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<a href="arith__theorem__producer3_8h.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_producer3.h</span>
<a name="l00004"></a>00004 <span class="comment"> * \brief TRUSTED implementation of arithmetic proof rules</span>
<a name="l00005"></a>00005 <span class="comment"> * </span>
<a name="l00006"></a>00006 <span class="comment"> * Author: Vijay Ganesh, Sergey Berezin</span>
<a name="l00007"></a>00007 <span class="comment"> * </span>
<a name="l00008"></a>00008 <span class="comment"> * Created: Dec 13 02:09:04 GMT 2002</span>
<a name="l00009"></a>00009 <span class="comment"> *</span>
<a name="l00010"></a>00010 <span class="comment"> * <hr></span>
<a name="l00011"></a>00011 <span class="comment"> *</span>
<a name="l00012"></a>00012 <span class="comment"> * License to use, copy, modify, sell and/or distribute this software</span>
<a name="l00013"></a>00013 <span class="comment"> * and its documentation for any purpose is hereby granted without</span>
<a name="l00014"></a>00014 <span class="comment"> * royalty, subject to the terms and conditions defined in the \ref</span>
<a name="l00015"></a>00015 <span class="comment"> * LICENSE file provided with this distribution.</span>
<a name="l00016"></a>00016 <span class="comment"> * </span>
<a name="l00017"></a>00017 <span class="comment"> * <hr></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">/*****************************************************************************/</span>
<a name="l00021"></a>00021
<a name="l00022"></a>00022 <span class="preprocessor">#ifndef _cvc3__arith_theorem_producer3_h_</span>
<a name="l00023"></a>00023 <span class="preprocessor"></span><span class="preprocessor">#define _cvc3__arith_theorem_producer3_h_</span>
<a name="l00024"></a>00024 <span class="preprocessor"></span>
<a name="l00025"></a>00025 <span class="preprocessor">#include "<a class="code" href="arith__proof__rules_8h.html" title="Arithmetic proof rules.">arith_proof_rules.h</a>"</span>
<a name="l00026"></a>00026 <span class="preprocessor">#include "<a class="code" href="theorem__producer_8h.html">theorem_producer.h</a>"</span>
<a name="l00027"></a>00027 <span class="preprocessor">#include "<a class="code" href="theory__arith3_8h.html">theory_arith3.h</a>"</span>
<a name="l00028"></a>00028
<a name="l00029"></a>00029 <span class="keyword">namespace </span>CVC3 {
<a name="l00030"></a>00030 <span class="keyword">class </span>TheoryArith3;
<a name="l00031"></a>00031
<a name="l00032"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer3.html">00032</a> <span class="keyword">class </span><a class="code" href="classCVC3_1_1ArithTheoremProducer3.html">ArithTheoremProducer3</a>: <span class="keyword">public</span> <a class="code" href="classCVC3_1_1ArithProofRules.html">ArithProofRules</a>, <span class="keyword">public</span> <a class="code" href="classCVC3_1_1TheoremProducer.html">TheoremProducer</a> {
<a name="l00033"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a75321b2dd304a716364b64d21ebf3d07">00033</a> <a class="code" href="classCVC3_1_1TheoryArith3.html">TheoryArith3</a>* <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a75321b2dd304a716364b64d21ebf3d07">d_theoryArith</a>;
<a name="l00034"></a>00034 <span class="keyword">private</span>:<span class="comment"></span>
<a name="l00035"></a>00035 <span class="comment"> /*! \name Auxiliary functions for eqElimIntRule()</span>
<a name="l00036"></a>00036 <span class="comment"> * Methods that compute the subterms used in eqElimIntRule()</span>
<a name="l00037"></a>00037 <span class="comment"> *@{</span>
<a name="l00038"></a>00038 <span class="comment"> */</span><span class="comment"></span>
<a name="l00039"></a>00039 <span class="comment"> //! Compute the special modulus: i - m*floor(i/m+1/2)</span>
<a name="l00040"></a>00040 <span class="comment"></span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ada3b48ce9720177b4a427237efe0453f" title="Compute the special modulus: i - m*floor(i/m+1/2)">modEq</a>(<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);<span class="comment"></span>
<a name="l00041"></a>00041 <span class="comment"> //! Create the term 't'. See eqElimIntRule().</span>
<a name="l00042"></a>00042 <span class="comment"></span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ab70323686fd8775952a2709a6c8c754b" title="Create the term 't'. See eqElimIntRule().">create_t</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& eqn);<span class="comment"></span>
<a name="l00043"></a>00043 <span class="comment"> //! Create the term 't2'. See eqElimIntRule().</span>
<a name="l00044"></a>00044 <span class="comment"></span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#adf974179ea62c2196a87fb9c2199f6cd" title="Create the term 't2'. See eqElimIntRule().">create_t2</a>(<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, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t);<span class="comment"></span>
<a name="l00045"></a>00045 <span class="comment"> //! Create the term 't3'. See eqElimIntRule().</span>
<a name="l00046"></a>00046 <span class="comment"></span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a6bad08f3833720448803251dfa234e36" title="Create the term 't3'. See eqElimIntRule().">create_t3</a>(<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, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t);<span class="comment"></span>
<a name="l00047"></a>00047 <span class="comment"> /*! @brief Takes sum = a_0 + a_1*x_1+...+a_n*x_n and returns the</span>
<a name="l00048"></a>00048 <span class="comment"> * vector of similar monomials (in 'summands') with coefficients</span>
<a name="l00049"></a>00049 <span class="comment"> * mod(a_i, m). If divide flag is true, the coefficients will be</span>
<a name="l00050"></a>00050 <span class="comment"> * mod(a_i,m)/m.</span>
<a name="l00051"></a>00051 <span class="comment"> */</span>
<a name="l00052"></a>00052 <span class="keywordtype">void</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aa21c4aa75f54e05bdc772b0e2d37b669" title="Takes sum = a_0 + a_1*x_1+...+a_n*x_n and returns the vector of similar monomials (in 'summands') wit...">sumModM</a>(std::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="l00053"></a>00053 <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="l00054"></a>00054 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a5245a34c6f9e903db87e17df1d33c09d" title="Compute the special modulus: i - m*floor(i/m+1/2)">monomialModM</a>(<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="l00055"></a>00055 <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="l00056"></a>00056 <span class="keywordtype">void</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a36838065b24c16503ef6cf8164de44a8" title="Compute the special modulus: i - m*floor(i/m+1/2)">sumMulF</a>(std::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="l00057"></a>00057 <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="l00058"></a>00058 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aea07da55e987ccd27d0f57e08558af01" title="Compute the special modulus: i - m*floor(i/m+1/2)">monomialMulF</a>(<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="l00059"></a>00059 <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);<span class="comment"></span>
<a name="l00060"></a>00060 <span class="comment"> //! Compute floor(i/m+1/2) + mod(i,m)</span>
<a name="l00061"></a>00061 <span class="comment"></span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a077f8d0dab986b01d390668f6af1afa2" title="Compute floor(i/m+1/2) + mod(i,m)">f</a>(<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="l00062"></a>00062 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a3d0129d121975b0141d77ba6f458c182" title="Compute the special modulus: i - m*floor(i/m+1/2)">substitute</a>(<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);<span class="comment"></span>
<a name="l00063"></a>00063 <span class="comment"> /*@}*/</span>
<a name="l00064"></a>00064 <span class="keyword">public</span>:<span class="comment"></span>
<a name="l00065"></a>00065 <span class="comment"> //! Constructor</span>
<a name="l00066"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a56fb5871062ffe12510c4cd4ba65b745">00066</a> <span class="comment"></span> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a56fb5871062ffe12510c4cd4ba65b745" title="Constructor.">ArithTheoremProducer3</a>(<a class="code" href="classCVC3_1_1TheoremManager.html">TheoremManager</a>* tm, <a class="code" href="classCVC3_1_1TheoryArith3.html">TheoryArith3</a>* theoryArith):
<a name="l00067"></a>00067 <a class="code" href="classCVC3_1_1TheoremProducer.html">TheoremProducer</a>(tm), <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a75321b2dd304a716364b64d21ebf3d07">d_theoryArith</a>(theoryArith) { }
<a name="l00068"></a>00068 <span class="comment"></span>
<a name="l00069"></a>00069 <span class="comment"> //! Create Expr from Rational (for convenience)</span>
<a name="l00070"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a4440979f29e7ec3519212ff1e23d758f">00070</a> <span class="comment"></span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a4440979f29e7ec3519212ff1e23d758f" title="Create Expr from Rational (for convenience)">rat</a>(<a class="code" href="classCVC3_1_1Rational.html">Rational</a> r) { <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1TheoremProducer.html#a1b706238281ad141a57363a6890f14a5">d_em</a>-><a class="code" href="group__EM__Priv.html#ga18423a42ce6557dc33287d3979ccc3c6">newRatExpr</a>(r); }
<a name="l00071"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ad010c33575ebd1dc229c2a1526c229c5">00071</a> <a class="code" href="classCVC3_1_1Type.html" title="MS C++ specific settings.">Type</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ad010c33575ebd1dc229c2a1526c229c5">realType</a>() { <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a75321b2dd304a716364b64d21ebf3d07">d_theoryArith</a>-><a class="code" href="classCVC3_1_1TheoryArith.html#a03fa81194322b92c488033695bec7204">realType</a>(); }
<a name="l00072"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a04f5df44759216fd1182bd745cfc6a82">00072</a> <a class="code" href="classCVC3_1_1Type.html" title="MS C++ specific settings.">Type</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a04f5df44759216fd1182bd745cfc6a82">intType</a>() { <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a75321b2dd304a716364b64d21ebf3d07">d_theoryArith</a>-><a class="code" href="classCVC3_1_1TheoryArith.html#ad3e47bba6c50745ad194cf273aa1d146">intType</a>(); }<span class="comment"></span>
<a name="l00073"></a>00073 <span class="comment"> //! Construct the dark shadow expression representing lhs <= rhs</span>
<a name="l00074"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#afe495b6c58dd0c89c84b64c5194eeeaa">00074</a> <span class="comment"></span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#afe495b6c58dd0c89c84b64c5194eeeaa" title="Construct the dark shadow expression representing lhs <= rhs.">darkShadow</a>(<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="l00075"></a>00075 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a75321b2dd304a716364b64d21ebf3d07">d_theoryArith</a>-><a class="code" href="classCVC3_1_1TheoryArith.html#abee62d97b0c60a1a44b7ede3c60b11b6" title="Construct the dark shadow expression representing lhs <= rhs.">darkShadow</a>(lhs, rhs);
<a name="l00076"></a>00076 }<span class="comment"></span>
<a name="l00077"></a>00077 <span class="comment"> //! Construct the gray shadow expression representing c1 <= v - e <= c2</span>
<a name="l00078"></a>00078 <span class="comment"></span><span class="comment"> /*! Alternatively, v = e + i for some i s.t. c1 <= i <= c2</span>
<a name="l00079"></a>00079 <span class="comment"> */</span>
<a name="l00080"></a><a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ab34039c1fcdbf7701cd0541dce2575c8">00080</a> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ab34039c1fcdbf7701cd0541dce2575c8" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& v, <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="l00081"></a>00081 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c2) {
<a name="l00082"></a>00082 <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a75321b2dd304a716364b64d21ebf3d07">d_theoryArith</a>-><a class="code" href="classCVC3_1_1TheoryArith.html#ae7d59b8b9bff1ae3cbb1b67a0baa3463" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>(v, e, c1, c2);
<a name="l00083"></a>00083 }
<a name="l00084"></a>00084 <span class="comment"></span>
<a name="l00085"></a>00085 <span class="comment"> ////////////////////////////////////////////////////////////////////</span>
<a name="l00086"></a>00086 <span class="comment"></span> <span class="comment">// Canonization rules</span><span class="comment"></span>
<a name="l00087"></a>00087 <span class="comment"> ////////////////////////////////////////////////////////////////////</span>
<a name="l00088"></a>00088 <span class="comment"></span>
<a name="l00089"></a>00089 <span class="comment">// ==> x = 1 * x</span>
<a name="l00090"></a>00090 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a23340f90880cb869fdcfe6e69a7a2631" title="==> e = 1 * e">varToMult</a>(<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="l00091"></a>00091
<a name="l00092"></a>00092 <span class="comment">// ==> -(e) = (-1) * e</span>
<a name="l00093"></a>00093 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a878e091ad5cfd2877ddce73d6f664e16" title="==> -(e) = (-1) * e">uMinusToMult</a>(<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="l00094"></a>00094
<a name="l00095"></a>00095 <span class="comment">// ==> x - y = x + (-1) * y</span>
<a name="l00096"></a>00096 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ab0d610d377cc20e3ce16823713d25403" title="==> x - y = x + (-1) * y">minusToPlus</a>(<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="l00097"></a>00097
<a name="l00098"></a>00098 <span class="comment">// Rule for unary minus: it just converts it to division by -1,</span>
<a name="l00099"></a>00099 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a9bf439248afb24bb63ea435193b68524">canonUMinusToDivide</a>(<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="l00100"></a>00100
<a name="l00101"></a>00101 <span class="comment">// Rules for division by constant 'd'</span>
<a name="l00102"></a>00102 <span class="comment">// (c) / d ==> (c/d), takes c and d</span>
<a name="l00103"></a>00103 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a3a2bf5e3b8c71543b1512f1606825a02" title="(c) / d ==> (c/d), takes c and d">canonDivideConst</a>(<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>& d);
<a name="l00104"></a>00104 <span class="comment">// (c * x) / d ==> (c/d) * x, takes (c*x) and d</span>
<a name="l00105"></a>00105 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a39a2efadcc13383fd860340c6d76db54" title="(c * x) / d ==> (c/d) * x, takes (c*x) and d">canonDivideMult</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& cx, <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="l00106"></a>00106 <span class="comment">// (+ c ...)/d ==> push division to all the coefficients.</span>
<a name="l00107"></a>00107 <span class="comment">// The result is not canonical, but canonizing the summands will</span>
<a name="l00108"></a>00108 <span class="comment">// make it canonical.</span>
<a name="l00109"></a>00109 <span class="comment">// Takes (+ c ...) and d</span>
<a name="l00110"></a>00110 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a897c950b6bb741189f1c33752159b587" title="(+ c ...)/d ==> push division to all the coefficients.">canonDividePlus</a>(<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="l00111"></a>00111 <span class="comment">// x / d ==> (1/d) * x, takes x and d</span>
<a name="l00112"></a>00112 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a9fddb49ed54796e6a5487be554eb14f4" title="x / d ==> (1/d) * x, takes x and d">canonDivideVar</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);
<a name="l00113"></a>00113
<a name="l00114"></a>00114 <span class="comment">// Canon Rules for multiplication</span>
<a name="l00115"></a>00115
<a name="l00116"></a>00116 <span class="comment">// TODO Deepak:</span>
<a name="l00117"></a>00117 <span class="comment">// t1 * t2 where t1 and t2 are canonized expressions, i.e. it can be a</span>
<a name="l00118"></a>00118 <span class="comment">// 1) Rational constant</span>
<a name="l00119"></a>00119 <span class="comment">// 2) Arithmetic Leaf (var or term from another theory)</span>
<a name="l00120"></a>00120 <span class="comment">// 3) (POW rational leaf)</span>
<a name="l00121"></a>00121 <span class="comment">// 4) (MULT rational mterm'_1 ...) where each mterm' is of type (2) or (3)</span>
<a name="l00122"></a>00122 <span class="comment">// 5) (PLUS rational sterm_1 sterm_2 ...) where each sterm is of </span>
<a name="l00123"></a>00123 <span class="comment">// type (2) or (3) or (4) </span>
<a name="l00124"></a>00124
<a name="l00125"></a>00125 <span class="keyword">static</span> <span class="keywordtype">bool</span> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a1923e590a205cefe9ef50d336e99c9e5">greaterthan</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> &, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> &);
<a name="l00126"></a>00126 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aea589889127864f327d4d71800f096b7">simplifiedMultExpr</a>(std::vector<Expr> & mulKids);
<a name="l00127"></a>00127 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ad49508debdf58df9d8333cd140c850a3">canonMultConstMult</a>(<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="l00128"></a>00128 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a747b71c44a0bad76328039a2fc123363">canonMultConstPlus</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);
<a name="l00129"></a>00129 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ae709408bffa6ff2016619a05febe63f5">canonMultPowPow</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);
<a name="l00130"></a>00130 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a1765748e34d12d99b3bdf57f3ba49d49">canonMultPowLeaf</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);
<a name="l00131"></a>00131 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ad9ff33794685a95c453d41bf1fd9d0aa">canonMultLeafLeaf</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);
<a name="l00132"></a>00132 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a9bf1d7c7d567deab2e5decc8c4e82fdc">canonMultLeafOrPowMult</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);
<a name="l00133"></a>00133 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#af61545eb36910fba4fa1b69e6febb354">canonCombineLikeTerms</a>(<span class="keyword">const</span> std::vector<Expr> & sumExprs);
<a name="l00134"></a>00134 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>
<a name="l00135"></a>00135 <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ad5dec14920bc52be7b9fdfb458ba2e1b">canonMultLeafOrPowOrMultPlus</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);
<a name="l00136"></a>00136 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ab327e6f313e952c0380fe7460bd7d36c">canonMultPlusPlus</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);
<a name="l00137"></a>00137 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aa1ab000ca8a6a2605b2cb57f8b881d91">canonMultMtermMterm</a>(<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="l00138"></a>00138 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#acbd2c2b8d5a0728aa00dcf55c7c646f2" title="Canonize (PLUS t1 ... tn)">canonPlus</a>(<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="l00139"></a>00139 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#addd3884d42a6e4637e9bda79d4af6574">canonInvertConst</a>(<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="l00140"></a>00140 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a84b1ec96629fa2ae52792a582ba7a63a">canonInvertLeaf</a>(<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="l00141"></a>00141 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a02b89064723281b69105ce11ecaf80c7">canonInvertPow</a>(<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="l00142"></a>00142 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a94090722e5ab797e97cdb14458c40742">canonInvertMult</a>(<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="l00143"></a>00143 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a1a4b78b01763b1ca5a80c0211bc3ba4b" title="==> 1/e = e' where e' is canonical; takes e.">canonInvert</a>(<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="l00144"></a>00144 <span class="comment"></span>
<a name="l00145"></a>00145 <span class="comment"> /**</span>
<a name="l00146"></a>00146 <span class="comment"> * Transform e = (SUM r t1 ... tn) @ 0 into (SUM t1 ... tn) @ -r. The first </span>
<a name="l00147"></a>00147 <span class="comment"> * sum term (r) must be a rational and t1 ... tn terms must be canonised.</span>
<a name="l00148"></a>00148 <span class="comment"> * </span>
<a name="l00149"></a>00149 <span class="comment"> * @param e the expression to transform </span>
<a name="l00150"></a>00150 <span class="comment"> * @return rewrite theorem representing the transformation </span>
<a name="l00151"></a>00151 <span class="comment"> */</span>
<a name="l00152"></a>00152 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aad289f36b55fe8be7f7af0f62aedaae8">moveSumConstantRight</a>(<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="l00153"></a>00153 <span class="comment"></span>
<a name="l00154"></a>00154 <span class="comment"> /** e[0]/e[1] ==> e[0]*(e[1])^-1 */</span>
<a name="l00155"></a>00155 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#acfe4060947cb28e9fc9c4ea859df565c">canonDivide</a>(<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="l00156"></a>00156 <span class="comment"></span>
<a name="l00157"></a>00157 <span class="comment"> /** Multiply out the operands of the multiplication (each of them is expected to be canonised */</span>
<a name="l00158"></a>00158 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a627a219305f83b200e36b28b1865729a">canonMult</a>(<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="l00159"></a>00159
<a name="l00160"></a>00160 <span class="comment">// t*c ==> c*t, takes constant c and term t</span>
<a name="l00161"></a>00161 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a401fca0c453a94c8c0053eb77e014af0" title="t*c ==> c*t, takes constant c and term t">canonMultTermConst</a>(<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="l00162"></a>00162 <span class="comment">// t1*t2 ==> Error, takes t1 and t2 where both are non-constants</span>
<a name="l00163"></a>00163 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a294916be1e9ac30e3c824b0b8e4ff093" title="t1*t2 ==> Error, takes t1 and t2 where both are non-constants">canonMultTerm1Term2</a>(<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="l00164"></a>00164 <span class="comment">// 0*t ==> 0, takes 0*t</span>
<a name="l00165"></a>00165 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a55fb07d5df2b4068bf5df327ae0d89d4" title="0*t ==> 0, takes 0*t">canonMultZero</a>(<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="l00166"></a>00166 <span class="comment">// 1*t ==> t, takes 1*t</span>
<a name="l00167"></a>00167 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aed0a2d1337910f3027ac867e0f18b8de" title="1*t ==> t, takes 1*t">canonMultOne</a>(<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="l00168"></a>00168 <span class="comment">// c1*c2 ==> c', takes constant c1*c2 </span>
<a name="l00169"></a>00169 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a4ea3884dff8c1606fd05e61eb78e379d" title="c1*c2 ==> c', takes constant c1*c2">canonMultConstConst</a>(<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="l00170"></a>00170 <span class="comment">// c1*(c2*t) ==> c'*t, takes c1 and c2 and t</span>
<a name="l00171"></a>00171 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00172"></a>00172 <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a9e5b7c75f1f662071942150df1a4d69e" title="c1*(c2*t) ==> c'*t, takes c1 and c2 and t">canonMultConstTerm</a>(<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, <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="l00173"></a>00173 <span class="comment">// c1*(+ c2 v1 ...) ==> (+ c' c1v1 ...), takes c1 and the sum</span>
<a name="l00174"></a>00174 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a2765c1485aac81cc42ed3186f7a1f244" title="c1*(+ c2 v1 ...) ==> (+ c' c1v1 ...), takes c1 and the sum">canonMultConstSum</a>(<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="l00175"></a>00175 <span class="comment">// c^n = c' (compute the constant power expression)</span>
<a name="l00176"></a>00176 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a5347a8208d4d7aa05fad463bd6da8c41" title="c^n = c' (compute the constant power expression)">canonPowConst</a>(<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#a28fc84bed3f9bc91ca9967de0f9cfa00" title="Raise 'base' into the power of 'pow' (pow must be an integer)">pow</a>);
<a name="l00177"></a>00177
<a name="l00178"></a>00178 <span class="comment">// Rules for addition</span>
<a name="l00179"></a>00179 <span class="comment">// flattens the input. accepts a PLUS expr</span>
<a name="l00180"></a>00180 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a5ec4889e730c0b1d4fb584d16af08a9d" title="flattens the input. accepts a PLUS expr">canonFlattenSum</a>(<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="l00181"></a>00181
<a name="l00182"></a>00182 <span class="comment">// Rules for addition</span>
<a name="l00183"></a>00183 <span class="comment">// combine like terms. accepts a flattened PLUS expr</span>
<a name="l00184"></a>00184 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a245f64776d0b1fbd14d18bb145f717e4" title="combine like terms. accepts a flattened PLUS expr">canonComboLikeTerms</a>(<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="l00185"></a>00185
<a name="l00186"></a>00186 <span class="comment">// 0 = (* e1 e2 ...) <=> 0 = e1 OR 0 = e2 OR ...</span>
<a name="l00187"></a>00187 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a57eafe7c2a127ca4b4706437b777d610">multEqZero</a>(<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="l00188"></a>00188
<a name="l00189"></a>00189 <span class="comment">// 0 = (^ c x) <=> false if c <=0</span>
<a name="l00190"></a>00190 <span class="comment">// <=> 0 = x if c > 0</span>
<a name="l00191"></a>00191 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#acbea7826fe54b91e8d4bc2c21f7137ae">powEqZero</a>(<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="l00192"></a>00192
<a name="l00193"></a>00193 <span class="comment">// x^n = y^n <=> x = y (if n is odd)</span>
<a name="l00194"></a>00194 <span class="comment">// x^n = y^n <=> x = y OR x = -y (if n is even)</span>
<a name="l00195"></a>00195 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ab29b63e40b7f2c624e6e4f11c4eff27e">elimPower</a>(<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="l00196"></a>00196
<a name="l00197"></a>00197 <span class="comment">// x^n = c <=> x = root (if n is odd and root^n = c)</span>
<a name="l00198"></a>00198 <span class="comment">// x^n = c <=> x = root OR x = -root (if n is even and root^n = c)</span>
<a name="l00199"></a>00199 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a942f9f0fc0ceff798b607e9fe032175a">elimPowerConst</a>(<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="l00200"></a>00200
<a name="l00201"></a>00201 <span class="comment">// x^n = c <=> false (if n is even and c is negative)</span>
<a name="l00202"></a>00202 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#abe913a6cc9430faf8f0ac50ec51aa36c">evenPowerEqNegConst</a>(<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="l00203"></a>00203
<a name="l00204"></a>00204 <span class="comment">// x^n = c <=> false (if x is an integer and c is not a perfect n power)</span>
<a name="l00205"></a>00205 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a946832931094bb746277d8b95c471690">intEqIrrational</a>(<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="namespaceCVC3.html#a8b193cc1fee34cb43707171b2ae6471e">isInt</a>);
<a name="l00206"></a>00206
<a name="l00207"></a>00207 <span class="comment">// e[0] kind e[1] <==> true when e[0] kind e[1],</span>
<a name="l00208"></a>00208 <span class="comment">// false when e[0] !kind e[1], for constants only</span>
<a name="l00209"></a>00209 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a7a2a8059fa49da5a8877b28b1cfa445a" title="e0 @ e1 <==> true | false, where @ is {=,<,<=,>,>=}">constPredicate</a>(<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="l00210"></a>00210
<a name="l00211"></a>00211 <span class="comment">// e[0] kind e[1] <==> 0 kind e[1] - e[0]</span>
<a name="l00212"></a>00212 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aca76a2dbee73d7ad9e2529ac8ce142a4" title="e[0] @ e[1] <==> 0 @ e[1] - e[0], where @ is {=,<,<=,>,>=}">rightMinusLeft</a>(<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="l00213"></a>00213
<a name="l00214"></a>00214 <span class="comment">// e[0] kind e[1] <==> e[0] - e[1] kind 0</span>
<a name="l00215"></a>00215 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aedad2be1c60515921f8c3761581afca5" title="e[0] @ e[1] <==> e[0] - e[1] @ 0, where @ is {=,<,<=,>,>=}">leftMinusRight</a>(<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="l00216"></a>00216
<a name="l00217"></a>00217 <span class="comment">// x kind y <==> x + z kind y + z</span>
<a name="l00218"></a>00218 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ab190e4d8fefb74f2a8117ca17ae49b48" title="x @ y <==> x + z @ y + z, where @ is {=,<,<=,>,>=} (given as 'kind')">plusPredicate</a>(<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="l00219"></a>00219 <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="l00220"></a>00220 <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="l00221"></a>00221
<a name="l00222"></a>00222 <span class="comment">// x = y <==> x * z = y * z</span>
<a name="l00223"></a>00223 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#afd7a6da45999fb3237cdbbbf9c5f19e8" title="x = y <==> x * z = y * z, where z is a non-zero constant">multEqn</a>(<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, <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="l00224"></a>00224
<a name="l00225"></a>00225 <span class="comment">// x = y <==> z=0 OR x * 1/z = y * 1/z</span>
<a name="l00226"></a>00226 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a7bf31f4d4bd6e3f7ff7e37dd5236a792">divideEqnNonConst</a>(<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, <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="l00227"></a>00227
<a name="l00228"></a>00228 <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="l00229"></a>00229 <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="l00230"></a>00230 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a8af6455fe4a8889cfb7b0b8c865b847c" title="Multiplying inequation by a non-zero constant.">multIneqn</a>(<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="l00231"></a>00231
<a name="l00232"></a>00232 <span class="comment">// x = y ==> x <= y and x >= y</span>
<a name="l00233"></a>00233 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ad2f144d3a2ffe108e0d8e7df8e263832" title="x = y ==> x <= y and x >= y">eqToIneq</a>(<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="l00234"></a>00234
<a name="l00235"></a>00235 <span class="comment">// "op1 GE|GT op2" <==> op2 LE|LT op1</span>
<a name="l00236"></a>00236 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a216a950228aad3cdef0c5dd5213be4fb" title=""op1 GE|GT op2" <==> op2 LE|LT op1">flipInequality</a>(<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="l00237"></a>00237
<a name="l00238"></a>00238 <span class="comment">// NOT (op1 LT op2) <==> (op1 GE op2)</span>
<a name="l00239"></a>00239 <span class="comment">// NOT (op1 LE op2) <==> (op1 GT op2)</span>
<a name="l00240"></a>00240 <span class="comment">// NOT (op1 GT op2) <==> (op1 LE op2)</span>
<a name="l00241"></a>00241 <span class="comment">// NOT (op1 GE op2) <==> (op1 LT op2)</span>
<a name="l00242"></a>00242 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a27bb939c33616b21a83aabdb5d47a660" title="Propagating negation over <,<=,>,>=.">negatedInequality</a>(<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="l00243"></a>00243
<a name="l00244"></a>00244 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a6f08ce700f85f9ba2967ecee42e7a550" title="Real shadow: a <(=) t, t <(=) b ==> a <(=) b.">realShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& alphaLTt, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& tLTbeta);
<a name="l00245"></a>00245 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a955e74558aee9ebc9de4c084819e93ac" title="alpha <= t <= alpha ==> t = alpha">realShadowEq</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& alphaLEt, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& tLEalpha);
<a name="l00246"></a>00246 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aaba7798eb77a93ac0de8978507dca731" title="Finite interval for integers: a <= t <= a + c ==> G(t, a, 0, c)">finiteInterval</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& aLEt, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& tLEac,
<a name="l00247"></a>00247 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isInta, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntt);
<a name="l00248"></a>00248
<a name="l00249"></a>00249 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a2ad479414c401fb8a4ea9631cbdd95c0" title="Dark & Gray shadows when a <= b.">darkGrayShadow2ab</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& betaLEbx,
<a name="l00250"></a>00250 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& axLEalpha,
<a name="l00251"></a>00251 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntAlpha,
<a name="l00252"></a>00252 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntBeta,
<a name="l00253"></a>00253 <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="l00254"></a>00254
<a name="l00255"></a>00255 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a8b2e8589d24fc69616ba431588c50b3e" title="Dark & Gray shadows when b <= a.">darkGrayShadow2ba</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& betaLEbx,
<a name="l00256"></a>00256 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& axLEalpha,
<a name="l00257"></a>00257 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntAlpha,
<a name="l00258"></a>00258 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntBeta,
<a name="l00259"></a>00259 <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="l00260"></a>00260
<a name="l00261"></a>00261 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a372efa694fb08c901deff55f5f108ffb">expandDarkShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#afe495b6c58dd0c89c84b64c5194eeeaa" title="Construct the dark shadow expression representing lhs <= rhs.">darkShadow</a>);
<a name="l00262"></a>00262 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aacc831490c52da277133fe625522216f" title="GRAY_SHADOW(v, e, c, c) ==> v=e+c.">expandGrayShadow0</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ab34039c1fcdbf7701cd0541dce2575c8" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>);
<a name="l00263"></a>00263 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ae609e58a7bee454d0f18dc1465cd2167" title="G(x, e, c1, c2) ==> (G1 or G2) and (!G1 or !G2)">splitGrayShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ab34039c1fcdbf7701cd0541dce2575c8" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>);
<a name="l00264"></a>00264 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aab0ccd490624628fa990b1dd473e7e8a">splitGrayShadowSmall</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ab34039c1fcdbf7701cd0541dce2575c8" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>);
<a name="l00265"></a>00265 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ab9dd38464b6e02af6d7c570119c6aec3" title="G(x, e, c1, c2) ==> e+c1 <= x AND x <= e+c2.">expandGrayShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ab34039c1fcdbf7701cd0541dce2575c8" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>);
<a name="l00266"></a>00266 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a43d1cf15faefe439c344508bf60e5e96" title="Optimized rules: GRAY_SHADOW(a*x, c, c1, c2) ==> [expansion].">expandGrayShadowConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ab34039c1fcdbf7701cd0541dce2575c8" title="Construct the gray shadow expression representing c1 <= v - e <= c2.">grayShadow</a>);
<a name="l00267"></a>00267 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a0a5eb9028805dd1ee141713b7c70be77" title="|- G(ax, c, c1, c2) ==> |- G(x, 0, ceil((c1+c)/a), floor((c2+c)/a))">grayShadowConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& g);
<a name="l00268"></a>00268 <span class="comment"></span>
<a name="l00269"></a>00269 <span class="comment"> //! Implements j(c,b,a)</span>
<a name="l00270"></a>00270 <span class="comment"></span><span class="comment"> /*! accepts 3 integers a,b,c and returns</span>
<a name="l00271"></a>00271 <span class="comment"> * (b > 0)? (c+b) mod a : (a - (c+b)) mod a</span>
<a name="l00272"></a>00272 <span class="comment"> */</span>
<a name="l00273"></a>00273 <a class="code" href="classCVC3_1_1Rational.html">Rational</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#afa3e14a6cb004a107d915df0088ed16c" title="Implements j(c,b,a)">constRHSGrayShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& c,
<a name="l00274"></a>00274 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& b,
<a name="l00275"></a>00275 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a>& a);
<a name="l00276"></a>00276
<a name="l00277"></a>00277 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a91447c7423622c037a2956114fd549f4">lessThanToLE</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& less, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntLHS,
<a name="l00278"></a>00278 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntRHS, <span class="keywordtype">bool</span> changeRight);
<a name="l00279"></a>00279
<a name="l00280"></a>00280 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a55c056040dc960b598706a94650acccb">lessThanToLERewrite</a>(<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>& isIntLHS,
<a name="l00281"></a>00281 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntRHS, <span class="keywordtype">bool</span> changeRight);
<a name="l00282"></a>00282
<a name="l00283"></a>00283 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a608b3a7da8f2824d3cc8188d7606396e">intVarEqnConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</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="l00284"></a>00284 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ad2438a34ff1edb7268495d4105cb6c9c">IsIntegerElim</a>(<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="l00285"></a>00285
<a name="l00286"></a>00286 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a1f5430f425efc533ca5881aaaeb42554" title="Equality elimination rule for integers: See the detailed description for explanations.">eqElimIntRule</a>(<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="l00287"></a>00287 <span class="keyword">const</span> std::vector<Theorem>& isIntVars);
<a name="l00288"></a>00288
<a name="l00289"></a>00289 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a24216d1be10b57272b918ba416783b76" title="return e <=> TRUE/FALSE for e == IS_INTEGER(c), where c is a constant">isIntConst</a>(<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="l00290"></a>00290
<a name="l00291"></a>00291 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#acb64cdcb59f042dd38a9bf9b70f043ad">equalLeaves1</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);
<a name="l00292"></a>00292 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ae97e571a8d541a31aef5c1c703190437">equalLeaves2</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);
<a name="l00293"></a>00293 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aba1a7d51f8b8291c30cc32c0f3ff5a4d">equalLeaves3</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);
<a name="l00294"></a>00294 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a5876760c9171eca18490c779cc2bbc73">equalLeaves4</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);
<a name="l00295"></a>00295
<a name="l00296"></a>00296 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a20fdbcbe80fa06a175aae548af7d2519" title="x /= y ==> (x < y) OR (x > y)">diseqToIneq</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& diseq);
<a name="l00297"></a>00297
<a name="l00298"></a>00298 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ae1e994559a2318ec45a758042371a71d">dummyTheorem</a>(<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="l00299"></a>00299
<a name="l00300"></a>00300 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a2caebbed8d00af9c80195413ed2cc568">oneElimination</a>(<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="l00301"></a>00301
<a name="l00302"></a>00302 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#af05299dbe2defe9679365201cd60c516">clashingBounds</a>(<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="l00303"></a>00303
<a name="l00304"></a>00304 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a301d62f207b9cfd50096417d1f5852df">addInequalities</a>(<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="l00305"></a>00305 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a301d62f207b9cfd50096417d1f5852df">addInequalities</a>(<span class="keyword">const</span> std::vector<Theorem>& thms);
<a name="l00306"></a>00306
<a name="l00307"></a>00307 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ae856ca9fab9699b655d7fd76cdf778d4">implyWeakerInequality</a>(<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="l00308"></a>00308
<a name="l00309"></a>00309 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a1797b422d1100edc2464666121d7017b">implyNegatedInequality</a>(<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="l00310"></a>00310
<a name="l00311"></a>00311 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ae25218af53e642382f30948adc991313">integerSplit</a>(<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="l00312"></a>00312
<a name="l00313"></a>00313 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#ad58ee7b299de278620860c9d67a2662b">trustedRewrite</a>(<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="l00314"></a>00314
<a name="l00315"></a>00315 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a7638b18d73c05e7bedad7c4cdfeca809">rafineStrictInteger</a>(<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="l00316"></a>00316
<a name="l00317"></a>00317 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a6fe0e5ebaf81278f55759fff05c275c1">simpleIneqInt</a>(<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="l00318"></a>00318
<a name="l00319"></a>00319 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a84ec7197bec26c33753e98b6adf55dce">intEqualityRationalConstant</a>(<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="l00320"></a>00320
<a name="l00321"></a>00321 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a5411413ef39cb6029a8e85fc03908de3">cycleConflict</a>(<span class="keyword">const</span> std::vector<Theorem>& inequalitites);
<a name="l00322"></a>00322
<a name="l00323"></a>00323 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a1efa679a45d71f60bf2be6f4f7a4430d">implyEqualities</a>(<span class="keyword">const</span> std::vector<Theorem>& inequalities);
<a name="l00324"></a>00324
<a name="l00325"></a>00325 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a8e90a0d0e2050a7f0eb1dde6df7f6842">implyWeakerInequalityDiffLogic</a>(<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="l00326"></a>00326
<a name="l00327"></a>00327 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a6ef98983cca8d3723f50fbea60c37cef">implyNegatedInequalityDiffLogic</a>(<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="l00328"></a>00328
<a name="l00329"></a>00329 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aa9b6fa1339b7e68cb730bdf2f63c0914">expandGrayShadowRewrite</a>(<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="l00330"></a>00330
<a name="l00331"></a>00331 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aac90a712f81d969d8aa0322b4d31de0b">compactNonLinearTerm</a>(<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="l00332"></a>00332
<a name="l00333"></a>00333 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#aaa91789edbf7fb936789379dd15a3a4f">nonLinearIneqSignSplit</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& ineqThm);
<a name="l00334"></a>00334
<a name="l00335"></a>00335 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#a9edd45196fbd8e61a4927134fde15e97">implyDiffLogicBothBounds</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& x, std::vector<Theorem>& c1_le_x, <a class="code" href="classCVC3_1_1Rational.html">Rational</a> c1,
<a name="l00336"></a>00336 std::vector<Theorem>& x_le_c2, <a class="code" href="classCVC3_1_1Rational.html">Rational</a> c2);
<a name="l00337"></a>00337
<a name="l00338"></a>00338 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducer3.html#abf49b0eeb6087702dd1a8e9c03f7379a">powerOfOne</a>(<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="l00339"></a>00339
<a name="l00340"></a>00340 }; <span class="comment">// end of class ArithTheoremProducer3</span>
<a name="l00341"></a>00341
<a name="l00342"></a>00342 } <span class="comment">// end of namespace CVC3</span>
<a name="l00343"></a>00343
<a name="l00344"></a>00344 <span class="preprocessor">#endif</span>
</pre></div></div>
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