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<a href="arith__theorem__producer__old_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_producer_old.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_producer_old_h_</span>
<a name="l00023"></a>00023 <span class="preprocessor"></span><span class="preprocessor">#define _cvc3__arith_theorem_producer_old_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__arith__old_8h.html">theory_arith_old.h</a>"</span>
<a name="l00028"></a>00028
<a name="l00029"></a>00029 <span class="keyword">namespace </span>CVC3 {
<a name="l00030"></a>00030
<a name="l00031"></a><a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html">00031</a> <span class="keyword">class </span><a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html">ArithTheoremProducerOld</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="l00032"></a><a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afd5a86810c4915fbe0223a122180a466">00032</a> <a class="code" href="classCVC3_1_1TheoryArithOld.html">TheoryArithOld</a>* <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afd5a86810c4915fbe0223a122180a466">d_theoryArith</a>;
<a name="l00033"></a>00033 <span class="keyword">private</span>:<span class="comment"></span>
<a name="l00034"></a>00034 <span class="comment"> /*! \name Auxiliary functions for eqElimIntRule()</span>
<a name="l00035"></a>00035 <span class="comment"> * Methods that compute the subterms used in eqElimIntRule()</span>
<a name="l00036"></a>00036 <span class="comment"> *@{</span>
<a name="l00037"></a>00037 <span class="comment"> */</span><span class="comment"></span>
<a name="l00038"></a>00038 <span class="comment"> //! Compute the special modulus: i - m*floor(i/m+1/2)</span>
<a name="l00039"></a>00039 <span class="comment"></span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a0f531ca3d0d71a1872e1519aeafa7700" 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="l00040"></a>00040 <span class="comment"> //! Create the term 't'. See eqElimIntRule().</span>
<a name="l00041"></a>00041 <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_1ArithTheoremProducerOld.html#a312dc8f65e3f19567e078035d1c67228" 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="l00042"></a>00042 <span class="comment"> //! Create the term 't2'. See eqElimIntRule().</span>
<a name="l00043"></a>00043 <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_1ArithTheoremProducerOld.html#a1e069e289a008b1becbd5aef9afdd386" 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="l00044"></a>00044 <span class="comment"> //! Create the term 't3'. See eqElimIntRule().</span>
<a name="l00045"></a>00045 <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_1ArithTheoremProducerOld.html#a7458e7bd26ab3c181402534228ddbcc0" 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="l00046"></a>00046 <span class="comment"> /*! @brief Takes sum = a_0 + a_1*x_1+...+a_n*x_n and returns the</span>
<a name="l00047"></a>00047 <span class="comment"> * vector of similar monomials (in 'summands') with coefficients</span>
<a name="l00048"></a>00048 <span class="comment"> * mod(a_i, m). If divide flag is true, the coefficients will be</span>
<a name="l00049"></a>00049 <span class="comment"> * mod(a_i,m)/m.</span>
<a name="l00050"></a>00050 <span class="comment"> */</span>
<a name="l00051"></a>00051 <span class="keywordtype">void</span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a8634bedfcede10ab17339fde0a72e5d6" 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="l00052"></a>00052 <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="l00053"></a>00053 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a9551aaeb071bd9c2b5703f69c2243e14" 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="l00054"></a>00054 <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="l00055"></a>00055 <span class="keywordtype">void</span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a3d81fdb3d2ac10bfc3f2c0d73a5258e1" 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="l00056"></a>00056 <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="l00057"></a>00057 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a2e2582c11f6547ed6faefaec6c9142f9" 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="l00058"></a>00058 <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="l00059"></a>00059 <span class="comment"> //! Compute floor(i/m+1/2) + mod(i,m)</span>
<a name="l00060"></a>00060 <span class="comment"></span> <a class="code" href="classCVC3_1_1Rational.html">Rational</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ad7af04a277cf5337c02182ee9bf055a4" 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="l00061"></a>00061 <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a77f3c348c3b6566fbae5c9750d568b9c" 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);
<a name="l00062"></a>00062 <span class="keywordtype">void</span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ae2174305ea66a5df62101bce0ada8d04" title="Compute the special modulus: i - m*floor(i/m+1/2)">getLeaves</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e, std::set<Rational>& s, <a class="code" href="classCVC3_1_1ExprHashMap.html">ExprHashMap<bool></a>& cache);<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_1ArithTheoremProducerOld.html#a4896b0d01e30e02300f74b9ae6b4d9d4">00066</a> <span class="comment"></span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a4896b0d01e30e02300f74b9ae6b4d9d4" title="Constructor.">ArithTheoremProducerOld</a>(<a class="code" href="classCVC3_1_1TheoremManager.html">TheoremManager</a>* tm, <a class="code" href="classCVC3_1_1TheoryArithOld.html">TheoryArithOld</a>* theoryArith):
<a name="l00067"></a>00067 <a class="code" href="classCVC3_1_1TheoremProducer.html">TheoremProducer</a>(tm), <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afd5a86810c4915fbe0223a122180a466">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_1ArithTheoremProducerOld.html#a8e7bf5bdb1872df7f21920c64a37c612">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_1ArithTheoremProducerOld.html#a8e7bf5bdb1872df7f21920c64a37c612" 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_1ArithTheoremProducerOld.html#ab22e2bf40e2473ab9dc34097c28a46a3">00071</a> <a class="code" href="classCVC3_1_1Type.html" title="MS C++ specific settings.">Type</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ab22e2bf40e2473ab9dc34097c28a46a3">realType</a>() { <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afd5a86810c4915fbe0223a122180a466">d_theoryArith</a>-><a class="code" href="classCVC3_1_1TheoryArith.html#a03fa81194322b92c488033695bec7204">realType</a>(); }
<a name="l00072"></a><a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a520ba37f3cc4129559fc32289a027b82">00072</a> <a class="code" href="classCVC3_1_1Type.html" title="MS C++ specific settings.">Type</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a520ba37f3cc4129559fc32289a027b82">intType</a>() { <span class="keywordflow">return</span> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afd5a86810c4915fbe0223a122180a466">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_1ArithTheoremProducerOld.html#a9437ab7589a35fa490136b4b917ad244">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_1ArithTheoremProducerOld.html#a9437ab7589a35fa490136b4b917ad244" 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_1ArithTheoremProducerOld.html#afd5a86810c4915fbe0223a122180a466">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_1ArithTheoremProducerOld.html#a4eade9939f609e974d0c5210404ba965">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_1ArithTheoremProducerOld.html#a4eade9939f609e974d0c5210404ba965" 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_1ArithTheoremProducerOld.html#afd5a86810c4915fbe0223a122180a466">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_1ArithTheoremProducerOld.html#aebcc9153d9e9bfff3678c271674a6053" 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_1ArithTheoremProducerOld.html#a8165eb2a8fea70e0d1d2c8ebb1358855" 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_1ArithTheoremProducerOld.html#ae3458f7b381a95e124e3204ed66904ef" 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_1ArithTheoremProducerOld.html#a693a5043cf100f13390b358290940dd5">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_1ArithTheoremProducerOld.html#a237d508b95295db21e9ce21172d4366a" 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_1ArithTheoremProducerOld.html#aea8367eb1c88d26b83aea3e5e63f66db" 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_1ArithTheoremProducerOld.html#a844e1fe500be8d1c083ddf6c06fcc85c" 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_1ArithTheoremProducerOld.html#af79a13a84e24d58135d13d7520726134" 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_1ArithTheoremProducerOld.html#ac6cae811b7bab0f2fc9aa62b94b461fd">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_1ArithTheoremProducerOld.html#aeebe92e51ed9f4f65fc949c66d240a1c">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_1ArithTheoremProducerOld.html#a4fe68827d0fd6cdccac139bc55416cb8">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_1ArithTheoremProducerOld.html#aa9f22909a2df31e9d59a96afecfa11dd">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_1ArithTheoremProducerOld.html#a5840677a1efc3ab4ef21840d57654c5f">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_1ArithTheoremProducerOld.html#ae7bb027487c9e8312c4ca194ecfd379d">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_1ArithTheoremProducerOld.html#a71d7308e50c892d691d504397f5a92c8">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_1ArithTheoremProducerOld.html#a040ec808dbbe743d9b138bfae33d24fc">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_1ArithTheoremProducerOld.html#aad39a4a6b01790e883d49e03e3b513a9">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_1ArithTheoremProducerOld.html#acf0ff17451a851136910015ea515ac2f">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_1ArithTheoremProducerOld.html#ae39478b27e22eee4837e7a132301b31a">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_1ArithTheoremProducerOld.html#ad7982dec66d9ebd08596c5b7d352604b">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_1ArithTheoremProducerOld.html#a4a213b741317120ee84b6e61f50e484f" 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_1ArithTheoremProducerOld.html#a7696b12b3bc3ab04fdbf284a9466364a">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_1ArithTheoremProducerOld.html#acd60e50d112e88d021974c0b70956db6">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_1ArithTheoremProducerOld.html#ad02b7e86f0f0edef419c4fe2adc74c99">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_1ArithTheoremProducerOld.html#a776468ac8d047b43cb460c9b3c600293">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_1ArithTheoremProducerOld.html#a67391e426738cbd4a15f6fbc5b2d19e1" 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_1ArithTheoremProducerOld.html#a2b44fabb65bb6748259aee8959be465e">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_1ArithTheoremProducerOld.html#aec48ed7710110960c6f87e6946500494">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_1ArithTheoremProducerOld.html#a50819c4cc053538490a2cbb535edf39d">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_1ArithTheoremProducerOld.html#a70d0d0fa8c08582a17399c0570812afa" 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_1ArithTheoremProducerOld.html#a10ed8952ec021d78cf1bc8b60e6634c6" 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_1ArithTheoremProducerOld.html#af62a070ed7a3a326db5b121b282bd47c" 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_1ArithTheoremProducerOld.html#abc03e832be081de0ca6f7f4e905e0f4f" 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_1ArithTheoremProducerOld.html#a3c1740f98f0ac4952c8d7a721767535e" 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_1ArithTheoremProducerOld.html#a8e0a636c4ee9bb70b8f36ee3f6acab49" 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_1ArithTheoremProducerOld.html#a5892d8574e2787b95005211cf0517952" 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_1ArithTheoremProducerOld.html#a7b083f1e452bd42475d9f0b313651fac" 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_1ArithTheoremProducerOld.html#aba0cab7c4879b336dfac9cd1673be1c8" 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_1ArithTheoremProducerOld.html#a7f2a1a065eac005fa6b47c32040d9401" 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_1ArithTheoremProducerOld.html#ad73622cdec4a472af97d68de6716fe0a">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_1ArithTheoremProducerOld.html#a9cc96dbb9ae7fa063146b9924f51fe68">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_1ArithTheoremProducerOld.html#aeed414c650deb9b1e619ffb8f3266ea4">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_1ArithTheoremProducerOld.html#a2483c968c6a4d7f8ae63595c839b70f2">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_1ArithTheoremProducerOld.html#afe5f71b9fdeb8be95e0e71e94df0b598">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_1ArithTheoremProducerOld.html#a75a67906db6381d408ea1a9830c36cf7">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_1ArithTheoremProducerOld.html#aefea69c7f808394db447b9ed658c59fa" 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_1ArithTheoremProducerOld.html#a088b20af694e737e1c7ff12d2ff74d7c" 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_1ArithTheoremProducerOld.html#a36301e14b9eb42fc9842a3a7f60f8b17" 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_1ArithTheoremProducerOld.html#a35577ad70c513422af5cbfca00cde1e2" 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_1ArithTheoremProducerOld.html#aeb54d03f4672718b7de6160a88bf33cb" 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_1ArithTheoremProducerOld.html#a16c7325daba5b9e8cea7284fafaa5382">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_1ArithTheoremProducerOld.html#aa425318a5846e14a94b2a3a34bb99b6d" 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_1ArithTheoremProducerOld.html#a8edb275846dc5d938d3a8716436f0e1e" 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_1ArithTheoremProducerOld.html#a86c578d9592d6782d2224118b755e0fa" 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_1ArithTheoremProducerOld.html#a0b1fba36612db00956767d73bb1b6623" 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_1ArithTheoremProducerOld.html#a8f7858787d55442d57e5924dd232f842" 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_1ArithTheoremProducerOld.html#a5033cb7a4be3d2e9bc1cd60582482c5f" 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_1ArithTheoremProducerOld.html#ae2869b5a206710a6c890d81ded080838" 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_1ArithTheoremProducerOld.html#a07e973f55e9daf1def982c84c3a078b1" 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_1ArithTheoremProducerOld.html#ae27df6e46accf919b67dda1cb914c160" 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_1ArithTheoremProducerOld.html#a0b28ed8d0e2ef812bcfc8bba931e46cd">expandDarkShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a9437ab7589a35fa490136b4b917ad244" 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_1ArithTheoremProducerOld.html#a273501b582758aca3ebabe6bd3ce83e4" 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_1ArithTheoremProducerOld.html#a4eade9939f609e974d0c5210404ba965" 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_1ArithTheoremProducerOld.html#a7fa5dbc59e8ce9a4315373092329a029" 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_1ArithTheoremProducerOld.html#a4eade9939f609e974d0c5210404ba965" 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_1ArithTheoremProducerOld.html#a0d76b8569909514e1f6a392a3778c04b">splitGrayShadowSmall</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a4eade9939f609e974d0c5210404ba965" 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_1ArithTheoremProducerOld.html#a0e43921a028cfe58d5b50acd0c4a70ed" 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_1ArithTheoremProducerOld.html#a4eade9939f609e974d0c5210404ba965" 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_1ArithTheoremProducerOld.html#ae8c25031e88732d3259cd8e33d75e094" 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_1ArithTheoremProducerOld.html#a4eade9939f609e974d0c5210404ba965" 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_1ArithTheoremProducerOld.html#a04d45720968a5ff4ccd6411413bd826e" 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_1ArithTheoremProducerOld.html#abd378d8d5a434e8df4809239bebc22fa" 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_1ArithTheoremProducerOld.html#a0ce54f8c725be25a6f6b11c7fbdc5321">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_1ArithTheoremProducerOld.html#ab872ead63494b4afa6571e61a5cdd977">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 name="l00284"></a>00284 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a99692dc40111d3082e7c583590c32188">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="l00285"></a>00285 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#adc3a59f76832fd2671407c85b4b721a5">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="l00286"></a>00286
<a name="l00287"></a>00287 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a85fd2ee0f7126d421fb53f4823ec8e77" 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="l00288"></a>00288 <span class="keyword">const</span> std::vector<Theorem>& isIntVars);
<a name="l00289"></a>00289
<a name="l00290"></a>00290 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a5ef5359db9aa12e8d196f7a39fc0fb55" 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="l00291"></a>00291
<a name="l00292"></a>00292 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a0a3f404013d038207a13103500e09c99">equalLeaves1</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_1ArithTheoremProducerOld.html#ae1820f8d68e98363139d77deae464f4f">equalLeaves2</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_1ArithTheoremProducerOld.html#a8e8ce7a2f17e5a855985bd0abfac6f12">equalLeaves3</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);
<a name="l00295"></a>00295 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a24c874d01ca341845373cd41851a5a1b">equalLeaves4</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e);
<a name="l00296"></a>00296
<a name="l00297"></a>00297 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ae723d1459d8c6f797ec08451f80f0798" 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="l00298"></a>00298
<a name="l00299"></a>00299 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a3a3dd2d9c47ec607c816a9004c3659a5">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="l00300"></a>00300
<a name="l00301"></a>00301 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aeb6d93e58c5c069ecbea38d013cbcf3e">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="l00302"></a>00302
<a name="l00303"></a>00303 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aa71bcce02e1c1ce0d6ae588b4f341e4a">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="l00304"></a>00304
<a name="l00305"></a>00305 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a582df53749ebc6fd4011c614ff767181">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="l00306"></a>00306 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a582df53749ebc6fd4011c614ff767181">addInequalities</a>(<span class="keyword">const</span> std::vector<Theorem>& thms);
<a name="l00307"></a>00307
<a name="l00308"></a>00308 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a08879e8160aca1424c12e098f78df383">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="l00309"></a>00309
<a name="l00310"></a>00310 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a3597b8abdecd9f22c11f3ed1b570b6e8">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="l00311"></a>00311
<a name="l00312"></a>00312 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ad6dec83ab198a011e429c0f4b3aa218f">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="l00313"></a>00313
<a name="l00314"></a>00314 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a929689864e6c95280fcf1caa08ae28e1">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="l00315"></a>00315
<a name="l00316"></a>00316 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#af6182f9b295bde40a9047b1651d979a5">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="l00317"></a>00317
<a name="l00318"></a>00318 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a21b67f29c32a44f6194d127feb316d99">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="l00319"></a>00319
<a name="l00320"></a>00320 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a33232797bdaaa27ecd2f077478605bf6">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="l00321"></a>00321
<a name="l00322"></a>00322 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aacf793e26f8917dbd96d235b9399a18e">cycleConflict</a>(<span class="keyword">const</span> std::vector<Theorem>& inequalitites);
<a name="l00323"></a>00323
<a name="l00324"></a>00324 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a6a98470138f38710024a7cc8f37706fb">implyEqualities</a>(<span class="keyword">const</span> std::vector<Theorem>& inequalities);
<a name="l00325"></a>00325
<a name="l00326"></a>00326 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#af6d982874e310ba4bdbc796fcbc720fc">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="l00327"></a>00327
<a name="l00328"></a>00328 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aee41f9c7c0f2a6b82383076327e316a0">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="l00329"></a>00329
<a name="l00330"></a>00330 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#abb0ca6212da8280b0026369e449f900e">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="l00331"></a>00331
<a name="l00332"></a>00332 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#ad54e479f1a44912397237a557590c597">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="l00333"></a>00333
<a name="l00334"></a>00334 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#afe7a4ea7cbce967d7f160c21995c8b39">nonLinearIneqSignSplit</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& ineqThm);
<a name="l00335"></a>00335
<a name="l00336"></a>00336 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a8581e89bb73352a8e368e7b87acd78f4">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="l00337"></a>00337 std::vector<Theorem>& x_le_c2, <a class="code" href="classCVC3_1_1Rational.html">Rational</a> c2);
<a name="l00338"></a>00338
<a name="l00339"></a>00339 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#aadb554e4e8877b135fb01d6e2471ccba">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="l00340"></a>00340
<a name="l00341"></a>00341 <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithTheoremProducerOld.html#a120563be6dbb828da3e9b6a9d4d35e32">rewriteLeavesConst</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="l00342"></a>00342
<a name="l00343"></a>00343 }; <span class="comment">// end of class ArithTheoremProducerOld</span>
<a name="l00344"></a>00344
<a name="l00345"></a>00345 } <span class="comment">// end of namespace CVC3</span>
<a name="l00346"></a>00346
<a name="l00347"></a>00347 <span class="preprocessor">#endif</span>
</pre></div></div>
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