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<div class="title">arith_theorem_producer.cpp</div> </div>
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<a href="arith__theorem__producer_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">/*****************************************************************************/</span><span class="comment"></span>
<a name="l00002"></a>00002 <span class="comment">/*!</span>
<a name="l00003"></a>00003 <span class="comment"> * \file arith_theorem_producer.cpp</span>
<a name="l00004"></a>00004 <span class="comment"> *</span>
<a name="l00005"></a>00005 <span class="comment"> * Author: Vijay Ganesh, Sergey Berezin</span>
<a name="l00006"></a>00006 <span class="comment"> *</span>
<a name="l00007"></a>00007 <span class="comment"> * Created: Dec 13 02:09:04 GMT 2002</span>
<a name="l00008"></a>00008 <span class="comment"> *</span>
<a name="l00009"></a>00009 <span class="comment"> * <hr></span>
<a name="l00010"></a>00010 <span class="comment"> *</span>
<a name="l00011"></a>00011 <span class="comment"> * License to use, copy, modify, sell and/or distribute this software</span>
<a name="l00012"></a>00012 <span class="comment"> * and its documentation for any purpose is hereby granted without</span>
<a name="l00013"></a>00013 <span class="comment"> * royalty, subject to the terms and conditions defined in the \ref</span>
<a name="l00014"></a>00014 <span class="comment"> * LICENSE file provided with this distribution.</span>
<a name="l00015"></a>00015 <span class="comment"> *</span>
<a name="l00016"></a>00016 <span class="comment"> * <hr></span>
<a name="l00017"></a>00017 <span class="comment"> *</span>
<a name="l00018"></a>00018 <span class="comment"> */</span>
<a name="l00019"></a>00019 <span class="comment">/*****************************************************************************/</span>
<a name="l00020"></a>00020 <span class="comment">// CLASS: ArithProofRules</span>
<a name="l00021"></a>00021 <span class="comment">//</span>
<a name="l00022"></a>00022 <span class="comment">// AUTHOR: Sergey Berezin, 12/11/2002</span>
<a name="l00023"></a>00023 <span class="comment">// AUTHOR: Vijay Ganesh, 05/30/2003</span>
<a name="l00024"></a>00024 <span class="comment">//</span>
<a name="l00025"></a>00025 <span class="comment">// Description: TRUSTED implementation of arithmetic proof rules.</span>
<a name="l00026"></a>00026 <span class="comment">//</span><span class="comment"></span>
<a name="l00027"></a>00027 <span class="comment">///////////////////////////////////////////////////////////////////////////////</span>
<a name="l00028"></a>00028 <span class="comment"></span>
<a name="l00029"></a>00029 <span class="comment">// This code is trusted</span>
<a name="l00030"></a><a class="code" href="arith__theorem__producer_8cpp.html#a8663c36bbf15bb5a0dcb01b97897fa95">00030</a> <span class="preprocessor">#define _CVC3_TRUSTED_</span>
<a name="l00031"></a>00031 <span class="preprocessor"></span>
<a name="l00032"></a>00032 <span class="preprocessor">#include "<a class="code" href="arith__theorem__producer_8h.html" title="TRUSTED implementation of arithmetic proof rules.">arith_theorem_producer.h</a>"</span>
<a name="l00033"></a>00033 <span class="preprocessor">#include "<a class="code" href="theory__core_8h.html">theory_core.h</a>"</span>
<a name="l00034"></a>00034 <span class="preprocessor">#include "<a class="code" href="theory__arith__new_8h.html">theory_arith_new.h</a>"</span>
<a name="l00035"></a>00035
<a name="l00036"></a>00036 <span class="keyword">using namespace </span>std;
<a name="l00037"></a>00037 <span class="keyword">using namespace </span>CVC3;
<a name="l00038"></a>00038 <span class="comment"></span>
<a name="l00039"></a>00039 <span class="comment">////////////////////////////////////////////////////////////////////</span>
<a name="l00040"></a>00040 <span class="comment"></span><span class="comment">// TheoryArith: trusted method for creating ArithTheoremProducer</span><span class="comment"></span>
<a name="l00041"></a>00041 <span class="comment">////////////////////////////////////////////////////////////////////</span>
<a name="l00042"></a>00042 <span class="comment"></span>
<a name="l00043"></a><a class="code" href="classCVC3_1_1TheoryArithNew.html#ac92f7d2a8db02ccf23fe15302dee278d">00043</a> <a class="code" href="classCVC3_1_1ArithProofRules.html">ArithProofRules</a>* TheoryArithNew::createProofRules() {
<a name="l00044"></a>00044 <span class="keywordflow">return</span> <span class="keyword">new</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer.html">ArithTheoremProducer</a>(theoryCore()->getTM(), <span class="keyword">this</span>);
<a name="l00045"></a>00045 }
<a name="l00046"></a>00046 <span class="comment"></span>
<a name="l00047"></a>00047 <span class="comment">////////////////////////////////////////////////////////////////////</span>
<a name="l00048"></a>00048 <span class="comment"></span><span class="comment">// Canonization rules</span><span class="comment"></span>
<a name="l00049"></a>00049 <span class="comment">////////////////////////////////////////////////////////////////////</span>
<a name="l00050"></a>00050 <span class="comment"></span>
<a name="l00051"></a>00051
<a name="l00052"></a><a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">00052</a> <span class="preprocessor">#define CLASS_NAME "ArithTheoremProducer"</span>
<a name="l00053"></a>00053 <span class="preprocessor"></span>
<a name="l00054"></a>00054 <span class="comment">// Rule for variables: e == 1 * e</span>
<a name="l00055"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a7568925b6c26f1c7ba882893f596d214">00055</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::varToMult(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00056"></a>00056 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00057"></a>00057 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"var_to_mult"</span>, e);
<a name="l00058"></a>00058 <span class="keywordflow">return</span> newRWTheorem(e, (rat(1) * e), Assumptions::emptyAssump(), pf);
<a name="l00059"></a>00059 }
<a name="l00060"></a>00060
<a name="l00061"></a>00061 <span class="comment">// Rule for unary minus: -e == (-1) * e</span>
<a name="l00062"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aaafdbe9dcc49728cc2bf16b43045c193">00062</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::uMinusToMult(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00063"></a>00063 <span class="comment">// The proof object to use</span>
<a name="l00064"></a>00064 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00065"></a>00065
<a name="l00066"></a>00066 <span class="comment">// If the proof is needed set it up</span>
<a name="l00067"></a>00067 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"uminus_to_mult"</span>, e);
<a name="l00068"></a>00068
<a name="l00069"></a>00069 <span class="comment">// Return the rewrite theorem explaining the rewrite</span>
<a name="l00070"></a>00070 <span class="keywordflow">return</span> newRWTheorem((-e), (rat(-1) * e), Assumptions::emptyAssump(), pf);
<a name="l00071"></a>00071 }
<a name="l00072"></a>00072
<a name="l00073"></a>00073
<a name="l00074"></a>00074 <span class="comment">// ==> x - y = x + (-1) * y</span>
<a name="l00075"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ab369e518fc2ee411503253fa0b1515d6">00075</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::minusToPlus(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& y) {
<a name="l00076"></a>00076 <span class="comment">// The proof object to use</span>
<a name="l00077"></a>00077 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00078"></a>00078
<a name="l00079"></a>00079 <span class="comment">// If proof is needed, set it up</span>
<a name="l00080"></a>00080 <span class="keywordflow">if</span> (withProof()) pf = newPf(<span class="stringliteral">"minus_to_plus"</span>, x, y);
<a name="l00081"></a>00081
<a name="l00082"></a>00082 <span class="comment">// Return a new rewrite theorem describing the change</span>
<a name="l00083"></a>00083 <span class="keywordflow">return</span> newRWTheorem((x-y), (x + (rat(-1) * y)), Assumptions::emptyAssump(), pf);
<a name="l00084"></a>00084 }
<a name="l00085"></a>00085
<a name="l00086"></a>00086
<a name="l00087"></a>00087 <span class="comment">// Rule for unary minus: -e == e/(-1)</span>
<a name="l00088"></a>00088 <span class="comment">// This is to reduce the number of almost identical rules for uminus and div</span>
<a name="l00089"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a4671174ae8ff61c52f16ddd53a3cdd27">00089</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::canonUMinusToDivide(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00090"></a>00090 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00091"></a>00091 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"canon_uminus"</span>, e);
<a name="l00092"></a>00092 <span class="keywordflow">return</span> newRWTheorem((-e), (e / rat(-1)), Assumptions::emptyAssump(), pf);
<a name="l00093"></a>00093 }
<a name="l00094"></a>00094
<a name="l00095"></a>00095 <span class="comment">// Rules for division by constant</span>
<a name="l00096"></a>00096
<a name="l00097"></a>00097 <span class="comment">// (c)/(d) ==> (c/d). When d==0, c/0 = 0 (our total extension).</span>
<a name="l00098"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a515e5d076ed135a6d943c2f5d5e34188">00098</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::canonDivideConst(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c,
<a name="l00099"></a>00099 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& d) {
<a name="l00100"></a>00100 <span class="comment">// Make sure c and d are a const</span>
<a name="l00101"></a>00101 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00102"></a>00102 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(c),
<a name="l00103"></a>00103 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonDivideConst:\n c not a constant: "</span>
<a name="l00104"></a>00104 + c.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00105"></a>00105 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(d),
<a name="l00106"></a>00106 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonDivideConst:\n d not a constant: "</span>
<a name="l00107"></a>00107 + d.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00108"></a>00108 }
<a name="l00109"></a>00109 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00110"></a>00110 <span class="keywordflow">if</span>(withProof())
<a name="l00111"></a>00111 pf = newPf(<span class="stringliteral">"canon_divide_const"</span>, c, d, d_hole);
<a name="l00112"></a>00112 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& dr = d.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l00113"></a>00113 <span class="keywordflow">return</span> newRWTheorem((c/d), (rat(dr==0? 0 : (c.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>()/dr))), Assumptions::emptyAssump(), pf);
<a name="l00114"></a>00114 }
<a name="l00115"></a>00115
<a name="l00116"></a>00116 <span class="comment">// (c * x)/d ==> (c/d) * x, takes (c*x) and d</span>
<a name="l00117"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a4d2d8da9de6d6faaa07758c01e3a9fe8">00117</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::canonDivideMult(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& cx,
<a name="l00118"></a>00118 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& d) {
<a name="l00119"></a>00119 <span class="comment">// Check the format of c*x</span>
<a name="l00120"></a>00120 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00121"></a>00121 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(cx) && <a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(cx[0]),
<a name="l00122"></a>00122 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonDivideMult:\n "</span>
<a name="l00123"></a>00123 <span class="stringliteral">"Not a (c * x) expression: "</span>
<a name="l00124"></a>00124 + cx.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00125"></a>00125 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(d),
<a name="l00126"></a>00126 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonDivideMult:\n "</span>
<a name="l00127"></a>00127 <span class="stringliteral">"d is not a constant: "</span> + d.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00128"></a>00128 }
<a name="l00129"></a>00129 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& dr = d.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l00130"></a>00130 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> cdr(dr==0? 0 : (cx[0].getRational()/dr));
<a name="l00131"></a>00131 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> cd(rat(cdr));
<a name="l00132"></a>00132 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00133"></a>00133 <span class="keywordflow">if</span>(withProof())
<a name="l00134"></a>00134 pf = newPf(<span class="stringliteral">"canon_divide_mult"</span>, cx[0], cx[1], d);
<a name="l00135"></a>00135 <span class="comment">// (c/d) may be == 1, so we also need to canonize 1*x to x</span>
<a name="l00136"></a>00136 <span class="keywordflow">if</span>(cdr == 1)
<a name="l00137"></a>00137 <span class="keywordflow">return</span> newRWTheorem((cx/d), (cx[1]), Assumptions::emptyAssump(), pf);
<a name="l00138"></a>00138 <span class="keywordflow">else</span> <span class="keywordflow">if</span>(cdr == 0) <span class="comment">// c/0 == 0 case</span>
<a name="l00139"></a>00139 <span class="keywordflow">return</span> newRWTheorem((cx/d), cd, Assumptions::emptyAssump(), pf);
<a name="l00140"></a>00140 <span class="keywordflow">else</span>
<a name="l00141"></a>00141 <span class="keywordflow">return</span> newRWTheorem((cx/d), (cd*cx[1]), Assumptions::emptyAssump(), pf);
<a name="l00142"></a>00142 }
<a name="l00143"></a>00143
<a name="l00144"></a>00144 <span class="comment">// (+ t1 ... tn)/d ==> (+ (t1/d) ... (tn/d))</span>
<a name="l00145"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a4338b85f1dd0fca0cc58e6b7259a20b4">00145</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::canonDividePlus(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& sum, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& d) {
<a name="l00146"></a>00146 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00147"></a>00147 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#afb0f7d15ddbd87f9abb128108101f557">isPlus</a>(sum) && sum.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() >= 2 && <a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(sum[0]),
<a name="l00148"></a>00148 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonUMinusPlus:\n "</span>
<a name="l00149"></a>00149 <span class="stringliteral">"Expr is not a canonical sum: "</span>
<a name="l00150"></a>00150 + sum.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00151"></a>00151 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(d),
<a name="l00152"></a>00152 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonUMinusPlus:\n "</span>
<a name="l00153"></a>00153 <span class="stringliteral">"d is not a const: "</span> + d.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00154"></a>00154 }
<a name="l00155"></a>00155 <span class="comment">// First, propagate '/d' down to the args</span>
<a name="l00156"></a>00156 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00157"></a>00157 <span class="keywordflow">if</span>(withProof())
<a name="l00158"></a>00158 pf = newPf(<span class="stringliteral">"canon_divide_plus"</span>, rat(sum.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>()),
<a name="l00159"></a>00159 sum.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>(), sum.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>());
<a name="l00160"></a>00160 vector<Expr> newKids;
<a name="l00161"></a>00161 <span class="keywordflow">for</span>(<a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i=sum.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>(), iend=sum.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); i!=iend; ++i)
<a name="l00162"></a>00162 newKids.push_back((*i)/d);
<a name="l00163"></a>00163 <span class="comment">// (+ t1 ... tn)/d == (+ (t1/d) ... (tn/d))</span>
<a name="l00164"></a>00164 <span class="keywordflow">return</span> newRWTheorem((sum/d), (<a class="code" href="namespaceCVC3.html#accd3d7d38b0e04136afbc3e5191bc8bb">plusExpr</a>(newKids)), Assumptions::emptyAssump(), pf);
<a name="l00165"></a>00165 }
<a name="l00166"></a>00166
<a name="l00167"></a>00167 <span class="comment">// x/(d) ==> (1/d) * x, unless d == 1</span>
<a name="l00168"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aa651eb7a4d20a77135efa2d3e984c355">00168</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::canonDivideVar(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& d) {
<a name="l00169"></a>00169 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00170"></a>00170 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(d),
<a name="l00171"></a>00171 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonDivideVar:\n "</span>
<a name="l00172"></a>00172 <span class="stringliteral">"d is not a const: "</span> + d.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00173"></a>00173 }
<a name="l00174"></a>00174 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00175"></a>00175
<a name="l00176"></a>00176 <span class="keywordflow">if</span>(withProof())
<a name="l00177"></a>00177 pf = newPf(<span class="stringliteral">"canon_divide_var"</span>, e);
<a name="l00178"></a>00178
<a name="l00179"></a>00179 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& dr = d.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l00180"></a>00180 <span class="keywordflow">if</span>(dr == 1)
<a name="l00181"></a>00181 <span class="keywordflow">return</span> newRWTheorem(e/d, e, Assumptions::emptyAssump(), pf);
<a name="l00182"></a>00182 <span class="keywordflow">if</span>(dr == 0) <span class="comment">// e/0 == 0 (total extension of division)</span>
<a name="l00183"></a>00183 <span class="keywordflow">return</span> newRWTheorem(e/d, d, Assumptions::emptyAssump(), pf);
<a name="l00184"></a>00184 <span class="keywordflow">else</span>
<a name="l00185"></a>00185 <span class="keywordflow">return</span> newRWTheorem(e/d, rat(1/dr) * e, Assumptions::emptyAssump(), pf);
<a name="l00186"></a>00186 }
<a name="l00187"></a>00187
<a name="l00188"></a>00188
<a name="l00189"></a>00189 <span class="comment">// Multiplication</span>
<a name="l00190"></a>00190 <span class="comment">// (MULT expr1 expr2 expr3 ...)</span>
<a name="l00191"></a>00191 <span class="comment">// Each expr is in canonical form, i.e. it can be a</span>
<a name="l00192"></a>00192 <span class="comment">// 1) Rational constant</span>
<a name="l00193"></a>00193 <span class="comment">// 2) Arithmetic Leaf (var or term from another theory)</span>
<a name="l00194"></a>00194 <span class="comment">// 3) (POW rational leaf)</span>
<a name="l00195"></a>00195 <span class="comment">// where rational cannot be 0 or 1</span>
<a name="l00196"></a>00196 <span class="comment">// 4) (MULT rational mterm'_1 ...) where each mterm' is of type (2) or (3)</span>
<a name="l00197"></a>00197 <span class="comment">// If rational == 1 then there should be at least two mterms</span>
<a name="l00198"></a>00198 <span class="comment">// 5) (PLUS rational sterm_1 ...) where each sterm is of</span>
<a name="l00199"></a>00199 <span class="comment">// type (2) or (3) or (4)</span>
<a name="l00200"></a>00200 <span class="comment">// if rational == 0 then there should be at least two sterms</span>
<a name="l00201"></a>00201
<a name="l00202"></a>00202
<a name="l00203"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#af24b2bc3bc03bc320707362f2460dd0e">00203</a> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ArithTheoremProducer::simplifiedMultExpr(std::vector<Expr> & mulKids) {
<a name="l00204"></a>00204
<a name="l00205"></a>00205 <span class="comment">// Check that the number of kids is at least 1 and that the first one is rational</span>
<a name="l00206"></a>00206 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(mulKids.size() >= 1 && mulKids[0].isRational(), <span class="stringliteral">""</span>);
<a name="l00207"></a>00207
<a name="l00208"></a>00208 <span class="comment">// If the number of kids is only one, return the kid, no multiplication is necessary</span>
<a name="l00209"></a>00209 <span class="keywordflow">if</span> (mulKids.size() == 1) <span class="keywordflow">return</span> mulKids[0];
<a name="l00210"></a>00210 <span class="comment">// Otherwise return the multiplication of given expression</span>
<a name="l00211"></a>00211 <span class="keywordflow">else</span> <span class="keywordflow">return</span> <a class="code" href="namespaceCVC3.html#adb35e0739f86730543924dbc8211a778">multExpr</a>(mulKids);
<a name="l00212"></a>00212 }
<a name="l00213"></a>00213
<a name="l00214"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a10ebfab26aa4ee1a147f08d8f6b94c45">00214</a> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ArithTheoremProducer::canonMultConstMult(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & c, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e) {
<a name="l00215"></a>00215
<a name="l00216"></a>00216 <span class="comment">// The constant must be a rational and e must be a multiplication</span>
<a name="l00217"></a>00217 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(c.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>() && e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>, <span class="stringliteral">"ArithTheoremProducer::canonMultConstMult: c must be a rational a e must be a MULT"</span>);
<a name="l00218"></a>00218
<a name="l00219"></a>00219 <span class="comment">// Multiplication must include a rational multiplier</span>
<a name="l00220"></a>00220 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a> ((e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 1) && (e[0].<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>()), <span class="stringliteral">"arith_theorem_producer::canonMultConstMult: a canonized MULT expression must have \</span>
<a name="l00221"></a>00221 <span class="stringliteral"> arity greater than 1: and first child must be rational "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00222"></a>00222
<a name="l00223"></a>00223 <span class="comment">// The kids of the new multiplication</span>
<a name="l00224"></a>00224 std::vector<Expr> mulKids;
<a name="l00225"></a>00225
<a name="l00226"></a>00226 <span class="comment">// Create new multiplication expression, multiplying the constant with the given constant</span>
<a name="l00227"></a>00227 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = e.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l00228"></a>00228 mulKids.push_back(rat(c.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() * (*i).getRational()));
<a name="l00229"></a>00229 <span class="comment">// All the rest, just push them to the kids vector</span>
<a name="l00230"></a>00230 <span class="keywordflow">for</span>(i ++; i != e.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); i ++)
<a name="l00231"></a>00231 mulKids.push_back(*i);
<a name="l00232"></a>00232
<a name="l00233"></a>00233 <span class="comment">// Return the simplified multiplication expression</span>
<a name="l00234"></a>00234 <span class="keywordflow">return</span> simplifiedMultExpr(mulKids);
<a name="l00235"></a>00235 }
<a name="l00236"></a>00236
<a name="l00237"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a48b21552a97a3a75ae469fb48c155e51">00237</a> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ArithTheoremProducer::canonMultConstPlus(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e2) {
<a name="l00238"></a>00238
<a name="l00239"></a>00239 <span class="comment">// e1 must be a rational and e2 must be a sum in canonic form</span>
<a name="l00240"></a>00240 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(e1.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>() && e2.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a> && e2.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 0, <span class="stringliteral">""</span>);
<a name="l00241"></a>00241
<a name="l00242"></a>00242 <span class="comment">// Vector to hold all the sum terms</span>
<a name="l00243"></a>00243 std::vector<Theorem> thmPlusVector;
<a name="l00244"></a>00244
<a name="l00245"></a>00245 <span class="comment">// Go through all the sum terms and multiply them with the constant</span>
<a name="l00246"></a>00246 <span class="keywordflow">for</span>(<a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = e2.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>(); i != e2.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); i++)
<a name="l00247"></a>00247 thmPlusVector.push_back(canonMultMtermMterm(e1*(*i)));
<a name="l00248"></a>00248
<a name="l00249"></a>00249 <span class="comment">// Substitute the canonized terms into the sum</span>
<a name="l00250"></a>00250 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> thmPlus1 = d_theoryArith->substitutivityRule(e2.<a class="code" href="group__ExprPkg.html#gace479f04faca399219496195152f7806" title="Get operator from expression.">getOp</a>(), thmPlusVector);
<a name="l00251"></a>00251
<a name="l00252"></a>00252 <span class="comment">// Return the resulting expression</span>
<a name="l00253"></a>00253 <span class="keywordflow">return</span> thmPlus1.<a class="code" href="classCVC3_1_1Theorem.html#a97d957fcbf9094480851b1d2e5d3729f">getRHS</a>();
<a name="l00254"></a>00254 }
<a name="l00255"></a>00255
<a name="l00256"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aebf0a0b539104e2190b53351efc6116b">00256</a> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ArithTheoremProducer::canonMultPowPow(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e1,
<a name="l00257"></a>00257 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e2)
<a name="l00258"></a>00258 {
<a name="l00259"></a>00259 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(e1.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a> && e2.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>, <span class="stringliteral">""</span>);
<a name="l00260"></a>00260 <span class="comment">// (POW r1 leaf1) * (POW r2 leaf2)</span>
<a name="l00261"></a>00261 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> leaf1 = e1[1];
<a name="l00262"></a>00262 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> leaf2 = e2[1];
<a name="l00263"></a>00263 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> can_expr;
<a name="l00264"></a>00264 <span class="keywordflow">if</span> (leaf1 == leaf2) {
<a name="l00265"></a>00265 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> rsum = e1[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() + e2[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l00266"></a>00266 <span class="keywordflow">if</span> (rsum == 0) {
<a name="l00267"></a>00267 <span class="keywordflow">return</span> rat(1);
<a name="l00268"></a>00268 }
<a name="l00269"></a>00269 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (rsum == 1) {
<a name="l00270"></a>00270 <span class="keywordflow">return</span> leaf1;
<a name="l00271"></a>00271 }
<a name="l00272"></a>00272 <span class="keywordflow">else</span>
<a name="l00273"></a>00273 {
<a name="l00274"></a>00274 <span class="keywordflow">return</span> <a class="code" href="namespaceCVC3.html#aa123bf4eb1751181baf16c5e80b47740" title="Power (x^n, or base^{pow}) expressions.">powExpr</a>(rat(rsum), leaf1);
<a name="l00275"></a>00275 }
<a name="l00276"></a>00276 }
<a name="l00277"></a>00277 <span class="keywordflow">else</span>
<a name="l00278"></a>00278 {
<a name="l00279"></a>00279 std::vector<Expr> mulKids;
<a name="l00280"></a>00280 mulKids.push_back(rat(1));
<a name="l00281"></a>00281 <span class="comment">// the leafs should be put in decreasing order</span>
<a name="l00282"></a>00282 <span class="keywordflow">if</span> (leaf1 < leaf2) {
<a name="l00283"></a>00283 mulKids.push_back(e2);
<a name="l00284"></a>00284 mulKids.push_back(e1);
<a name="l00285"></a>00285 }
<a name="l00286"></a>00286 <span class="keywordflow">else</span>
<a name="l00287"></a>00287 {
<a name="l00288"></a>00288 mulKids.push_back(e1);
<a name="l00289"></a>00289 mulKids.push_back(e2);
<a name="l00290"></a>00290 }
<a name="l00291"></a>00291 <span class="comment">// FIXME: don't really need to simplify, just wrap up a MULT?</span>
<a name="l00292"></a>00292 <span class="keywordflow">return</span> simplifiedMultExpr(mulKids);
<a name="l00293"></a>00293 }
<a name="l00294"></a>00294 }
<a name="l00295"></a>00295
<a name="l00296"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aabc24cdaf5d3a390f9880937bac17311">00296</a> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ArithTheoremProducer::canonMultPowLeaf(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e1,
<a name="l00297"></a>00297 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e2)
<a name="l00298"></a>00298 {
<a name="l00299"></a>00299 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(e1.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>, <span class="stringliteral">""</span>);
<a name="l00300"></a>00300 <span class="comment">// (POW r1 leaf1) * leaf2</span>
<a name="l00301"></a>00301 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> leaf1 = e1[1];
<a name="l00302"></a>00302 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> leaf2 = e2;
<a name="l00303"></a>00303 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> can_expr;
<a name="l00304"></a>00304 <span class="keywordflow">if</span> (leaf1 == leaf2) {
<a name="l00305"></a>00305 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> rsum = e1[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() + 1;
<a name="l00306"></a>00306 <span class="keywordflow">if</span> (rsum == 0) {
<a name="l00307"></a>00307 <span class="keywordflow">return</span> rat(1);
<a name="l00308"></a>00308 }
<a name="l00309"></a>00309 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (rsum == 1) {
<a name="l00310"></a>00310 <span class="keywordflow">return</span> leaf1;
<a name="l00311"></a>00311 }
<a name="l00312"></a>00312 <span class="keywordflow">else</span>
<a name="l00313"></a>00313 {
<a name="l00314"></a>00314 <span class="keywordflow">return</span> <a class="code" href="namespaceCVC3.html#aa123bf4eb1751181baf16c5e80b47740" title="Power (x^n, or base^{pow}) expressions.">powExpr</a>(rat(rsum), leaf1);
<a name="l00315"></a>00315 }
<a name="l00316"></a>00316 }
<a name="l00317"></a>00317 <span class="keywordflow">else</span>
<a name="l00318"></a>00318 {
<a name="l00319"></a>00319 std::vector<Expr> mulKids;
<a name="l00320"></a>00320 mulKids.push_back(rat(1));
<a name="l00321"></a>00321 <span class="comment">// the leafs should be put in decreasing order</span>
<a name="l00322"></a>00322 <span class="keywordflow">if</span> (leaf1 < leaf2) {
<a name="l00323"></a>00323 mulKids.push_back(e2);
<a name="l00324"></a>00324 mulKids.push_back(e1);
<a name="l00325"></a>00325 }
<a name="l00326"></a>00326 <span class="keywordflow">else</span>
<a name="l00327"></a>00327 {
<a name="l00328"></a>00328 mulKids.push_back(e1);
<a name="l00329"></a>00329 mulKids.push_back(e2);
<a name="l00330"></a>00330 }
<a name="l00331"></a>00331 <span class="keywordflow">return</span> simplifiedMultExpr(mulKids);
<a name="l00332"></a>00332 }
<a name="l00333"></a>00333 }
<a name="l00334"></a>00334
<a name="l00335"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aae1bc41d54f8b148ce5cf9425ac688af">00335</a> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ArithTheoremProducer::canonMultLeafLeaf(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e1,
<a name="l00336"></a>00336 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e2)
<a name="l00337"></a>00337 {
<a name="l00338"></a>00338 <span class="comment">// leaf1 * leaf2</span>
<a name="l00339"></a>00339 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> leaf1 = e1;
<a name="l00340"></a>00340 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> leaf2 = e2;
<a name="l00341"></a>00341 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> can_expr;
<a name="l00342"></a>00342 <span class="keywordflow">if</span> (leaf1 == leaf2) {
<a name="l00343"></a>00343 <span class="keywordflow">return</span> <a class="code" href="namespaceCVC3.html#aa123bf4eb1751181baf16c5e80b47740" title="Power (x^n, or base^{pow}) expressions.">powExpr</a>(rat(2), leaf1);
<a name="l00344"></a>00344 }
<a name="l00345"></a>00345 <span class="keywordflow">else</span>
<a name="l00346"></a>00346 {
<a name="l00347"></a>00347 std::vector<Expr> mulKids;
<a name="l00348"></a>00348 mulKids.push_back(rat(1));
<a name="l00349"></a>00349 <span class="comment">// the leafs should be put in decreasing order</span>
<a name="l00350"></a>00350 <span class="keywordflow">if</span> (leaf1 < leaf2) {
<a name="l00351"></a>00351 mulKids.push_back(e2);
<a name="l00352"></a>00352 mulKids.push_back(e1);
<a name="l00353"></a>00353 }
<a name="l00354"></a>00354 <span class="keywordflow">else</span>
<a name="l00355"></a>00355 {
<a name="l00356"></a>00356 mulKids.push_back(e1);
<a name="l00357"></a>00357 mulKids.push_back(e2);
<a name="l00358"></a>00358 }
<a name="l00359"></a>00359 <span class="keywordflow">return</span> simplifiedMultExpr(mulKids);
<a name="l00360"></a>00360 }
<a name="l00361"></a>00361 }
<a name="l00362"></a>00362
<a name="l00363"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a05b2608fd280890cb49bf4534a54e304">00363</a> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ArithTheoremProducer::canonMultLeafOrPowMult(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e1,
<a name="l00364"></a>00364 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e2)
<a name="l00365"></a>00365 {
<a name="l00366"></a>00366 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(e2.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>, <span class="stringliteral">""</span>);
<a name="l00367"></a>00367 <span class="comment">// Leaf * (MULT rat1 mterm1 ...)</span>
<a name="l00368"></a>00368 <span class="comment">// (POW r1 leaf1) * (MULT rat1 mterm1 ...) where</span>
<a name="l00369"></a>00369 <span class="comment">// each mterm is a leaf or (POW r leaf). Furthermore the leafs</span>
<a name="l00370"></a>00370 <span class="comment">// in the mterms are in descending order</span>
<a name="l00371"></a>00371 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> leaf1 = e1.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a> ? e1[1] : e1;
<a name="l00372"></a>00372 std::vector<Expr> mulKids;
<a name="l00373"></a>00373 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(e2.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 1, <span class="stringliteral">"MULT expr must have arity 2 or more"</span>);
<a name="l00374"></a>00374 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = e2.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l00375"></a>00375 <span class="comment">// push the rational</span>
<a name="l00376"></a>00376 mulKids.push_back(*i);
<a name="l00377"></a>00377 ++i;
<a name="l00378"></a>00378 <span class="comment">// Now i points to the first mterm</span>
<a name="l00379"></a>00379 <span class="keywordflow">for</span>(; i != e2.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); ++i) {
<a name="l00380"></a>00380 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> leaf2 = ((*i).getKind() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>) ? (*i)[1] : (*i);
<a name="l00381"></a>00381 <span class="keywordflow">if</span> (leaf1 == leaf2) {
<a name="l00382"></a>00382 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> r1 = e1.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a> ? e1[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() : 1;
<a name="l00383"></a>00383 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> r2 =
<a name="l00384"></a>00384 ((*i).getKind() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a> ? (*i)[0].getRational() : 1);
<a name="l00385"></a>00385 <span class="comment">// if r1 + r2 == 0 then it is the case of x^n * x^{-n}</span>
<a name="l00386"></a>00386 <span class="comment">// So, nothing needs to be added</span>
<a name="l00387"></a>00387 <span class="keywordflow">if</span> (r1 + r2 != 0) {
<a name="l00388"></a>00388 <span class="keywordflow">if</span> (r1 + r2 == 1) {
<a name="l00389"></a>00389 mulKids.push_back(leaf1);
<a name="l00390"></a>00390 }
<a name="l00391"></a>00391 <span class="keywordflow">else</span>
<a name="l00392"></a>00392 {
<a name="l00393"></a>00393 mulKids.push_back(<a class="code" href="namespaceCVC3.html#aa123bf4eb1751181baf16c5e80b47740" title="Power (x^n, or base^{pow}) expressions.">powExpr</a>(rat(r1 + r2), leaf1));
<a name="l00394"></a>00394 }
<a name="l00395"></a>00395 }
<a name="l00396"></a>00396 <span class="keywordflow">break</span>;
<a name="l00397"></a>00397 }
<a name="l00398"></a>00398 <span class="comment">// This ensures that the leaves in the mterms are also arranged</span>
<a name="l00399"></a>00399 <span class="comment">// in decreasing order</span>
<a name="l00400"></a>00400 <span class="comment">// Note that this will need to be changed if we want the order to</span>
<a name="l00401"></a>00401 <span class="comment">// be increasing order.</span>
<a name="l00402"></a>00402 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (leaf2 < leaf1) {
<a name="l00403"></a>00403 mulKids.push_back(e1);
<a name="l00404"></a>00404 mulKids.push_back(*i);
<a name="l00405"></a>00405 <span class="keywordflow">break</span>;
<a name="l00406"></a>00406 }
<a name="l00407"></a>00407 <span class="keywordflow">else</span> <span class="comment">// leaf1 < leaf2</span>
<a name="l00408"></a>00408 mulKids.push_back(*i);
<a name="l00409"></a>00409 }
<a name="l00410"></a>00410 <span class="keywordflow">if</span> (i == e2.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>()) {
<a name="l00411"></a>00411 mulKids.push_back(e1);
<a name="l00412"></a>00412 }
<a name="l00413"></a>00413 <span class="keywordflow">else</span>
<a name="l00414"></a>00414 {
<a name="l00415"></a>00415 <span class="comment">// e1 and *i have already been added</span>
<a name="l00416"></a>00416 <span class="keywordflow">for</span> (++i; i != e2.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); ++i) {
<a name="l00417"></a>00417 mulKids.push_back(*i);
<a name="l00418"></a>00418 }
<a name="l00419"></a>00419 }
<a name="l00420"></a>00420 <span class="keywordflow">return</span> simplifiedMultExpr(mulKids);
<a name="l00421"></a>00421 }
<a name="l00422"></a>00422
<a name="l00423"></a>00423 <span class="comment">// Local class for ordering monomials; note, that it flips the</span>
<a name="l00424"></a>00424 <span class="comment">// ordering given by greaterthan(), to sort in ascending order.</span>
<a name="l00425"></a><a class="code" href="classMonomialLess.html">00425</a> <span class="keyword">class </span><a class="code" href="classMonomialLess.html">MonomialLess</a> {
<a name="l00426"></a>00426 <span class="keyword">public</span>:
<a name="l00427"></a><a class="code" href="classMonomialLess.html#a69db32fbde99647b028bbab4a6e61126">00427</a> <span class="keywordtype">bool</span> <a class="code" href="classMonomialLess.html#a69db32fbde99647b028bbab4a6e61126">operator()</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e2)<span class="keyword"> const </span>{
<a name="l00428"></a>00428 <span class="keywordflow">return</span> ArithTheoremProducer::greaterthan(e1,e2);
<a name="l00429"></a>00429 }
<a name="l00430"></a>00430 };
<a name="l00431"></a>00431
<a name="l00432"></a><a class="code" href="arith__theorem__producer_8cpp.html#a24fc78b84aff5214bf8b65ff0a2a99a3">00432</a> <span class="keyword">typedef</span> map<Expr,Rational,MonomialLess> <a class="code" href="arith__theorem__producer_8cpp.html#a24fc78b84aff5214bf8b65ff0a2a99a3">MonomMap</a>;
<a name="l00433"></a>00433
<a name="l00434"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a9548361051bb6febc314faa107d2c2f5">00434</a> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ArithTheoremProducer::canonCombineLikeTerms(<span class="keyword">const</span> std::vector<Expr> & sumExprs) {
<a name="l00435"></a>00435
<a name="l00436"></a>00436 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> constant = 0; <span class="comment">// The constant at the begining of the sum</span>
<a name="l00437"></a>00437 <a class="code" href="arith__theorem__producer_8cpp.html#a24fc78b84aff5214bf8b65ff0a2a99a3">MonomMap</a> sumHashMap; <span class="comment">// The hash map of the summands, so that we can gather them and sum in the right order</span>
<a name="l00438"></a>00438 vector<Expr> sumKids; <span class="comment">// The kids of the sum</span>
<a name="l00439"></a>00439
<a name="l00440"></a>00440 <span class="comment">// Add each distinct mterm (not including the rational) into an appropriate hash map entry</span>
<a name="l00441"></a>00441 std::vector<Expr>::const_iterator i = sumExprs.begin();
<a name="l00442"></a>00442 std::vector<Expr>::const_iterator i_end = sumExprs.end();
<a name="l00443"></a>00443 <span class="keywordflow">for</span> (; i != i_end; i++) {
<a name="l00444"></a>00444 <span class="comment">// Take the current expression (it must be a multiplication, a leaf or a rational number)</span>
<a name="l00445"></a>00445 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> mul = *i;
<a name="l00446"></a>00446
<a name="l00447"></a>00447 <span class="comment">// If it's a rational, just add it to the constant factor c</span>
<a name="l00448"></a>00448 <span class="keywordflow">if</span> (mul.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>())
<a name="l00449"></a>00449 constant = constant + mul.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l00450"></a>00450 <span class="keywordflow">else</span> {
<a name="l00451"></a>00451 <span class="comment">// Depending on the type of the expression decide what to do with this sum term</span>
<a name="l00452"></a>00452 <span class="keywordflow">switch</span> (mul.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>()) {
<a name="l00453"></a>00453
<a name="l00454"></a>00454 <span class="comment">// Multiplication is</span>
<a name="l00455"></a>00455 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>: {
<a name="l00456"></a>00456
<a name="l00457"></a>00457 <span class="comment">// The multiplication must be of arity > 1 and the first one must be rational</span>
<a name="l00458"></a>00458 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(mul.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 1 && mul[0].<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>(),<span class="stringliteral">"If sum term is multiplication it must have the first term a rational, and at least another one"</span>);
<a name="l00459"></a>00459
<a name="l00460"></a>00460 <span class="comment">// Get the rational constant of multiplication</span>
<a name="l00461"></a>00461 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> r = mul[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l00462"></a>00462
<a name="l00463"></a>00463 <span class="comment">// Make a new multiplication term with a 1 instead of the rational r</span>
<a name="l00464"></a>00464 vector<Expr> newKids;
<a name="l00465"></a>00465 <span class="comment">// Copy the children to the newKids vector (including the rational)</span>
<a name="l00466"></a>00466 <span class="keywordflow">for</span>(<a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> m = mul.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>(); m != mul.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); m ++) newKids.push_back(*m);
<a name="l00467"></a>00467 <span class="comment">// Change the rational to 1</span>
<a name="l00468"></a>00468 newKids[0] = rat(1);
<a name="l00469"></a>00469 <span class="comment">// Make the newMul expression</span>
<a name="l00470"></a>00470 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> newMul = <a class="code" href="namespaceCVC3.html#adb35e0739f86730543924dbc8211a778">multExpr</a>(newKids);
<a name="l00471"></a>00471
<a name="l00472"></a>00472 <span class="comment">// Find the term in the hashmap, so that we can add the coefficient (a*t + b*t = (a+b)*t)</span>
<a name="l00473"></a>00473 MonomMap::iterator i = sumHashMap.find(newMul);
<a name="l00474"></a>00474
<a name="l00475"></a>00475 <span class="comment">// If not found, just add the rational to the hash map</span>
<a name="l00476"></a>00476 <span class="keywordflow">if</span> (i == sumHashMap.end()) sumHashMap[newMul] = r;
<a name="l00477"></a>00477 <span class="comment">// Otherwise, add it to the existing coefficient</span>
<a name="l00478"></a>00478 <span class="keywordflow">else</span> (*i).second += r;
<a name="l00479"></a>00479
<a name="l00480"></a>00480 <span class="comment">// MULT case break</span>
<a name="l00481"></a>00481 <span class="keywordflow">break</span>;
<a name="l00482"></a>00482 }
<a name="l00483"></a>00483
<a name="l00484"></a>00484 <span class="keywordflow">default</span>: {
<a name="l00485"></a>00485
<a name="l00486"></a>00486 <span class="comment">// Find the term in the hashmap (add the 1*mul for being canonical)</span>
<a name="l00487"></a>00487 MonomMap::iterator i = sumHashMap.find(<a class="code" href="namespaceCVC3.html#adb35e0739f86730543924dbc8211a778">multExpr</a>(rat(1), mul));
<a name="l00488"></a>00488
<a name="l00489"></a>00489 <span class="comment">// covers the case of POW, leaf</span>
<a name="l00490"></a>00490 <span class="keywordflow">if</span> (i == sumHashMap.end()) sumHashMap[<a class="code" href="namespaceCVC3.html#adb35e0739f86730543924dbc8211a778">multExpr</a>(rat(1), mul)] = 1;
<a name="l00491"></a>00491 <span class="keywordflow">else</span> (*i).second += 1;
<a name="l00492"></a>00492
<a name="l00493"></a>00493 <span class="comment">// Default break</span>
<a name="l00494"></a>00494 <span class="keywordflow">break</span>;
<a name="l00495"></a>00495 }
<a name="l00496"></a>00496 }
<a name="l00497"></a>00497 }
<a name="l00498"></a>00498 }
<a name="l00499"></a>00499
<a name="l00500"></a>00500 <span class="comment">// Now transfer to sumKids, first adding the rational constant if different from 0 (b + a_1*x_1 + a_2*x_2 + ... + a_n*x_n)</span>
<a name="l00501"></a>00501 <span class="keywordflow">if</span> (constant != 0) sumKids.push_back(rat(constant));
<a name="l00502"></a>00502
<a name="l00503"></a>00503 <span class="comment">// After the constant, add all the other summands, in the right order (the hashmap order)</span>
<a name="l00504"></a>00504 MonomMap::iterator j = sumHashMap.begin(), jend=sumHashMap.end();
<a name="l00505"></a>00505 <span class="keywordflow">for</span>(; j != jend; j++) {
<a name="l00506"></a>00506 <span class="comment">// If the corresponding coefficient is non-zero, add the term to the sum</span>
<a name="l00507"></a>00507 <span class="keywordflow">if</span> ((*j).second != 0) {
<a name="l00508"></a>00508 <span class="comment">// Again, make a new multiplication term with a the coefficient instead of the rational one (1)</span>
<a name="l00509"></a>00509 vector<Expr> newKids;
<a name="l00510"></a>00510 <span class="comment">// Copy the children to the newKids vector (including the rational)</span>
<a name="l00511"></a>00511 <span class="keywordflow">for</span>(<a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> m = (*j).first.begin(); m != (*j).first.end(); m ++) newKids.push_back(*m);
<a name="l00512"></a>00512 <span class="comment">// Change the rational to the summed rationals for this term</span>
<a name="l00513"></a>00513 newKids[0] = rat((*j).second);
<a name="l00514"></a>00514 <span class="comment">// Make the newMul expression and add it to the sum</span>
<a name="l00515"></a>00515 sumKids.push_back(<a class="code" href="namespaceCVC3.html#adb35e0739f86730543924dbc8211a778">multExpr</a>(newKids));
<a name="l00516"></a>00516 }
<a name="l00517"></a>00517 }
<a name="l00518"></a>00518
<a name="l00519"></a>00519 <span class="comment">// If the whole sum is only the constant, the whole sum is only the constant (TODO: CLEAN THIS UP, ITS HORRIBLE)</span>
<a name="l00520"></a>00520 <span class="keywordflow">if</span> (constant != 0 && sumKids.size() == 1) <span class="keywordflow">return</span> sumKids[0];
<a name="l00521"></a>00521
<a name="l00522"></a>00522 <span class="comment">// If the constant is 0 and there is only one more summand, return only the summand</span>
<a name="l00523"></a>00523 <span class="keywordflow">if</span> (constant == 0 && sumKids.size() == 1) <span class="keywordflow">return</span> sumKids[0];
<a name="l00524"></a>00524
<a name="l00525"></a>00525 <span class="comment">// If the constant is 0 and there are no summands, return 0</span>
<a name="l00526"></a>00526 <span class="keywordflow">if</span> (constant == 0 && sumKids.size() == 0) <span class="keywordflow">return</span> rat(0);
<a name="l00527"></a>00527
<a name="l00528"></a>00528 <span class="comment">// Otherwise return the sum of the sumkids</span>
<a name="l00529"></a>00529 <span class="keywordflow">return</span> <a class="code" href="namespaceCVC3.html#accd3d7d38b0e04136afbc3e5191bc8bb">plusExpr</a>(sumKids);
<a name="l00530"></a>00530 }
<a name="l00531"></a>00531
<a name="l00532"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a0b344f367f01d240d997df7edfe1a12c">00532</a> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ArithTheoremProducer::canonMultLeafOrPowOrMultPlus(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e1,
<a name="l00533"></a>00533 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e2)
<a name="l00534"></a>00534 {
<a name="l00535"></a>00535 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(e2.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>, <span class="stringliteral">""</span>);
<a name="l00536"></a>00536 <span class="comment">// Leaf * (PLUS rational sterm1 ...)</span>
<a name="l00537"></a>00537 <span class="comment">// or</span>
<a name="l00538"></a>00538 <span class="comment">// (POW n1 x1) * (PLUS rational sterm1 ...)</span>
<a name="l00539"></a>00539 <span class="comment">// or</span>
<a name="l00540"></a>00540 <span class="comment">// (MULT r1 m1 m2 ...) * (PLUS rational sterm1 ...)</span>
<a name="l00541"></a>00541 <span class="comment">// assume that e1 and e2 are themselves canonized</span>
<a name="l00542"></a>00542 std::vector<Expr> sumExprs;
<a name="l00543"></a>00543 <span class="comment">// Multiply each term in turn.</span>
<a name="l00544"></a>00544 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = e2.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l00545"></a>00545 <span class="keywordflow">for</span> (; i != e2.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); ++i) {
<a name="l00546"></a>00546 sumExprs.push_back(canonMultMtermMterm(e1 * (*i)).getRHS());
<a name="l00547"></a>00547 }
<a name="l00548"></a>00548 <span class="keywordflow">return</span> canonCombineLikeTerms(sumExprs);
<a name="l00549"></a>00549 }
<a name="l00550"></a>00550
<a name="l00551"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ac0363ff2f51ad1173ed1e46046b0654a">00551</a> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ArithTheoremProducer::canonMultPlusPlus(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e1,
<a name="l00552"></a>00552 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & e2)
<a name="l00553"></a>00553 {
<a name="l00554"></a>00554 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(e1.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a> && e2.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>, <span class="stringliteral">""</span>);
<a name="l00555"></a>00555 <span class="comment">// (PLUS r1 .... ) * (PLUS r1' ...)</span>
<a name="l00556"></a>00556 <span class="comment">// assume that e1 and e2 are themselves canonized</span>
<a name="l00557"></a>00557
<a name="l00558"></a>00558 std::vector<Expr> sumExprs;
<a name="l00559"></a>00559 <span class="comment">// Multiply each term in turn.</span>
<a name="l00560"></a>00560 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = e1.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l00561"></a>00561 <span class="keywordflow">for</span> (; i != e1.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); ++i) {
<a name="l00562"></a>00562 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> j = e2.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l00563"></a>00563 <span class="keywordflow">for</span> (; j != e2.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); ++j) {
<a name="l00564"></a>00564 sumExprs.push_back(canonMultMtermMterm((*i) * (*j)).getRHS());
<a name="l00565"></a>00565 }
<a name="l00566"></a>00566 }
<a name="l00567"></a>00567 <span class="keywordflow">return</span> canonCombineLikeTerms(sumExprs);
<a name="l00568"></a>00568 }
<a name="l00569"></a>00569
<a name="l00570"></a>00570
<a name="l00571"></a>00571
<a name="l00572"></a>00572 <span class="comment">// The following produces a Theorem which is the result of multiplication</span>
<a name="l00573"></a>00573 <span class="comment">// of two canonized mterms. e = e1*e2</span>
<a name="l00574"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ab5166b206f49897a6a49ba0014c0b808">00574</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::canonMultMtermMterm(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00575"></a>00575
<a name="l00576"></a>00576 <span class="comment">// Check if the rule is sound</span>
<a name="l00577"></a>00577 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00578"></a>00578 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(e) && e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 2, <span class="stringliteral">"canonMultMtermMterm: e = "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00579"></a>00579 }
<a name="l00580"></a>00580
<a name="l00581"></a>00581 <span class="comment">// The proof we are using</span>
<a name="l00582"></a>00582 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00583"></a>00583
<a name="l00584"></a>00584 <span class="comment">// The resulting expression</span>
<a name="l00585"></a>00585 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> rhs;
<a name="l00586"></a>00586
<a name="l00587"></a>00587 <span class="comment">// Get the parts of the multiplication</span>
<a name="l00588"></a>00588 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e1 = e[0];
<a name="l00589"></a>00589 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e2 = e[1];
<a name="l00590"></a>00590
<a name="l00591"></a>00591 <span class="comment">// The name of the proof</span>
<a name="l00592"></a>00592 <span class="keywordtype">string</span> cmmm = <span class="stringliteral">"canon_mult_mterm_mterm"</span>;
<a name="l00593"></a>00593
<a name="l00594"></a>00594 <span class="keywordflow">if</span> (e1.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>()) {
<a name="l00595"></a>00595 <span class="comment">// e1 is a Rational</span>
<a name="l00596"></a>00596 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c = e1.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l00597"></a>00597 <span class="keywordflow">if</span> (c == 0)
<a name="l00598"></a>00598 <span class="keywordflow">return</span> canonMultZero(e2);
<a name="l00599"></a>00599 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (c == 1)
<a name="l00600"></a>00600 <span class="keywordflow">return</span> canonMultOne(e2);
<a name="l00601"></a>00601 <span class="keywordflow">else</span> {
<a name="l00602"></a>00602 <span class="keywordflow">switch</span> (e2.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>()) {
<a name="l00603"></a>00603 <span class="keywordflow">case</span> <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a> :
<a name="l00604"></a>00604 <span class="comment">// rat * rat</span>
<a name="l00605"></a>00605 <span class="keywordflow">return</span> canonMultConstConst(e1,e2);
<a name="l00606"></a>00606 <span class="keywordflow">break</span>;
<a name="l00607"></a>00607 <span class="comment">// TODO case of leaf</span>
<a name="l00608"></a>00608 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>:
<a name="l00609"></a>00609 <span class="comment">// rat * (POW rat leaf)</span>
<a name="l00610"></a>00610 <span class="comment">// nothing to simplify</span>
<a name="l00611"></a>00611 <span class="keywordflow">return</span> d_theoryArith->reflexivityRule (e);
<a name="l00612"></a>00612
<a name="l00613"></a>00613 <span class="keywordflow">break</span>;
<a name="l00614"></a>00614 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>:
<a name="l00615"></a>00615 rhs = canonMultConstMult(e1,e2);
<a name="l00616"></a>00616 <span class="keywordflow">if</span>(withProof()) pf = newPf(cmmm,e,rhs);
<a name="l00617"></a>00617 <span class="keywordflow">return</span> newRWTheorem(e, rhs, Assumptions::emptyAssump(), pf);
<a name="l00618"></a>00618 <span class="keywordflow">break</span>;
<a name="l00619"></a>00619 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>:
<a name="l00620"></a>00620 rhs = canonMultConstPlus(e1,e2);
<a name="l00621"></a>00621 <span class="keywordflow">if</span>(withProof()) pf = newPf(cmmm,e,rhs);
<a name="l00622"></a>00622 <span class="keywordflow">return</span> newRWTheorem(e, rhs, Assumptions::emptyAssump(), pf);
<a name="l00623"></a>00623 <span class="keywordflow">break</span>;
<a name="l00624"></a>00624 <span class="keywordflow">default</span>:
<a name="l00625"></a>00625 <span class="comment">// TODO: I am going to assume that this is just a leaf</span>
<a name="l00626"></a>00626 <span class="comment">// i.e., a variable or term from another theory</span>
<a name="l00627"></a>00627 <span class="keywordflow">return</span> d_theoryArith->reflexivityRule(e);
<a name="l00628"></a>00628 <span class="keywordflow">break</span>;
<a name="l00629"></a>00629 }
<a name="l00630"></a>00630 }
<a name="l00631"></a>00631 }
<a name="l00632"></a>00632 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (e1.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>) {
<a name="l00633"></a>00633 <span class="keywordflow">switch</span> (e2.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>()) {
<a name="l00634"></a>00634 <span class="keywordflow">case</span> <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a>:
<a name="l00635"></a>00635 <span class="comment">// switch the order of the two arguments</span>
<a name="l00636"></a>00636 <span class="keywordflow">return</span> canonMultMtermMterm(e2 * e1);
<a name="l00637"></a>00637 <span class="keywordflow">break</span>;
<a name="l00638"></a>00638 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>:
<a name="l00639"></a>00639 rhs = canonMultPowPow(e1,e2);
<a name="l00640"></a>00640 <span class="keywordflow">if</span>(withProof()) pf = newPf(cmmm,e,rhs);
<a name="l00641"></a>00641 <span class="keywordflow">return</span> newRWTheorem(e,rhs, Assumptions::emptyAssump(), pf);
<a name="l00642"></a>00642 <span class="keywordflow">break</span>;
<a name="l00643"></a>00643 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>:
<a name="l00644"></a>00644 rhs = canonMultLeafOrPowMult(e1,e2);
<a name="l00645"></a>00645 <span class="keywordflow">if</span>(withProof()) pf = newPf(cmmm,e,rhs);
<a name="l00646"></a>00646 <span class="keywordflow">return</span> newRWTheorem(e, rhs, Assumptions::emptyAssump(), pf);
<a name="l00647"></a>00647 <span class="keywordflow">break</span>;
<a name="l00648"></a>00648 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>:
<a name="l00649"></a>00649 rhs = canonMultLeafOrPowOrMultPlus(e1,e2);
<a name="l00650"></a>00650 <span class="keywordflow">if</span>(withProof()) pf = newPf(cmmm,e,rhs);
<a name="l00651"></a>00651 <span class="keywordflow">return</span> newRWTheorem(e, rhs, Assumptions::emptyAssump(), pf);
<a name="l00652"></a>00652 <span class="keywordflow">break</span>;
<a name="l00653"></a>00653 <span class="keywordflow">default</span>:
<a name="l00654"></a>00654 rhs = canonMultPowLeaf(e1,e2);
<a name="l00655"></a>00655 <span class="keywordflow">if</span>(withProof()) pf = newPf(cmmm,e,rhs);
<a name="l00656"></a>00656 <span class="keywordflow">return</span> newRWTheorem(e,rhs, Assumptions::emptyAssump(), pf);
<a name="l00657"></a>00657 <span class="keywordflow">break</span>;
<a name="l00658"></a>00658 }
<a name="l00659"></a>00659 }
<a name="l00660"></a>00660 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (e1.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>) {
<a name="l00661"></a>00661 <span class="keywordflow">switch</span> (e2.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>()) {
<a name="l00662"></a>00662 <span class="keywordflow">case</span> <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a>:
<a name="l00663"></a>00663 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>:
<a name="l00664"></a>00664 <span class="comment">// switch the order of the two arguments</span>
<a name="l00665"></a>00665 <span class="keywordflow">return</span> canonMultMtermMterm(e2 * e1);
<a name="l00666"></a>00666 <span class="keywordflow">break</span>;
<a name="l00667"></a>00667 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>:
<a name="l00668"></a>00668 {
<a name="l00669"></a>00669 <span class="comment">// (Mult r m1 m2 ...) (Mult r' m1' m2' ...)</span>
<a name="l00670"></a>00670 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> result = e2;
<a name="l00671"></a>00671 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = e1.begin();
<a name="l00672"></a>00672 <span class="keywordflow">for</span> (; i != e1.end(); ++i) {
<a name="l00673"></a>00673 result = canonMultMtermMterm((*i) * result).getRHS();
<a name="l00674"></a>00674 }
<a name="l00675"></a>00675 <span class="keywordflow">if</span>(withProof()) pf = newPf(cmmm,e,result);
<a name="l00676"></a>00676 <span class="keywordflow">return</span> newRWTheorem(e, result, Assumptions::emptyAssump(), pf);
<a name="l00677"></a>00677 }
<a name="l00678"></a>00678 <span class="keywordflow">break</span>;
<a name="l00679"></a>00679 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>:
<a name="l00680"></a>00680 rhs = canonMultLeafOrPowOrMultPlus(e1,e2);
<a name="l00681"></a>00681 <span class="keywordflow">if</span>(withProof()) pf = newPf(cmmm,e,rhs);
<a name="l00682"></a>00682 <span class="keywordflow">return</span> newRWTheorem(e,rhs, Assumptions::emptyAssump(), pf);
<a name="l00683"></a>00683 <span class="keywordflow">break</span>;
<a name="l00684"></a>00684 <span class="keywordflow">default</span>:
<a name="l00685"></a>00685 <span class="comment">// leaf</span>
<a name="l00686"></a>00686 <span class="comment">// switch the order of the two arguments</span>
<a name="l00687"></a>00687 <span class="keywordflow">return</span> canonMultMtermMterm(e2 * e1);
<a name="l00688"></a>00688 <span class="keywordflow">break</span>;
<a name="l00689"></a>00689 }
<a name="l00690"></a>00690 }
<a name="l00691"></a>00691 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (e1.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>) {
<a name="l00692"></a>00692 <span class="keywordflow">switch</span> (e2.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>()) {
<a name="l00693"></a>00693 <span class="keywordflow">case</span> <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a>:
<a name="l00694"></a>00694 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>:
<a name="l00695"></a>00695 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>:
<a name="l00696"></a>00696 <span class="comment">// switch the order of the two arguments</span>
<a name="l00697"></a>00697 <span class="keywordflow">return</span> canonMultMtermMterm(e2 * e1);
<a name="l00698"></a>00698 <span class="keywordflow">break</span>;
<a name="l00699"></a>00699 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>:
<a name="l00700"></a>00700 rhs = canonMultPlusPlus(e1,e2);
<a name="l00701"></a>00701 <span class="keywordflow">if</span>(withProof()) pf = newPf(cmmm,e,rhs);
<a name="l00702"></a>00702 <span class="keywordflow">return</span> newRWTheorem(e, rhs, Assumptions::emptyAssump(), pf);
<a name="l00703"></a>00703 <span class="keywordflow">break</span>;
<a name="l00704"></a>00704 <span class="keywordflow">default</span>:
<a name="l00705"></a>00705 <span class="comment">// leaf</span>
<a name="l00706"></a>00706 <span class="comment">// switch the order of the two arguments</span>
<a name="l00707"></a>00707 <span class="keywordflow">return</span> canonMultMtermMterm(e2 * e1);
<a name="l00708"></a>00708 <span class="keywordflow">break</span>;
<a name="l00709"></a>00709 }
<a name="l00710"></a>00710 }
<a name="l00711"></a>00711 <span class="keywordflow">else</span> {
<a name="l00712"></a>00712 <span class="comment">// leaf</span>
<a name="l00713"></a>00713 <span class="keywordflow">switch</span> (e2.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>()) {
<a name="l00714"></a>00714 <span class="keywordflow">case</span> <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a>:
<a name="l00715"></a>00715 <span class="comment">// switch the order of the two arguments</span>
<a name="l00716"></a>00716 <span class="keywordflow">return</span> canonMultMtermMterm(e2 * e1);
<a name="l00717"></a>00717 <span class="keywordflow">break</span>;
<a name="l00718"></a>00718 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>:
<a name="l00719"></a>00719 rhs = canonMultPowLeaf(e2,e1);
<a name="l00720"></a>00720 <span class="keywordflow">if</span>(withProof()) pf = newPf(cmmm,e,rhs);
<a name="l00721"></a>00721 <span class="keywordflow">return</span> newRWTheorem(e, rhs, Assumptions::emptyAssump(), pf);
<a name="l00722"></a>00722 <span class="keywordflow">break</span>;
<a name="l00723"></a>00723 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>:
<a name="l00724"></a>00724 rhs = canonMultLeafOrPowMult(e1,e2);;
<a name="l00725"></a>00725 <span class="keywordflow">if</span>(withProof()) pf = newPf(cmmm,e,rhs);
<a name="l00726"></a>00726 <span class="keywordflow">return</span> newRWTheorem(e, rhs, Assumptions::emptyAssump(), pf);
<a name="l00727"></a>00727 <span class="keywordflow">break</span>;
<a name="l00728"></a>00728 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>:
<a name="l00729"></a>00729 rhs = canonMultLeafOrPowOrMultPlus(e1,e2);
<a name="l00730"></a>00730 <span class="keywordflow">if</span>(withProof()) pf = newPf(cmmm,e,rhs);
<a name="l00731"></a>00731 <span class="keywordflow">return</span> newRWTheorem(e, rhs, Assumptions::emptyAssump(), pf);
<a name="l00732"></a>00732 <span class="keywordflow">break</span>;
<a name="l00733"></a>00733 <span class="keywordflow">default</span>:
<a name="l00734"></a>00734 <span class="comment">// leaf * leaf</span>
<a name="l00735"></a>00735 rhs = canonMultLeafLeaf(e1,e2);
<a name="l00736"></a>00736 <span class="keywordflow">if</span>(withProof()) pf = newPf(cmmm,e,rhs);
<a name="l00737"></a>00737 <span class="keywordflow">return</span> newRWTheorem(e, rhs, Assumptions::emptyAssump(), pf);
<a name="l00738"></a>00738 <span class="keywordflow">break</span>;
<a name="l00739"></a>00739 }
<a name="l00740"></a>00740 }
<a name="l00741"></a>00741 <a class="code" href="debug_8h.html#a2637b2fffa22e3c9fad40cda8fcc3bce" title="If something goes horribly wrong, print a message and abort immediately with exit(1).">FatalAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Unreachable"</span>);
<a name="l00742"></a>00742 <span class="keywordflow">return</span> newRWTheorem(e, rhs, Assumptions::emptyAssump(), pf);
<a name="l00743"></a>00743 }
<a name="l00744"></a>00744
<a name="l00745"></a>00745 <span class="comment">// (PLUS expr1 expr2 ...) where each expr is itself in canonic form</span>
<a name="l00746"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a41f7000c783a82e9a86cad823b06bff4">00746</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::canonPlus(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00747"></a>00747 {
<a name="l00748"></a>00748 <span class="comment">// Create the proof object in case we need it</span>
<a name="l00749"></a>00749 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00750"></a>00750
<a name="l00751"></a>00751 <span class="comment">// The operation must be PLUS</span>
<a name="l00752"></a>00752 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>, <span class="stringliteral">""</span>);
<a name="l00753"></a>00753
<a name="l00754"></a>00754 <span class="comment">// Add all the summands to the sumKids vector</span>
<a name="l00755"></a>00755 std::vector<Expr> sumKids;
<a name="l00756"></a>00756 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = e.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l00757"></a>00757 <span class="keywordflow">for</span>(; i != e.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); ++i) {
<a name="l00758"></a>00758 <span class="keywordflow">if</span> ((*i).getKind() != <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>)
<a name="l00759"></a>00759 sumKids.push_back(*i);
<a name="l00760"></a>00760 <span class="keywordflow">else</span> {
<a name="l00761"></a>00761 <span class="comment">// If the kid is also a sum, add it to the sumKids vector (no need for recursion, kids are already canonized)</span>
<a name="l00762"></a>00762 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> j = (*i).begin();
<a name="l00763"></a>00763 <span class="keywordflow">for</span>(; j != (*i).end(); ++j)
<a name="l00764"></a>00764 sumKids.push_back(*j);
<a name="l00765"></a>00765 }
<a name="l00766"></a>00766 }
<a name="l00767"></a>00767
<a name="l00768"></a>00768 <span class="comment">// Combine all the kids to sum (gather the same variables and stuff)</span>
<a name="l00769"></a>00769 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> val = canonCombineLikeTerms(sumKids);
<a name="l00770"></a>00770
<a name="l00771"></a>00771 <span class="comment">// If proofs needed set it up with starting expression and the value</span>
<a name="l00772"></a>00772 <span class="keywordflow">if</span> (withProof()) {
<a name="l00773"></a>00773 pf = newPf(<span class="stringliteral">"canon_plus"</span>, e, val);
<a name="l00774"></a>00774 }
<a name="l00775"></a>00775
<a name="l00776"></a>00776 <span class="comment">// Return the explaining rewrite theorem</span>
<a name="l00777"></a>00777 <span class="keywordflow">return</span> newRWTheorem(e, val, Assumptions::emptyAssump(), pf);
<a name="l00778"></a>00778 }
<a name="l00779"></a>00779
<a name="l00780"></a>00780 <span class="comment">// (MULT expr1 expr2 ...) where each expr is itself in canonic form</span>
<a name="l00781"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a9bd77385dd0cbaac271aaab4b6c6ec09">00781</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::canonMult(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00782"></a>00782 {
<a name="l00783"></a>00783 <span class="comment">// The proof we might need</span>
<a name="l00784"></a>00784 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00785"></a>00785
<a name="l00786"></a>00786 <span class="comment">// Expression must be of kind MULT</span>
<a name="l00787"></a>00787 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a> && e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 1, <span class="stringliteral">""</span>);
<a name="l00788"></a>00788
<a name="l00789"></a>00789 <span class="comment">// Get the first operand of the multiplication</span>
<a name="l00790"></a>00790 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = e.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l00791"></a>00791
<a name="l00792"></a>00792 <span class="comment">// Set the result to the first element</span>
<a name="l00793"></a>00793 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> result = *i;
<a name="l00794"></a>00794
<a name="l00795"></a>00795 <span class="comment">// Skip to the next one</span>
<a name="l00796"></a>00796 ++i;
<a name="l00797"></a>00797
<a name="l00798"></a>00798 <span class="comment">// For all the other elements</span>
<a name="l00799"></a>00799 <span class="keywordflow">for</span> (; i != e.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); ++i) {
<a name="l00800"></a>00800 <span class="comment">// Multiply each element into the result</span>
<a name="l00801"></a>00801 result = canonMultMtermMterm(result * (*i)).getRHS();
<a name="l00802"></a>00802 }
<a name="l00803"></a>00803
<a name="l00804"></a>00804 <span class="comment">// If the proof is needed, create one</span>
<a name="l00805"></a>00805 <span class="keywordflow">if</span> (withProof()) {
<a name="l00806"></a>00806 pf = newPf(<span class="stringliteral">"canon_mult"</span>, e,result);
<a name="l00807"></a>00807 }
<a name="l00808"></a>00808
<a name="l00809"></a>00809 <span class="comment">// Return a new rewrite theorem with the result</span>
<a name="l00810"></a>00810 <span class="keywordflow">return</span> newRWTheorem(e, result, Assumptions::emptyAssump(), pf);
<a name="l00811"></a>00811 }
<a name="l00812"></a>00812
<a name="l00813"></a>00813
<a name="l00814"></a>00814 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00815"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a7b07ab799dbdf80254df3ec7fc35d36d">00815</a> ArithTheoremProducer::canonInvertConst(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00816"></a>00816 {
<a name="l00817"></a>00817 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l00818"></a>00818 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(e), <span class="stringliteral">"expecting a rational: e = "</span>+e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00819"></a>00819
<a name="l00820"></a>00820 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00821"></a>00821
<a name="l00822"></a>00822 <span class="keywordflow">if</span> (withProof()) {
<a name="l00823"></a>00823 pf = newPf(<span class="stringliteral">"canon_invert_const"</span>, e);
<a name="l00824"></a>00824 }
<a name="l00825"></a>00825 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& er = e.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l00826"></a>00826 <span class="keywordflow">return</span> newRWTheorem((rat(1)/e), rat(er==0? 0 : (1/er)), Assumptions::emptyAssump(), pf);
<a name="l00827"></a>00827 }
<a name="l00828"></a>00828
<a name="l00829"></a>00829
<a name="l00830"></a>00830 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00831"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#afb0c2a89f3373dcb26cd516714d0e49a">00831</a> ArithTheoremProducer::canonInvertLeaf(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00832"></a>00832 {
<a name="l00833"></a>00833 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00834"></a>00834
<a name="l00835"></a>00835 <span class="keywordflow">if</span> (withProof()) {
<a name="l00836"></a>00836 pf = newPf(<span class="stringliteral">"canon_invert_leaf"</span>, e);
<a name="l00837"></a>00837 }
<a name="l00838"></a>00838 <span class="keywordflow">return</span> newRWTheorem((rat(1)/e), <a class="code" href="namespaceCVC3.html#aa123bf4eb1751181baf16c5e80b47740" title="Power (x^n, or base^{pow}) expressions.">powExpr</a>(rat(-1), e), Assumptions::emptyAssump(), pf);
<a name="l00839"></a>00839 }
<a name="l00840"></a>00840
<a name="l00841"></a>00841
<a name="l00842"></a>00842 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00843"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a6a829cb16f960f9e7c2f25ea4906eaba">00843</a> ArithTheoremProducer::canonInvertPow(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00844"></a>00844 {
<a name="l00845"></a>00845 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>, <span class="stringliteral">"expecting a rational"</span>+e[0].<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00846"></a>00846
<a name="l00847"></a>00847 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00848"></a>00848
<a name="l00849"></a>00849 <span class="keywordflow">if</span> (withProof()) {
<a name="l00850"></a>00850 pf = newPf(<span class="stringliteral">"canon_invert_pow"</span>, e);
<a name="l00851"></a>00851 }
<a name="l00852"></a>00852 <span class="keywordflow">if</span> (e[0].getRational() == -1)
<a name="l00853"></a>00853 <span class="keywordflow">return</span> newRWTheorem((rat(1)/e), e[1], Assumptions::emptyAssump(), pf);
<a name="l00854"></a>00854 <span class="keywordflow">else</span>
<a name="l00855"></a>00855 <span class="keywordflow">return</span> newRWTheorem((rat(1)/e),
<a name="l00856"></a>00856 <a class="code" href="namespaceCVC3.html#aa123bf4eb1751181baf16c5e80b47740" title="Power (x^n, or base^{pow}) expressions.">powExpr</a>(rat(-e[0].getRational()), e),
<a name="l00857"></a>00857 Assumptions::emptyAssump(),
<a name="l00858"></a>00858 pf);
<a name="l00859"></a>00859 }
<a name="l00860"></a>00860
<a name="l00861"></a>00861 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00862"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a70a381c22184655fb6d4f3b621bf216b">00862</a> ArithTheoremProducer::canonInvertMult(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00863"></a>00863 {
<a name="l00864"></a>00864 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>, <span class="stringliteral">"expecting a rational"</span>+e[0].<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00865"></a>00865
<a name="l00866"></a>00866 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00867"></a>00867
<a name="l00868"></a>00868 <span class="keywordflow">if</span> (withProof()) {
<a name="l00869"></a>00869 pf = newPf(<span class="stringliteral">"canon_invert_mult"</span>, e);
<a name="l00870"></a>00870 }
<a name="l00871"></a>00871
<a name="l00872"></a>00872 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 1, <span class="stringliteral">"MULT should have arity > 1"</span>+e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00873"></a>00873 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> result = canonInvert(e[0]).getRHS();
<a name="l00874"></a>00874 <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i < e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>(); ++i) {
<a name="l00875"></a>00875 result =
<a name="l00876"></a>00876 canonMultMtermMterm(result * canonInvert(e[i]).getRHS()).getRHS();
<a name="l00877"></a>00877 }
<a name="l00878"></a>00878 <span class="keywordflow">return</span> newRWTheorem((rat(1)/e), result, Assumptions::emptyAssump(), pf);
<a name="l00879"></a>00879 }
<a name="l00880"></a>00880
<a name="l00881"></a>00881
<a name="l00882"></a>00882 <span class="comment">// Given an expression e in Canonic form generate 1/e in canonic form</span>
<a name="l00883"></a>00883 <span class="comment">// This function assumes that e is not a PLUS expression</span>
<a name="l00884"></a>00884 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00885"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a7c7c860b193ec63a776dd13613aeca25">00885</a> ArithTheoremProducer::canonInvert(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00886"></a>00886 {
<a name="l00887"></a>00887 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() != <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>,
<a name="l00888"></a>00888 <span class="stringliteral">"Cannot do inverse on a PLUS"</span>+e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00889"></a>00889 <span class="keywordflow">switch</span> (e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>()) {
<a name="l00890"></a>00890 <span class="keywordflow">case</span> <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a>:
<a name="l00891"></a>00891 <span class="keywordflow">return</span> canonInvertConst(e);
<a name="l00892"></a>00892 <span class="keywordflow">break</span>;
<a name="l00893"></a>00893 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>:
<a name="l00894"></a>00894 <span class="keywordflow">return</span> canonInvertPow(e);
<a name="l00895"></a>00895 <span class="keywordflow">break</span>;
<a name="l00896"></a>00896 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>:
<a name="l00897"></a>00897 <span class="keywordflow">return</span> canonInvertMult(e);
<a name="l00898"></a>00898 <span class="keywordflow">break</span>;
<a name="l00899"></a>00899 <span class="keywordflow">default</span>:
<a name="l00900"></a>00900 <span class="comment">// leaf</span>
<a name="l00901"></a>00901 <span class="keywordflow">return</span> canonInvertLeaf(e);
<a name="l00902"></a>00902 <span class="keywordflow">break</span>;
<a name="l00903"></a>00903 }
<a name="l00904"></a>00904 }
<a name="l00905"></a>00905
<a name="l00906"></a>00906
<a name="l00907"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a92540cc58f6203c2904fc2bd197190da">00907</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::canonDivide(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l00908"></a>00908 {
<a name="l00909"></a>00909 <span class="comment">// The expression should be of type DIVIDE</span>
<a name="l00910"></a>00910 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ac3c38ad296d5671b7fde3373fdd87ea1">DIVIDE</a>, <span class="stringliteral">"Expecting Divide"</span>+e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00911"></a>00911
<a name="l00912"></a>00912 <span class="comment">// The proof if we need one</span>
<a name="l00913"></a>00913 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00914"></a>00914
<a name="l00915"></a>00915 <span class="comment">// If the proof is needed make it</span>
<a name="l00916"></a>00916 <span class="keywordflow">if</span> (withProof()) {
<a name="l00917"></a>00917 pf = newPf(<span class="stringliteral">"canon_invert_divide"</span>, e);
<a name="l00918"></a>00918 }
<a name="l00919"></a>00919
<a name="l00920"></a>00920 <span class="comment">// Rewrite e[0] / e[1] as e[0]*(e[1])^-1</span>
<a name="l00921"></a>00921 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> thm = newRWTheorem(e, e[0]*(canonInvert(e[1]).getRHS()), Assumptions::emptyAssump(), pf);
<a name="l00922"></a>00922
<a name="l00923"></a>00923 <span class="comment">// Return the proof with canonizing the above multiplication</span>
<a name="l00924"></a>00924 <span class="keywordflow">return</span> d_theoryArith->transitivityRule(thm, canonMult(thm.<a class="code" href="classCVC3_1_1Theorem.html#a97d957fcbf9094480851b1d2e5d3729f">getRHS</a>()));
<a name="l00925"></a>00925 }
<a name="l00926"></a>00926
<a name="l00927"></a>00927
<a name="l00928"></a>00928 <span class="comment">// Rules for multiplication</span>
<a name="l00929"></a>00929 <span class="comment">// t*c ==> c*t, takes constant c and term t</span>
<a name="l00930"></a>00930 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00931"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#af6ba91fa47c4c9139c4d93fe3de0112f">00931</a> ArithTheoremProducer::canonMultTermConst(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t) {
<a name="l00932"></a>00932 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00933"></a>00933 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00934"></a>00934 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(c),
<a name="l00935"></a>00935 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonMultTermConst:\n "</span>
<a name="l00936"></a>00936 <span class="stringliteral">"c is not a constant: "</span> + c.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00937"></a>00937 }
<a name="l00938"></a>00938 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"canon_mult_term_const"</span>, c, t);
<a name="l00939"></a>00939 <span class="keywordflow">return</span> newRWTheorem((t*c), (c*t), Assumptions::emptyAssump(), pf);
<a name="l00940"></a>00940 }
<a name="l00941"></a>00941
<a name="l00942"></a>00942 <span class="comment">// Rules for multiplication</span>
<a name="l00943"></a>00943 <span class="comment">// t1*t2 ==> Error, takes t1 and t2 where both are non-constants</span>
<a name="l00944"></a>00944 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00945"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a529fe89fea243d932879a1a74e9d36a7">00945</a> ArithTheoremProducer::canonMultTerm1Term2(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t2) {
<a name="l00946"></a>00946 <span class="comment">// Proof pf;</span>
<a name="l00947"></a>00947 <span class="comment">// if(withProof()) pf = newPf("canon_mult_term1_term2", t1, t2);</span>
<a name="l00948"></a>00948 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00949"></a>00949 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<span class="keyword">false</span>, <span class="stringliteral">"Fatal Error: We don't support multiplication"</span>
<a name="l00950"></a>00950 <span class="stringliteral">"of two non constant terms at this time "</span>
<a name="l00951"></a>00951 + t1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">" and "</span> + t2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00952"></a>00952 }
<a name="l00953"></a>00953 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l00954"></a>00954 }
<a name="l00955"></a>00955
<a name="l00956"></a>00956 <span class="comment">// Rules for multiplication</span>
<a name="l00957"></a>00957 <span class="comment">// 0*x = 0, takes x</span>
<a name="l00958"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a55ec89d6cf310694e9f4b1013a795ce2">00958</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::canonMultZero(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00959"></a>00959 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00960"></a>00960 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"canon_mult_zero"</span>, e);
<a name="l00961"></a>00961 <span class="keywordflow">return</span> newRWTheorem((rat(0)*e), rat(0), Assumptions::emptyAssump(), pf);
<a name="l00962"></a>00962 }
<a name="l00963"></a>00963
<a name="l00964"></a>00964 <span class="comment">// Rules for multiplication</span>
<a name="l00965"></a>00965 <span class="comment">// 1*x ==> x, takes x (if x is other than a leaf)</span>
<a name="l00966"></a>00966 <span class="comment">// otherwise 1*x ==> 1*x</span>
<a name="l00967"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ae5a6e1b2c7b9239b7e53027c51a2dc7e">00967</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::canonMultOne(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l00968"></a>00968
<a name="l00969"></a>00969 <span class="comment">// Setup the proof object</span>
<a name="l00970"></a>00970 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00971"></a>00971 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"canon_mult_one"</span>, e);
<a name="l00972"></a>00972
<a name="l00973"></a>00973 <span class="comment">// If it is a leaf multiply it by one</span>
<a name="l00974"></a>00974 <span class="keywordflow">if</span> (d_theoryArith->isLeaf(e)) <span class="keywordflow">return</span> d_theoryArith->reflexivityRule (rat(1)*e);
<a name="l00975"></a>00975
<a name="l00976"></a>00976 <span class="comment">// Otherwise, just return the expression itself</span>
<a name="l00977"></a>00977 <span class="keywordflow">return</span> newRWTheorem((rat(1)*e), e, Assumptions::emptyAssump(), pf);
<a name="l00978"></a>00978 }
<a name="l00979"></a>00979
<a name="l00980"></a>00980 <span class="comment">// Rules for multiplication</span>
<a name="l00981"></a>00981 <span class="comment">// c1*c2 ==> c', takes constant c1*c2</span>
<a name="l00982"></a>00982 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00983"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#affbdf02016310d8cd6a9037fdd9eddc6">00983</a> ArithTheoremProducer::canonMultConstConst(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c2) {
<a name="l00984"></a>00984 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l00985"></a>00985 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l00986"></a>00986 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(c1),
<a name="l00987"></a>00987 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonMultConstConst:\n "</span>
<a name="l00988"></a>00988 <span class="stringliteral">"c1 is not a constant: "</span> + c1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00989"></a>00989 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(c2),
<a name="l00990"></a>00990 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonMultConstConst:\n "</span>
<a name="l00991"></a>00991 <span class="stringliteral">"c2 is not a constant: "</span> + c2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l00992"></a>00992 }
<a name="l00993"></a>00993 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"canon_mult_const_const"</span>, c1, c2);
<a name="l00994"></a>00994 <span class="keywordflow">return</span>
<a name="l00995"></a>00995 newRWTheorem((c1*c2), rat(c1.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>()*c2.getRational()), Assumptions::emptyAssump(), pf);
<a name="l00996"></a>00996 }
<a name="l00997"></a>00997
<a name="l00998"></a>00998 <span class="comment">// Rules for multiplication</span>
<a name="l00999"></a>00999 <span class="comment">// c1*(c2*t) ==> c'*t, takes c1 and c2 and t</span>
<a name="l01000"></a>01000 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l01001"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ad51f0d5c3232b6c247939a10e253f53d">01001</a> ArithTheoremProducer::canonMultConstTerm(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c1,
<a name="l01002"></a>01002 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c2,<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t) {
<a name="l01003"></a>01003 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01004"></a>01004 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01005"></a>01005 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(c1),
<a name="l01006"></a>01006 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonMultConstTerm:\n "</span>
<a name="l01007"></a>01007 <span class="stringliteral">"c1 is not a constant: "</span> + c1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01008"></a>01008 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(c2),
<a name="l01009"></a>01009 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonMultConstTerm:\n "</span>
<a name="l01010"></a>01010 <span class="stringliteral">"c2 is not a constant: "</span> + c2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01011"></a>01011 }
<a name="l01012"></a>01012
<a name="l01013"></a>01013 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"canon_mult_const_term"</span>, c1, c2, t);
<a name="l01014"></a>01014 <span class="keywordflow">return</span>
<a name="l01015"></a>01015 newRWTheorem(c1*(c2*t), rat(c1.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>()*c2.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>())*t, Assumptions::emptyAssump(), pf);
<a name="l01016"></a>01016 }
<a name="l01017"></a>01017
<a name="l01018"></a>01018 <span class="comment">// Rules for multiplication</span>
<a name="l01019"></a>01019 <span class="comment">// c1*(+ c2 v1 ...) ==> (+ c1c2 c1v1 ...), takes c1 and the sum</span>
<a name="l01020"></a>01020 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l01021"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ab0e0e14c71501a9f8208963c54010fe4">01021</a> ArithTheoremProducer::canonMultConstSum(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& sum) {
<a name="l01022"></a>01022 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01023"></a>01023 std::vector<Expr> sumKids;
<a name="l01024"></a>01024
<a name="l01025"></a>01025 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01026"></a>01026 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(c1),
<a name="l01027"></a>01027 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonMultConstTerm:\n "</span>
<a name="l01028"></a>01028 <span class="stringliteral">"c1 is not a constant: "</span> + c1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01029"></a>01029 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a> == sum.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>(),
<a name="l01030"></a>01030 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonMultConstTerm:\n "</span>
<a name="l01031"></a>01031 <span class="stringliteral">"the kind must be a PLUS: "</span> + sum.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01032"></a>01032 }
<a name="l01033"></a>01033 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = sum.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l01034"></a>01034 <span class="keywordflow">for</span>(; i != sum.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); ++i)
<a name="l01035"></a>01035 sumKids.push_back(c1*(*i));
<a name="l01036"></a>01036 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ret = <a class="code" href="namespaceCVC3.html#accd3d7d38b0e04136afbc3e5191bc8bb">plusExpr</a>(sumKids);
<a name="l01037"></a>01037 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"canon_mult_const_sum"</span>, c1, sum, ret);
<a name="l01038"></a>01038 <span class="keywordflow">return</span> newRWTheorem((c1*sum),ret , Assumptions::emptyAssump(), pf);
<a name="l01039"></a>01039 }
<a name="l01040"></a>01040
<a name="l01041"></a>01041
<a name="l01042"></a>01042 <span class="comment">// c^n = c' (compute the constant power expression)</span>
<a name="l01043"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#af673275ae1c3dc606b29979b60df35c5">01043</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::canonPowConst(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l01044"></a>01044 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01045"></a>01045 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a> && e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 2
<a name="l01046"></a>01046 && e[0].<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>() && e[1].<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>(),
<a name="l01047"></a>01047 <span class="stringliteral">"ArithTheoremProducer::canonPowConst("</span>+e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l01048"></a>01048 }
<a name="l01049"></a>01049 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& p = e[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l01050"></a>01050 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& base = e[1].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l01051"></a>01051 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01052"></a>01052 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(p.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>(),
<a name="l01053"></a>01053 <span class="stringliteral">"ArithTheoremProducer::canonPowConst("</span>+e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l01054"></a>01054 }
<a name="l01055"></a>01055 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> res;
<a name="l01056"></a>01056 <span class="keywordflow">if</span> (base == 0 && p < 0) {
<a name="l01057"></a>01057 res = rat(0);
<a name="l01058"></a>01058 }
<a name="l01059"></a>01059 <span class="keywordflow">else</span> res = rat(<a class="code" href="namespaceCVC3.html#a28fc84bed3f9bc91ca9967de0f9cfa00" title="Raise 'base' into the power of 'pow' (pow must be an integer)">pow</a>(p, base));
<a name="l01060"></a>01060 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01061"></a>01061 <span class="keywordflow">if</span>(withProof())
<a name="l01062"></a>01062 pf = newPf(<span class="stringliteral">"canon_pow_const"</span>, e);
<a name="l01063"></a>01063 <span class="keywordflow">return</span> newRWTheorem(e, res, Assumptions::emptyAssump(), pf);
<a name="l01064"></a>01064 }
<a name="l01065"></a>01065
<a name="l01066"></a>01066
<a name="l01067"></a>01067 <span class="comment">// Rules for addition</span>
<a name="l01068"></a>01068 <span class="comment">// flattens the input. accepts a PLUS expr</span>
<a name="l01069"></a>01069 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l01070"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a19964269c705bafbe69cb1052fe7bec8">01070</a> ArithTheoremProducer::canonFlattenSum(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l01071"></a>01071 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01072"></a>01072 std::vector<Expr> sumKids;
<a name="l01073"></a>01073 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01074"></a>01074 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a> == e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>(),
<a name="l01075"></a>01075 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonFlattenSum:\n"</span>
<a name="l01076"></a>01076 <span class="stringliteral">"input must be a PLUS:"</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01077"></a>01077 }
<a name="l01078"></a>01078
<a name="l01079"></a>01079 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = e.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l01080"></a>01080 <span class="keywordflow">for</span>(; i != e.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); ++i){
<a name="l01081"></a>01081 <span class="keywordflow">if</span> (<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a> != (*i).getKind())
<a name="l01082"></a>01082 sumKids.push_back(*i);
<a name="l01083"></a>01083 <span class="keywordflow">else</span> {
<a name="l01084"></a>01084 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> j = (*i).begin();
<a name="l01085"></a>01085 <span class="keywordflow">for</span>(; j != (*i).end(); ++j)
<a name="l01086"></a>01086 sumKids.push_back(*j);
<a name="l01087"></a>01087 }
<a name="l01088"></a>01088 }
<a name="l01089"></a>01089 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ret = <a class="code" href="namespaceCVC3.html#accd3d7d38b0e04136afbc3e5191bc8bb">plusExpr</a>(sumKids);
<a name="l01090"></a>01090 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"canon_flatten_sum"</span>, e,ret);
<a name="l01091"></a>01091 <span class="keywordflow">return</span> newRWTheorem(e,ret, Assumptions::emptyAssump(), pf);
<a name="l01092"></a>01092 }
<a name="l01093"></a>01093
<a name="l01094"></a>01094 <span class="comment">// Rules for addition</span>
<a name="l01095"></a>01095 <span class="comment">// combine like terms. accepts a flattened PLUS expr</span>
<a name="l01096"></a>01096 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l01097"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ac9ee451992ab00f200ee8aee26e99e0c">01097</a> ArithTheoremProducer::canonComboLikeTerms(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l01098"></a>01098 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01099"></a>01099 std::vector<Expr> sumKids;
<a name="l01100"></a>01100 <a class="code" href="classCVC3_1_1ExprMap.html">ExprMap<Rational></a> sumHashMap;
<a name="l01101"></a>01101 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> constant = 0;
<a name="l01102"></a>01102
<a name="l01103"></a>01103 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01104"></a>01104 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> k = e.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l01105"></a>01105 <span class="keywordflow">for</span>(; k != e.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); ++k)
<a name="l01106"></a>01106 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(!<a class="code" href="namespaceCVC3.html#afb0f7d15ddbd87f9abb128108101f557">isPlus</a>(*k),
<a name="l01107"></a>01107 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::canonComboLikeTerms:\n"</span>
<a name="l01108"></a>01108 <span class="stringliteral">"input must be a flattened PLUS:"</span> + k->toString());
<a name="l01109"></a>01109 }
<a name="l01110"></a>01110 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = e.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l01111"></a>01111 <span class="keywordflow">for</span>(; i != e.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); ++i){
<a name="l01112"></a>01112 <span class="keywordflow">if</span>(i->isRational())
<a name="l01113"></a>01113 constant = constant + i->getRational();
<a name="l01114"></a>01114 <span class="keywordflow">else</span> {
<a name="l01115"></a>01115 <span class="keywordflow">if</span> (!<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(*i)) {
<a name="l01116"></a>01116 <span class="keywordflow">if</span>(0 == sumHashMap.<a class="code" href="classCVC3_1_1ExprMap.html#aa96dfa3a54a131cdb0964ef4b80e324f">count</a>((*i)))
<a name="l01117"></a>01117 sumHashMap[*i] = 1;
<a name="l01118"></a>01118 <span class="keywordflow">else</span>
<a name="l01119"></a>01119 sumHashMap[*i] += 1;
<a name="l01120"></a>01120 }
<a name="l01121"></a>01121 <span class="keywordflow">else</span> {
<a name="l01122"></a>01122 <span class="keywordflow">if</span>(0 == sumHashMap.<a class="code" href="classCVC3_1_1ExprMap.html#aa96dfa3a54a131cdb0964ef4b80e324f">count</a>((*i)[1]))
<a name="l01123"></a>01123 sumHashMap[(*i)[1]] = (*i)[0].getRational();
<a name="l01124"></a>01124 <span class="keywordflow">else</span>
<a name="l01125"></a>01125 sumHashMap[(*i)[1]] = sumHashMap[(*i)[1]] + (*i)[0].getRational();
<a name="l01126"></a>01126 }
<a name="l01127"></a>01127 }
<a name="l01128"></a>01128 }
<a name="l01129"></a>01129
<a name="l01130"></a>01130 sumKids.push_back(rat(constant));
<a name="l01131"></a>01131 <a class="code" href="classCVC3_1_1ExprMap.html">ExprMap<Rational>::iterator</a> j = sumHashMap.<a class="code" href="classCVC3_1_1ExprMap.html#a3db85401f8535daf4054fde531cd46b1">begin</a>();
<a name="l01132"></a>01132 <span class="keywordflow">for</span>(; j != sumHashMap.<a class="code" href="classCVC3_1_1ExprMap.html#a283ae6c44308cbdda0d82da5a16e52c8">end</a>(); ++j) {
<a name="l01133"></a>01133 <span class="keywordflow">if</span>(0 == (*j).second)
<a name="l01134"></a>01134 ;<span class="comment">//do nothing</span>
<a name="l01135"></a>01135 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (1 == (*j).second)
<a name="l01136"></a>01136 sumKids.push_back((*j).first);
<a name="l01137"></a>01137 <span class="keywordflow">else</span>
<a name="l01138"></a>01138 sumKids.push_back(rat((*j).second) * (*j).first);
<a name="l01139"></a>01139 }
<a name="l01140"></a>01140
<a name="l01141"></a>01141 <span class="comment">//constant is same as sumKids[0].</span>
<a name="l01142"></a>01142 <span class="comment">//corner cases: "0 + monomial" and "constant"(no monomials)</span>
<a name="l01143"></a>01143
<a name="l01144"></a>01144 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ret;
<a name="l01145"></a>01145 <span class="keywordflow">if</span>(2 == sumKids.size() && 0 == constant) ret = sumKids[1];
<a name="l01146"></a>01146 <span class="keywordflow">else</span> <span class="keywordflow">if</span> (1 == sumKids.size()) ret = sumKids[0];
<a name="l01147"></a>01147 <span class="keywordflow">else</span> ret = <a class="code" href="namespaceCVC3.html#accd3d7d38b0e04136afbc3e5191bc8bb">plusExpr</a>(sumKids);
<a name="l01148"></a>01148
<a name="l01149"></a>01149 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"canon_combo_like_terms"</span>,e,ret);
<a name="l01150"></a>01150 <span class="keywordflow">return</span> newRWTheorem(e, ret, Assumptions::emptyAssump(), pf);
<a name="l01151"></a>01151 }
<a name="l01152"></a>01152
<a name="l01153"></a>01153
<a name="l01154"></a>01154 <span class="comment">// 0 = (* e1 e2 ...) <=> 0 = e1 OR 0 = e2 OR ...</span>
<a name="l01155"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a0040d5d848f7040df940b92d95a75930">01155</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::multEqZero(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr)
<a name="l01156"></a>01156 {
<a name="l01157"></a>01157 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01158"></a>01158 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr.<a class="code" href="group__ExprPkg.html#gac4af2026c180da0f18d66ac616f61f3a">isEq</a>() && expr[0].<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>() &&
<a name="l01159"></a>01159 expr[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() == 0 &&
<a name="l01160"></a>01160 <a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(expr[1]) && expr[1].<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 1,
<a name="l01161"></a>01161 <span class="stringliteral">"multEqZero invariant violated"</span>+expr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01162"></a>01162 }
<a name="l01163"></a>01163 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01164"></a>01164 vector<Expr> kids;
<a name="l01165"></a>01165 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = expr[1].<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>(), iend = expr[1].<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>();
<a name="l01166"></a>01166 <span class="keywordflow">for</span> (; i != iend; ++i) {
<a name="l01167"></a>01167 kids.push_back(rat(0).eqExpr(*i));
<a name="l01168"></a>01168 }
<a name="l01169"></a>01169 <span class="keywordflow">if</span> (withProof()) {
<a name="l01170"></a>01170 pf = newPf(<span class="stringliteral">"multEqZero"</span>, expr);
<a name="l01171"></a>01171 }
<a name="l01172"></a>01172 <span class="keywordflow">return</span> newRWTheorem(expr, <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(<a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba96727447c0ad447987df1c6415aef074">OR</a>, kids), Assumptions::emptyAssump(), pf);
<a name="l01173"></a>01173 }
<a name="l01174"></a>01174
<a name="l01175"></a>01175
<a name="l01176"></a>01176 <span class="comment">// 0 = (^ c x) <=> false if c <=0</span>
<a name="l01177"></a>01177 <span class="comment">// <=> 0 = x if c > 0</span>
<a name="l01178"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a9cd618abf322c0389f1fc40f274059c2">01178</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::powEqZero(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr)
<a name="l01179"></a>01179 {
<a name="l01180"></a>01180 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01181"></a>01181 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr.<a class="code" href="group__ExprPkg.html#gac4af2026c180da0f18d66ac616f61f3a">isEq</a>() && expr[0].<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>() &&
<a name="l01182"></a>01182 expr[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() == 0 &&
<a name="l01183"></a>01183 <a class="code" href="namespaceCVC3.html#a7c2a9996013597a3e00c7562074f590b">isPow</a>(expr[1]) && expr[1].<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 2 &&
<a name="l01184"></a>01184 expr[1][0].<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>(),
<a name="l01185"></a>01185 <span class="stringliteral">"powEqZero invariant violated"</span>+expr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01186"></a>01186 }
<a name="l01187"></a>01187 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01188"></a>01188 <span class="keywordflow">if</span> (withProof()) {
<a name="l01189"></a>01189 pf = newPf(<span class="stringliteral">"powEqZero"</span>, expr);
<a name="l01190"></a>01190 }
<a name="l01191"></a>01191 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> r = expr[1][0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l01192"></a>01192 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> res;
<a name="l01193"></a>01193 <span class="keywordflow">if</span> (r <= 0) {
<a name="l01194"></a>01194 res = d_em->falseExpr();
<a name="l01195"></a>01195 }
<a name="l01196"></a>01196 <span class="keywordflow">else</span> {
<a name="l01197"></a>01197 res = rat(0).<a class="code" href="group__ExprPkg.html#gacb48495ca445c895f95d0c3c1ae2070b">eqExpr</a>(expr[1][1]);
<a name="l01198"></a>01198 }
<a name="l01199"></a>01199 <span class="keywordflow">return</span> newRWTheorem(expr, res, Assumptions::emptyAssump(), pf);
<a name="l01200"></a>01200 }
<a name="l01201"></a>01201
<a name="l01202"></a>01202
<a name="l01203"></a>01203 <span class="comment">// x^n = y^n <=> x = y (if n is odd)</span>
<a name="l01204"></a>01204 <span class="comment">// x^n = y^n <=> x = y OR x = -y (if n is even)</span>
<a name="l01205"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a3c454b863142345e1093663fbb89d306">01205</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::elimPower(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr)
<a name="l01206"></a>01206 {
<a name="l01207"></a>01207 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01208"></a>01208 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr.<a class="code" href="group__ExprPkg.html#gac4af2026c180da0f18d66ac616f61f3a">isEq</a>() && <a class="code" href="namespaceCVC3.html#a7c2a9996013597a3e00c7562074f590b">isPow</a>(expr[0]) &&
<a name="l01209"></a>01209 <a class="code" href="namespaceCVC3.html#a7c2a9996013597a3e00c7562074f590b">isPow</a>(expr[1]) &&
<a name="l01210"></a>01210 <a class="code" href="namespaceCVC3.html#aef45cea7af354d2928a8224f7ae8ae4f">isIntegerConst</a>(expr[0][0]) &&
<a name="l01211"></a>01211 expr[0][0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() > 0 &&
<a name="l01212"></a>01212 expr[0][0] == expr[1][0],
<a name="l01213"></a>01213 <span class="stringliteral">"elimPower invariant violated"</span>+expr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01214"></a>01214 }
<a name="l01215"></a>01215 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01216"></a>01216 <span class="keywordflow">if</span> (withProof()) {
<a name="l01217"></a>01217 pf = newPf(<span class="stringliteral">"elimPower"</span>, expr);
<a name="l01218"></a>01218 }
<a name="l01219"></a>01219 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> r = expr[0][0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l01220"></a>01220 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> res = expr[0][1].<a class="code" href="group__ExprPkg.html#gacb48495ca445c895f95d0c3c1ae2070b">eqExpr</a>(expr[1][1]);
<a name="l01221"></a>01221 <span class="keywordflow">if</span> (r % 2 == 0) {
<a name="l01222"></a>01222 res = res.<a class="code" href="group__ExprPkg.html#gaf310870d783fff343e77ba9c2277c626">orExpr</a>(expr[0][1].eqExpr(-expr[1][1]));
<a name="l01223"></a>01223 }
<a name="l01224"></a>01224 <span class="keywordflow">return</span> newRWTheorem(expr, res, Assumptions::emptyAssump(), pf);
<a name="l01225"></a>01225 }
<a name="l01226"></a>01226
<a name="l01227"></a>01227
<a name="l01228"></a>01228 <span class="comment">// x^n = c <=> x = root (if n is odd and root^n = c)</span>
<a name="l01229"></a>01229 <span class="comment">// x^n = c <=> x = root OR x = -root (if n is even and root^n = c)</span>
<a name="l01230"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a21456f49d3a6711f21e3c13fb3c0d34a">01230</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::elimPowerConst(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& root)
<a name="l01231"></a>01231 {
<a name="l01232"></a>01232 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01233"></a>01233 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr.<a class="code" href="group__ExprPkg.html#gac4af2026c180da0f18d66ac616f61f3a">isEq</a>() && <a class="code" href="namespaceCVC3.html#a7c2a9996013597a3e00c7562074f590b">isPow</a>(expr[0]) &&
<a name="l01234"></a>01234 <a class="code" href="namespaceCVC3.html#aef45cea7af354d2928a8224f7ae8ae4f">isIntegerConst</a>(expr[0][0]) &&
<a name="l01235"></a>01235 expr[0][0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() > 0 &&
<a name="l01236"></a>01236 expr[1].<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>() &&
<a name="l01237"></a>01237 <a class="code" href="namespaceCVC3.html#a28fc84bed3f9bc91ca9967de0f9cfa00" title="Raise 'base' into the power of 'pow' (pow must be an integer)">pow</a>(expr[0][0].getRational(), root) == expr[1].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>(),
<a name="l01238"></a>01238 <span class="stringliteral">"elimPowerConst invariant violated"</span>+expr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01239"></a>01239 }
<a name="l01240"></a>01240 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01241"></a>01241 <span class="keywordflow">if</span> (withProof()) {
<a name="l01242"></a>01242 pf = newPf(<span class="stringliteral">"elimPowerConst"</span>, expr, rat(root));
<a name="l01243"></a>01243 }
<a name="l01244"></a>01244 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> r = expr[0][0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l01245"></a>01245 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> res = expr[0][1].<a class="code" href="group__ExprPkg.html#gacb48495ca445c895f95d0c3c1ae2070b">eqExpr</a>(rat(root));
<a name="l01246"></a>01246 <span class="keywordflow">if</span> (r % 2 == 0) {
<a name="l01247"></a>01247 res = res.<a class="code" href="group__ExprPkg.html#gaf310870d783fff343e77ba9c2277c626">orExpr</a>(expr[0][1].eqExpr(rat(-root)));
<a name="l01248"></a>01248 }
<a name="l01249"></a>01249 <span class="keywordflow">return</span> newRWTheorem(expr, res, Assumptions::emptyAssump(), pf);
<a name="l01250"></a>01250 }
<a name="l01251"></a>01251
<a name="l01252"></a>01252
<a name="l01253"></a>01253 <span class="comment">// x^n = c <=> false (if n is even and c is negative)</span>
<a name="l01254"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#afbf059903de8b1e87aef9a4a75340d6c">01254</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::evenPowerEqNegConst(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr)
<a name="l01255"></a>01255 {
<a name="l01256"></a>01256 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01257"></a>01257 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr.<a class="code" href="group__ExprPkg.html#gac4af2026c180da0f18d66ac616f61f3a">isEq</a>() && <a class="code" href="namespaceCVC3.html#a7c2a9996013597a3e00c7562074f590b">isPow</a>(expr[0]) &&
<a name="l01258"></a>01258 expr[1].<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>() &&
<a name="l01259"></a>01259 <a class="code" href="namespaceCVC3.html#aef45cea7af354d2928a8224f7ae8ae4f">isIntegerConst</a>(expr[0][0]) &&
<a name="l01260"></a>01260 expr[0][0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() % 2 == 0 &&
<a name="l01261"></a>01261 expr[1].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() < 0,
<a name="l01262"></a>01262 <span class="stringliteral">"evenPowerEqNegConst invariant violated"</span>+expr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01263"></a>01263 }
<a name="l01264"></a>01264 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01265"></a>01265 <span class="keywordflow">if</span> (withProof()) {
<a name="l01266"></a>01266 pf = newPf(<span class="stringliteral">"evenPowerEqNegConst"</span>, expr);
<a name="l01267"></a>01267 }
<a name="l01268"></a>01268 <span class="keywordflow">return</span> newRWTheorem(expr, d_em->falseExpr(), Assumptions::emptyAssump(), pf);
<a name="l01269"></a>01269 }
<a name="l01270"></a>01270
<a name="l01271"></a>01271
<a name="l01272"></a>01272 <span class="comment">// x^n = c <=> false (if x is an integer and c is not a perfect n power)</span>
<a name="l01273"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aa3838fe1c003a9f47f3ec8344d192dea">01273</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::intEqIrrational(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="theory__quant_8cpp.html#ac9940420b1f3427ebe821902adbb578d">isIntx</a>)
<a name="l01274"></a>01274 {
<a name="l01275"></a>01275 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01276"></a>01276 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr.<a class="code" href="group__ExprPkg.html#gac4af2026c180da0f18d66ac616f61f3a">isEq</a>() && <a class="code" href="namespaceCVC3.html#a7c2a9996013597a3e00c7562074f590b">isPow</a>(expr[0]) &&
<a name="l01277"></a>01277 expr[1].<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>() &&
<a name="l01278"></a>01278 expr[1].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() != 0 &&
<a name="l01279"></a>01279 <a class="code" href="namespaceCVC3.html#aef45cea7af354d2928a8224f7ae8ae4f">isIntegerConst</a>(expr[0][0]) &&
<a name="l01280"></a>01280 expr[0][0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() > 0 &&
<a name="l01281"></a>01281 <a class="code" href="namespaceCVC3.html#aad16f7bcc4d7a86af9b253e8587d264b" title="take nth root of base, return result if it is exact, 0 otherwise">ratRoot</a>(expr[1].getRational(), expr[0][0].getRational().getUnsigned()) == 0,
<a name="l01282"></a>01282 <span class="stringliteral">"intEqIrrational invariant violated"</span>+expr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01283"></a>01283 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntx.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>()) && isIntx.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>()[0] == expr[0][1],
<a name="l01284"></a>01284 <span class="stringliteral">"ArithTheoremProducerOld::intEqIrrational:\n "</span>
<a name="l01285"></a>01285 <span class="stringliteral">"wrong integrality constraint:\n expr = "</span>
<a name="l01286"></a>01286 +expr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n isIntx = "</span>
<a name="l01287"></a>01287 +isIntx.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>().<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01288"></a>01288 }
<a name="l01289"></a>01289 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a>& assump(isIntx.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>());
<a name="l01290"></a>01290 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01291"></a>01291 <span class="keywordflow">if</span> (withProof()) {
<a name="l01292"></a>01292 pf = newPf(<span class="stringliteral">"int_eq_irr"</span>, expr, isIntx.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01293"></a>01293 }
<a name="l01294"></a>01294 <span class="keywordflow">return</span> newRWTheorem(expr, d_em->falseExpr(), assump, pf);
<a name="l01295"></a>01295 }
<a name="l01296"></a>01296
<a name="l01297"></a>01297
<a name="l01298"></a>01298 <span class="comment">// e[0] kind e[1] <==> true when e[0] kind e[1],</span>
<a name="l01299"></a>01299 <span class="comment">// false when e[0] !kind e[1], for constants only</span>
<a name="l01300"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a621015d4894231ecd9ab465494e9c9c8">01300</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::constPredicate(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l01301"></a>01301 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01302"></a>01302 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 2 && <a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(e[0]) && <a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(e[1]),
<a name="l01303"></a>01303 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::constPredicate:\n "</span>
<a name="l01304"></a>01304 <span class="stringliteral">"non-const parameters: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01305"></a>01305 }
<a name="l01306"></a>01306 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01307"></a>01307 <span class="keywordtype">bool</span> result(<span class="keyword">false</span>);
<a name="l01308"></a>01308 <span class="keywordtype">int</span> kind = e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>();
<a name="l01309"></a>01309 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> r1 = e[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>(), r2 = e[1].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l01310"></a>01310 <span class="keywordflow">switch</span>(kind) {
<a name="l01311"></a>01311 <span class="keywordflow">case</span> <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba9efdc855f3c1477957fb50affec07f8f">EQ</a>:
<a name="l01312"></a>01312 result = (r1 == r2)?<span class="keyword">true</span> : <span class="keyword">false</span>;
<a name="l01313"></a>01313 <span class="keywordflow">break</span>;
<a name="l01314"></a>01314 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9e29ecc77281f945fb50c183cfae6749">LT</a>:
<a name="l01315"></a>01315 result = (r1 < r2)?<span class="keyword">true</span> : <span class="keyword">false</span>;
<a name="l01316"></a>01316 <span class="keywordflow">break</span>;
<a name="l01317"></a>01317 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a1b768cf71a18713c90cd71f82488ffb1">LE</a>:
<a name="l01318"></a>01318 result = (r1 <= r2)?<span class="keyword">true</span> : <span class="keyword">false</span>;
<a name="l01319"></a>01319 <span class="keywordflow">break</span>;
<a name="l01320"></a>01320 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a589b68b2d271254aa9fd3d89b4bf33b9">GT</a>:
<a name="l01321"></a>01321 result = (r1 > r2)?<span class="keyword">true</span> : <span class="keyword">false</span>;
<a name="l01322"></a>01322 <span class="keywordflow">break</span>;
<a name="l01323"></a>01323 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024aad2afa561f31a801e12ab3fdd50a6229">GE</a>:
<a name="l01324"></a>01324 result = (r1 >= r2)?<span class="keyword">true</span> : <span class="keyword">false</span>;
<a name="l01325"></a>01325 <span class="keywordflow">break</span>;
<a name="l01326"></a>01326 <span class="keywordflow">default</span>:
<a name="l01327"></a>01327 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01328"></a>01328 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<span class="keyword">false</span>,
<a name="l01329"></a>01329 <span class="stringliteral">"ArithTheoremProducer::constPredicate: wrong kind"</span>);
<a name="l01330"></a>01330 }
<a name="l01331"></a>01331 <span class="keywordflow">break</span>;
<a name="l01332"></a>01332 }
<a name="l01333"></a>01333 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ret = (result) ? d_em->trueExpr() : d_em->falseExpr();
<a name="l01334"></a>01334 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"const_predicate"</span>, e,ret);
<a name="l01335"></a>01335 <span class="keywordflow">return</span> newRWTheorem(e, ret, Assumptions::emptyAssump(), pf);
<a name="l01336"></a>01336 }
<a name="l01337"></a>01337
<a name="l01338"></a>01338
<a name="l01339"></a>01339 <span class="comment">// e[0] kind e[1] <==> 0 kind e[1] - e[0]</span>
<a name="l01340"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a3eb1309c184247837239c098d9c9100a">01340</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::rightMinusLeft(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l01341"></a>01341 {
<a name="l01342"></a>01342 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01343"></a>01343 <span class="keywordtype">int</span> kind = e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>();
<a name="l01344"></a>01344 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01345"></a>01345 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>((<a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba9efdc855f3c1477957fb50affec07f8f">EQ</a>==kind) ||
<a name="l01346"></a>01346 (<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9e29ecc77281f945fb50c183cfae6749">LT</a>==kind) ||
<a name="l01347"></a>01347 (<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a1b768cf71a18713c90cd71f82488ffb1">LE</a>==kind) ||
<a name="l01348"></a>01348 (<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024aad2afa561f31a801e12ab3fdd50a6229">GE</a>==kind) ||
<a name="l01349"></a>01349 (<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a589b68b2d271254aa9fd3d89b4bf33b9">GT</a>==kind),
<a name="l01350"></a>01350 <span class="stringliteral">"ArithTheoremProduder::rightMinusLeft: wrong kind"</span>);
<a name="l01351"></a>01351 }
<a name="l01352"></a>01352 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"right_minus_left"</span>,e);
<a name="l01353"></a>01353 <span class="keywordflow">return</span> newRWTheorem(e, <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(e.<a class="code" href="group__ExprPkg.html#gace479f04faca399219496195152f7806" title="Get operator from expression.">getOp</a>(), rat(0), e[1] - e[0]), Assumptions::emptyAssump(), pf);
<a name="l01354"></a>01354 }
<a name="l01355"></a>01355
<a name="l01356"></a>01356 <span class="comment">// e[0] kind e[1] <==> 0 kind e[1] - e[0]</span>
<a name="l01357"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a8196042ba713a7c782ee4b5eb4c69ccc">01357</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::leftMinusRight(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l01358"></a>01358 {
<a name="l01359"></a>01359 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01360"></a>01360 <span class="keywordtype">int</span> kind = e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>();
<a name="l01361"></a>01361 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01362"></a>01362 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>((<a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba9efdc855f3c1477957fb50affec07f8f">EQ</a>==kind) ||
<a name="l01363"></a>01363 (<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9e29ecc77281f945fb50c183cfae6749">LT</a>==kind) ||
<a name="l01364"></a>01364 (<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a1b768cf71a18713c90cd71f82488ffb1">LE</a>==kind) ||
<a name="l01365"></a>01365 (<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024aad2afa561f31a801e12ab3fdd50a6229">GE</a>==kind) ||
<a name="l01366"></a>01366 (<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a589b68b2d271254aa9fd3d89b4bf33b9">GT</a>==kind),
<a name="l01367"></a>01367 <span class="stringliteral">"ArithTheoremProduder::rightMinusLeft: wrong kind"</span>);
<a name="l01368"></a>01368 }
<a name="l01369"></a>01369 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"left_minus_right"</span>,e);
<a name="l01370"></a>01370 <span class="keywordflow">return</span> newRWTheorem(e, <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(e.<a class="code" href="group__ExprPkg.html#gace479f04faca399219496195152f7806" title="Get operator from expression.">getOp</a>(), e[0] - e[1], rat(0)), Assumptions::emptyAssump(), pf);
<a name="l01371"></a>01371 }
<a name="l01372"></a>01372
<a name="l01373"></a>01373
<a name="l01374"></a>01374
<a name="l01375"></a>01375 <span class="comment">// x kind y <==> x + z kind y + z</span>
<a name="l01376"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a3c3041eb3b0144e21d72ffe6999953e2">01376</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::plusPredicate(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x,
<a name="l01377"></a>01377 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& y,
<a name="l01378"></a>01378 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& z, <span class="keywordtype">int</span> kind) {
<a name="l01379"></a>01379 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01380"></a>01380 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>((<a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba9efdc855f3c1477957fb50affec07f8f">EQ</a>==kind) ||
<a name="l01381"></a>01381 (<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9e29ecc77281f945fb50c183cfae6749">LT</a>==kind) ||
<a name="l01382"></a>01382 (<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a1b768cf71a18713c90cd71f82488ffb1">LE</a>==kind) ||
<a name="l01383"></a>01383 (<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024aad2afa561f31a801e12ab3fdd50a6229">GE</a>==kind) ||
<a name="l01384"></a>01384 (<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a589b68b2d271254aa9fd3d89b4bf33b9">GT</a>==kind),
<a name="l01385"></a>01385 <span class="stringliteral">"ArithTheoremProduder::plusPredicate: wrong kind"</span>);
<a name="l01386"></a>01386 }
<a name="l01387"></a>01387 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01388"></a>01388 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="namespaceMiniSat.html#ad93cb56673487974071ed3b75bf4ea83">left</a> = <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(kind, x, y);
<a name="l01389"></a>01389 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="namespaceMiniSat.html#a82558b7a36c52f5d3211d5d14bed99d4">right</a> = <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(kind, x + z, y + z);
<a name="l01390"></a>01390 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"plus_predicate"</span>,left,right);
<a name="l01391"></a>01391 <span class="keywordflow">return</span> newRWTheorem(left, right, Assumptions::emptyAssump(), pf);
<a name="l01392"></a>01392 }
<a name="l01393"></a>01393
<a name="l01394"></a>01394 <span class="comment">// x = y <==> x * z = y * z</span>
<a name="l01395"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ae66ddbc1457e3c032ea9059625059992">01395</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::multEqn(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x,
<a name="l01396"></a>01396 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& y,
<a name="l01397"></a>01397 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& z) {
<a name="l01398"></a>01398 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01399"></a>01399 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l01400"></a>01400 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(z.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>() && z.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() != 0,
<a name="l01401"></a>01401 <span class="stringliteral">"ArithTheoremProducer::multEqn(): multiplying equation by 0"</span>);
<a name="l01402"></a>01402 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"mult_eqn"</span>, x, y, z);
<a name="l01403"></a>01403 <span class="keywordflow">return</span> newRWTheorem(x.<a class="code" href="group__ExprPkg.html#gacb48495ca445c895f95d0c3c1ae2070b">eqExpr</a>(y), (x * z).eqExpr(y * z), Assumptions::emptyAssump(), pf);
<a name="l01404"></a>01404 }
<a name="l01405"></a>01405
<a name="l01406"></a>01406
<a name="l01407"></a>01407 <span class="comment">// x = y <==> z=0 OR x * 1/z = y * 1/z</span>
<a name="l01408"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aa371616db9ac1a4a9c7a4b1ce0f2a05c">01408</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::divideEqnNonConst(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x,
<a name="l01409"></a>01409 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& y,
<a name="l01410"></a>01410 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& z) {
<a name="l01411"></a>01411 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01412"></a>01412 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"mult_eqn_nonconst"</span>, x, y, z);
<a name="l01413"></a>01413 <span class="keywordflow">return</span> newRWTheorem(x.<a class="code" href="group__ExprPkg.html#gacb48495ca445c895f95d0c3c1ae2070b">eqExpr</a>(y), (z.<a class="code" href="group__ExprPkg.html#gacb48495ca445c895f95d0c3c1ae2070b">eqExpr</a>(rat(0))).<a class="code" href="namespaceCVC3.html#a30f30b6e20c174f21ae63acea8618294">orExpr</a>((x / z).eqExpr(y / z)),
<a name="l01414"></a>01414 Assumptions::emptyAssump(), pf);
<a name="l01415"></a>01415 }
<a name="l01416"></a>01416
<a name="l01417"></a>01417
<a name="l01418"></a>01418 <span class="comment">// if z is +ve, return e[0] LT|LE|GT|GE e[1] <==> e[0]*z LT|LE|GT|GE e[1]*z</span>
<a name="l01419"></a>01419 <span class="comment">// if z is -ve, return e[0] LT|LE|GT|GE e[1] <==> e[1]*z LT|LE|GT|GE e[0]*z</span>
<a name="l01420"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a3d245f36a2e42684ec2fd9356d89111f">01420</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::multIneqn(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& z) {
<a name="l01421"></a>01421
<a name="l01422"></a>01422 <span class="comment">// Check the proofs in necessary</span>
<a name="l01423"></a>01423 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01424"></a>01424 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#abbae617aaff89a9e5deb84ab649e14a0">isIneq</a>(e), <span class="stringliteral">"ArithTheoremProduder::multIneqn: wrong kind"</span>);
<a name="l01425"></a>01425 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(z.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>() && z.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() != 0, <span class="stringliteral">"ArithTheoremProduder::multIneqn: z must be non-zero rational: "</span> + z.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01426"></a>01426 }
<a name="l01427"></a>01427
<a name="l01428"></a>01428 <span class="comment">// Operation of the expression</span>
<a name="l01429"></a>01429 <a class="code" href="classCVC3_1_1Op.html">Op</a> op(e.<a class="code" href="group__ExprPkg.html#gace479f04faca399219496195152f7806" title="Get operator from expression.">getOp</a>());
<a name="l01430"></a>01430
<a name="l01431"></a>01431 <span class="comment">// Calculate the returning expression</span>
<a name="l01432"></a>01432 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ret;
<a name="l01433"></a>01433 <span class="comment">// If constant is positive, just multiply both sides</span>
<a name="l01434"></a>01434 <span class="keywordflow">if</span>(0 < z.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>())
<a name="l01435"></a>01435 ret = <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(op, e[0]*z, e[1]*z);
<a name="l01436"></a>01436 <span class="keywordflow">else</span>
<a name="l01437"></a>01437 <span class="comment">// The constant is negative, reverse the relation</span>
<a name="l01438"></a>01438 <span class="keywordflow">switch</span> (e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>()) {
<a name="l01439"></a>01439 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a1b768cf71a18713c90cd71f82488ffb1">LE</a>: ret = <a class="code" href="namespaceCVC3.html#a520cf0df288be321d27ea6fa77ded2d2">geExpr</a>(e[0]*z, e[1]*z); <span class="keywordflow">break</span>;
<a name="l01440"></a>01440 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9e29ecc77281f945fb50c183cfae6749">LT</a>: ret = <a class="code" href="namespaceCVC3.html#a8ad355d6650f2dfa754419c634e36afb">gtExpr</a>(e[0]*z, e[1]*z); <span class="keywordflow">break</span>;
<a name="l01441"></a>01441 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024aad2afa561f31a801e12ab3fdd50a6229">GE</a>: ret = <a class="code" href="namespaceCVC3.html#aebfd8a82800bd3dff4c8db461a52cdea">leExpr</a>(e[0]*z, e[1]*z); <span class="keywordflow">break</span>;
<a name="l01442"></a>01442 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a589b68b2d271254aa9fd3d89b4bf33b9">GT</a>: ret = <a class="code" href="namespaceCVC3.html#ac9ccba18a3c725634b1f8ba8e99e627f">ltExpr</a>(e[0]*z, e[1]*z); <span class="keywordflow">break</span>;
<a name="l01443"></a>01443 <span class="keywordflow">default</span>:
<a name="l01444"></a>01444 <span class="comment">//TODO: exception, we shouldn't be here</span>
<a name="l01445"></a>01445 <span class="keywordflow">break</span>;
<a name="l01446"></a>01446 }
<a name="l01447"></a>01447
<a name="l01448"></a>01448 <span class="comment">// If we need the proof, set it up</span>
<a name="l01449"></a>01449 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01450"></a>01450 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"mult_ineqn"</span>, e, ret);
<a name="l01451"></a>01451
<a name="l01452"></a>01452 <span class="comment">// Return the explaining rewrite theorem</span>
<a name="l01453"></a>01453 <span class="keywordflow">return</span> newRWTheorem(e, ret, Assumptions::emptyAssump(), pf);
<a name="l01454"></a>01454 }
<a name="l01455"></a>01455 <span class="comment"></span>
<a name="l01456"></a>01456 <span class="comment">//// multiply a canonised expression e = e[0] @ 0 with a constant c</span>
<a name="l01457"></a>01457 <span class="comment"></span><span class="comment">//Theorem ArithTheoremProducer::multConst(const Expr& e, const Rational c)</span>
<a name="l01458"></a>01458 <span class="comment">//{</span>
<a name="l01459"></a>01459 <span class="comment">// // The proof object</span>
<a name="l01460"></a>01460 <span class="comment">// Proof pf;</span>
<a name="l01461"></a>01461 <span class="comment">//</span>
<a name="l01462"></a>01462 <span class="comment">// // The resulting expression</span>
<a name="l01463"></a>01463 <span class="comment">// Expr ret;</span>
<a name="l01464"></a>01464 <span class="comment">//</span>
<a name="l01465"></a>01465 <span class="comment">// // If expression is just a rational multiply it and thats it</span>
<a name="l01466"></a>01466 <span class="comment">// if (e[0].isRational())</span>
<a name="l01467"></a>01467 <span class="comment">// ret = rat(e[0].getRational() * c);</span>
<a name="l01468"></a>01468 <span class="comment">// // The expression is a canonised sum, multiply each one</span>
<a name="l01469"></a>01469 <span class="comment">// else {</span>
<a name="l01470"></a>01470 <span class="comment">// // Vector to hold all the sum children</span>
<a name="l01471"></a>01471 <span class="comment">// vector<Expr> sumKids;</span>
<a name="l01472"></a>01472 <span class="comment">//</span>
<a name="l01473"></a>01473 <span class="comment">// // Put all the sum children to the sumKids vector</span>
<a name="l01474"></a>01474 <span class="comment">// for(Expression::iterator m = e[0].begin(); m != e[0].end(); m ++) {</span>
<a name="l01475"></a>01475 <span class="comment">// // The current term in the sum</span>
<a name="l01476"></a>01476 <span class="comment">// const Expr& sumTerm = (*m);</span>
<a name="l01477"></a>01477 <span class="comment">//</span>
<a name="l01478"></a>01478 <span class="comment">// // If the child is rational, just multiply it</span>
<a name="l01479"></a>01479 <span class="comment">// if (sumTerm.isRational()) sumKids.push_back(rat(sumTerm.getRational() * c));</span>
<a name="l01480"></a>01480 <span class="comment">// // Otherwise multiply the coefficient with c and add it to the sumKids (TODO: Is the multiplication binary???)</span>
<a name="l01481"></a>01481 <span class="comment">// else sumKids.pushBack(multExpr(rat(c * sumTerm[0].getRational()), sumTerm[1]));</span>
<a name="l01482"></a>01482 <span class="comment">// }</span>
<a name="l01483"></a>01483 <span class="comment">//</span>
<a name="l01484"></a>01484 <span class="comment">// // The resulting expression is the sum of the sumKids</span>
<a name="l01485"></a>01485 <span class="comment">// ret = plusExpr(sumKids);</span>
<a name="l01486"></a>01486 <span class="comment">// }</span>
<a name="l01487"></a>01487 <span class="comment">//</span>
<a name="l01488"></a>01488 <span class="comment">// // If proof is needed set it up</span>
<a name="l01489"></a>01489 <span class="comment">// if(withProof()) pf = newPf("arith_mult_const", e, ret);</span>
<a name="l01490"></a>01490 <span class="comment">//</span>
<a name="l01491"></a>01491 <span class="comment">// // Return the theorem explaining the multiplication</span>
<a name="l01492"></a>01492 <span class="comment">// return newRWTheorem(e, ret, Assumptions::emptyAssump(), pf);</span>
<a name="l01493"></a>01493 <span class="comment">//}</span>
<a name="l01494"></a>01494
<a name="l01495"></a>01495
<a name="l01496"></a>01496
<a name="l01497"></a>01497 <span class="comment">// "op1 GE|GT op2" <==> op2 LE|LT op1</span>
<a name="l01498"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#af069fc1b320c0455ec7cde192668884b">01498</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::flipInequality(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l01499"></a>01499 {
<a name="l01500"></a>01500 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01501"></a>01501 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01502"></a>01502 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a7306d7566ccb21380f05058477aba009">isGT</a>(e) || <a class="code" href="namespaceCVC3.html#af85f3152a3b2fe195d795bc0aefaec71">isGE</a>(e),
<a name="l01503"></a>01503 <span class="stringliteral">"ArithTheoremProducer::flipInequality: wrong kind: "</span> +
<a name="l01504"></a>01504 e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01505"></a>01505 }
<a name="l01506"></a>01506
<a name="l01507"></a>01507 <span class="keywordtype">int</span> kind = <a class="code" href="namespaceCVC3.html#af85f3152a3b2fe195d795bc0aefaec71">isGE</a>(e) ? <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a1b768cf71a18713c90cd71f82488ffb1">LE</a> : <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9e29ecc77281f945fb50c183cfae6749">LT</a>;
<a name="l01508"></a>01508 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ret = <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(kind, e[1], e[0]);
<a name="l01509"></a>01509 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"flip_inequality"</span>, e,ret);
<a name="l01510"></a>01510 <span class="keywordflow">return</span> newRWTheorem(e,ret, Assumptions::emptyAssump(), pf);
<a name="l01511"></a>01511 }
<a name="l01512"></a>01512
<a name="l01513"></a>01513
<a name="l01514"></a>01514 <span class="comment">// NOT (op1 LT op2) <==> (op1 GE op2)</span>
<a name="l01515"></a>01515 <span class="comment">// NOT (op1 LE op2) <==> (op1 GT op2)</span>
<a name="l01516"></a>01516 <span class="comment">// NOT (op1 GT op2) <==> (op1 LE op2)</span>
<a name="l01517"></a>01517 <span class="comment">// NOT (op1 GE op2) <==> (op1 LT op2)</span>
<a name="l01518"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a07368f8a2e12b5c189645a99bc934102">01518</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::negatedInequality(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e)
<a name="l01519"></a>01519 {
<a name="l01520"></a>01520 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& ineq = e[0];
<a name="l01521"></a>01521 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01522"></a>01522 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga1a898858ccadce833df5a294c7740f11">isNot</a>(),
<a name="l01523"></a>01523 <span class="stringliteral">"ArithTheoremProducer::negatedInequality: wrong kind: "</span> +
<a name="l01524"></a>01524 e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01525"></a>01525 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#abbae617aaff89a9e5deb84ab649e14a0">isIneq</a>(ineq),
<a name="l01526"></a>01526 <span class="stringliteral">"ArithTheoremProducer::negatedInequality: wrong kind: "</span> +
<a name="l01527"></a>01527 (ineq).toString());
<a name="l01528"></a>01528 }
<a name="l01529"></a>01529 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01530"></a>01530 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"negated_inequality"</span>, e);
<a name="l01531"></a>01531
<a name="l01532"></a>01532 <span class="keywordtype">int</span> kind;
<a name="l01533"></a>01533 <span class="comment">// NOT (op1 LT op2) <==> (op1 GE op2)</span>
<a name="l01534"></a>01534 <span class="comment">// NOT (op1 LE op2) <==> (op1 GT op2)</span>
<a name="l01535"></a>01535 <span class="comment">// NOT (op1 GT op2) <==> (op1 LE op2)</span>
<a name="l01536"></a>01536 <span class="comment">// NOT (op1 GE op2) <==> (op1 LT op2)</span>
<a name="l01537"></a>01537 kind =
<a name="l01538"></a>01538 <a class="code" href="namespaceCVC3.html#a448b6e0d541113608bba5a7a005609e3">isLT</a>(ineq) ? <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024aad2afa561f31a801e12ab3fdd50a6229">GE</a> :
<a name="l01539"></a>01539 <a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(ineq) ? <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a589b68b2d271254aa9fd3d89b4bf33b9">GT</a> :
<a name="l01540"></a>01540 <a class="code" href="namespaceCVC3.html#a7306d7566ccb21380f05058477aba009">isGT</a>(ineq) ? <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a1b768cf71a18713c90cd71f82488ffb1">LE</a> :
<a name="l01541"></a>01541 <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9e29ecc77281f945fb50c183cfae6749">LT</a>;
<a name="l01542"></a>01542 <span class="keywordflow">return</span> newRWTheorem(e, <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(kind, ineq[0], ineq[1]), Assumptions::emptyAssump(), pf);
<a name="l01543"></a>01543 }
<a name="l01544"></a>01544
<a name="l01545"></a>01545 <span class="comment">//takes two ineqs "|- alpha LT|LE t" and "|- t LT|LE beta"</span>
<a name="l01546"></a>01546 <span class="comment">//and returns "|- alpha LT|LE beta"</span>
<a name="l01547"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a8092c96a87d952fc1e572bb9237ff994">01547</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::realShadow(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& alphaLTt,
<a name="l01548"></a>01548 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& tLTbeta)
<a name="l01549"></a>01549 {
<a name="l01550"></a>01550 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr1 = alphaLTt.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01551"></a>01551 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr2 = tLTbeta.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01552"></a>01552 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01553"></a>01553 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>((<a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr1) || <a class="code" href="namespaceCVC3.html#a448b6e0d541113608bba5a7a005609e3">isLT</a>(expr1)) &&
<a name="l01554"></a>01554 (<a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr2) || <a class="code" href="namespaceCVC3.html#a448b6e0d541113608bba5a7a005609e3">isLT</a>(expr2)),
<a name="l01555"></a>01555 <span class="stringliteral">"ArithTheoremProducer::realShadow: Wrong Kind: "</span> +
<a name="l01556"></a>01556 alphaLTt.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>() + tLTbeta.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>());
<a name="l01557"></a>01557
<a name="l01558"></a>01558 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr1[1] == expr2[0],
<a name="l01559"></a>01559 <span class="stringliteral">"ArithTheoremProducer::realShadow:"</span>
<a name="l01560"></a>01560 <span class="stringliteral">" t must be same for both inputs: "</span> +
<a name="l01561"></a>01561 expr1[1].toString() + <span class="stringliteral">" , "</span> + expr2[0].toString());
<a name="l01562"></a>01562 }
<a name="l01563"></a>01563 <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a> a(alphaLTt, tLTbeta);
<a name="l01564"></a>01564 <span class="keywordtype">int</span> firstKind = expr1.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>();
<a name="l01565"></a>01565 <span class="keywordtype">int</span> secondKind = expr2.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>();
<a name="l01566"></a>01566 <span class="keywordtype">int</span> kind = (firstKind == secondKind) ? firstKind : <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9e29ecc77281f945fb50c183cfae6749">LT</a>;
<a name="l01567"></a>01567 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01568"></a>01568 <span class="keywordflow">if</span>(withProof()) {
<a name="l01569"></a>01569 vector<Proof> pfs;
<a name="l01570"></a>01570 pfs.push_back(alphaLTt.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01571"></a>01571 pfs.push_back(tLTbeta.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01572"></a>01572 pf = newPf(<span class="stringliteral">"real_shadow"</span>,expr1, expr2, pfs);
<a name="l01573"></a>01573 }
<a name="l01574"></a>01574 <span class="keywordflow">return</span> newTheorem(<a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(kind, expr1[0], expr2[1]), a, pf);
<a name="l01575"></a>01575 }
<a name="l01576"></a>01576 <span class="comment"></span>
<a name="l01577"></a>01577 <span class="comment">//! alpha <= t <= alpha ==> t = alpha</span>
<a name="l01578"></a>01578 <span class="comment"></span><span class="comment"></span>
<a name="l01579"></a>01579 <span class="comment">/*! takes two ineqs "|- alpha LE t" and "|- t LE alpha"</span>
<a name="l01580"></a>01580 <span class="comment"> and returns "|- t = alpha"</span>
<a name="l01581"></a>01581 <span class="comment">*/</span>
<a name="l01582"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a6e14251c516153e14539a34598daca04">01582</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::realShadowEq(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& alphaLEt,
<a name="l01583"></a>01583 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& tLEalpha)
<a name="l01584"></a>01584 {
<a name="l01585"></a>01585 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr1 = alphaLEt.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01586"></a>01586 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr2 = tLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01587"></a>01587 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01588"></a>01588 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr1) && <a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr2),
<a name="l01589"></a>01589 <span class="stringliteral">"ArithTheoremProducer::realShadowLTLE: Wrong Kind: "</span> +
<a name="l01590"></a>01590 alphaLEt.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>() + tLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>());
<a name="l01591"></a>01591
<a name="l01592"></a>01592 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr1[1] == expr2[0],
<a name="l01593"></a>01593 <span class="stringliteral">"ArithTheoremProducer::realShadowLTLE:"</span>
<a name="l01594"></a>01594 <span class="stringliteral">" t must be same for both inputs: "</span> +
<a name="l01595"></a>01595 alphaLEt.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>() + <span class="stringliteral">" , "</span> + tLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>());
<a name="l01596"></a>01596
<a name="l01597"></a>01597 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr1[0] == expr2[1],
<a name="l01598"></a>01598 <span class="stringliteral">"ArithTheoremProducer::realShadowLTLE:"</span>
<a name="l01599"></a>01599 <span class="stringliteral">" alpha must be same for both inputs: "</span> +
<a name="l01600"></a>01600 alphaLEt.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>() + <span class="stringliteral">" , "</span> + tLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>());
<a name="l01601"></a>01601 }
<a name="l01602"></a>01602 <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a> a(alphaLEt, tLEalpha);
<a name="l01603"></a>01603 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01604"></a>01604 <span class="keywordflow">if</span>(withProof()) {
<a name="l01605"></a>01605 vector<Proof> pfs;
<a name="l01606"></a>01606 pfs.push_back(alphaLEt.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01607"></a>01607 pfs.push_back(tLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01608"></a>01608 pf = newPf(<span class="stringliteral">"real_shadow_eq"</span>, alphaLEt.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>(), tLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>(), pfs);
<a name="l01609"></a>01609 }
<a name="l01610"></a>01610 <span class="keywordflow">return</span> newRWTheorem(expr1[0], expr1[1], a, pf);
<a name="l01611"></a>01611 }
<a name="l01612"></a>01612
<a name="l01613"></a>01613 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l01614"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a7f4c82e18e7a3ed3b5b22a6ce7d7cf27">01614</a> ArithTheoremProducer::finiteInterval(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& aLEt,
<a name="l01615"></a>01615 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& tLEac,
<a name="l01616"></a>01616 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isInta,
<a name="l01617"></a>01617 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntt) {
<a name="l01618"></a>01618 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e1 = aLEt.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01619"></a>01619 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e2 = tLEac.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01620"></a>01620 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01621"></a>01621 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(e1) && <a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(e2),
<a name="l01622"></a>01622 <span class="stringliteral">"ArithTheoremProducer::finiteInterval:\n e1 = "</span>
<a name="l01623"></a>01623 +e1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n e2 = "</span>+e2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01624"></a>01624 <span class="comment">// term 't' is the same in both inequalities</span>
<a name="l01625"></a>01625 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e1[1] == e2[0],
<a name="l01626"></a>01626 <span class="stringliteral">"ArithTheoremProducer::finiteInterval:\n e1 = "</span>
<a name="l01627"></a>01627 +e1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n e2 = "</span>+e2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01628"></a>01628 <span class="comment">// RHS in e2 is (a+c)</span>
<a name="l01629"></a>01629 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#afb0f7d15ddbd87f9abb128108101f557">isPlus</a>(e2[1]) && e2[1].arity() == 2,
<a name="l01630"></a>01630 <span class="stringliteral">"ArithTheoremProducer::finiteInterval:\n e1 = "</span>
<a name="l01631"></a>01631 +e1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n e2 = "</span>+e2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01632"></a>01632 <span class="comment">// term 'a' in LHS of e1 and RHS of e2 is the same</span>
<a name="l01633"></a>01633 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e1[0] == e2[1][0],
<a name="l01634"></a>01634 <span class="stringliteral">"ArithTheoremProducer::finiteInterval:\n e1 = "</span>
<a name="l01635"></a>01635 +e1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n e2 = "</span>+e2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01636"></a>01636 <span class="comment">// 'c' in the RHS of e2 is a positive integer constant</span>
<a name="l01637"></a>01637 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e2[1][1].<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>() && e2[1][1].getRational().isInteger()
<a name="l01638"></a>01638 && e2[1][1].getRational() >= 1,
<a name="l01639"></a>01639 <span class="stringliteral">"ArithTheoremProducer::finiteInterval:\n e1 = "</span>
<a name="l01640"></a>01640 +e1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n e2 = "</span>+e2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01641"></a>01641 <span class="comment">// Integrality constraints</span>
<a name="l01642"></a>01642 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& isIntaExpr = isInta.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01643"></a>01643 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& isInttExpr = isIntt.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01644"></a>01644 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntaExpr) && isIntaExpr[0] == e1[0],
<a name="l01645"></a>01645 <span class="stringliteral">"Wrong integrality constraint:\n e1 = "</span>
<a name="l01646"></a>01646 +e1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n isInta = "</span>+isIntaExpr.toString());
<a name="l01647"></a>01647 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isInttExpr) && isInttExpr[0] == e1[1],
<a name="l01648"></a>01648 <span class="stringliteral">"Wrong integrality constraint:\n e1 = "</span>
<a name="l01649"></a>01649 +e1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n isIntt = "</span>+isInttExpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01650"></a>01650 }
<a name="l01651"></a>01651 vector<Theorem> thms;
<a name="l01652"></a>01652 thms.push_back(aLEt);
<a name="l01653"></a>01653 thms.push_back(tLEac);
<a name="l01654"></a>01654 thms.push_back(isInta);
<a name="l01655"></a>01655 thms.push_back(isIntt);
<a name="l01656"></a>01656 <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a> a(thms);
<a name="l01657"></a>01657 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01658"></a>01658 <span class="keywordflow">if</span>(withProof()) {
<a name="l01659"></a>01659 vector<Expr> es;
<a name="l01660"></a>01660 vector<Proof> pfs;
<a name="l01661"></a>01661 es.push_back(e1);
<a name="l01662"></a>01662 es.push_back(e2);
<a name="l01663"></a>01663 es.push_back(isInta.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>());
<a name="l01664"></a>01664 es.push_back(isIntt.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>());
<a name="l01665"></a>01665 pfs.push_back(aLEt.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01666"></a>01666 pfs.push_back(tLEac.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01667"></a>01667 pfs.push_back(isInta.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01668"></a>01668 pfs.push_back(isIntt.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01669"></a>01669 pf = newPf(<span class="stringliteral">"finite_interval"</span>, es, pfs);
<a name="l01670"></a>01670 }
<a name="l01671"></a>01671 <span class="comment">// Construct GRAY_SHADOW(t, a, 0, c)</span>
<a name="l01672"></a>01672 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> g(grayShadow(e1[1], e1[0], 0, e2[1][1].getRational()));
<a name="l01673"></a>01673 <span class="keywordflow">return</span> newTheorem(g, a, pf);
<a name="l01674"></a>01674 }
<a name="l01675"></a>01675
<a name="l01676"></a>01676
<a name="l01677"></a>01677 <span class="comment">// Dark & Gray shadows when a <= b</span>
<a name="l01678"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aef6fd1261bea182d4554d0423803b05e">01678</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::darkGrayShadow2ab(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& betaLEbx,
<a name="l01679"></a>01679 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& axLEalpha,
<a name="l01680"></a>01680 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntAlpha,
<a name="l01681"></a>01681 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntBeta,
<a name="l01682"></a>01682 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="theory__quant_8cpp.html#ac9940420b1f3427ebe821902adbb578d">isIntx</a>) {
<a name="l01683"></a>01683 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr1 = betaLEbx.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01684"></a>01684 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr2 = axLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01685"></a>01685 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& isIntAlphaExpr = isIntAlpha.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01686"></a>01686 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& isIntBetaExpr = isIntBeta.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01687"></a>01687 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& isIntxExpr = isIntx.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01688"></a>01688
<a name="l01689"></a>01689 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01690"></a>01690 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr1) && <a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr2),
<a name="l01691"></a>01691 <span class="stringliteral">"ArithTheoremProducer::darkGrayShadow2ab: Wrong Kind: "</span> +
<a name="l01692"></a>01692 betaLEbx.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>() + axLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>());
<a name="l01693"></a>01693 }
<a name="l01694"></a>01694
<a name="l01695"></a>01695 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& beta = expr1[0];
<a name="l01696"></a>01696 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& bx = expr1[1];
<a name="l01697"></a>01697 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& ax = expr2[0];
<a name="l01698"></a>01698 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& alpha = expr2[1];
<a name="l01699"></a>01699 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> a = <a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(ax)? ax[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() : 1;
<a name="l01700"></a>01700 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> b = <a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(bx)? bx[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() : 1;
<a name="l01701"></a>01701 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x = <a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(ax)? ax[1] : ax;
<a name="l01702"></a>01702
<a name="l01703"></a>01703 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01704"></a>01704 <span class="comment">// Integrality constraints</span>
<a name="l01705"></a>01705 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntAlphaExpr) && isIntAlphaExpr[0] == alpha,
<a name="l01706"></a>01706 <span class="stringliteral">"ArithTheoremProducer::darkGrayShadow2ab:\n "</span>
<a name="l01707"></a>01707 <span class="stringliteral">"wrong integrality constraint:\n alpha = "</span>
<a name="l01708"></a>01708 +alpha.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n isIntAlpha = "</span>
<a name="l01709"></a>01709 +isIntAlphaExpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01710"></a>01710 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntBetaExpr) && isIntBetaExpr[0] == beta,
<a name="l01711"></a>01711 <span class="stringliteral">"ArithTheoremProducer::darkGrayShadow2ab:\n "</span>
<a name="l01712"></a>01712 <span class="stringliteral">"wrong integrality constraint:\n beta = "</span>
<a name="l01713"></a>01713 +beta.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n isIntBeta = "</span>
<a name="l01714"></a>01714 +isIntBetaExpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01715"></a>01715 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntxExpr) && isIntxExpr[0] == x,
<a name="l01716"></a>01716 <span class="stringliteral">"ArithTheoremProducer::darkGrayShadow2ab:\n "</span>
<a name="l01717"></a>01717 <span class="stringliteral">"wrong integrality constraint:\n x = "</span>
<a name="l01718"></a>01718 +x.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n isIntx = "</span>
<a name="l01719"></a>01719 +isIntxExpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01720"></a>01720 <span class="comment">// Expressions ax and bx should match on x</span>
<a name="l01721"></a>01721 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(!<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(ax) || ax.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 2,
<a name="l01722"></a>01722 <span class="stringliteral">"ArithTheoremProducer::darkGrayShadow2ab:\n ax<=alpha: "</span> +
<a name="l01723"></a>01723 axLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>());
<a name="l01724"></a>01724 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(!<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(bx) || (bx.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 2 && bx[1] == x),
<a name="l01725"></a>01725 <span class="stringliteral">"ArithTheoremProducer::darkGrayShadow2ab:\n beta<=bx: "</span>
<a name="l01726"></a>01726 +betaLEbx.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>()
<a name="l01727"></a>01727 +<span class="stringliteral">"\n ax<=alpha: "</span>+ axLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>());
<a name="l01728"></a>01728 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(1 <= a && a <= b && 2 <= b,
<a name="l01729"></a>01729 <span class="stringliteral">"ArithTheoremProducer::darkGrayShadow2ab:\n beta<=bx: "</span>
<a name="l01730"></a>01730 +betaLEbx.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>()
<a name="l01731"></a>01731 +<span class="stringliteral">"\n ax<=alpha: "</span>+ axLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>());
<a name="l01732"></a>01732 }
<a name="l01733"></a>01733 vector<Theorem> thms;
<a name="l01734"></a>01734 thms.push_back(betaLEbx);
<a name="l01735"></a>01735 thms.push_back(axLEalpha);
<a name="l01736"></a>01736 thms.push_back(isIntAlpha);
<a name="l01737"></a>01737 thms.push_back(isIntBeta);
<a name="l01738"></a>01738 thms.push_back(isIntx);
<a name="l01739"></a>01739 <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a> A(thms);
<a name="l01740"></a>01740
<a name="l01741"></a>01741 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> bAlpha = <a class="code" href="namespaceCVC3.html#adb35e0739f86730543924dbc8211a778">multExpr</a>(rat(b), alpha);
<a name="l01742"></a>01742 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> aBeta = <a class="code" href="namespaceCVC3.html#adb35e0739f86730543924dbc8211a778">multExpr</a>(rat(a), beta);
<a name="l01743"></a>01743 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> t = <a class="code" href="namespaceCVC3.html#a9ba326c305c5aeb61de515009aaa61f8">minusExpr</a>(bAlpha, aBeta);
<a name="l01744"></a>01744 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> d = darkShadow(rat(a*b-1), t);
<a name="l01745"></a>01745 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> g = grayShadow(ax, alpha, -a+1, 0);
<a name="l01746"></a>01746
<a name="l01747"></a>01747 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01748"></a>01748 <span class="keywordflow">if</span>(withProof()) {
<a name="l01749"></a>01749 vector<Expr> exprs;
<a name="l01750"></a>01750 exprs.push_back(expr1);
<a name="l01751"></a>01751 exprs.push_back(expr2);
<a name="l01752"></a>01752 exprs.push_back(d);
<a name="l01753"></a>01753 exprs.push_back(g);
<a name="l01754"></a>01754
<a name="l01755"></a>01755 vector<Proof> pfs;
<a name="l01756"></a>01756 pfs.push_back(betaLEbx.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01757"></a>01757 pfs.push_back(axLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01758"></a>01758 pfs.push_back(isIntAlpha.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01759"></a>01759 pfs.push_back(isIntBeta.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01760"></a>01760 pfs.push_back(isIntx.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01761"></a>01761
<a name="l01762"></a>01762 pf = newPf(<span class="stringliteral">"dark_grayshadow_2ab"</span>, exprs, pfs);
<a name="l01763"></a>01763 }
<a name="l01764"></a>01764
<a name="l01765"></a>01765 <span class="keywordflow">return</span> newTheorem((d || g) && (!d || !g), A, pf);
<a name="l01766"></a>01766 }
<a name="l01767"></a>01767
<a name="l01768"></a>01768 <span class="comment">// Dark & Gray shadows when b <= a</span>
<a name="l01769"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aaf64935bb620ab79fd7383f1913bd8b8">01769</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::darkGrayShadow2ba(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& betaLEbx,
<a name="l01770"></a>01770 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& axLEalpha,
<a name="l01771"></a>01771 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntAlpha,
<a name="l01772"></a>01772 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntBeta,
<a name="l01773"></a>01773 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="theory__quant_8cpp.html#ac9940420b1f3427ebe821902adbb578d">isIntx</a>) {
<a name="l01774"></a>01774 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr1 = betaLEbx.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01775"></a>01775 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr2 = axLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01776"></a>01776 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& isIntAlphaExpr = isIntAlpha.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01777"></a>01777 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& isIntBetaExpr = isIntBeta.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01778"></a>01778 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& isIntxExpr = isIntx.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01779"></a>01779
<a name="l01780"></a>01780 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01781"></a>01781 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr1) && <a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr2),
<a name="l01782"></a>01782 <span class="stringliteral">"ArithTheoremProducer::darkGrayShadow2ba: Wrong Kind: "</span> +
<a name="l01783"></a>01783 betaLEbx.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>() + axLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>());
<a name="l01784"></a>01784 }
<a name="l01785"></a>01785
<a name="l01786"></a>01786 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& beta = expr1[0];
<a name="l01787"></a>01787 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& bx = expr1[1];
<a name="l01788"></a>01788 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& ax = expr2[0];
<a name="l01789"></a>01789 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& alpha = expr2[1];
<a name="l01790"></a>01790 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> a = <a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(ax)? ax[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() : 1;
<a name="l01791"></a>01791 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> b = <a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(bx)? bx[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() : 1;
<a name="l01792"></a>01792 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x = <a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(ax)? ax[1] : ax;
<a name="l01793"></a>01793
<a name="l01794"></a>01794 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01795"></a>01795 <span class="comment">// Integrality constraints</span>
<a name="l01796"></a>01796 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntAlphaExpr) && isIntAlphaExpr[0] == alpha,
<a name="l01797"></a>01797 <span class="stringliteral">"ArithTheoremProducer::darkGrayShadow2ab:\n "</span>
<a name="l01798"></a>01798 <span class="stringliteral">"wrong integrality constraint:\n alpha = "</span>
<a name="l01799"></a>01799 +alpha.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n isIntAlpha = "</span>
<a name="l01800"></a>01800 +isIntAlphaExpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01801"></a>01801 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntBetaExpr) && isIntBetaExpr[0] == beta,
<a name="l01802"></a>01802 <span class="stringliteral">"ArithTheoremProducer::darkGrayShadow2ab:\n "</span>
<a name="l01803"></a>01803 <span class="stringliteral">"wrong integrality constraint:\n beta = "</span>
<a name="l01804"></a>01804 +beta.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n isIntBeta = "</span>
<a name="l01805"></a>01805 +isIntBetaExpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01806"></a>01806 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntxExpr) && isIntxExpr[0] == x,
<a name="l01807"></a>01807 <span class="stringliteral">"ArithTheoremProducer::darkGrayShadow2ab:\n "</span>
<a name="l01808"></a>01808 <span class="stringliteral">"wrong integrality constraint:\n x = "</span>
<a name="l01809"></a>01809 +x.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n isIntx = "</span>
<a name="l01810"></a>01810 +isIntxExpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01811"></a>01811 <span class="comment">// Expressions ax and bx should match on x</span>
<a name="l01812"></a>01812 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(!<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(ax) || ax.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 2,
<a name="l01813"></a>01813 <span class="stringliteral">"ArithTheoremProducer::darkGrayShadow2ba:\n ax<=alpha: "</span> +
<a name="l01814"></a>01814 axLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>());
<a name="l01815"></a>01815 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(!<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(bx) || (bx.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 2 && bx[1] == x),
<a name="l01816"></a>01816 <span class="stringliteral">"ArithTheoremProducer::darkGrayShadow2ba:\n beta<=bx: "</span>
<a name="l01817"></a>01817 +betaLEbx.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>()
<a name="l01818"></a>01818 +<span class="stringliteral">"\n ax<=alpha: "</span>+ axLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>());
<a name="l01819"></a>01819 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(1 <= b && b <= a && 2 <= a,
<a name="l01820"></a>01820 <span class="stringliteral">"ArithTheoremProducer::darkGrayShadow2ba:\n beta<=bx: "</span>
<a name="l01821"></a>01821 +betaLEbx.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>()
<a name="l01822"></a>01822 +<span class="stringliteral">"\n ax<=alpha: "</span>+ axLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>());
<a name="l01823"></a>01823 }
<a name="l01824"></a>01824 vector<Theorem> thms;
<a name="l01825"></a>01825 thms.push_back(betaLEbx);
<a name="l01826"></a>01826 thms.push_back(axLEalpha);
<a name="l01827"></a>01827 thms.push_back(isIntAlpha);
<a name="l01828"></a>01828 thms.push_back(isIntBeta);
<a name="l01829"></a>01829 thms.push_back(isIntx);
<a name="l01830"></a>01830 <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a> A(thms);
<a name="l01831"></a>01831 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01832"></a>01832 <span class="keywordflow">if</span>(withProof()) {
<a name="l01833"></a>01833 vector<Proof> pfs;
<a name="l01834"></a>01834 pfs.push_back(betaLEbx.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01835"></a>01835 pfs.push_back(axLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01836"></a>01836 pfs.push_back(isIntAlpha.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01837"></a>01837 pfs.push_back(isIntBeta.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01838"></a>01838 pfs.push_back(isIntx.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01839"></a>01839
<a name="l01840"></a>01840 pf = newPf(<span class="stringliteral">"dark_grayshadow_2ba"</span>, betaLEbx.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>(),
<a name="l01841"></a>01841 axLEalpha.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>(), pfs);
<a name="l01842"></a>01842 }
<a name="l01843"></a>01843
<a name="l01844"></a>01844 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> bAlpha = <a class="code" href="namespaceCVC3.html#adb35e0739f86730543924dbc8211a778">multExpr</a>(rat(b), alpha);
<a name="l01845"></a>01845 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> aBeta = <a class="code" href="namespaceCVC3.html#adb35e0739f86730543924dbc8211a778">multExpr</a>(rat(a), beta);
<a name="l01846"></a>01846 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> t = <a class="code" href="namespaceCVC3.html#a9ba326c305c5aeb61de515009aaa61f8">minusExpr</a>(bAlpha, aBeta);
<a name="l01847"></a>01847 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> d = darkShadow(rat(a*b-1), t);
<a name="l01848"></a>01848 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> g = grayShadow(bx, beta, 0, b-1);
<a name="l01849"></a>01849 <span class="keywordflow">return</span> newTheorem((d || g) && (!d || !g), A, pf);
<a name="l01850"></a>01850 }
<a name="l01851"></a>01851 <span class="comment"></span>
<a name="l01852"></a>01852 <span class="comment">/*! takes a dark shadow and expands it into an inequality.</span>
<a name="l01853"></a>01853 <span class="comment">*/</span>
<a name="l01854"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#aafadfc6ae6013ab18a7b4ee570cce16a">01854</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::expandDarkShadow(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& darkShadow) {
<a name="l01855"></a>01855 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& theShadow = darkShadow.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01856"></a>01856 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>){
<a name="l01857"></a>01857 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a61ff5938806e85a64c55e42c6fca5255">isDarkShadow</a>(theShadow),
<a name="l01858"></a>01858 <span class="stringliteral">"ArithTheoremProducer::expandDarkShadow: not DARK_SHADOW: "</span> +
<a name="l01859"></a>01859 theShadow.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01860"></a>01860 }
<a name="l01861"></a>01861 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01862"></a>01862 <span class="keywordflow">if</span>(withProof())
<a name="l01863"></a>01863 pf = newPf(<span class="stringliteral">"expand_dark_shadow"</span>, theShadow, darkShadow.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01864"></a>01864 <span class="keywordflow">return</span> newTheorem(<a class="code" href="namespaceCVC3.html#aebfd8a82800bd3dff4c8db461a52cdea">leExpr</a>(theShadow[0], theShadow[1]), darkShadow.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>(), pf);
<a name="l01865"></a>01865 }
<a name="l01866"></a>01866
<a name="l01867"></a>01867
<a name="l01868"></a>01868 <span class="comment">// takes a grayShadow (c1==c2) and expands it into an equality</span>
<a name="l01869"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ac8a2c0a97ace8f17153ad784c87ba5a2">01869</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::expandGrayShadow0(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& grayShadow) {
<a name="l01870"></a>01870 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& theShadow = grayShadow.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01871"></a>01871 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01872"></a>01872 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ab9a9fba0a64da2bd1ee5194fdedffb07">isGrayShadow</a>(theShadow),
<a name="l01873"></a>01873 <span class="stringliteral">"ArithTheoremProducer::expandGrayShadowConst0:"</span>
<a name="l01874"></a>01874 <span class="stringliteral">" not GRAY_SHADOW: "</span> +
<a name="l01875"></a>01875 theShadow.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01876"></a>01876 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(theShadow[2] == theShadow[3],
<a name="l01877"></a>01877 <span class="stringliteral">"ArithTheoremProducer::expandGrayShadow0: c1!=c2: "</span> +
<a name="l01878"></a>01878 theShadow.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01879"></a>01879 }
<a name="l01880"></a>01880 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01881"></a>01881 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"expand_gray_shadowconst0"</span>, theShadow,
<a name="l01882"></a>01882 grayShadow.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01883"></a>01883 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& v = theShadow[0];
<a name="l01884"></a>01884 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e = theShadow[1];
<a name="l01885"></a>01885 <span class="keywordflow">return</span> newRWTheorem(v, e + theShadow[2], grayShadow.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>(), pf);
<a name="l01886"></a>01886 }
<a name="l01887"></a>01887
<a name="l01888"></a>01888
<a name="l01889"></a>01889 <span class="comment">// G ==> (G1 or G2) and (!G1 or !G2),</span>
<a name="l01890"></a>01890 <span class="comment">// where G = G(x, e, c1, c2),</span>
<a name="l01891"></a>01891 <span class="comment">// G1 = G(x,e,c1,c)</span>
<a name="l01892"></a>01892 <span class="comment">// G2 = G(x,e,c+1,c2),</span>
<a name="l01893"></a>01893 <span class="comment">// and c = floor((c1+c2)/2)</span>
<a name="l01894"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a14af8b5ecbfaaee4600453bd9d681838">01894</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::splitGrayShadow(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& gThm) {
<a name="l01895"></a>01895 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& theShadow = gThm.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01896"></a>01896 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01897"></a>01897 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ab9a9fba0a64da2bd1ee5194fdedffb07">isGrayShadow</a>(theShadow),
<a name="l01898"></a>01898 <span class="stringliteral">"ArithTheoremProducer::expandGrayShadowConst: not a shadow"</span> +
<a name="l01899"></a>01899 theShadow.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01900"></a>01900 }
<a name="l01901"></a>01901
<a name="l01902"></a>01902 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c1 = theShadow[2].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l01903"></a>01903 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c2 = theShadow[3].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l01904"></a>01904
<a name="l01905"></a>01905 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01906"></a>01906 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(c1.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>() && c2.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>() && c1 < c2,
<a name="l01907"></a>01907 <span class="stringliteral">"ArithTheoremProducer::expandGrayShadow: "</span> +
<a name="l01908"></a>01908 theShadow.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01909"></a>01909 }
<a name="l01910"></a>01910
<a name="l01911"></a>01911 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& v = theShadow[0];
<a name="l01912"></a>01912 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e = theShadow[1];
<a name="l01913"></a>01913
<a name="l01914"></a>01914 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01915"></a>01915 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> c(floor((c1+c2) / 2));
<a name="l01916"></a>01916 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> g1(grayShadow(v, e, c1, c));
<a name="l01917"></a>01917 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> g2(grayShadow(v, e, c+1, c2));
<a name="l01918"></a>01918
<a name="l01919"></a>01919 <span class="keywordflow">if</span>(withProof()){
<a name="l01920"></a>01920 vector<Expr> exprs;
<a name="l01921"></a>01921 exprs.push_back(theShadow);
<a name="l01922"></a>01922 exprs.push_back(g1);
<a name="l01923"></a>01923 exprs.push_back(g2);
<a name="l01924"></a>01924 pf = newPf(<span class="stringliteral">"split_gray_shadow"</span>, exprs, gThm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01925"></a>01925 }
<a name="l01926"></a>01926
<a name="l01927"></a>01927 <span class="keywordflow">return</span> newTheorem((g1 || g2) && (!g1 || !g2), gThm.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>(), pf);
<a name="l01928"></a>01928 }
<a name="l01929"></a>01929
<a name="l01930"></a>01930
<a name="l01931"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ac6714d4922aea3413f9aeed742bc645e">01931</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::expandGrayShadow(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& gThm) {
<a name="l01932"></a>01932 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& theShadow = gThm.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01933"></a>01933 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01934"></a>01934 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ab9a9fba0a64da2bd1ee5194fdedffb07">isGrayShadow</a>(theShadow),
<a name="l01935"></a>01935 <span class="stringliteral">"ArithTheoremProducer::expandGrayShadowConst: not a shadow"</span> +
<a name="l01936"></a>01936 theShadow.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01937"></a>01937 }
<a name="l01938"></a>01938
<a name="l01939"></a>01939 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c1 = theShadow[2].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l01940"></a>01940 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c2 = theShadow[3].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l01941"></a>01941
<a name="l01942"></a>01942 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01943"></a>01943 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(c1.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>() && c2.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>() && c1 < c2,
<a name="l01944"></a>01944 <span class="stringliteral">"ArithTheoremProducer::expandGrayShadow: "</span> +
<a name="l01945"></a>01945 theShadow.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01946"></a>01946 }
<a name="l01947"></a>01947
<a name="l01948"></a>01948 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& v = theShadow[0];
<a name="l01949"></a>01949 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e = theShadow[1];
<a name="l01950"></a>01950
<a name="l01951"></a>01951 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l01952"></a>01952 <span class="keywordflow">if</span>(withProof())
<a name="l01953"></a>01953 pf = newPf(<span class="stringliteral">"expand_gray_shadow"</span>, theShadow, gThm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l01954"></a>01954 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ineq1(<a class="code" href="namespaceCVC3.html#aebfd8a82800bd3dff4c8db461a52cdea">leExpr</a>(e+rat(c1), v));
<a name="l01955"></a>01955 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> ineq2(<a class="code" href="namespaceCVC3.html#aebfd8a82800bd3dff4c8db461a52cdea">leExpr</a>(v, e+rat(c2)));
<a name="l01956"></a>01956 <span class="keywordflow">return</span> newTheorem(ineq1 && ineq2, gThm.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>(), pf);
<a name="l01957"></a>01957 }
<a name="l01958"></a>01958
<a name="l01959"></a>01959
<a name="l01960"></a>01960 <span class="comment">// Expanding GRAY_SHADOW(a*x, c, b), where c is a constant</span>
<a name="l01961"></a>01961 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l01962"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#af091e13254c983370c46707a03b1ad30">01962</a> ArithTheoremProducer::expandGrayShadowConst(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& gThm) {
<a name="l01963"></a>01963 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& theShadow = gThm.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l01964"></a>01964 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& ax = theShadow[0];
<a name="l01965"></a>01965 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& cExpr = theShadow[1];
<a name="l01966"></a>01966 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& bExpr = theShadow[2];
<a name="l01967"></a>01967
<a name="l01968"></a>01968 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01969"></a>01969 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(!<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(ax) || ax[0].<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(),
<a name="l01970"></a>01970 <span class="stringliteral">"ArithTheoremProducer::expandGrayShadowConst: "</span>
<a name="l01971"></a>01971 <span class="stringliteral">"'a' in a*x is not a const: "</span> +theShadow.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01972"></a>01972 }
<a name="l01973"></a>01973
<a name="l01974"></a>01974 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> a = <a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(ax)? ax[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() : 1;
<a name="l01975"></a>01975
<a name="l01976"></a>01976 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l01977"></a>01977 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ab9a9fba0a64da2bd1ee5194fdedffb07">isGrayShadow</a>(theShadow),
<a name="l01978"></a>01978 <span class="stringliteral">"ArithTheoremProducer::expandGrayShadowConst: "</span>
<a name="l01979"></a>01979 <span class="stringliteral">"not a GRAY_SHADOW: "</span> +theShadow.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01980"></a>01980 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(a.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>() && a >= 1,
<a name="l01981"></a>01981 <span class="stringliteral">"ArithTheoremProducer::expandGrayShadowConst: "</span>
<a name="l01982"></a>01982 <span class="stringliteral">"'a' is not integer: "</span> +theShadow.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01983"></a>01983 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(cExpr.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>(),
<a name="l01984"></a>01984 <span class="stringliteral">"ArithTheoremProducer::expandGrayShadowConst: "</span>
<a name="l01985"></a>01985 <span class="stringliteral">"'c' is not rational"</span> +theShadow.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01986"></a>01986 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(bExpr.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>() && bExpr.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>().<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>(),
<a name="l01987"></a>01987 <span class="stringliteral">"ArithTheoremProducer::expandGrayShadowConst: b not integer: "</span>
<a name="l01988"></a>01988 +theShadow.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l01989"></a>01989 }
<a name="l01990"></a>01990
<a name="l01991"></a>01991 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& b = bExpr.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l01992"></a>01992 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c = cExpr.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l01993"></a>01993 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> j = constRHSGrayShadow(c,b,a);
<a name="l01994"></a>01994 <span class="comment">// Compute sign(b)*j(c,b,a)</span>
<a name="l01995"></a>01995 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> signB = (b>0)? 1 : -1;
<a name="l01996"></a>01996 <span class="comment">// |b| (absolute value of b)</span>
<a name="l01997"></a>01997 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> bAbs = <a class="code" href="namespaceCVC3.html#a39fc111339d6dffdc98d6a25b68dff0e">abs</a>(b);
<a name="l01998"></a>01998
<a name="l01999"></a>01999 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a>& assump(gThm.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>());
<a name="l02000"></a>02000 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02001"></a>02001 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> conc; <span class="comment">// Conclusion of the rule</span>
<a name="l02002"></a>02002
<a name="l02003"></a>02003 <span class="keywordflow">if</span>(bAbs < j) {
<a name="l02004"></a>02004 <span class="keywordflow">if</span>(withProof())
<a name="l02005"></a>02005 pf = newPf(<span class="stringliteral">"expand_gray_shadow_const_0"</span>, theShadow,
<a name="l02006"></a>02006 gThm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02007"></a>02007 conc = newTheorem(d_em->falseExpr(), assump, pf);
<a name="l02008"></a>02008 } <span class="keywordflow">else</span> <span class="keywordflow">if</span>(bAbs < a+j) {
<a name="l02009"></a>02009 <span class="keywordflow">if</span>(withProof())
<a name="l02010"></a>02010 pf = newPf(<span class="stringliteral">"expand_gray_shadow_const_1"</span>, theShadow,
<a name="l02011"></a>02011 gThm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02012"></a>02012 conc = newRWTheorem(ax, rat(c+b-signB*j), assump, pf);
<a name="l02013"></a>02013 } <span class="keywordflow">else</span> {
<a name="l02014"></a>02014 <span class="keywordflow">if</span>(withProof())
<a name="l02015"></a>02015 pf = newPf(<span class="stringliteral">"expand_gray_shadow_const"</span>, theShadow,
<a name="l02016"></a>02016 gThm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02017"></a>02017 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> newGrayShadow(<a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ae88f497d92023928ed529d704ecb1881">GRAY_SHADOW</a>, ax, cExpr, rat(b-signB*(a+j))));
<a name="l02018"></a>02018 conc = newTheorem(ax.<a class="code" href="group__ExprPkg.html#gacb48495ca445c895f95d0c3c1ae2070b">eqExpr</a>(rat(c+b-signB*j)).<a class="code" href="group__ExprPkg.html#gaf310870d783fff343e77ba9c2277c626">orExpr</a>(newGrayShadow),
<a name="l02019"></a>02019 assump, pf);
<a name="l02020"></a>02020 }
<a name="l02021"></a>02021
<a name="l02022"></a>02022 <span class="keywordflow">return</span> conc;
<a name="l02023"></a>02023 }
<a name="l02024"></a>02024
<a name="l02025"></a>02025
<a name="l02026"></a>02026 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l02027"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#af0070c5da95d33029e54b1d669d5b1f0">02027</a> ArithTheoremProducer::grayShadowConst(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& gThm) {
<a name="l02028"></a>02028 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& g = gThm.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l02029"></a>02029 <span class="keywordtype">bool</span> checkProofs(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>);
<a name="l02030"></a>02030 <span class="keywordflow">if</span>(checkProofs) {
<a name="l02031"></a>02031 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ab9a9fba0a64da2bd1ee5194fdedffb07">isGrayShadow</a>(g), <span class="stringliteral">"ArithTheoremProducer::grayShadowConst("</span>
<a name="l02032"></a>02032 +g.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l02033"></a>02033 }
<a name="l02034"></a>02034
<a name="l02035"></a>02035 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& ax = g[0];
<a name="l02036"></a>02036 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e = g[1];
<a name="l02037"></a>02037 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c1 = g[2].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l02038"></a>02038 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c2 = g[3].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l02039"></a>02039 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> aExpr, x;
<a name="l02040"></a>02040 d_theoryArith->separateMonomial(ax, aExpr, x);
<a name="l02041"></a>02041
<a name="l02042"></a>02042 <span class="keywordflow">if</span>(checkProofs) {
<a name="l02043"></a>02043 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>() && e.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>().<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>(),
<a name="l02044"></a>02044 <span class="stringliteral">"ArithTheoremProducer::grayShadowConst("</span>+g.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l02045"></a>02045 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(aExpr.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>(),
<a name="l02046"></a>02046 <span class="stringliteral">"ArithTheoremProducer::grayShadowConst("</span>+g.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l02047"></a>02047 }
<a name="l02048"></a>02048
<a name="l02049"></a>02049 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& a = aExpr.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l02050"></a>02050 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c = e.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l02051"></a>02051
<a name="l02052"></a>02052 <span class="keywordflow">if</span>(checkProofs) {
<a name="l02053"></a>02053 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(a.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>() && a >= 2,
<a name="l02054"></a>02054 <span class="stringliteral">"ArithTheoremProducer::grayShadowConst("</span>+g.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l02055"></a>02055 }
<a name="l02056"></a>02056
<a name="l02057"></a>02057 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> newC1 = ceil((c1+c)/a), newC2 = floor((c2+c)/a);
<a name="l02058"></a>02058 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> newG((newC1 > newC2)? d_em->falseExpr()
<a name="l02059"></a>02059 : grayShadow(x, rat(0), newC1, newC2));
<a name="l02060"></a>02060 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02061"></a>02061 <span class="keywordflow">if</span>(withProof())
<a name="l02062"></a>02062 pf = newPf(<span class="stringliteral">"gray_shadow_const"</span>, g, newG, gThm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02063"></a>02063 <span class="keywordflow">return</span> newTheorem(newG, gThm.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>(), pf);
<a name="l02064"></a>02064 }
<a name="l02065"></a>02065
<a name="l02066"></a>02066
<a name="l02067"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a529e92e59e9009e3330a8592c9cb56fe">02067</a> <a class="code" href="classCVC3_1_1Rational.html">Rational</a> ArithTheoremProducer::constRHSGrayShadow(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c,
<a name="l02068"></a>02068 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& b,
<a name="l02069"></a>02069 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& a) {
<a name="l02070"></a>02070 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(c.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>() &&
<a name="l02071"></a>02071 b.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>() &&
<a name="l02072"></a>02072 a.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>() &&
<a name="l02073"></a>02073 b != 0,
<a name="l02074"></a>02074 <span class="stringliteral">"ArithTheoremProducer::constRHSGrayShadow: a, b, c must be ints"</span>);
<a name="l02075"></a>02075 <span class="keywordflow">if</span> (b > 0)
<a name="l02076"></a>02076 <span class="keywordflow">return</span> mod(c+b, a);
<a name="l02077"></a>02077 <span class="keywordflow">else</span>
<a name="l02078"></a>02078 <span class="keywordflow">return</span> mod(a-(c+b), a);
<a name="l02079"></a>02079 }
<a name="l02080"></a>02080 <span class="comment"></span>
<a name="l02081"></a>02081 <span class="comment">/*! Takes a Theorem(\\alpha < \\beta) and returns</span>
<a name="l02082"></a>02082 <span class="comment"> * Theorem(\\alpha < \\beta <==> \\alpha <= \\beta -1)</span>
<a name="l02083"></a>02083 <span class="comment"> * where \\alpha and \\beta are integer expressions</span>
<a name="l02084"></a>02084 <span class="comment"> */</span>
<a name="l02085"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ac5d4056f00cee80d73b5b46f63bd5b3d">02085</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::lessThanToLE(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& less,
<a name="l02086"></a>02086 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntLHS,
<a name="l02087"></a>02087 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntRHS,
<a name="l02088"></a>02088 <span class="keywordtype">bool</span> changeRight) {
<a name="l02089"></a>02089 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& ineq = less.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l02090"></a>02090 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& isIntLHSexpr = isIntLHS.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l02091"></a>02091 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& isIntRHSexpr = isIntRHS.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l02092"></a>02092
<a name="l02093"></a>02093 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02094"></a>02094 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a448b6e0d541113608bba5a7a005609e3">isLT</a>(ineq),
<a name="l02095"></a>02095 <span class="stringliteral">"ArithTheoremProducer::LTtoLE: ineq must be <"</span>);
<a name="l02096"></a>02096 <span class="comment">// Integrality check</span>
<a name="l02097"></a>02097 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntLHSexpr) && isIntLHSexpr[0] == ineq[0],
<a name="l02098"></a>02098 <span class="stringliteral">"ArithTheoremProducer::lessThanToLE: bad integrality check:\n"</span>
<a name="l02099"></a>02099 <span class="stringliteral">" ineq = "</span>+ineq.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n isIntLHS = "</span>
<a name="l02100"></a>02100 +isIntLHSexpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02101"></a>02101 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntRHSexpr) && isIntRHSexpr[0] == ineq[1],
<a name="l02102"></a>02102 <span class="stringliteral">"ArithTheoremProducer::lessThanToLE: bad integrality check:\n"</span>
<a name="l02103"></a>02103 <span class="stringliteral">" ineq = "</span>+ineq.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n isIntRHS = "</span>
<a name="l02104"></a>02104 +isIntRHSexpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02105"></a>02105 }
<a name="l02106"></a>02106 vector<Theorem> thms;
<a name="l02107"></a>02107 thms.push_back(less);
<a name="l02108"></a>02108 thms.push_back(isIntLHS);
<a name="l02109"></a>02109 thms.push_back(isIntRHS);
<a name="l02110"></a>02110 <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a> a(thms);
<a name="l02111"></a>02111 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02112"></a>02112 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> le = changeRight?
<a name="l02113"></a>02113 <a class="code" href="namespaceCVC3.html#aebfd8a82800bd3dff4c8db461a52cdea">leExpr</a>(ineq[0], ineq[1] + rat(-1))
<a name="l02114"></a>02114 : <a class="code" href="namespaceCVC3.html#aebfd8a82800bd3dff4c8db461a52cdea">leExpr</a>(ineq[0] + rat(1), ineq[1]);
<a name="l02115"></a>02115
<a name="l02116"></a>02116 <span class="keywordflow">if</span>(withProof()) {
<a name="l02117"></a>02117 vector<Proof> pfs;
<a name="l02118"></a>02118 pfs.push_back(less.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02119"></a>02119 pfs.push_back(isIntLHS.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02120"></a>02120 pfs.push_back(isIntRHS.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02121"></a>02121 pf = newPf(changeRight? <span class="stringliteral">"lessThan_To_LE_rhs"</span> : <span class="stringliteral">"lessThan_To_LE_lhs"</span>,
<a name="l02122"></a>02122 ineq, le, pfs);
<a name="l02123"></a>02123 }
<a name="l02124"></a>02124
<a name="l02125"></a>02125 <span class="keywordflow">return</span> newRWTheorem(ineq, le, a, pf);
<a name="l02126"></a>02126 }
<a name="l02127"></a>02127
<a name="l02128"></a>02128 <span class="comment"></span>
<a name="l02129"></a>02129 <span class="comment">/*! \param eqn is an equation 0 = a.x or 0 = c + a.x</span>
<a name="l02130"></a>02130 <span class="comment"> * \param isIntx is a proof of IS_INTEGER(x)</span>
<a name="l02131"></a>02131 <span class="comment"> *</span>
<a name="l02132"></a>02132 <span class="comment"> * \return the theorem 0 = c + a.x <==> x=-c/a if -c/a is int else</span>
<a name="l02133"></a>02133 <span class="comment"> * return the theorem 0 = c + a.x <==> false.</span>
<a name="l02134"></a>02134 <span class="comment"> *</span>
<a name="l02135"></a>02135 <span class="comment"> * It also handles the special case of 0 = a.x <==> x = 0</span>
<a name="l02136"></a>02136 <span class="comment"> */</span>
<a name="l02137"></a>02137 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l02138"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a92936e3de514c430659486b00e84b0a9">02138</a> ArithTheoremProducer::intVarEqnConst(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& eqn,
<a name="l02139"></a>02139 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="theory__quant_8cpp.html#ac9940420b1f3427ebe821902adbb578d">isIntx</a>) {
<a name="l02140"></a>02140 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& <a class="code" href="namespaceMiniSat.html#ad93cb56673487974071ed3b75bf4ea83">left</a>(eqn[0]);
<a name="l02141"></a>02141 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& <a class="code" href="namespaceMiniSat.html#a82558b7a36c52f5d3211d5d14bed99d4">right</a>(eqn[1]);
<a name="l02142"></a>02142 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& isIntxexpr(isIntx.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>());
<a name="l02143"></a>02143
<a name="l02144"></a>02144 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02145"></a>02145 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>((<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(right) && right[0].<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>())
<a name="l02146"></a>02146 || (right.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 2 && <a class="code" href="namespaceCVC3.html#afb0f7d15ddbd87f9abb128108101f557">isPlus</a>(right)
<a name="l02147"></a>02147 && right[0].<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>()
<a name="l02148"></a>02148 && ((!<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(right[1]) || right[1][0].<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>()))),
<a name="l02149"></a>02149 <span class="stringliteral">"ArithTheoremProducer::intVarEqnConst: "</span>
<a name="l02150"></a>02150 <span class="stringliteral">"rhs has a wrong format: "</span> + right.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02151"></a>02151 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(left.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>() && 0 == left.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>(),
<a name="l02152"></a>02152 <span class="stringliteral">"ArithTheoremProducer:intVarEqnConst:left is not a zero: "</span> +
<a name="l02153"></a>02153 left.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02154"></a>02154 }
<a name="l02155"></a>02155 <span class="comment">// Integrality constraint</span>
<a name="l02156"></a>02156 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> x(right);
<a name="l02157"></a>02157 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> a(1), c(0);
<a name="l02158"></a>02158 <span class="keywordflow">if</span>(<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(right)) {
<a name="l02159"></a>02159 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> aExpr;
<a name="l02160"></a>02160 d_theoryArith->separateMonomial(right, aExpr, x);
<a name="l02161"></a>02161 a = aExpr.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l02162"></a>02162 } <span class="keywordflow">else</span> { <span class="comment">// right is a PLUS</span>
<a name="l02163"></a>02163 c = right[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l02164"></a>02164 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> aExpr;
<a name="l02165"></a>02165 d_theoryArith->separateMonomial(right[1], aExpr, x);
<a name="l02166"></a>02166 a = aExpr.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l02167"></a>02167 }
<a name="l02168"></a>02168 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02169"></a>02169 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntxexpr) && isIntxexpr[0] == x,
<a name="l02170"></a>02170 <span class="stringliteral">"ArithTheoremProducer:intVarEqnConst: "</span>
<a name="l02171"></a>02171 <span class="stringliteral">"bad integrality constraint:\n right = "</span> +
<a name="l02172"></a>02172 right.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n isIntx = "</span>+isIntxexpr.toString());
<a name="l02173"></a>02173 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(a!=0, <span class="stringliteral">"ArithTheoremProducer:intVarEqnConst: eqn = "</span>
<a name="l02174"></a>02174 +eqn.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02175"></a>02175 }
<a name="l02176"></a>02176 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a>& assump(isIntx.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>());
<a name="l02177"></a>02177 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02178"></a>02178 <span class="keywordflow">if</span>(withProof())
<a name="l02179"></a>02179 pf = newPf(<span class="stringliteral">"int_const_eq"</span>, eqn, isIntx.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02180"></a>02180
<a name="l02181"></a>02181 <span class="comment">// Solve for x: x = r = -c/a</span>
<a name="l02182"></a>02182 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> r(-c/a);
<a name="l02183"></a>02183
<a name="l02184"></a>02184 <span class="keywordflow">if</span>(r.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>())
<a name="l02185"></a>02185 <span class="keywordflow">return</span> newRWTheorem(eqn, x.<a class="code" href="group__ExprPkg.html#gacb48495ca445c895f95d0c3c1ae2070b">eqExpr</a>(rat(r)), assump, pf);
<a name="l02186"></a>02186 <span class="keywordflow">else</span>
<a name="l02187"></a>02187 <span class="keywordflow">return</span> newRWTheorem(eqn, d_em->falseExpr(), assump, pf);
<a name="l02188"></a>02188 }
<a name="l02189"></a>02189
<a name="l02190"></a>02190
<a name="l02191"></a>02191 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>
<a name="l02192"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a47a517c15b57ba19b7759a4ba925e306">02192</a> ArithTheoremProducer::create_t(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& eqn) {
<a name="l02193"></a>02193 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& lhs = eqn[0];
<a name="l02194"></a>02194 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(lhs),
<a name="l02195"></a>02195 <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"create_t : lhs must be a MULT"</span>
<a name="l02196"></a>02196 + lhs.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02197"></a>02197 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x = lhs[1];
<a name="l02198"></a>02198 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> m = lhs[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>()+1;
<a name="l02199"></a>02199 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(m > 0, <span class="stringliteral">"ArithTheoremProducer::create_t: m = "</span>+m.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>());
<a name="l02200"></a>02200 vector<Expr> kids;
<a name="l02201"></a>02201 <span class="keywordflow">if</span>(<a class="code" href="namespaceCVC3.html#afb0f7d15ddbd87f9abb128108101f557">isPlus</a>(eqn[1]))
<a name="l02202"></a>02202 sumModM(kids, eqn[1], m, m);
<a name="l02203"></a>02203 <span class="keywordflow">else</span>
<a name="l02204"></a>02204 kids.push_back(monomialModM(eqn[1], m, m));
<a name="l02205"></a>02205
<a name="l02206"></a>02206 kids.push_back(<a class="code" href="namespaceCVC3.html#adb35e0739f86730543924dbc8211a778">multExpr</a>(rat(1/m), x));
<a name="l02207"></a>02207 <span class="keywordflow">return</span> <a class="code" href="namespaceCVC3.html#accd3d7d38b0e04136afbc3e5191bc8bb">plusExpr</a>(kids);
<a name="l02208"></a>02208 }
<a name="l02209"></a>02209
<a name="l02210"></a>02210 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>
<a name="l02211"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ab20380e74e431d9956c588d45d5121a4">02211</a> ArithTheoremProducer::create_t2(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& lhs, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& rhs,
<a name="l02212"></a>02212 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& sigma) {
<a name="l02213"></a>02213 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> m = lhs[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>()+1;
<a name="l02214"></a>02214 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(m > 0, <span class="stringliteral">"ArithTheoremProducer::create_t2: m = "</span>+m.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>());
<a name="l02215"></a>02215 vector<Expr> kids;
<a name="l02216"></a>02216 <span class="keywordflow">if</span>(<a class="code" href="namespaceCVC3.html#afb0f7d15ddbd87f9abb128108101f557">isPlus</a>(rhs))
<a name="l02217"></a>02217 sumModM(kids, rhs, m, -1);
<a name="l02218"></a>02218 <span class="keywordflow">else</span> {
<a name="l02219"></a>02219 kids.push_back(rat(0)); <span class="comment">// For canonical form</span>
<a name="l02220"></a>02220 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> monom = monomialModM(rhs, m, -1);
<a name="l02221"></a>02221 <span class="keywordflow">if</span>(!monom.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>())
<a name="l02222"></a>02222 kids.push_back(monom);
<a name="l02223"></a>02223 <span class="keywordflow">else</span>
<a name="l02224"></a>02224 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(monom.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() == 0, <span class="stringliteral">""</span>);
<a name="l02225"></a>02225 }
<a name="l02226"></a>02226 kids.push_back(rat(m)*sigma);
<a name="l02227"></a>02227 <span class="keywordflow">return</span> <a class="code" href="namespaceCVC3.html#accd3d7d38b0e04136afbc3e5191bc8bb">plusExpr</a>(kids);
<a name="l02228"></a>02228 }
<a name="l02229"></a>02229
<a name="l02230"></a>02230 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>
<a name="l02231"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a77e9c5681a02ab61f1311628e843d3db">02231</a> ArithTheoremProducer::create_t3(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& lhs, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& rhs,
<a name="l02232"></a>02232 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& sigma) {
<a name="l02233"></a>02233 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& a = lhs[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l02234"></a>02234 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> m = a+1;
<a name="l02235"></a>02235 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(m > 0, <span class="stringliteral">"ArithTheoremProducer::create_t3: m = "</span>+m.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>());
<a name="l02236"></a>02236 vector<Expr> kids;
<a name="l02237"></a>02237 <span class="keywordflow">if</span>(<a class="code" href="namespaceCVC3.html#afb0f7d15ddbd87f9abb128108101f557">isPlus</a>(rhs))
<a name="l02238"></a>02238 sumMulF(kids, rhs, m, 1);
<a name="l02239"></a>02239 <span class="keywordflow">else</span> {
<a name="l02240"></a>02240 kids.push_back(rat(0)); <span class="comment">// For canonical form</span>
<a name="l02241"></a>02241 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> monom = monomialMulF(rhs, m, 1);
<a name="l02242"></a>02242 <span class="keywordflow">if</span>(!monom.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>())
<a name="l02243"></a>02243 kids.push_back(monom);
<a name="l02244"></a>02244 <span class="keywordflow">else</span>
<a name="l02245"></a>02245 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(monom.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() == 0, <span class="stringliteral">""</span>);
<a name="l02246"></a>02246 }
<a name="l02247"></a>02247 kids.push_back(rat(-a)*sigma);
<a name="l02248"></a>02248 <span class="keywordflow">return</span> <a class="code" href="namespaceCVC3.html#accd3d7d38b0e04136afbc3e5191bc8bb">plusExpr</a>(kids);
<a name="l02249"></a>02249 }
<a name="l02250"></a>02250
<a name="l02251"></a>02251 <a class="code" href="classCVC3_1_1Rational.html">Rational</a>
<a name="l02252"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a3cb8580c7627250ffe999de9a1b2c8c3">02252</a> ArithTheoremProducer::modEq(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& i, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& m) {
<a name="l02253"></a>02253 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(m > 0, <span class="stringliteral">"ArithTheoremProducer::modEq: m = "</span>+m.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>());
<a name="l02254"></a>02254 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> half(1,2);
<a name="l02255"></a>02255 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> res((i - m*(floor((i/m) + half))));
<a name="l02256"></a>02256 <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba7fa27e82c6c4f69434225ed81e5d151e">TRACE</a>(<span class="stringliteral">"arith eq"</span>, <span class="stringliteral">"modEq("</span>+i.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>()+<span class="stringliteral">", "</span>+m.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>()+<span class="stringliteral">") = "</span>, res, <span class="stringliteral">""</span>);
<a name="l02257"></a>02257 <span class="keywordflow">return</span> res;
<a name="l02258"></a>02258 }
<a name="l02259"></a>02259
<a name="l02260"></a>02260 <a class="code" href="classCVC3_1_1Rational.html">Rational</a>
<a name="l02261"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ad727620082aea32b487863ac5888eb1b">02261</a> ArithTheoremProducer::f(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& i, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& m) {
<a name="l02262"></a>02262 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(m > 0, <span class="stringliteral">"ArithTheoremProducer::f: m = "</span>+m.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>());
<a name="l02263"></a>02263 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> half(1,2);
<a name="l02264"></a>02264 <span class="keywordflow">return</span> (floor(i/m + half)+modEq(i,m));
<a name="l02265"></a>02265 }
<a name="l02266"></a>02266
<a name="l02267"></a>02267 <span class="keywordtype">void</span>
<a name="l02268"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a10c569edc893a67b42af659633b3f20d">02268</a> ArithTheoremProducer::sumModM(vector<Expr>& summands, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& sum,
<a name="l02269"></a>02269 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& m, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& divisor) {
<a name="l02270"></a>02270 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(divisor != 0, <span class="stringliteral">"ArithTheoremProducer::sumModM: divisor = "</span>
<a name="l02271"></a>02271 +divisor.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>());
<a name="l02272"></a>02272 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = sum.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l02273"></a>02273 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(i != sum.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(), <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::sumModM"</span>);
<a name="l02274"></a>02274 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> C = i->getRational();
<a name="l02275"></a>02275 C = modEq(C,m)/divisor;
<a name="l02276"></a>02276 summands.push_back(rat(C));
<a name="l02277"></a>02277 i++;
<a name="l02278"></a>02278 <span class="keywordflow">for</span>(<a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> iend=sum.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); i!=iend; ++i) {
<a name="l02279"></a>02279 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> monom = monomialModM(*i, m, divisor);
<a name="l02280"></a>02280 <span class="keywordflow">if</span>(!monom.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>())
<a name="l02281"></a>02281 summands.push_back(monom);
<a name="l02282"></a>02282 <span class="keywordflow">else</span>
<a name="l02283"></a>02283 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(monom.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() == 0, <span class="stringliteral">""</span>);
<a name="l02284"></a>02284 }
<a name="l02285"></a>02285 }
<a name="l02286"></a>02286
<a name="l02287"></a>02287 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>
<a name="l02288"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a69adf7d70a6a71e5c0e3489535a18108">02288</a> ArithTheoremProducer::monomialModM(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& i,
<a name="l02289"></a>02289 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& m, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& divisor)
<a name="l02290"></a>02290 {
<a name="l02291"></a>02291 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(divisor != 0, <span class="stringliteral">"ArithTheoremProducer::monomialModM: divisor = "</span>
<a name="l02292"></a>02292 +divisor.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>());
<a name="l02293"></a>02293 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> res;
<a name="l02294"></a>02294 <span class="keywordflow">if</span>(<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(i)) {
<a name="l02295"></a>02295 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> ai = i[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l02296"></a>02296 ai = modEq(ai,m)/divisor;
<a name="l02297"></a>02297 <span class="keywordflow">if</span>(0 == ai) res = rat(0);
<a name="l02298"></a>02298 <span class="keywordflow">else</span> <span class="keywordflow">if</span>(1 == ai && i.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 2) res = i[1];
<a name="l02299"></a>02299 <span class="keywordflow">else</span> {
<a name="l02300"></a>02300 vector<Expr> kids = i.<a class="code" href="group__ExprPkg.html#ga1e18ae89889e781591eb2874a4196b73">getKids</a>();
<a name="l02301"></a>02301 kids[0] = rat(ai);
<a name="l02302"></a>02302 res = <a class="code" href="namespaceCVC3.html#adb35e0739f86730543924dbc8211a778">multExpr</a>(kids);
<a name="l02303"></a>02303 }
<a name="l02304"></a>02304 } <span class="keywordflow">else</span> { <span class="comment">// It's a single variable</span>
<a name="l02305"></a>02305 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> ai = modEq(1,m)/divisor;
<a name="l02306"></a>02306 <span class="keywordflow">if</span>(1 == ai) res = i;
<a name="l02307"></a>02307 <span class="keywordflow">else</span> res = rat(ai)*i;
<a name="l02308"></a>02308 }
<a name="l02309"></a>02309 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(!res.isNull(), <span class="stringliteral">"ArithTheoremProducer::monomialModM()"</span>);
<a name="l02310"></a>02310 <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba7fa27e82c6c4f69434225ed81e5d151e">TRACE</a>(<span class="stringliteral">"arith eq"</span>, <span class="stringliteral">"monomialModM(i="</span>+i.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">", m="</span>+m.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>()
<a name="l02311"></a>02311 +<span class="stringliteral">", div="</span>+divisor.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>()+<span class="stringliteral">") = "</span>, res, <span class="stringliteral">""</span>);
<a name="l02312"></a>02312 <span class="keywordflow">return</span> res;
<a name="l02313"></a>02313 }
<a name="l02314"></a>02314
<a name="l02315"></a>02315 <span class="keywordtype">void</span>
<a name="l02316"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a32e61136df79a76fe1ed853ee6b8dc2e">02316</a> ArithTheoremProducer::sumMulF(vector<Expr>& summands, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& sum,
<a name="l02317"></a>02317 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& m, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& divisor) {
<a name="l02318"></a>02318 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(divisor != 0, <span class="stringliteral">"ArithTheoremProducer::sumMulF: divisor = "</span>
<a name="l02319"></a>02319 +divisor.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>());
<a name="l02320"></a>02320 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = sum.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l02321"></a>02321 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(i != sum.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(), <a class="code" href="arith__theorem__producer_8cpp.html#a79f2713d570c7065f61a160134ea765b">CLASS_NAME</a> <span class="stringliteral">"::sumModM"</span>);
<a name="l02322"></a>02322 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> C = i->getRational();
<a name="l02323"></a>02323 C = f(C,m)/divisor;
<a name="l02324"></a>02324 summands.push_back(rat(C));
<a name="l02325"></a>02325 i++;
<a name="l02326"></a>02326 <span class="keywordflow">for</span>(<a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> iend=sum.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); i!=iend; ++i) {
<a name="l02327"></a>02327 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> monom = monomialMulF(*i, m, divisor);
<a name="l02328"></a>02328 <span class="keywordflow">if</span>(!monom.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>())
<a name="l02329"></a>02329 summands.push_back(monom);
<a name="l02330"></a>02330 <span class="keywordflow">else</span>
<a name="l02331"></a>02331 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(monom.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() == 0, <span class="stringliteral">""</span>);
<a name="l02332"></a>02332 }
<a name="l02333"></a>02333 }
<a name="l02334"></a>02334
<a name="l02335"></a>02335 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>
<a name="l02336"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a41da83b4624daa43a84bc049b5b7d836">02336</a> ArithTheoremProducer::monomialMulF(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& i,
<a name="l02337"></a>02337 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& m, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& divisor)
<a name="l02338"></a>02338 {
<a name="l02339"></a>02339 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(divisor != 0, <span class="stringliteral">"ArithTheoremProducer::monomialMulF: divisor = "</span>
<a name="l02340"></a>02340 +divisor.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>());
<a name="l02341"></a>02341 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> ai = <a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(i) ? (i)[0].getRational() : 1;
<a name="l02342"></a>02342 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> xi = <a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(i) ? (i)[1] : (i);
<a name="l02343"></a>02343 ai = f(ai,m)/divisor;
<a name="l02344"></a>02344 <span class="keywordflow">if</span>(0 == ai) <span class="keywordflow">return</span> rat(0);
<a name="l02345"></a>02345 <span class="keywordflow">if</span>(1 == ai) <span class="keywordflow">return</span> xi;
<a name="l02346"></a>02346 <span class="keywordflow">return</span> <a class="code" href="namespaceCVC3.html#adb35e0739f86730543924dbc8211a778">multExpr</a>(rat(ai), xi);
<a name="l02347"></a>02347 }
<a name="l02348"></a>02348
<a name="l02349"></a>02349 <span class="comment">// This recursive function accepts a term, t, and a 'map' of</span>
<a name="l02350"></a>02350 <span class="comment">// substitutions [x1/t1, x2/t2,...,xn/tn]. it returns a t' which is</span>
<a name="l02351"></a>02351 <span class="comment">// basically t[x1/t1,x2/t2...xn/tn]</span>
<a name="l02352"></a>02352 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>
<a name="l02353"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a073ec1476668043be44ae96519eae36d">02353</a> ArithTheoremProducer::substitute(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& term, <a class="code" href="classCVC3_1_1ExprMap.html">ExprMap<Expr></a>& eMap)
<a name="l02354"></a>02354 {
<a name="l02355"></a>02355 <a class="code" href="classCVC3_1_1ExprMap.html">ExprMap<Expr>::iterator</a> i, iend = eMap.<a class="code" href="classCVC3_1_1ExprMap.html#a283ae6c44308cbdda0d82da5a16e52c8">end</a>();
<a name="l02356"></a>02356
<a name="l02357"></a>02357 i = eMap.<a class="code" href="classCVC3_1_1ExprMap.html#ae50ab1874dd63b575553e7db769abe28">find</a>(term);
<a name="l02358"></a>02358 <span class="keywordflow">if</span>(iend != i)
<a name="l02359"></a>02359 <span class="keywordflow">return</span> (*i).second;
<a name="l02360"></a>02360
<a name="l02361"></a>02361 if (<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(term)) {
<a name="l02362"></a>02362 <span class="comment">//in this case term is of the form c.x</span>
<a name="l02363"></a>02363 i = eMap.<a class="code" href="classCVC3_1_1ExprMap.html#ae50ab1874dd63b575553e7db769abe28">find</a>(term[1]);
<a name="l02364"></a>02364 <span class="keywordflow">if</span>(iend != i)
<a name="l02365"></a>02365 <span class="keywordflow">return</span> term[0]*(*i).second;
<a name="l02366"></a>02366 <span class="keywordflow">else</span>
<a name="l02367"></a>02367 <span class="keywordflow">return</span> term;
<a name="l02368"></a>02368 }
<a name="l02369"></a>02369
<a name="l02370"></a>02370 <span class="keywordflow">if</span>(<a class="code" href="namespaceCVC3.html#afb0f7d15ddbd87f9abb128108101f557">isPlus</a>(term)) {
<a name="l02371"></a>02371 vector<Expr> output;
<a name="l02372"></a>02372 <span class="keywordflow">for</span>(<a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> j = term.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>(), jend = term.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); j != jend; ++j)
<a name="l02373"></a>02373 output.push_back(substitute(*j, eMap));
<a name="l02374"></a>02374 <span class="keywordflow">return</span> <a class="code" href="namespaceCVC3.html#accd3d7d38b0e04136afbc3e5191bc8bb">plusExpr</a>(output);
<a name="l02375"></a>02375 }
<a name="l02376"></a>02376 <span class="keywordflow">return</span> term;
<a name="l02377"></a>02377 }
<a name="l02378"></a>02378
<a name="l02379"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a23faa6b30e4b01d7540ac1e22e6e06ce">02379</a> <span class="keywordtype">bool</span> ArithTheoremProducer::greaterthan(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & l, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & r)
<a name="l02380"></a>02380 {
<a name="l02381"></a>02381 <span class="comment">// DebugAssert(l != r, "");</span>
<a name="l02382"></a>02382 <span class="keywordflow">if</span> (l==r) <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l02383"></a>02383
<a name="l02384"></a>02384 <span class="keywordflow">switch</span>(l.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>()) {
<a name="l02385"></a>02385 <span class="keywordflow">case</span> <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a>:
<a name="l02386"></a>02386 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(!r.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>(), <span class="stringliteral">""</span>);
<a name="l02387"></a>02387 <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l02388"></a>02388 <span class="keywordflow">break</span>;
<a name="l02389"></a>02389 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>:
<a name="l02390"></a>02390 <span class="keywordflow">switch</span> (r.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>()) {
<a name="l02391"></a>02391 <span class="keywordflow">case</span> <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a>:
<a name="l02392"></a>02392 <span class="comment">// TODO:</span>
<a name="l02393"></a>02393 <span class="comment">// alternately I could return (not greaterthan(r,l))</span>
<a name="l02394"></a>02394 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l02395"></a>02395 <span class="keywordflow">break</span>;
<a name="l02396"></a>02396 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>:
<a name="l02397"></a>02397 <span class="comment">// x^n > y^n if x > y</span>
<a name="l02398"></a>02398 <span class="comment">// x^n1 > x^n2 if n1 > n2</span>
<a name="l02399"></a>02399 <span class="keywordflow">return</span>
<a name="l02400"></a>02400 ((r[1] < l[1]) ||
<a name="l02401"></a>02401 ((r[1]==l[1]) && (r[0].getRational() < l[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>())));
<a name="l02402"></a>02402 <span class="keywordflow">break</span>;
<a name="l02403"></a>02403
<a name="l02404"></a>02404 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>:
<a name="l02405"></a>02405 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(r.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 1, <span class="stringliteral">""</span>);
<a name="l02406"></a>02406 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>((r.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 2) || (r[1] != l), <span class="stringliteral">""</span>);
<a name="l02407"></a>02407 <span class="keywordflow">if</span> (r[1] == l) <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l02408"></a>02408 <span class="keywordflow">return</span> greaterthan(l, r[1]);
<a name="l02409"></a>02409 <span class="keywordflow">break</span>;
<a name="l02410"></a>02410 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>:
<a name="l02411"></a>02411 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">""</span>);
<a name="l02412"></a>02412 <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l02413"></a>02413 <span class="keywordflow">break</span>;
<a name="l02414"></a>02414 <span class="keywordflow">default</span>:
<a name="l02415"></a>02415 <span class="comment">// leaf</span>
<a name="l02416"></a>02416 <span class="keywordflow">return</span> ((r < l[1]) || ((r == l[1]) && l[0].getRational() > 1));
<a name="l02417"></a>02417 <span class="keywordflow">break</span>;
<a name="l02418"></a>02418 }
<a name="l02419"></a>02419 <span class="keywordflow">break</span>;
<a name="l02420"></a>02420 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>:
<a name="l02421"></a>02421 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(l.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 1, <span class="stringliteral">""</span>);
<a name="l02422"></a>02422 <span class="keywordflow">switch</span> (r.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>()) {
<a name="l02423"></a>02423 <span class="keywordflow">case</span> <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a>:
<a name="l02424"></a>02424 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l02425"></a>02425 <span class="keywordflow">break</span>;
<a name="l02426"></a>02426 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>:
<a name="l02427"></a>02427 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(l.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 1, <span class="stringliteral">""</span>);
<a name="l02428"></a>02428 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>((l.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 2) || (l[1] != r), <span class="stringliteral">""</span>);
<a name="l02429"></a>02429 <span class="comment">// TODO:</span>
<a name="l02430"></a>02430 <span class="comment">// alternately return (not greaterthan(r,l)</span>
<a name="l02431"></a>02431 <span class="keywordflow">return</span> ((l[1] == r) || greaterthan(l[1], r));
<a name="l02432"></a>02432 <span class="keywordflow">break</span>;
<a name="l02433"></a>02433 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>:
<a name="l02434"></a>02434 {
<a name="l02435"></a>02435
<a name="l02436"></a>02436 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(r.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 1, <span class="stringliteral">""</span>);
<a name="l02437"></a>02437 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> i = l.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l02438"></a>02438 <a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> j = r.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>();
<a name="l02439"></a>02439 ++i;
<a name="l02440"></a>02440 ++j;
<a name="l02441"></a>02441 <span class="keywordflow">for</span> (; i != l.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>() && j != r.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); ++i, ++j) {
<a name="l02442"></a>02442 <span class="keywordflow">if</span> (*i == *j)
<a name="l02443"></a>02443 <span class="keywordflow">continue</span>;
<a name="l02444"></a>02444 <span class="keywordflow">return</span> greaterthan(*i,*j);
<a name="l02445"></a>02445 }
<a name="l02446"></a>02446 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(i != l.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>() || j != r.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(), <span class="stringliteral">""</span>);
<a name="l02447"></a>02447 <span class="keywordflow">if</span> (i == l.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>()) {
<a name="l02448"></a>02448 <span class="comment">// r is bigger</span>
<a name="l02449"></a>02449 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l02450"></a>02450 }
<a name="l02451"></a>02451 <span class="keywordflow">else</span>
<a name="l02452"></a>02452 {
<a name="l02453"></a>02453 <span class="comment">// l is bigger</span>
<a name="l02454"></a>02454 <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l02455"></a>02455 }
<a name="l02456"></a>02456 }
<a name="l02457"></a>02457 <span class="keywordflow">break</span>;
<a name="l02458"></a>02458 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>:
<a name="l02459"></a>02459 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">""</span>);
<a name="l02460"></a>02460 <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l02461"></a>02461 <span class="keywordflow">break</span>;
<a name="l02462"></a>02462 <span class="keywordflow">default</span>:
<a name="l02463"></a>02463 <span class="comment">// leaf</span>
<a name="l02464"></a>02464 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>((l.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 2) || (l[1] != r), <span class="stringliteral">""</span>);
<a name="l02465"></a>02465 <span class="keywordflow">return</span> ((l[1] == r) || greaterthan(l[1], r));
<a name="l02466"></a>02466 <span class="keywordflow">break</span>;
<a name="l02467"></a>02467 }
<a name="l02468"></a>02468 <span class="keywordflow">break</span>;
<a name="l02469"></a>02469 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>:
<a name="l02470"></a>02470 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">""</span>);
<a name="l02471"></a>02471 <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l02472"></a>02472 <span class="keywordflow">break</span>;
<a name="l02473"></a>02473 <span class="keywordflow">default</span>:
<a name="l02474"></a>02474 <span class="comment">// leaf</span>
<a name="l02475"></a>02475 <span class="keywordflow">switch</span> (r.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>()) {
<a name="l02476"></a>02476 <span class="keywordflow">case</span> <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a>:
<a name="l02477"></a>02477 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l02478"></a>02478 <span class="keywordflow">break</span>;
<a name="l02479"></a>02479 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a880283f7bbc366efe54c9ea074c9f5e5">POW</a>:
<a name="l02480"></a>02480 <span class="keywordflow">return</span> ((r[1] < l) || ((r[1] == l) && (r[0].getRational() < 1)));
<a name="l02481"></a>02481 <span class="keywordflow">break</span>;
<a name="l02482"></a>02482 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a>:
<a name="l02483"></a>02483 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(r.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 1, <span class="stringliteral">""</span>);
<a name="l02484"></a>02484 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>((r.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() > 2) || (r[1] != l), <span class="stringliteral">""</span>);
<a name="l02485"></a>02485 <span class="keywordflow">if</span> (l == r[1]) <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l02486"></a>02486 <span class="keywordflow">return</span> greaterthan(l,r[1]);
<a name="l02487"></a>02487 <span class="keywordflow">break</span>;
<a name="l02488"></a>02488 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a>:
<a name="l02489"></a>02489 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">""</span>);
<a name="l02490"></a>02490 <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l02491"></a>02491 <span class="keywordflow">break</span>;
<a name="l02492"></a>02492 <span class="keywordflow">default</span>:
<a name="l02493"></a>02493 <span class="comment">// leaf</span>
<a name="l02494"></a>02494 <span class="keywordflow">return</span> (r < l);
<a name="l02495"></a>02495 <span class="keywordflow">break</span>;
<a name="l02496"></a>02496 }
<a name="l02497"></a>02497 <span class="keywordflow">break</span>;
<a name="l02498"></a>02498 }
<a name="l02499"></a>02499 }
<a name="l02500"></a>02500
<a name="l02501"></a>02501 <span class="comment"></span>
<a name="l02502"></a>02502 <span class="comment">/*! IS_INTEGER(x) |= EXISTS (y : INT) y = x</span>
<a name="l02503"></a>02503 <span class="comment"> * where x is not already known to be an integer.</span>
<a name="l02504"></a>02504 <span class="comment"> */</span>
<a name="l02505"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a85e9c7d93d6d1433fea606b0c3878e25">02505</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::IsIntegerElim(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="theory__quant_8cpp.html#ac9940420b1f3427ebe821902adbb578d">isIntx</a>)
<a name="l02506"></a>02506 {
<a name="l02507"></a>02507 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> expr = isIntx.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l02508"></a>02508 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02509"></a>02509 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a3193c0a76bedff5b39b32531195ef779">IS_INTEGER</a>,
<a name="l02510"></a>02510 <span class="stringliteral">"Expected IS_INTEGER predicate"</span>);
<a name="l02511"></a>02511 }
<a name="l02512"></a>02512 expr = expr[0];
<a name="l02513"></a>02513 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(!d_theoryArith->isInteger(expr), <span class="stringliteral">"Expected non-integer"</span>);
<a name="l02514"></a>02514
<a name="l02515"></a>02515 <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a> a(isIntx);
<a name="l02516"></a>02516 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02517"></a>02517
<a name="l02518"></a>02518 <span class="keywordflow">if</span> (withProof())
<a name="l02519"></a>02519 {
<a name="l02520"></a>02520 pf = newPf(<span class="stringliteral">"isIntElim"</span>, isIntx.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02521"></a>02521 }
<a name="l02522"></a>02522
<a name="l02523"></a>02523 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> newVar = d_em->newBoundVarExpr(d_theoryArith->intType());
<a name="l02524"></a>02524 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> res = d_em->newClosureExpr(<a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba3197625a1bb2264943f5a95f236d9973">EXISTS</a>, newVar, newVar.<a class="code" href="group__ExprPkg.html#gacb48495ca445c895f95d0c3c1ae2070b">eqExpr</a>(expr));
<a name="l02525"></a>02525
<a name="l02526"></a>02526 <span class="keywordflow">return</span> newTheorem(res, a, pf);
<a name="l02527"></a>02527 }
<a name="l02528"></a>02528
<a name="l02529"></a>02529
<a name="l02530"></a>02530 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l02531"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a49d6559f50d51cde3c2e723c2a254cff">02531</a> ArithTheoremProducer::eqElimIntRule(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& eqn, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="theory__quant_8cpp.html#ac9940420b1f3427ebe821902adbb578d">isIntx</a>,
<a name="l02532"></a>02532 <span class="keyword">const</span> vector<Theorem>& isIntVars) {
<a name="l02533"></a>02533 <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba7fa27e82c6c4f69434225ed81e5d151e">TRACE</a>(<span class="stringliteral">"arith eq"</span>, <span class="stringliteral">"eqElimIntRule("</span>, eqn.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>(), <span class="stringliteral">") {"</span>);
<a name="l02534"></a>02534 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02535"></a>02535
<a name="l02536"></a>02536 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l02537"></a>02537 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(eqn.<a class="code" href="classCVC3_1_1Theorem.html#a362c1d70e03803d804bbe300e5f6dc87">isRewrite</a>(),
<a name="l02538"></a>02538 <span class="stringliteral">"ArithTheoremProducer::eqElimInt: input must be an equation"</span> +
<a name="l02539"></a>02539 eqn.<a class="code" href="classCVC3_1_1Theorem.html#ac4b1c9570ffb9cc901627ef2abb9ff77">toString</a>());
<a name="l02540"></a>02540
<a name="l02541"></a>02541 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& lhs = eqn.<a class="code" href="classCVC3_1_1Theorem.html#a206c04f39fbbcacef2337148675553f4">getLHS</a>();
<a name="l02542"></a>02542 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& rhs = eqn.<a class="code" href="classCVC3_1_1Theorem.html#a97d957fcbf9094480851b1d2e5d3729f">getRHS</a>();
<a name="l02543"></a>02543 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> a, x;
<a name="l02544"></a>02544 d_theoryArith->separateMonomial(lhs, a, x);
<a name="l02545"></a>02545
<a name="l02546"></a>02546 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02547"></a>02547 <span class="comment">// Checking LHS</span>
<a name="l02548"></a>02548 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& isIntxe = isIntx.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l02549"></a>02549 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntxe) && isIntxe[0] == x,
<a name="l02550"></a>02550 <span class="stringliteral">"ArithTheoremProducer::eqElimInt\n eqn = "</span>
<a name="l02551"></a>02551 +eqn.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>().<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()
<a name="l02552"></a>02552 +<span class="stringliteral">"\n isIntx = "</span>+isIntxe.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02553"></a>02553 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(a) && a.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>().<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>()
<a name="l02554"></a>02554 && a.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() >= 2,
<a name="l02555"></a>02555 <span class="stringliteral">"ArithTheoremProducer::eqElimInt:\n lhs = "</span>+lhs.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>());
<a name="l02556"></a>02556 <span class="comment">// Checking RHS</span>
<a name="l02557"></a>02557 <span class="comment">// It cannot be a division (we don't handle it)</span>
<a name="l02558"></a>02558 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(!<a class="code" href="namespaceCVC3.html#a10c6762fa24ef8adf8b5a5c3d6e4dad3">isDivide</a>(rhs),
<a name="l02559"></a>02559 <span class="stringliteral">"ArithTheoremProducer::eqElimInt:\n rhs = "</span>+rhs.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02560"></a>02560 <span class="comment">// If it's a single monomial, then it's the only "variable"</span>
<a name="l02561"></a>02561 <span class="keywordflow">if</span>(!<a class="code" href="namespaceCVC3.html#afb0f7d15ddbd87f9abb128108101f557">isPlus</a>(rhs)) {
<a name="l02562"></a>02562 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> c, v;
<a name="l02563"></a>02563 d_theoryArith->separateMonomial(rhs, c, v);
<a name="l02564"></a>02564 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(isIntVars.size() == 1
<a name="l02565"></a>02565 && <a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntVars[0].getExpr())
<a name="l02566"></a>02566 && isIntVars[0].getExpr()[0] == v
<a name="l02567"></a>02567 && <a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(c) && c.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>().<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>(),
<a name="l02568"></a>02568 <span class="stringliteral">"ArithTheoremProducer::eqElimInt:\n rhs = "</span>+rhs.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()
<a name="l02569"></a>02569 +<span class="stringliteral">"isIntVars.size = "</span>+<a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(isIntVars.size()));
<a name="l02570"></a>02570 } <span class="keywordflow">else</span> { <span class="comment">// RHS is a plus</span>
<a name="l02571"></a>02571 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(isIntVars.size() + 1 == (size_t)rhs.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>(),
<a name="l02572"></a>02572 <span class="stringliteral">"ArithTheoremProducer::eqElimInt: rhs = "</span>+rhs.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02573"></a>02573 <span class="comment">// Check the free constant</span>
<a name="l02574"></a>02574 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(rhs[0]) && rhs[0].getRational().isInteger(),
<a name="l02575"></a>02575 <span class="stringliteral">"ArithTheoremProducer::eqElimInt: rhs = "</span>+rhs.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02576"></a>02576 <span class="comment">// Check the vars</span>
<a name="l02577"></a>02577 <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i=0, iend=isIntVars.size(); i<iend; ++i) {
<a name="l02578"></a>02578 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> c, v;
<a name="l02579"></a>02579 d_theoryArith->separateMonomial(rhs[i+1], c, v);
<a name="l02580"></a>02580 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& <a class="code" href="namespaceCVC3.html#a8b193cc1fee34cb43707171b2ae6471e">isInt</a>(isIntVars[i].getExpr());
<a name="l02581"></a>02581 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isInt) && isInt[0] == v
<a name="l02582"></a>02582 && <a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(c) && c.<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>().<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>(),
<a name="l02583"></a>02583 <span class="stringliteral">"ArithTheoremProducer::eqElimInt:\n rhs["</span>+<a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(i+1)
<a name="l02584"></a>02584 +<span class="stringliteral">"] = "</span>+rhs[i+1].<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()
<a name="l02585"></a>02585 +<span class="stringliteral">"\n isInt = "</span>+isInt.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02586"></a>02586 }
<a name="l02587"></a>02587 }
<a name="l02588"></a>02588 }
<a name="l02589"></a>02589
<a name="l02590"></a>02590 <span class="comment">// Creating a fresh bound variable</span>
<a name="l02591"></a>02591 <span class="keyword">static</span> <span class="keywordtype">int</span> varCount(0);
<a name="l02592"></a>02592 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> newVar = d_em->newBoundVarExpr(<span class="stringliteral">"_int_var"</span>, <a class="code" href="namespaceCVC3.html#af69618103f1f0f2eadada0796a2a940c">int2string</a>(varCount++));
<a name="l02593"></a>02593 newVar.<a class="code" href="group__ExprPkg.html#ga07d47f902598e00097086deabf04d9c5" title="Set the cached type.">setType</a>(intType());
<a name="l02594"></a>02594 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> t2 = create_t2(lhs, rhs, newVar);
<a name="l02595"></a>02595 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> t3 = create_t3(lhs, rhs, newVar);
<a name="l02596"></a>02596 vector<Expr> vars;
<a name="l02597"></a>02597 vars.push_back(newVar);
<a name="l02598"></a>02598 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> res = d_em->newClosureExpr(<a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba3197625a1bb2264943f5a95f236d9973">EXISTS</a>, vars,
<a name="l02599"></a>02599 x.<a class="code" href="group__ExprPkg.html#gacb48495ca445c895f95d0c3c1ae2070b">eqExpr</a>(t2) && rat(0).<a class="code" href="group__ExprPkg.html#gacb48495ca445c895f95d0c3c1ae2070b">eqExpr</a>(t3));
<a name="l02600"></a>02600
<a name="l02601"></a>02601 vector<Theorem> thms(isIntVars);
<a name="l02602"></a>02602 thms.push_back(isIntx);
<a name="l02603"></a>02603 thms.push_back(eqn);
<a name="l02604"></a>02604 <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a> assump(thms);
<a name="l02605"></a>02605
<a name="l02606"></a>02606 <span class="keywordflow">if</span>(withProof()) {
<a name="l02607"></a>02607 vector<Proof> pfs;
<a name="l02608"></a>02608 pfs.push_back(eqn.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02609"></a>02609 pfs.push_back(isIntx.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02610"></a>02610 vector<Theorem>::const_iterator i=isIntVars.begin(), iend=isIntVars.end();
<a name="l02611"></a>02611 <span class="keywordflow">for</span>(; i!=iend; ++i)
<a name="l02612"></a>02612 pfs.push_back(i->getProof());
<a name="l02613"></a>02613 pf = newPf(<span class="stringliteral">"eq_elim_int"</span>, eqn.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>(), res , pfs);
<a name="l02614"></a>02614 }
<a name="l02615"></a>02615
<a name="l02616"></a>02616 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> thm(newTheorem(res, assump, pf));
<a name="l02617"></a>02617 <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5ba7fa27e82c6c4f69434225ed81e5d151e">TRACE</a>(<span class="stringliteral">"arith eq"</span>, <span class="stringliteral">"eqElimIntRule => "</span>, thm.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>(), <span class="stringliteral">" }"</span>);
<a name="l02618"></a>02618 <span class="keywordflow">return</span> thm;
<a name="l02619"></a>02619 }
<a name="l02620"></a>02620
<a name="l02621"></a>02621
<a name="l02622"></a>02622 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l02623"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#af1baf70d6108dc52cbb9704e2a8889ec">02623</a> ArithTheoremProducer::isIntConst(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l02624"></a>02624 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02625"></a>02625
<a name="l02626"></a>02626 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02627"></a>02627 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(e) && e[0].<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(),
<a name="l02628"></a>02628 <span class="stringliteral">"ArithTheoremProducer::isIntConst(e = "</span>
<a name="l02629"></a>02629 +e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">")"</span>);
<a name="l02630"></a>02630 }
<a name="l02631"></a>02631 <span class="keywordflow">if</span>(withProof())
<a name="l02632"></a>02632 pf = newPf(<span class="stringliteral">"is_int_const"</span>, e);
<a name="l02633"></a>02633 <span class="keywordtype">bool</span> <a class="code" href="namespaceCVC3.html#a8b193cc1fee34cb43707171b2ae6471e">isInt</a> = e[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>().<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>();
<a name="l02634"></a>02634 <span class="keywordflow">return</span> newRWTheorem(e, isInt? d_em->trueExpr() : d_em->falseExpr(), Assumptions::emptyAssump(), pf);
<a name="l02635"></a>02635 }
<a name="l02636"></a>02636
<a name="l02637"></a>02637
<a name="l02638"></a>02638 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l02639"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a512f22a4a025477ced8c27f3d62809d7">02639</a> ArithTheoremProducer::equalLeaves1(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm)
<a name="l02640"></a>02640 {
<a name="l02641"></a>02641 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02642"></a>02642 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e = thm.<a class="code" href="classCVC3_1_1Theorem.html#a97d957fcbf9094480851b1d2e5d3729f">getRHS</a>();
<a name="l02643"></a>02643
<a name="l02644"></a>02644 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02645"></a>02645 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e[1].getKind() == <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a> &&
<a name="l02646"></a>02646 e[1].getRational() == <a class="code" href="classCVC3_1_1Rational.html">Rational</a>(0) &&
<a name="l02647"></a>02647 e[0].getKind() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a> &&
<a name="l02648"></a>02648 e[0].arity() == 3 &&
<a name="l02649"></a>02649 e[0][0].getKind() == <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a> &&
<a name="l02650"></a>02650 e[0][0].getRational() == <a class="code" href="classCVC3_1_1Rational.html">Rational</a>(0) &&
<a name="l02651"></a>02651 e[0][1].getKind() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a> &&
<a name="l02652"></a>02652 e[0][1].arity() == 2 &&
<a name="l02653"></a>02653 e[0][1][0].getKind() == <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a> &&
<a name="l02654"></a>02654 e[0][1][0].getRational() == <a class="code" href="classCVC3_1_1Rational.html">Rational</a>(-1),
<a name="l02655"></a>02655 <span class="stringliteral">"equalLeaves1"</span>);
<a name="l02656"></a>02656 }
<a name="l02657"></a>02657 <span class="keywordflow">if</span> (withProof())
<a name="l02658"></a>02658 {
<a name="l02659"></a>02659 vector<Proof> pfs;
<a name="l02660"></a>02660 pfs.push_back(thm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02661"></a>02661 pf = newPf(<span class="stringliteral">"equalLeaves1"</span>, e, pfs);
<a name="l02662"></a>02662 }
<a name="l02663"></a>02663 <span class="keywordflow">return</span> newRWTheorem(e, e[0][1][1].eqExpr(e[0][2]), thm.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>(), pf);
<a name="l02664"></a>02664 }
<a name="l02665"></a>02665
<a name="l02666"></a>02666
<a name="l02667"></a>02667 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l02668"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a77ae567431bf98e20cc08903deb2ec99">02668</a> ArithTheoremProducer::equalLeaves2(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm)
<a name="l02669"></a>02669 {
<a name="l02670"></a>02670 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02671"></a>02671 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e = thm.<a class="code" href="classCVC3_1_1Theorem.html#a97d957fcbf9094480851b1d2e5d3729f">getRHS</a>();
<a name="l02672"></a>02672
<a name="l02673"></a>02673 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02674"></a>02674 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e[0].getKind() == <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a> &&
<a name="l02675"></a>02675 e[0].getRational() == <a class="code" href="classCVC3_1_1Rational.html">Rational</a>(0) &&
<a name="l02676"></a>02676 e[1].getKind() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a> &&
<a name="l02677"></a>02677 e[1].arity() == 3 &&
<a name="l02678"></a>02678 e[1][0].getKind() == <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a> &&
<a name="l02679"></a>02679 e[1][0].getRational() == <a class="code" href="classCVC3_1_1Rational.html">Rational</a>(0) &&
<a name="l02680"></a>02680 e[1][1].getKind() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a> &&
<a name="l02681"></a>02681 e[1][1].arity() == 2 &&
<a name="l02682"></a>02682 e[1][1][0].getKind() == <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a> &&
<a name="l02683"></a>02683 e[1][1][0].getRational() == <a class="code" href="classCVC3_1_1Rational.html">Rational</a>(-1),
<a name="l02684"></a>02684 <span class="stringliteral">"equalLeaves2"</span>);
<a name="l02685"></a>02685 }
<a name="l02686"></a>02686 <span class="keywordflow">if</span> (withProof())
<a name="l02687"></a>02687 {
<a name="l02688"></a>02688 vector<Proof> pfs;
<a name="l02689"></a>02689 pfs.push_back(thm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02690"></a>02690 pf = newPf(<span class="stringliteral">"equalLeaves2"</span>, e, pfs);
<a name="l02691"></a>02691 }
<a name="l02692"></a>02692 <span class="keywordflow">return</span> newRWTheorem(e, e[1][1][1].eqExpr(e[1][2]), thm.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>(), pf);
<a name="l02693"></a>02693 }
<a name="l02694"></a>02694
<a name="l02695"></a>02695
<a name="l02696"></a>02696 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l02697"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a8de6b6b44c60cf495b455b980a7c681b">02697</a> ArithTheoremProducer::equalLeaves3(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm)
<a name="l02698"></a>02698 {
<a name="l02699"></a>02699 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02700"></a>02700 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e = thm.<a class="code" href="classCVC3_1_1Theorem.html#a97d957fcbf9094480851b1d2e5d3729f">getRHS</a>();
<a name="l02701"></a>02701
<a name="l02702"></a>02702 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02703"></a>02703 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e[1].getKind() == <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a> &&
<a name="l02704"></a>02704 e[1].getRational() == <a class="code" href="classCVC3_1_1Rational.html">Rational</a>(0) &&
<a name="l02705"></a>02705 e[0].getKind() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a> &&
<a name="l02706"></a>02706 e[0].arity() == 3 &&
<a name="l02707"></a>02707 e[0][0].getKind() == <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a> &&
<a name="l02708"></a>02708 e[0][0].getRational() == <a class="code" href="classCVC3_1_1Rational.html">Rational</a>(0) &&
<a name="l02709"></a>02709 e[0][2].getKind() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a> &&
<a name="l02710"></a>02710 e[0][2].arity() == 2 &&
<a name="l02711"></a>02711 e[0][2][0].getKind() == <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a> &&
<a name="l02712"></a>02712 e[0][2][0].getRational() == <a class="code" href="classCVC3_1_1Rational.html">Rational</a>(-1),
<a name="l02713"></a>02713 <span class="stringliteral">"equalLeaves3"</span>);
<a name="l02714"></a>02714 }
<a name="l02715"></a>02715 <span class="keywordflow">if</span> (withProof())
<a name="l02716"></a>02716 {
<a name="l02717"></a>02717 vector<Proof> pfs;
<a name="l02718"></a>02718 pfs.push_back(thm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02719"></a>02719 pf = newPf(<span class="stringliteral">"equalLeaves3"</span>, e, pfs);
<a name="l02720"></a>02720 }
<a name="l02721"></a>02721 <span class="keywordflow">return</span> newRWTheorem(e, e[0][2][1].eqExpr(e[0][1]), thm.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>(), pf);
<a name="l02722"></a>02722 }
<a name="l02723"></a>02723
<a name="l02724"></a>02724
<a name="l02725"></a>02725 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l02726"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a97768870957319cdc68eb94694a37dc5">02726</a> ArithTheoremProducer::equalLeaves4(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm)
<a name="l02727"></a>02727 {
<a name="l02728"></a>02728 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02729"></a>02729 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e = thm.<a class="code" href="classCVC3_1_1Theorem.html#a97d957fcbf9094480851b1d2e5d3729f">getRHS</a>();
<a name="l02730"></a>02730
<a name="l02731"></a>02731 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02732"></a>02732 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e[0].getKind() == <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a> &&
<a name="l02733"></a>02733 e[0].getRational() == <a class="code" href="classCVC3_1_1Rational.html">Rational</a>(0) &&
<a name="l02734"></a>02734 e[1].getKind() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9a12fbdcaa45ef17eaa1802161f9ca98">PLUS</a> &&
<a name="l02735"></a>02735 e[1].arity() == 3 &&
<a name="l02736"></a>02736 e[1][0].getKind() == <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a> &&
<a name="l02737"></a>02737 e[1][0].getRational() == <a class="code" href="classCVC3_1_1Rational.html">Rational</a>(0) &&
<a name="l02738"></a>02738 e[1][2].getKind() == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024ad77e825b0133e40de2760344377ee1fa">MULT</a> &&
<a name="l02739"></a>02739 e[1][2].arity() == 2 &&
<a name="l02740"></a>02740 e[1][2][0].getKind() == <a class="code" href="kinds_8h.html#aa10c9e8951b8ccf714a59ec321bdac5bae07a708ec52c578b62f8b0f701571d56">RATIONAL_EXPR</a> &&
<a name="l02741"></a>02741 e[1][2][0].getRational() == <a class="code" href="classCVC3_1_1Rational.html">Rational</a>(-1),
<a name="l02742"></a>02742 <span class="stringliteral">"equalLeaves4"</span>);
<a name="l02743"></a>02743 }
<a name="l02744"></a>02744 <span class="keywordflow">if</span> (withProof())
<a name="l02745"></a>02745 {
<a name="l02746"></a>02746 vector<Proof> pfs;
<a name="l02747"></a>02747 pfs.push_back(thm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02748"></a>02748 pf = newPf(<span class="stringliteral">"equalLeaves4"</span>, e, pfs);
<a name="l02749"></a>02749 }
<a name="l02750"></a>02750 <span class="keywordflow">return</span> newRWTheorem(e, e[1][2][1].eqExpr(e[1][1]), thm.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>(), pf);
<a name="l02751"></a>02751 }
<a name="l02752"></a>02752
<a name="l02753"></a>02753 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l02754"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a3d6e1d8668360c20b5a6a47e3fcc4612">02754</a> ArithTheoremProducer::diseqToIneq(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& diseq) {
<a name="l02755"></a>02755 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02756"></a>02756
<a name="l02757"></a>02757 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e = diseq.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l02758"></a>02758
<a name="l02759"></a>02759 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02760"></a>02760 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#ga1a898858ccadce833df5a294c7740f11">isNot</a>() && e[0].<a class="code" href="group__ExprPkg.html#gac4af2026c180da0f18d66ac616f61f3a">isEq</a>(),
<a name="l02761"></a>02761 <span class="stringliteral">"ArithTheoremProducer::diseqToIneq: expected disequality:\n"</span>
<a name="l02762"></a>02762 <span class="stringliteral">" e = "</span>+e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02763"></a>02763 }
<a name="l02764"></a>02764
<a name="l02765"></a>02765 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x = e[0][0];
<a name="l02766"></a>02766 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& y = e[0][1];
<a name="l02767"></a>02767
<a name="l02768"></a>02768 <span class="keywordflow">if</span>(withProof())
<a name="l02769"></a>02769 pf = newPf(e, diseq.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02770"></a>02770 <span class="keywordflow">return</span> newTheorem(<a class="code" href="namespaceCVC3.html#ac9ccba18a3c725634b1f8ba8e99e627f">ltExpr</a>(x,y).<a class="code" href="namespaceCVC3.html#a30f30b6e20c174f21ae63acea8618294">orExpr</a>(<a class="code" href="namespaceCVC3.html#a8ad355d6650f2dfa754419c634e36afb">gtExpr</a>(x,y)), diseq.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>(), pf);
<a name="l02771"></a>02771 }
<a name="l02772"></a>02772
<a name="l02773"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a77b99e94956d407e5cd20701e6771120">02773</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::moveSumConstantRight(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l02774"></a>02774
<a name="l02775"></a>02775 <span class="comment">// Check soundness of the rule if necessary</span>
<a name="l02776"></a>02776 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02777"></a>02777 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#abbae617aaff89a9e5deb84ab649e14a0">isIneq</a>(e) || e.<a class="code" href="group__ExprPkg.html#gac4af2026c180da0f18d66ac616f61f3a">isEq</a>(), <span class="stringliteral">"moveSumConstantRight: input must be Eq or Ineq: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02778"></a>02778 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(e[0]) || <a class="code" href="namespaceCVC3.html#afb0f7d15ddbd87f9abb128108101f557">isPlus</a>(e[0]), <span class="stringliteral">"moveSumConstantRight: left side must be a canonised sum: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02779"></a>02779 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(e[1]) && e[1].getRational() == 0, <span class="stringliteral">"moveSumConstantRight: right side must be 0: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02780"></a>02780 }
<a name="l02781"></a>02781
<a name="l02782"></a>02782 <span class="comment">// The rational constant of the sum</span>
<a name="l02783"></a>02783 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> r = 0;
<a name="l02784"></a>02784
<a name="l02785"></a>02785 <span class="comment">// The right hand side of the expression</span>
<a name="l02786"></a>02786 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="namespaceMiniSat.html#a82558b7a36c52f5d3211d5d14bed99d4">right</a> = e[0];
<a name="l02787"></a>02787
<a name="l02788"></a>02788 <span class="comment">// The vector of sum terms</span>
<a name="l02789"></a>02789 vector<Expr> sumTerms;
<a name="l02790"></a>02790
<a name="l02791"></a>02791 <span class="comment">// Get all the non rational children and</span>
<a name="l02792"></a>02792 <span class="keywordflow">if</span> (!right.<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>())
<a name="l02793"></a>02793 <span class="keywordflow">for</span>(<a class="code" href="classCVC3_1_1Expr_1_1iterator.html">Expr::iterator</a> it = right.<a class="code" href="group__ExprPkg.html#gac890e13db184610276fc533fa4b4fe99" title="Begin iterator.">begin</a>(); it != right.<a class="code" href="group__ExprPkg.html#gaf6048a5030c8fa2511bf5dfee868e653" title="End iterator.">end</a>(); it ++) {
<a name="l02794"></a>02794 <span class="comment">// If the term is rational then add the rational number to r</span>
<a name="l02795"></a>02795 <span class="keywordflow">if</span> ((*it).isRational()) r = r + (*it).getRational();
<a name="l02796"></a>02796 <span class="comment">// Otherwise just add the sumTerm to the sumTerms</span>
<a name="l02797"></a>02797 <span class="keywordflow">else</span> sumTerms.push_back((*it));
<a name="l02798"></a>02798 }
<a name="l02799"></a>02799
<a name="l02800"></a>02800 <span class="comment">// Setup the new expression</span>
<a name="l02801"></a>02801 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> transformed;
<a name="l02802"></a>02802 <span class="keywordflow">if</span> (sumTerms.size() > 1)
<a name="l02803"></a>02803 <span class="comment">// If the number of summands is > 1 return the sum of them</span>
<a name="l02804"></a>02804 transformed = <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>(), <a class="code" href="namespaceCVC3.html#accd3d7d38b0e04136afbc3e5191bc8bb">plusExpr</a>(sumTerms), rat(-r));
<a name="l02805"></a>02805 <span class="keywordflow">else</span>
<a name="l02806"></a>02806 <span class="comment">// Otherwise return the one summand as itself</span>
<a name="l02807"></a>02807 transformed = <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(e.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>(), sumTerms[0], rat(-r));
<a name="l02808"></a>02808
<a name="l02809"></a>02809
<a name="l02810"></a>02810 <span class="comment">// If proof is needed set it up</span>
<a name="l02811"></a>02811 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02812"></a>02812 <span class="keywordflow">if</span> (withProof()) pf = newPf(<span class="stringliteral">"arithm_sum_constant_right"</span>, e);
<a name="l02813"></a>02813
<a name="l02814"></a>02814 <span class="comment">// Retrun the theorem explaining the transformation</span>
<a name="l02815"></a>02815 <span class="keywordflow">return</span> newRWTheorem(e, transformed, Assumptions::emptyAssump(), pf);
<a name="l02816"></a>02816 }
<a name="l02817"></a>02817
<a name="l02818"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a517d45514aefcab0dc6aabb400f149fd">02818</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::eqToIneq(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l02819"></a>02819
<a name="l02820"></a>02820 <span class="comment">// Check soundness of the rule if necessary</span>
<a name="l02821"></a>02821 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l02822"></a>02822 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(e.<a class="code" href="group__ExprPkg.html#gac4af2026c180da0f18d66ac616f61f3a">isEq</a>(), <span class="stringliteral">"eqToIneq: input must be an equality: "</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02823"></a>02823
<a name="l02824"></a>02824 <span class="comment">// The proof object we will use</span>
<a name="l02825"></a>02825 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02826"></a>02826
<a name="l02827"></a>02827 <span class="comment">// The parts of the equality x = y</span>
<a name="l02828"></a>02828 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x = e[0];
<a name="l02829"></a>02829 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& y = e[1];
<a name="l02830"></a>02830
<a name="l02831"></a>02831 <span class="comment">// Setup the proof if needed</span>
<a name="l02832"></a>02832 <span class="keywordflow">if</span> (withProof())
<a name="l02833"></a>02833 pf = newPf(<span class="stringliteral">"eqToIneq"</span>, e);
<a name="l02834"></a>02834
<a name="l02835"></a>02835 <span class="comment">// Retrun the theorem explaining the transformation</span>
<a name="l02836"></a>02836 <span class="keywordflow">return</span> newRWTheorem(e, <a class="code" href="namespaceCVC3.html#aebfd8a82800bd3dff4c8db461a52cdea">leExpr</a>(x,y).<a class="code" href="namespaceCVC3.html#ad4258158bba138eb54b9080af7f8223a">andExpr</a>(<a class="code" href="namespaceCVC3.html#a520cf0df288be321d27ea6fa77ded2d2">geExpr</a>(x,y)), Assumptions::emptyAssump(), pf);
<a name="l02837"></a>02837 }
<a name="l02838"></a>02838
<a name="l02839"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a753c339b31e38915ae6f06e0fe6e48da">02839</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::dummyTheorem(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l02840"></a>02840 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02841"></a>02841 <span class="keywordflow">return</span> newRWTheorem(e, d_em->trueExpr(), Assumptions::emptyAssump(), pf);
<a name="l02842"></a>02842 }
<a name="l02843"></a>02843
<a name="l02844"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a23051d23d509f9cda35c64d4a5ff1dbf">02844</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::oneElimination(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l02845"></a>02845
<a name="l02846"></a>02846 <span class="comment">// Check soundness</span>
<a name="l02847"></a>02847 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>)
<a name="l02848"></a>02848 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a28ae8672047db708e99602ebaca89777">isMult</a>(e) &&
<a name="l02849"></a>02849 e.<a class="code" href="group__ExprPkg.html#ga28b901d05e52a5c646f83a95cc74f94b">arity</a>() == 2 &&
<a name="l02850"></a>02850 e[0].<a class="code" href="group__ExprPkg.html#gac5ced6adc7a60945ea6707ef494aa28f">isRational</a>() &&
<a name="l02851"></a>02851 e[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>() == 1,
<a name="l02852"></a>02852 <span class="stringliteral">"oneElimination: input must be a multiplication by one"</span> + e.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02853"></a>02853
<a name="l02854"></a>02854 <span class="comment">// The proof object that we will us</span>
<a name="l02855"></a>02855 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02856"></a>02856
<a name="l02857"></a>02857 <span class="comment">// Setup the proof if needed</span>
<a name="l02858"></a>02858 <span class="keywordflow">if</span> (withProof())
<a name="l02859"></a>02859 pf = newPf(<span class="stringliteral">"oneElimination"</span>, e);
<a name="l02860"></a>02860
<a name="l02861"></a>02861 <span class="comment">// Return the rewrite theorem that explains the phenomenon</span>
<a name="l02862"></a>02862 <span class="keywordflow">return</span> newRWTheorem(e, e[1], Assumptions::emptyAssump(), pf);
<a name="l02863"></a>02863 }
<a name="l02864"></a>02864
<a name="l02865"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ad4513630a9eec6c841b527222a79ea1d">02865</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::clashingBounds(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& lowerBound, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& upperBound) {
<a name="l02866"></a>02866
<a name="l02867"></a>02867 <span class="comment">// Get the expressions</span>
<a name="l02868"></a>02868 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& lowerBoundExpr = lowerBound.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l02869"></a>02869 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& upperBoundExpr = upperBound.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l02870"></a>02870
<a name="l02871"></a>02871 <span class="comment">// Check soundness</span>
<a name="l02872"></a>02872 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02873"></a>02873 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(lowerBoundExpr) || <a class="code" href="namespaceCVC3.html#a448b6e0d541113608bba5a7a005609e3">isLT</a>(lowerBoundExpr), <span class="stringliteral">"clashingBounds: lowerBound should be >= or > "</span> + lowerBoundExpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02874"></a>02874 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#af85f3152a3b2fe195d795bc0aefaec71">isGE</a>(upperBoundExpr) || <a class="code" href="namespaceCVC3.html#a7306d7566ccb21380f05058477aba009">isGT</a>(upperBoundExpr), <span class="stringliteral">"clashingBounds: upperBound should be <= or < "</span> + upperBoundExpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02875"></a>02875 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(lowerBoundExpr[0].<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(), <span class="stringliteral">"clashingBounds: lowerBound left side should be a rational "</span> + lowerBoundExpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02876"></a>02876 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(upperBoundExpr[0].<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(), <span class="stringliteral">"clashingBounds: upperBound left side should be a rational "</span> + upperBoundExpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02877"></a>02877 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(lowerBoundExpr[1] == upperBoundExpr[1], <span class="stringliteral">"clashingBounds: bounds not on the same term "</span> + lowerBoundExpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">", "</span> + upperBoundExpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02878"></a>02878
<a name="l02879"></a>02879 <span class="comment">// Get the bounds</span>
<a name="l02880"></a>02880 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> lowerBoundR = lowerBoundExpr[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l02881"></a>02881 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> upperBoundR = upperBoundExpr[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l02882"></a>02882
<a name="l02883"></a>02883 <span class="keywordflow">if</span> (<a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(lowerBoundExpr) && <a class="code" href="namespaceCVC3.html#af85f3152a3b2fe195d795bc0aefaec71">isGE</a>(upperBoundExpr)) {
<a name="l02884"></a>02884 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(upperBoundR < lowerBoundR, <span class="stringliteral">"clashingBounds: bounds are satisfiable"</span>);
<a name="l02885"></a>02885 } <span class="keywordflow">else</span> {
<a name="l02886"></a>02886 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(upperBoundR <= lowerBoundR, <span class="stringliteral">"clashingBounds: bounds are satisfiable"</span>);
<a name="l02887"></a>02887 }
<a name="l02888"></a>02888 }
<a name="l02889"></a>02889
<a name="l02890"></a>02890 <span class="comment">// The proof object that we will use</span>
<a name="l02891"></a>02891 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02892"></a>02892 <span class="comment">// Setup the proof if needed</span>
<a name="l02893"></a>02893 <span class="keywordflow">if</span> (withProof())
<a name="l02894"></a>02894 pf = newPf(<span class="stringliteral">"clashingBounds"</span>, lowerBoundExpr, upperBoundExpr);
<a name="l02895"></a>02895
<a name="l02896"></a>02896 <span class="comment">// Put the bounds expressions in the assumptions</span>
<a name="l02897"></a>02897 <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a> assumptions;
<a name="l02898"></a>02898 assumptions.<a class="code" href="classCVC3_1_1Assumptions.html#a72ece655220d8976c4090006eb7b0b40">add</a>(lowerBound);
<a name="l02899"></a>02899 assumptions.<a class="code" href="classCVC3_1_1Assumptions.html#a72ece655220d8976c4090006eb7b0b40">add</a>(upperBound);
<a name="l02900"></a>02900
<a name="l02901"></a>02901 <span class="comment">// Return the theorem</span>
<a name="l02902"></a>02902 <span class="keywordflow">return</span> newTheorem(d_em->falseExpr(), assumptions, pf);
<a name="l02903"></a>02903 }
<a name="l02904"></a>02904
<a name="l02905"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a3b2bea72cd9163daa7c41388037bca29">02905</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::addInequalities(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm2) {
<a name="l02906"></a>02906
<a name="l02907"></a>02907 <span class="comment">// Get the expressions of the theorem</span>
<a name="l02908"></a>02908 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr1 = thm1.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l02909"></a>02909 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr2 = thm2.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l02910"></a>02910
<a name="l02911"></a>02911 <span class="comment">// Check soundness</span>
<a name="l02912"></a>02912 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02913"></a>02913
<a name="l02914"></a>02914 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#abbae617aaff89a9e5deb84ab649e14a0">isIneq</a>(expr1), <span class="stringliteral">"addInequalities: expecting an inequality for thm1, got "</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02915"></a>02915 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#abbae617aaff89a9e5deb84ab649e14a0">isIneq</a>(expr2), <span class="stringliteral">"addInequalities: expecting an inequality for thm2, got "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02916"></a>02916
<a name="l02917"></a>02917 <span class="keywordflow">if</span> (<a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr1) || <a class="code" href="namespaceCVC3.html#a448b6e0d541113608bba5a7a005609e3">isLT</a>(expr1))
<a name="l02918"></a>02918 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr2) || <a class="code" href="namespaceCVC3.html#a448b6e0d541113608bba5a7a005609e3">isLT</a>(expr2), <span class="stringliteral">"addInequalities: expr2 should be <(=) also "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02919"></a>02919 <span class="keywordflow">if</span> (<a class="code" href="namespaceCVC3.html#af85f3152a3b2fe195d795bc0aefaec71">isGE</a>(expr1) || <a class="code" href="namespaceCVC3.html#a7306d7566ccb21380f05058477aba009">isGT</a>(expr1))
<a name="l02920"></a>02920 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#af85f3152a3b2fe195d795bc0aefaec71">isGE</a>(expr2) || <a class="code" href="namespaceCVC3.html#a7306d7566ccb21380f05058477aba009">isGT</a>(expr2), <span class="stringliteral">"addInequalities: expr2 should be >(=) also"</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02921"></a>02921 }
<a name="l02922"></a>02922
<a name="l02923"></a>02923 <span class="comment">// Create the assumptions</span>
<a name="l02924"></a>02924 <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a> a(thm1, thm2);
<a name="l02925"></a>02925
<a name="l02926"></a>02926 <span class="comment">// Get the kinds of the inequalitites</span>
<a name="l02927"></a>02927 <span class="keywordtype">int</span> kind1 = expr1.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>();
<a name="l02928"></a>02928 <span class="keywordtype">int</span> kind2 = expr2.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>();
<a name="l02929"></a>02929
<a name="l02930"></a>02930 <span class="comment">// Set-up the resulting inequality</span>
<a name="l02931"></a>02931 <span class="keywordtype">int</span> kind = (kind1 == kind2) ? kind1 : ((kind1 == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9e29ecc77281f945fb50c183cfae6749">LT</a>) || (kind2 == <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9e29ecc77281f945fb50c183cfae6749">LT</a>))? <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9e29ecc77281f945fb50c183cfae6749">LT</a> : <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a589b68b2d271254aa9fd3d89b4bf33b9">GT</a>;
<a name="l02932"></a>02932
<a name="l02933"></a>02933 <span class="comment">// Create the proof object</span>
<a name="l02934"></a>02934 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02935"></a>02935 <span class="keywordflow">if</span>(withProof()) {
<a name="l02936"></a>02936 vector<Proof> pfs;
<a name="l02937"></a>02937 pfs.push_back(thm1.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02938"></a>02938 pfs.push_back(thm2.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l02939"></a>02939 pf = newPf(<span class="stringliteral">"addInequalities"</span>, expr1, expr2, pfs);
<a name="l02940"></a>02940 }
<a name="l02941"></a>02941
<a name="l02942"></a>02942 <span class="comment">// Create the new expressions</span>
<a name="l02943"></a>02943 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> leftSide = <a class="code" href="namespaceCVC3.html#accd3d7d38b0e04136afbc3e5191bc8bb">plusExpr</a>(expr1[0], expr2[0]);
<a name="l02944"></a>02944 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> rightSide = <a class="code" href="namespaceCVC3.html#accd3d7d38b0e04136afbc3e5191bc8bb">plusExpr</a>(expr1[1], expr2[1]);
<a name="l02945"></a>02945
<a name="l02946"></a>02946 <span class="comment">// Return the theorem</span>
<a name="l02947"></a>02947 <span class="keywordflow">return</span> newTheorem(<a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(kind, leftSide, rightSide), a, pf);
<a name="l02948"></a>02948 }
<a name="l02949"></a>02949
<a name="l02950"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a364ef37224bae3afb4f62a5c0f75d02c">02950</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::implyWeakerInequality(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr2) {
<a name="l02951"></a>02951
<a name="l02952"></a>02952 <span class="comment">// Check soundness</span>
<a name="l02953"></a>02953 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l02954"></a>02954
<a name="l02955"></a>02955 <span class="comment">// Both must be inequalitites</span>
<a name="l02956"></a>02956 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#abbae617aaff89a9e5deb84ab649e14a0">isIneq</a>(expr1), <span class="stringliteral">"implyWeakerInequality: expr1 should be an inequality"</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02957"></a>02957 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#abbae617aaff89a9e5deb84ab649e14a0">isIneq</a>(expr2), <span class="stringliteral">"implyWeakerInequality: expr1 should be an inequality"</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02958"></a>02958
<a name="l02959"></a>02959 <span class="keywordtype">bool</span> type_less_than = <span class="keyword">true</span>;
<a name="l02960"></a>02960
<a name="l02961"></a>02961 <span class="comment">// Should be of the same type</span>
<a name="l02962"></a>02962 <span class="keywordflow">if</span> (<a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr1) || <a class="code" href="namespaceCVC3.html#a448b6e0d541113608bba5a7a005609e3">isLT</a>(expr1))
<a name="l02963"></a>02963 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr2) || <a class="code" href="namespaceCVC3.html#a448b6e0d541113608bba5a7a005609e3">isLT</a>(expr2), <span class="stringliteral">"implyWeakerInequality: expr2 should be <(=) also "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02964"></a>02964 <span class="keywordflow">if</span> (<a class="code" href="namespaceCVC3.html#af85f3152a3b2fe195d795bc0aefaec71">isGE</a>(expr1) || <a class="code" href="namespaceCVC3.html#a7306d7566ccb21380f05058477aba009">isGT</a>(expr1)) {
<a name="l02965"></a>02965 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#af85f3152a3b2fe195d795bc0aefaec71">isGE</a>(expr2) || <a class="code" href="namespaceCVC3.html#a7306d7566ccb21380f05058477aba009">isGT</a>(expr2), <span class="stringliteral">"implyWeakerInequality: expr2 should be >(=) also"</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02966"></a>02966 type_less_than = <span class="keyword">false</span>;
<a name="l02967"></a>02967 }
<a name="l02968"></a>02968
<a name="l02969"></a>02969 <span class="comment">// Left sides must be rational numbers</span>
<a name="l02970"></a>02970 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr1[0].<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(), <span class="stringliteral">"implyWeakerInequality: expr1 should have a rational on the left side"</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02971"></a>02971 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr2[0].<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(), <span class="stringliteral">"implyWeakerInequality: expr2 should have a rational on the left side"</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02972"></a>02972
<a name="l02973"></a>02973 <span class="comment">// Right sides must be identical</span>
<a name="l02974"></a>02974 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr1[1] == expr2[1], <span class="stringliteral">"implyWeakerInequality: the expression must be the same"</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">" and "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02975"></a>02975
<a name="l02976"></a>02976 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> expr1rat = expr1[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l02977"></a>02977 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> expr2rat = expr2[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l02978"></a>02978
<a name="l02979"></a>02979
<a name="l02980"></a>02980 <span class="comment">// Check the bounds</span>
<a name="l02981"></a>02981 <span class="keywordflow">if</span> (type_less_than) {
<a name="l02982"></a>02982 <span class="keywordflow">if</span> (<a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr1) || <a class="code" href="namespaceCVC3.html#a448b6e0d541113608bba5a7a005609e3">isLT</a>(expr2)) {
<a name="l02983"></a>02983 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr2rat < expr1rat, <span class="stringliteral">"implyWeakerInequality: the implication doesn't apply"</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">" and "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02984"></a>02984 } <span class="keywordflow">else</span> {
<a name="l02985"></a>02985 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr2rat <= expr1rat, <span class="stringliteral">"implyWeakerInequality: the implication doesn't apply"</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">" and "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02986"></a>02986 }
<a name="l02987"></a>02987 } <span class="keywordflow">else</span> {
<a name="l02988"></a>02988 <span class="keywordflow">if</span> (<a class="code" href="namespaceCVC3.html#af85f3152a3b2fe195d795bc0aefaec71">isGE</a>(expr1) || <a class="code" href="namespaceCVC3.html#a7306d7566ccb21380f05058477aba009">isGT</a>(expr2)) {
<a name="l02989"></a>02989 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr2rat > expr1rat, <span class="stringliteral">"implyWeakerInequality: the implication doesn't apply"</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">" and "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02990"></a>02990 } <span class="keywordflow">else</span> {
<a name="l02991"></a>02991 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr2rat >= expr1rat, <span class="stringliteral">"implyWeakerInequality: the implication doesn't apply"</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">" and "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l02992"></a>02992 }
<a name="l02993"></a>02993 }
<a name="l02994"></a>02994 }
<a name="l02995"></a>02995
<a name="l02996"></a>02996 <span class="comment">// Create the proof object</span>
<a name="l02997"></a>02997 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l02998"></a>02998 <span class="keywordflow">if</span>(withProof()) pf = newPf(<span class="stringliteral">"implyWeakerInequality"</span>, expr1, expr2);
<a name="l02999"></a>02999
<a name="l03000"></a>03000 <span class="comment">// Return the theorem</span>
<a name="l03001"></a>03001 <span class="keywordflow">return</span> newTheorem(expr1.<a class="code" href="group__ExprPkg.html#ga8dd97bcdeb9d8870238f94a263fd083b">impExpr</a>(expr2), Assumptions::emptyAssump(), pf);
<a name="l03002"></a>03002 }
<a name="l03003"></a>03003
<a name="l03004"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a1bf4d45330b587882e726daa9117cdfb">03004</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::implyNegatedInequality(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr2) {
<a name="l03005"></a>03005
<a name="l03006"></a>03006 <span class="comment">// Check soundness</span>
<a name="l03007"></a>03007 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l03008"></a>03008 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#abbae617aaff89a9e5deb84ab649e14a0">isIneq</a>(expr1), <span class="stringliteral">"implyNegatedInequality: lowerBound should be an inequality "</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l03009"></a>03009 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#abbae617aaff89a9e5deb84ab649e14a0">isIneq</a>(expr2), <span class="stringliteral">"implyNegatedInequality: upperBound should be be an inequality "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l03010"></a>03010 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr1[0].<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(), <span class="stringliteral">"implyNegatedInequality: lowerBound left side should be a rational "</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l03011"></a>03011 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr2[0].<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(), <span class="stringliteral">"implyNegatedInequality: upperBound left side should be a rational "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l03012"></a>03012 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(expr1[1] == expr2[1], <span class="stringliteral">"implyNegatedInequality: bounds not on the same term "</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">", "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l03013"></a>03013
<a name="l03014"></a>03014 <span class="comment">// Get the bounds</span>
<a name="l03015"></a>03015 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> lowerBoundR = expr1[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l03016"></a>03016 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> upperBoundR = expr2[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l03017"></a>03017
<a name="l03018"></a>03018 <span class="keywordflow">if</span> (<a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr1) && <a class="code" href="namespaceCVC3.html#af85f3152a3b2fe195d795bc0aefaec71">isGE</a>(expr2))
<a name="l03019"></a>03019 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(upperBoundR < lowerBoundR, <span class="stringliteral">"implyNegatedInequality: cant imply negation"</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">", "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l03020"></a>03020 <span class="keywordflow">if</span> (<a class="code" href="namespaceCVC3.html#a448b6e0d541113608bba5a7a005609e3">isLT</a>(expr1) || <a class="code" href="namespaceCVC3.html#a7306d7566ccb21380f05058477aba009">isGT</a>(expr2))
<a name="l03021"></a>03021 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(upperBoundR <= lowerBoundR, <span class="stringliteral">"implyNegatedInequality: cant imply negation"</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">", "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l03022"></a>03022 <span class="keywordflow">if</span> (<a class="code" href="namespaceCVC3.html#af85f3152a3b2fe195d795bc0aefaec71">isGE</a>(expr1) && <a class="code" href="namespaceCVC3.html#a8ef991dfa16ee3a209b7f38014153101">isLE</a>(expr2))
<a name="l03023"></a>03023 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(upperBoundR > lowerBoundR, <span class="stringliteral">"implyNegatedInequality: cant imply negation"</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">", "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l03024"></a>03024 <span class="keywordflow">if</span> (<a class="code" href="namespaceCVC3.html#a7306d7566ccb21380f05058477aba009">isGT</a>(expr1) || <a class="code" href="namespaceCVC3.html#a448b6e0d541113608bba5a7a005609e3">isLT</a>(expr2))
<a name="l03025"></a>03025 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(upperBoundR >= lowerBoundR, <span class="stringliteral">"implyNegatedInequality: cant imply negation"</span> + expr1.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>() + <span class="stringliteral">", "</span> + expr2.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l03026"></a>03026 }
<a name="l03027"></a>03027
<a name="l03028"></a>03028 <span class="comment">// The proof object that we will use</span>
<a name="l03029"></a>03029 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l03030"></a>03030 <span class="keywordflow">if</span> (withProof()) pf = newPf(<span class="stringliteral">"implyNegatedInequality"</span>, expr1, expr2);
<a name="l03031"></a>03031
<a name="l03032"></a>03032 <span class="comment">// Return the theorem</span>
<a name="l03033"></a>03033 <span class="keywordflow">return</span> newTheorem(expr1.<a class="code" href="group__ExprPkg.html#ga8dd97bcdeb9d8870238f94a263fd083b">impExpr</a>(expr2.<a class="code" href="group__ExprPkg.html#gab1ce461dc931af73bf04e88c8d37dcbc">negate</a>()), Assumptions::emptyAssump(), pf);
<a name="l03034"></a>03034 }
<a name="l03035"></a>03035
<a name="l03036"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a43fa5f7c8c3ad3915de7f068ac8cefbd">03036</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::trustedRewrite(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& expr2) {
<a name="l03037"></a>03037
<a name="l03038"></a>03038 <span class="comment">// The proof object that we will us</span>
<a name="l03039"></a>03039 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l03040"></a>03040
<a name="l03041"></a>03041 <span class="comment">// Setup the proof if needed</span>
<a name="l03042"></a>03042 <span class="keywordflow">if</span> (withProof()) pf = newPf(<span class="stringliteral">"trustedRewrite"</span>, expr1, expr2);
<a name="l03043"></a>03043
<a name="l03044"></a>03044 <span class="comment">// Return the rewrite theorem that explains the phenomenon</span>
<a name="l03045"></a>03045 <span class="keywordflow">return</span> newRWTheorem(expr1, expr2, Assumptions::emptyAssump(), pf);
<a name="l03046"></a>03046
<a name="l03047"></a>03047 }
<a name="l03048"></a>03048
<a name="l03049"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ab9395a2ee958d70c780df2514e517320">03049</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::integerSplit(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& intVar, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& intPoint) {
<a name="l03050"></a>03050
<a name="l03051"></a>03051 <span class="comment">// Check soundness</span>
<a name="l03052"></a>03052 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l03053"></a>03053 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(intPoint.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>(), <span class="stringliteral">"integerSplit: we can only split on integer points, given"</span> + intPoint.<a class="code" href="classCVC3_1_1Rational.html#a195c125a76cb9a6c5731369e244a2de3">toString</a>());
<a name="l03054"></a>03054 }
<a name="l03055"></a>03055
<a name="l03056"></a>03056 <span class="comment">// Create the expression</span>
<a name="l03057"></a>03057 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& split = <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>(<a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a3193c0a76bedff5b39b32531195ef779">IS_INTEGER</a>, intVar).<a class="code" href="group__ExprPkg.html#ga8dd97bcdeb9d8870238f94a263fd083b">impExpr</a>(<a class="code" href="namespaceCVC3.html#aebfd8a82800bd3dff4c8db461a52cdea">leExpr</a>(intVar, rat(intPoint)).<a class="code" href="namespaceCVC3.html#a30f30b6e20c174f21ae63acea8618294">orExpr</a>(<a class="code" href="namespaceCVC3.html#a520cf0df288be321d27ea6fa77ded2d2">geExpr</a>(intVar, rat(intPoint + 1))));
<a name="l03058"></a>03058
<a name="l03059"></a>03059 <span class="comment">// The proof object that we will use</span>
<a name="l03060"></a>03060 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l03061"></a>03061 <span class="keywordflow">if</span> (withProof()) pf = newPf(<span class="stringliteral">"integerSplit"</span>, intVar, rat(intPoint));
<a name="l03062"></a>03062
<a name="l03063"></a>03063 <span class="comment">// Return the theorem</span>
<a name="l03064"></a>03064 <span class="keywordflow">return</span> newTheorem(split, Assumptions::emptyAssump(), pf);
<a name="l03065"></a>03065 }
<a name="l03066"></a>03066
<a name="l03067"></a>03067
<a name="l03068"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a4b28aa17702ca3f9703e61ca012ca236">03068</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::rafineStrictInteger(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntConstrThm, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& constr) {
<a name="l03069"></a>03069
<a name="l03070"></a>03070
<a name="l03071"></a>03071 <span class="comment">// Check soundness</span>
<a name="l03072"></a>03072 <span class="keywordflow">if</span> (<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l03073"></a>03073 <span class="comment">// Right side of the constraint should correspond to the proved integer expression</span>
<a name="l03074"></a>03074 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#abbae617aaff89a9e5deb84ab649e14a0">isIneq</a>(constr), <span class="stringliteral">"rafineStrictInteger: expected a constraint got : "</span> + constr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l03075"></a>03075 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(isIntConstrThm.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>()[0] == constr[1], <span class="stringliteral">"rafineStrictInteger: proof of intger doesn't correspond to the constarint right side"</span>);
<a name="l03076"></a>03076 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(constr[0].<a class="code" href="namespaceCVC3.html#ac0334a083d6782caa17ca0d337fddddf">isRational</a>(), <span class="stringliteral">"rafineStrictInteger: right side of the constraint muts be a rational"</span>);
<a name="l03077"></a>03077 }
<a name="l03078"></a>03078
<a name="l03079"></a>03079 <span class="comment">// Get the contraint bound</span>
<a name="l03080"></a>03080 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> bound = constr[0].<a class="code" href="group__ExprPkg.html#gab0eee70e4a7f97c09954dc61b71b65e5" title="Get the Rational value out of RATIONAL_EXPR.">getRational</a>();
<a name="l03081"></a>03081
<a name="l03082"></a>03082 <span class="comment">// Get the kind of the constraint</span>
<a name="l03083"></a>03083 <span class="keywordtype">int</span> kind = constr.<a class="code" href="group__ExprPkg.html#ga7814e4f55f65c7ca860c637413df5f4d">getKind</a>();
<a name="l03084"></a>03084
<a name="l03085"></a>03085 <span class="comment">// If the bound is strict, make it non-strict</span>
<a name="l03086"></a>03086 <span class="keywordflow">switch</span> (kind) {
<a name="l03087"></a>03087 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a9e29ecc77281f945fb50c183cfae6749">LT</a>:
<a name="l03088"></a>03088 kind = <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a1b768cf71a18713c90cd71f82488ffb1">LE</a>;
<a name="l03089"></a>03089 <span class="keywordflow">if</span> (bound.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>()) bound ++; <span class="comment">// 3 < x --> 4 <= x</span>
<a name="l03090"></a>03090 <span class="keywordflow">else</span> bound = ceil(bound); <span class="comment">// 3.4 < x --> 4 <= x</span>
<a name="l03091"></a>03091 <span class="keywordflow">break</span>;
<a name="l03092"></a>03092 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a1b768cf71a18713c90cd71f82488ffb1">LE</a>:
<a name="l03093"></a>03093 kind = <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a1b768cf71a18713c90cd71f82488ffb1">LE</a>;
<a name="l03094"></a>03094 <span class="keywordflow">if</span> (!bound.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>()) bound = ceil(bound); <span class="comment">// 3.5 <= x --> 4 <= x</span>
<a name="l03095"></a>03095 <span class="keywordflow">break</span>;
<a name="l03096"></a>03096 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024a589b68b2d271254aa9fd3d89b4bf33b9">GT</a>:
<a name="l03097"></a>03097 kind = <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024aad2afa561f31a801e12ab3fdd50a6229">GE</a>;
<a name="l03098"></a>03098 <span class="keywordflow">if</span> (bound.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>()) bound --; <span class="comment">// 3 > x --> 2 >= x</span>
<a name="l03099"></a>03099 <span class="keywordflow">else</span> bound = floor(bound); <span class="comment">// 3.4 > x --> 3 >= x</span>
<a name="l03100"></a>03100 <span class="keywordflow">break</span>;
<a name="l03101"></a>03101 <span class="keywordflow">case</span> <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024aad2afa561f31a801e12ab3fdd50a6229">GE</a>:
<a name="l03102"></a>03102 kind = <a class="code" href="namespaceCVC3.html#a32d50a30de0e9e5bc4c2451de0107024aad2afa561f31a801e12ab3fdd50a6229">GE</a>;
<a name="l03103"></a>03103 <span class="keywordflow">if</span> (!bound.<a class="code" href="classCVC3_1_1Rational.html#a1366320f4de558bb964c67f8aecedb36">isInteger</a>()) bound = floor(bound); <span class="comment">// 3.4 >= x --> 3 >= x</span>
<a name="l03104"></a>03104 <span class="keywordflow">break</span>;
<a name="l03105"></a>03105 }
<a name="l03106"></a>03106
<a name="l03107"></a>03107 <span class="comment">// The new constraint</span>
<a name="l03108"></a>03108 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> newConstr(kind, rat(bound), constr[1]);
<a name="l03109"></a>03109
<a name="l03110"></a>03110 <span class="comment">// Pick up the assumptions from the integer proof</span>
<a name="l03111"></a>03111 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a>& assump(isIntConstrThm.<a class="code" href="classCVC3_1_1Theorem.html#a5e9ab00a613df15cc02f55edb55a67b3">getAssumptionsRef</a>());
<a name="l03112"></a>03112
<a name="l03113"></a>03113 <span class="comment">// Construct the proof object if necessary</span>
<a name="l03114"></a>03114 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l03115"></a>03115 <span class="keywordflow">if</span> (withProof()) pf = newPf(<span class="stringliteral">"rafineStrictInteger"</span>, constr, newConstr,isIntConstrThm.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l03116"></a>03116
<a name="l03117"></a>03117 <span class="comment">// Return the rewrite theorem that explains the phenomenon</span>
<a name="l03118"></a>03118 <span class="keywordflow">return</span> newRWTheorem(constr, newConstr, assump, pf);
<a name="l03119"></a>03119 }
<a name="l03120"></a>03120
<a name="l03121"></a>03121 <span class="comment">//</span>
<a name="l03122"></a>03122 <span class="comment">// This one is here just to compile... the code is in old arithmetic</span>
<a name="l03123"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#afd5bca9b136254b904b931680180ac83">03123</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::simpleIneqInt(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& ineq, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntRHS)
<a name="l03124"></a>03124 {
<a name="l03125"></a>03125 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Not implemented!!!"</span>);
<a name="l03126"></a>03126 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l03127"></a>03127 }
<a name="l03128"></a>03128
<a name="l03129"></a>03129 <span class="comment">// Given:</span>
<a name="l03130"></a>03130 <span class="comment">// 0 = c + t</span>
<a name="l03131"></a>03131 <span class="comment">// where t is integer and c is not</span>
<a name="l03132"></a>03132 <span class="comment">// deduce bot</span>
<a name="l03133"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ad5f121b6b7d6b8ae951dfb4cce064575">03133</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::intEqualityRationalConstant(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntConstrThm, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& constr) {
<a name="l03134"></a>03134 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Not implemented!!!"</span>);
<a name="l03135"></a>03135 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l03136"></a>03136 }
<a name="l03137"></a>03137
<a name="l03138"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a0111aa5645658dbd6a4bc030178edb94">03138</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::cycleConflict(<span class="keyword">const</span> vector<Theorem>& inequalitites) {
<a name="l03139"></a>03139 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Not implemented!!!"</span>);
<a name="l03140"></a>03140 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l03141"></a>03141 }
<a name="l03142"></a>03142
<a name="l03143"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#abb8aff055ea56ad8de2b66fd9a7aeba9">03143</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::implyEqualities(<span class="keyword">const</span> vector<Theorem>& inequalitites) {
<a name="l03144"></a>03144 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Not implemented!!!"</span>);
<a name="l03145"></a>03145 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l03146"></a>03146 }
<a name="l03147"></a>03147 <span class="comment"></span>
<a name="l03148"></a>03148 <span class="comment">/*! Takes a Theorem(\\alpha < \\beta) and returns</span>
<a name="l03149"></a>03149 <span class="comment"> * Theorem(\\alpha < \\beta <==> \\alpha <= \\beta -1)</span>
<a name="l03150"></a>03150 <span class="comment"> * where \\alpha and \\beta are integer expressions</span>
<a name="l03151"></a>03151 <span class="comment"> */</span>
<a name="l03152"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#af55c5d0a2626f955b0843381ca8b50f3">03152</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::lessThanToLERewrite(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& ineq,
<a name="l03153"></a>03153 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntLHS,
<a name="l03154"></a>03154 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntRHS,
<a name="l03155"></a>03155 <span class="keywordtype">bool</span> changeRight) {
<a name="l03156"></a>03156
<a name="l03157"></a>03157 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& isIntLHSexpr = isIntLHS.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l03158"></a>03158 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& isIntRHSexpr = isIntRHS.<a class="code" href="classCVC3_1_1Theorem.html#af2b97ae5d270ddf1013bf4f3867a7e5d">getExpr</a>();
<a name="l03159"></a>03159
<a name="l03160"></a>03160 <span class="keywordflow">if</span>(<a class="code" href="theorem__producer_8h.html#a74a97b789e1a9e6c016291960c657445">CHECK_PROOFS</a>) {
<a name="l03161"></a>03161 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#a448b6e0d541113608bba5a7a005609e3">isLT</a>(ineq), <span class="stringliteral">"ArithTheoremProducerOld::LTtoLE: ineq must be <"</span>);
<a name="l03162"></a>03162 <span class="comment">// Integrality check</span>
<a name="l03163"></a>03163 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntLHSexpr) && isIntLHSexpr[0] == ineq[0],
<a name="l03164"></a>03164 <span class="stringliteral">"ArithTheoremProducerOld::lessThanToLE: bad integrality check:\n"</span>
<a name="l03165"></a>03165 <span class="stringliteral">" ineq = "</span>+ineq.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n isIntLHS = "</span>
<a name="l03166"></a>03166 +isIntLHSexpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l03167"></a>03167 <a class="code" href="theorem__producer_8h.html#a03dbe872f723d32fd975528f811d646e">CHECK_SOUND</a>(<a class="code" href="namespaceCVC3.html#aff7910c172ccdd1afb5e42964e2f248d">isIntPred</a>(isIntRHSexpr) && isIntRHSexpr[0] == ineq[1],
<a name="l03168"></a>03168 <span class="stringliteral">"ArithTheoremProducerOld::lessThanToLE: bad integrality check:\n"</span>
<a name="l03169"></a>03169 <span class="stringliteral">" ineq = "</span>+ineq.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>()+<span class="stringliteral">"\n isIntRHS = "</span>
<a name="l03170"></a>03170 +isIntRHSexpr.<a class="code" href="group__ExprPkg.html#gaf3028bb1619f8cc69b66ec712e1adb54" title="Print the expression to a string.">toString</a>());
<a name="l03171"></a>03171 }
<a name="l03172"></a>03172
<a name="l03173"></a>03173 vector<Theorem> thms;
<a name="l03174"></a>03174 thms.push_back(isIntLHS);
<a name="l03175"></a>03175 thms.push_back(isIntRHS);
<a name="l03176"></a>03176 <a class="code" href="classCVC3_1_1Assumptions.html">Assumptions</a> a(thms);
<a name="l03177"></a>03177 <a class="code" href="classCVC3_1_1Proof.html">Proof</a> pf;
<a name="l03178"></a>03178 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> le = changeRight? <a class="code" href="namespaceCVC3.html#aebfd8a82800bd3dff4c8db461a52cdea">leExpr</a>(ineq[0], ineq[1] + rat(-1)) : <a class="code" href="namespaceCVC3.html#aebfd8a82800bd3dff4c8db461a52cdea">leExpr</a>(ineq[0] + rat(1), ineq[1]);
<a name="l03179"></a>03179 <span class="keywordflow">if</span>(withProof()) {
<a name="l03180"></a>03180 vector<Proof> pfs;
<a name="l03181"></a>03181 pfs.push_back(isIntLHS.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l03182"></a>03182 pfs.push_back(isIntRHS.<a class="code" href="classCVC3_1_1Theorem.html#a2d8352c07a756c3837683a27a1e659ef">getProof</a>());
<a name="l03183"></a>03183 pf = newPf(changeRight? <span class="stringliteral">"lessThan_To_LE_rhs_rwr"</span> : <span class="stringliteral">"lessThan_To_LE_lhs_rwr"</span>, ineq, le, pfs);
<a name="l03184"></a>03184 }
<a name="l03185"></a>03185
<a name="l03186"></a>03186 <span class="keywordflow">return</span> newRWTheorem(ineq, le, a, pf);
<a name="l03187"></a>03187 }
<a name="l03188"></a>03188
<a name="l03189"></a>03189
<a name="l03190"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#acaa835c8569f6667fa26bfedb0502cf1">03190</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::splitGrayShadowSmall(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& gThm) {
<a name="l03191"></a>03191 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Not implemented!!!"</span>);
<a name="l03192"></a>03192 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l03193"></a>03193 }
<a name="l03194"></a>03194
<a name="l03195"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ae3a7aa0ebe8e84b806efaa59278ea75e">03195</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::implyWeakerInequalityDiffLogic(<span class="keyword">const</span> std::vector<Theorem>& antecedentThms, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& implied) {
<a name="l03196"></a>03196 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Not implemented!!!"</span>);
<a name="l03197"></a>03197 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l03198"></a>03198 }
<a name="l03199"></a>03199
<a name="l03200"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ab794c1f9d6e971ac56e0063f409b4774">03200</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::implyNegatedInequalityDiffLogic(<span class="keyword">const</span> std::vector<Theorem>& antecedentThms, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& implied) {
<a name="l03201"></a>03201 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Not implemented!!!"</span>);
<a name="l03202"></a>03202 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l03203"></a>03203 }
<a name="l03204"></a>03204
<a name="l03205"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a84a9652acc5908e5d1ead5c54c1f2d90">03205</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::expandGrayShadowRewrite(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& theShadow) {
<a name="l03206"></a>03206 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Not implemented!!!"</span>);
<a name="l03207"></a>03207 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l03208"></a>03208 }
<a name="l03209"></a>03209
<a name="l03210"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#ae43400e7e4c9e3695a75da3bd5718eda">03210</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::compactNonLinearTerm(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& nonLinear) {
<a name="l03211"></a>03211 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Not implemented!!!"</span>);
<a name="l03212"></a>03212 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l03213"></a>03213 }
<a name="l03214"></a>03214
<a name="l03215"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a9edd8b9ee6a8b4d14e9a2f967b78d52f">03215</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::nonLinearIneqSignSplit(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& ineqThm) {
<a name="l03216"></a>03216 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Not implemented!!!"</span>);
<a name="l03217"></a>03217 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l03218"></a>03218 }
<a name="l03219"></a>03219
<a name="l03220"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a45d8f89bdb0e57ddbaec273a24bf34b4">03220</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::implyDiffLogicBothBounds(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x,
<a name="l03221"></a>03221 std::vector<Theorem>& c1_le_x, <a class="code" href="classCVC3_1_1Rational.html">Rational</a> c1,
<a name="l03222"></a>03222 std::vector<Theorem>& x_le_c2, <a class="code" href="classCVC3_1_1Rational.html">Rational</a> c2) {
<a name="l03223"></a>03223 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Not implemented!!!"</span>);
<a name="l03224"></a>03224 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l03225"></a>03225 }
<a name="l03226"></a>03226
<a name="l03227"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a0eb949bb19e618a8318f236b249fadd5">03227</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::addInequalities(<span class="keyword">const</span> vector<Theorem>& thms) {
<a name="l03228"></a>03228 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Not implemented!!!"</span>);
<a name="l03229"></a>03229 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l03230"></a>03230 }
<a name="l03231"></a>03231
<a name="l03232"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer.html#a0433b1ba53a33275015c26450acb09d0">03232</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithTheoremProducer::powerOfOne(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l03233"></a>03233 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Not implemented!!!"</span>);
<a name="l03234"></a>03234 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l03235"></a>03235 }
<a name="l03236"></a>03236
<a name="l03237"></a>03237 <span class="comment"></span>
<a name="l03238"></a>03238 <span class="comment">////////////////////////////////////////////////////////////////////</span>
<a name="l03239"></a>03239 <span class="comment"></span><span class="comment">// Stubs for ArithProofRules</span><span class="comment"></span>
<a name="l03240"></a>03240 <span class="comment">////////////////////////////////////////////////////////////////////</span>
<a name="l03241"></a>03241 <span class="comment"></span>
<a name="l03242"></a>03242
<a name="l03243"></a><a class="code" href="classCVC3_1_1ArithProofRules.html#a81d9ea1e5c2d42c2b60a893c879145bd">03243</a> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> ArithProofRules::rewriteLeavesConst(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) {
<a name="l03244"></a>03244 <a class="code" href="debug_8h.html#a40dac3bdb2166ffc852ee8b1489d2b56">DebugAssert</a>(<span class="keyword">false</span>, <span class="stringliteral">"Not implemented!!!"</span>);
<a name="l03245"></a>03245 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>();
<a name="l03246"></a>03246 }
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