<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<title>CVC3: common_proof_rules.h Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<link href="doxygen.css" rel="stylesheet" type="text/css"/>
</head>
<body>
<!-- Generated by Doxygen 1.7.4 -->
<div id="top">
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr style="height: 56px;">
<td style="padding-left: 0.5em;">
<div id="projectname">CVC3 <span id="projectnumber">2.4.1</span></div>
</td>
</tr>
</tbody>
</table>
</div>
<div id="navrow1" class="tabs">
<ul class="tablist">
<li><a href="index.html"><span>Main Page</span></a></li>
<li><a href="pages.html"><span>Related Pages</span></a></li>
<li><a href="modules.html"><span>Modules</span></a></li>
<li><a href="namespaces.html"><span>Namespaces</span></a></li>
<li><a href="annotated.html"><span>Classes</span></a></li>
<li class="current"><a href="files.html"><span>Files</span></a></li>
</ul>
</div>
<div id="navrow2" class="tabs2">
<ul class="tablist">
<li><a href="files.html"><span>File List</span></a></li>
<li><a href="globals.html"><span>File Members</span></a></li>
</ul>
</div>
<div class="header">
<div class="headertitle">
<div class="title">common_proof_rules.h</div> </div>
</div>
<div class="contents">
<a href="common__proof__rules_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 common_proof_rules.h</span>
<a name="l00004"></a>00004 <span class="comment"> * </span>
<a name="l00005"></a>00005 <span class="comment"> * Author: Sergey Berezin</span>
<a name="l00006"></a>00006 <span class="comment"> * </span>
<a name="l00007"></a>00007 <span class="comment"> * Created: Dec 11 18:15:37 GMT 2002</span>
<a name="l00008"></a>00008 <span class="comment"> *</span>
<a name="l00009"></a>00009 <span class="comment"> * <hr></span>
<a name="l00010"></a>00010 <span class="comment"> *</span>
<a name="l00011"></a>00011 <span class="comment"> * License to use, copy, modify, sell and/or distribute this software</span>
<a name="l00012"></a>00012 <span class="comment"> * and its documentation for any purpose is hereby granted without</span>
<a name="l00013"></a>00013 <span class="comment"> * royalty, subject to the terms and conditions defined in the \ref</span>
<a name="l00014"></a>00014 <span class="comment"> * LICENSE file provided with this distribution.</span>
<a name="l00015"></a>00015 <span class="comment"> * </span>
<a name="l00016"></a>00016 <span class="comment"> * <hr></span>
<a name="l00017"></a>00017 <span class="comment"> * </span>
<a name="l00018"></a>00018 <span class="comment"> */</span>
<a name="l00019"></a>00019 <span class="comment">/*****************************************************************************/</span>
<a name="l00020"></a>00020 <span class="comment">// CLASS: CommonProofRules</span>
<a name="l00021"></a>00021 <span class="comment">//</span>
<a name="l00022"></a>00022 <span class="comment">// AUTHOR: Sergey Berezin, 12/09/2002</span>
<a name="l00023"></a>00023 <span class="comment">//</span>
<a name="l00024"></a>00024 <span class="comment">// Description: Commonly used proof rules (reflexivity, symmetry,</span>
<a name="l00025"></a>00025 <span class="comment">// transitivity, substitutivity, etc.).</span>
<a name="l00026"></a>00026 <span class="comment">//</span>
<a name="l00027"></a>00027 <span class="comment">// Normally, proof rule interfaces belong to their decision</span>
<a name="l00028"></a>00028 <span class="comment">// procedures. However, in the case of equational logic, the rules</span>
<a name="l00029"></a>00029 <span class="comment">// are so useful, that even some basic classes like Transformer use</span>
<a name="l00030"></a>00030 <span class="comment">// these rules under the hood. Therefore, it is made public, and its</span>
<a name="l00031"></a>00031 <span class="comment">// implementation is provided by the 'theorem' module.</span><span class="comment"></span>
<a name="l00032"></a>00032 <span class="comment">///////////////////////////////////////////////////////////////////////////////</span>
<a name="l00033"></a>00033 <span class="comment"></span>
<a name="l00034"></a>00034 <span class="preprocessor">#ifndef _cvc3__common_proof_rules_h_</span>
<a name="l00035"></a>00035 <span class="preprocessor"></span><span class="preprocessor">#define _cvc3__common_proof_rules_h_</span>
<a name="l00036"></a>00036 <span class="preprocessor"></span>
<a name="l00037"></a>00037 <span class="preprocessor">#include <vector></span>
<a name="l00038"></a>00038
<a name="l00039"></a>00039 <span class="keyword">namespace </span>CVC3 {
<a name="l00040"></a>00040
<a name="l00041"></a>00041 <span class="keyword">class </span>Theorem;
<a name="l00042"></a>00042 <span class="keyword">class </span>Theorem3;
<a name="l00043"></a>00043 <span class="keyword">class </span>Expr;
<a name="l00044"></a>00044 <span class="keyword">class </span>Op;
<a name="l00045"></a>00045
<a name="l00046"></a><a class="code" href="classCVC3_1_1CommonProofRules.html">00046</a> <span class="keyword">class </span><a class="code" href="classCVC3_1_1CommonProofRules.html">CommonProofRules</a> {
<a name="l00047"></a>00047 <span class="keyword">public</span>:<span class="comment"></span>
<a name="l00048"></a>00048 <span class="comment"> //! Destructor</span>
<a name="l00049"></a><a class="code" href="classCVC3_1_1CommonProofRules.html#a334ad50333e9323968df2bc286de7a8f">00049</a> <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1CommonProofRules.html#a334ad50333e9323968df2bc286de7a8f" title="Destructor.">~CommonProofRules</a>() { }
<a name="l00050"></a>00050 <span class="comment"></span>
<a name="l00051"></a>00051 <span class="comment"> ////////////////////////////////////////////////////////////////////////</span>
<a name="l00052"></a>00052 <span class="comment"></span> <span class="comment">// TCC rules (3-valued logic)</span><span class="comment"></span>
<a name="l00053"></a>00053 <span class="comment"> ////////////////////////////////////////////////////////////////////////</span>
<a name="l00054"></a>00054 <span class="comment"></span>
<a name="l00055"></a>00055 <span class="comment">// G1 |- phi G2 |- D_phi</span>
<a name="l00056"></a>00056 <span class="comment">// -------------------------</span>
<a name="l00057"></a>00057 <span class="comment">// G1,G2 |-_3 phi</span><span class="comment"></span>
<a name="l00058"></a>00058 <span class="comment"> /*!</span>
<a name="l00059"></a>00059 <span class="comment"> * @brief Convert 2-valued formula to 3-valued by discharging its</span>
<a name="l00060"></a>00060 <span class="comment"> * TCC (\f$D_\phi\f$):</span>
<a name="l00061"></a>00061 <span class="comment"> * \f[\frac{\Gamma_1\vdash_2 \phi\quad \Gamma_2\vdash_2 D_{\phi}}</span>
<a name="l00062"></a>00062 <span class="comment"> * {\Gamma_1,\,\Gamma_2\vdash_3\phi}\f]</span>
<a name="l00063"></a>00063 <span class="comment"> */</span>
<a name="l00064"></a>00064 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem3.html" title="Theorem3.">Theorem3</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a758fe978ff00099419c459914a0af5ba" title="Convert 2-valued formula to 3-valued by discharging its TCC ( ): .">queryTCC</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& phi, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& D_phi) = 0;
<a name="l00065"></a>00065
<a name="l00066"></a>00066 <span class="comment">// G0,a1,...,an |-_3 phi G1 |- D_a1 ... Gn |- D_an</span>
<a name="l00067"></a>00067 <span class="comment">// -------------------------------------------------</span>
<a name="l00068"></a>00068 <span class="comment">// G0,G1,...,Gn |-_3 (a1 & ... & an) -> phi</span><span class="comment"></span>
<a name="l00069"></a>00069 <span class="comment"> /*!</span>
<a name="l00070"></a>00070 <span class="comment"> * @brief 3-valued implication introduction rule:</span>
<a name="l00071"></a>00071 <span class="comment"> * \f[\frac{\Gamma_0,\,\alpha_1\,\ldots,\,\alpha_n\vdash_3\phi\quad</span>
<a name="l00072"></a>00072 <span class="comment"> * (\Gamma_i\vdash D_{\alpha_i})_{i\in[1..n]}}</span>
<a name="l00073"></a>00073 <span class="comment"> * {\Gamma_0,\,\Gamma_1, \ldots, \Gamma_n\vdash_3</span>
<a name="l00074"></a>00074 <span class="comment"> * (\bigwedge_{i=1}^n\alpha_i)\to\phi}\f]</span>
<a name="l00075"></a>00075 <span class="comment"> *</span>
<a name="l00076"></a>00076 <span class="comment"> * \param phi is the formula \f$\phi\f$</span>
<a name="l00077"></a>00077 <span class="comment"> * \param assump is the vector of assumptions \f$\alpha_1\ldots\alpha_n\f$</span>
<a name="l00078"></a>00078 <span class="comment"> * \param tccs is the vector of TCCs for assumptions</span>
<a name="l00079"></a>00079 <span class="comment"> * \f$D_{\alpha_1}\ldots D_{\alpha_n}\f$</span>
<a name="l00080"></a>00080 <span class="comment"> */</span>
<a name="l00081"></a>00081 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem3.html" title="Theorem3.">Theorem3</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#afe561cfd6d5ee752fbc1c3cafe9b68a5" title="3-valued implication introduction rule: ">implIntro3</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem3.html" title="Theorem3.">Theorem3</a>& phi,
<a name="l00082"></a>00082 <span class="keyword">const</span> std::vector<Expr>& assump,
<a name="l00083"></a>00083 <span class="keyword">const</span> std::vector<Theorem>& tccs) = 0;
<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">// Common 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">// ==> u:a |- a</span><span class="comment"></span>
<a name="l00090"></a>00090 <span class="comment"> //! \f[\frac{}{a\vdash a}\f]</span>
<a name="l00091"></a>00091 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#ab4527c48e9f88d94d7ca076757a6f3ba">assumpRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& a, <span class="keywordtype">int</span> scope = -1) = 0;
<a name="l00092"></a>00092
<a name="l00093"></a>00093 <span class="comment">// ==> a == a or ==> a IFF a</span><span class="comment"></span>
<a name="l00094"></a>00094 <span class="comment"> //! \f[\frac{}{a = a}\quad or \quad\frac{}{a \Leftrightarrow a}\f]</span>
<a name="l00095"></a>00095 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a61c1fe56b4ed9744006883a7784ddb71">reflexivityRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& a) = 0;
<a name="l00096"></a>00096 <span class="comment"></span>
<a name="l00097"></a>00097 <span class="comment"> //! ==> (a == a) IFF TRUE</span>
<a name="l00098"></a>00098 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#ad078b5d25129b200fe04b20c5962aa34" title="==> (a == a) IFF TRUE">rewriteReflexivity</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& a_eq_a) = 0;
<a name="l00099"></a>00099
<a name="l00100"></a>00100 <span class="comment">// a1 == a2 ==> a2 == a1 (same for IFF)</span><span class="comment"></span>
<a name="l00101"></a>00101 <span class="comment"> //! \f[\frac{a_1=a_2}{a_2=a_1}\f] (same for IFF)</span>
<a name="l00102"></a>00102 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a0a87e88508f49b73037e0024afa841bf" title=" (same for IFF)">symmetryRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& a1_eq_a2) = 0;
<a name="l00103"></a>00103
<a name="l00104"></a>00104 <span class="comment">// ==> (a1 == a2) IFF (a2 == a1)</span><span class="comment"></span>
<a name="l00105"></a>00105 <span class="comment"> //! \f[\frac{}{(a_1=a_2)\Leftrightarrow (a_2=a_1)}\f]</span>
<a name="l00106"></a>00106 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a338cafc978d9b6a447e8d58af42d7e5b">rewriteUsingSymmetry</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& a1_eq_a2) = 0;
<a name="l00107"></a>00107
<a name="l00108"></a>00108 <span class="comment">// (a1 == a2) & (a2 == a3) ==> (a1 == a3) [same for IFF]</span><span class="comment"></span>
<a name="l00109"></a>00109 <span class="comment"> //! \f[\frac{a_1=a_2\quad a_2=a_3}{a_1=a_3}\f] (same for IFF)</span>
<a name="l00110"></a>00110 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a4a4e90cd69ce24e83ba2c217907c277a" title=" (same for IFF)">transitivityRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& a1_eq_a2,
<a name="l00111"></a>00111 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& a2_eq_a3) = 0;
<a name="l00112"></a>00112 <span class="comment"></span>
<a name="l00113"></a>00113 <span class="comment"> //! Optimized case for expr with one child</span>
<a name="l00114"></a>00114 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a776c827bb6e3b889234429c49ae9ad6f" title="Optimized case for expr with one child.">substitutivityRule</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_1Theorem.html">Theorem</a>& thm) = 0;
<a name="l00115"></a>00115 <span class="comment"></span>
<a name="l00116"></a>00116 <span class="comment"> //! Optimized case for expr with two children</span>
<a name="l00117"></a>00117 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a776c827bb6e3b889234429c49ae9ad6f" title="Optimized case for expr with one child.">substitutivityRule</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_1Theorem.html">Theorem</a>& thm1,
<a name="l00118"></a>00118 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm2) = 0;
<a name="l00119"></a>00119
<a name="l00120"></a>00120 <span class="comment">// (c_1 == d_1) & ... & (c_n == d_n)</span>
<a name="l00121"></a>00121 <span class="comment">// ==> op(c_1,...,c_n) == op(d_1,...,d_n)</span><span class="comment"></span>
<a name="l00122"></a>00122 <span class="comment"> /*! @brief </span>
<a name="l00123"></a>00123 <span class="comment"> \f[\frac{(c_1=d_1)\wedge\ldots\wedge(c_n=d_n)}</span>
<a name="l00124"></a>00124 <span class="comment"> {op(c_1,\ldots,c_n)=op(d_1,\ldots,d_n)}\f]</span>
<a name="l00125"></a>00125 <span class="comment"> */</span>
<a name="l00126"></a>00126 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a776c827bb6e3b889234429c49ae9ad6f" title="Optimized case for expr with one child.">substitutivityRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Op.html">Op</a>& op,
<a name="l00127"></a>00127 <span class="keyword">const</span> std::vector<Theorem>& thms) = 0;
<a name="l00128"></a>00128
<a name="l00129"></a>00129 <span class="comment">// (c_1 == d_1) & ... & (c_n == d_n)</span>
<a name="l00130"></a>00130 <span class="comment">// ==> op(c_1,...,c_n) == op(d_1,...,d_n)</span><span class="comment"></span>
<a name="l00131"></a>00131 <span class="comment"> /*! @brief </span>
<a name="l00132"></a>00132 <span class="comment"> \f[\frac{(c_1=d_1)\wedge\ldots\wedge(c_n=d_n)}</span>
<a name="l00133"></a>00133 <span class="comment"> {op(c_1,\ldots,c_n)=op(d_1,\ldots,d_n)}\f]</span>
<a name="l00134"></a>00134 <span class="comment"> except that only those arguments are given that \f$c_i\not=d_i\f$.</span>
<a name="l00135"></a>00135 <span class="comment"> \param e is the original expression \f$op(c_1,\ldots,c_n)\f$.</span>
<a name="l00136"></a>00136 <span class="comment"> \param changed is the vector of indices of changed kids</span>
<a name="l00137"></a>00137 <span class="comment"> \param thms are the theorems \f$c_i=d_i\f$ for the changed kids.</span>
<a name="l00138"></a>00138 <span class="comment"> */</span>
<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_1CommonProofRules.html#a776c827bb6e3b889234429c49ae9ad6f" title="Optimized case for expr with one child.">substitutivityRule</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">const</span> std::vector<unsigned>& changed,
<a name="l00141"></a>00141 <span class="keyword">const</span> std::vector<Theorem>& thms) = 0;
<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_1CommonProofRules.html#a776c827bb6e3b889234429c49ae9ad6f" title="Optimized case for expr with one child.">substitutivityRule</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> <span class="keywordtype">int</span> changed, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm) = 0;
<a name="l00143"></a>00143
<a name="l00144"></a>00144 <span class="comment">// |- e, |- !e ==> |- FALSE</span><span class="comment"></span>
<a name="l00145"></a>00145 <span class="comment"> /*! @brief</span>
<a name="l00146"></a>00146 <span class="comment"> \f[\frac{\Gamma_1\vdash e\quad\Gamma_2\vdash \neg e}</span>
<a name="l00147"></a>00147 <span class="comment"> {\Gamma_1\cup\Gamma_2\vdash \mathrm{FALSE}}</span>
<a name="l00148"></a>00148 <span class="comment"> \f]</span>
<a name="l00149"></a>00149 <span class="comment"> */</span>
<a name="l00150"></a>00150 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a1074822d52c22daacaa78b34ac0635ba">contradictionRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e,
<a name="l00151"></a>00151 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& not_e) = 0;
<a name="l00152"></a>00152
<a name="l00153"></a>00153 <span class="comment">// |- e OR !e</span>
<a name="l00154"></a>00154 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#aec56ab0fbac82267ff202ae328fe801f">excludedMiddle</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00155"></a>00155
<a name="l00156"></a>00156 <span class="comment">// e ==> e IFF TRUE</span><span class="comment"></span>
<a name="l00157"></a>00157 <span class="comment"> //! \f[\frac{\Gamma\vdash e}{\Gamma\vdash e\Leftrightarrow\mathrm{TRUE}}\f]</span>
<a name="l00158"></a>00158 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#ae5a0a67c59ba15d84e900fdccc7653ca">iffTrue</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e) = 0;
<a name="l00159"></a>00159
<a name="l00160"></a>00160 <span class="comment">// e ==> !e IFF FALSE</span><span class="comment"></span>
<a name="l00161"></a>00161 <span class="comment"> //! \f[\frac{\Gamma\vdash e}{\Gamma\vdash\neg e\Leftrightarrow\mathrm{FALSE}}\f]</span>
<a name="l00162"></a>00162 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a5a56b6f9544841fe86255e5bc35e8449">iffNotFalse</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e) = 0;
<a name="l00163"></a>00163
<a name="l00164"></a>00164 <span class="comment">// e IFF TRUE ==> e</span><span class="comment"></span>
<a name="l00165"></a>00165 <span class="comment"> //! \f[\frac{\Gamma\vdash e\Leftrightarrow\mathrm{TRUE}}{\Gamma\vdash e}\f]</span>
<a name="l00166"></a>00166 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#ad2edb920405666bf6e9d21ae496ff6b3">iffTrueElim</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e) = 0;
<a name="l00167"></a>00167
<a name="l00168"></a>00168 <span class="comment">// e IFF FALSE ==> !e</span><span class="comment"></span>
<a name="l00169"></a>00169 <span class="comment"> //! \f[\frac{\Gamma\vdash e\Leftrightarrow\mathrm{FALSE}}{\Gamma\vdash\neg e}\f]</span>
<a name="l00170"></a>00170 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a11b56754024b56844336954cf789a63a">iffFalseElim</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e) = 0;
<a name="l00171"></a>00171 <span class="comment"></span>
<a name="l00172"></a>00172 <span class="comment"> //! e1 <=> e2 ==> ~e1 <=> ~e2</span>
<a name="l00173"></a>00173 <span class="comment"></span><span class="comment"> /*! \f[\frac{\Gamma\vdash e_1\Leftrightarrow e_2}</span>
<a name="l00174"></a>00174 <span class="comment"> * {\Gamma\vdash\sim e_1\Leftrightarrow\sim e_2}\f]</span>
<a name="l00175"></a>00175 <span class="comment"> * Where ~e is the <em>inverse</em> of e (that is, ~(!e') = e').</span>
<a name="l00176"></a>00176 <span class="comment"> */</span>
<a name="l00177"></a>00177 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#af38f25446a561384c3de66392c4d3544" title="e1 <=> e2 ==> ~e1 <=> ~e2">iffContrapositive</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm) = 0;
<a name="l00178"></a>00178
<a name="l00179"></a>00179 <span class="comment">// !!e ==> e</span><span class="comment"></span>
<a name="l00180"></a>00180 <span class="comment"> //! \f[\frac{\Gamma\vdash\neg\neg e}{\Gamma\vdash e}\f]</span>
<a name="l00181"></a>00181 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#ace6786234994faf89bc1b0ac8575278a">notNotElim</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& not_not_e) = 0;
<a name="l00182"></a>00182
<a name="l00183"></a>00183 <span class="comment">// e1 AND (e1 IFF e2) ==> e2</span><span class="comment"></span>
<a name="l00184"></a>00184 <span class="comment"> /*! @brief</span>
<a name="l00185"></a>00185 <span class="comment"> \f[\frac{\Gamma_1\vdash e_1\quad \Gamma_2\vdash(e_1\Leftrightarrow e_2)}</span>
<a name="l00186"></a>00186 <span class="comment"> {\Gamma_1\cup\Gamma_2\vdash e_2}</span>
<a name="l00187"></a>00187 <span class="comment"> \f]</span>
<a name="l00188"></a>00188 <span class="comment"> */</span>
<a name="l00189"></a>00189 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#aebbcd4a194e4fdca0bcd16143fb03a75">iffMP</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e1_iff_e2) = 0;
<a name="l00190"></a>00190
<a name="l00191"></a>00191 <span class="comment">// e1 AND (e1 IMPLIES e2) ==> e2</span><span class="comment"></span>
<a name="l00192"></a>00192 <span class="comment"> /*! @brief</span>
<a name="l00193"></a>00193 <span class="comment"> \f[\frac{\Gamma_1\vdash e_1\quad \Gamma_2\vdash(e_1\Rightarrow e_2)}</span>
<a name="l00194"></a>00194 <span class="comment"> {\Gamma_1\cup\Gamma_2\vdash e_2}</span>
<a name="l00195"></a>00195 <span class="comment"> \f]</span>
<a name="l00196"></a>00196 <span class="comment"> */</span>
<a name="l00197"></a>00197 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a86416b3ccec1ddf1ce534b53d6af1ec9">implMP</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e1_impl_e2) = 0;
<a name="l00198"></a>00198
<a name="l00199"></a>00199 <span class="comment">// AND(e_1,...e_n) ==> e_i</span><span class="comment"></span>
<a name="l00200"></a>00200 <span class="comment"> //! \f[\frac{\vdash e_1\wedge\cdots\wedge e_n}{\vdash e_i}\f]</span>
<a name="l00201"></a>00201 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a3f3592ac74d0aa0caa3b9224ea7e61f4">andElim</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e, <span class="keywordtype">int</span> i) = 0;
<a name="l00202"></a>00202
<a name="l00203"></a>00203 <span class="comment">// e1, e2 ==> AND(e1, e2)</span><span class="comment"></span>
<a name="l00204"></a>00204 <span class="comment"> /*! @brief</span>
<a name="l00205"></a>00205 <span class="comment"> \f[\frac{\Gamma_1\vdash e_1\quad \Gamma_2\vdash e_2}</span>
<a name="l00206"></a>00206 <span class="comment"> {\Gamma_1\cup\Gamma_2\vdash e_1\wedge e_2}</span>
<a name="l00207"></a>00207 <span class="comment"> \f]</span>
<a name="l00208"></a>00208 <span class="comment"> */</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_1CommonProofRules.html#a4aa193bfeb969c96b63db39a70470015">andIntro</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e1, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e2) = 0;
<a name="l00210"></a>00210
<a name="l00211"></a>00211 <span class="comment">// e1, ..., en ==> AND(e1, ..., en)</span><span class="comment"></span>
<a name="l00212"></a>00212 <span class="comment"> /*! @brief</span>
<a name="l00213"></a>00213 <span class="comment"> \f[\frac{\Gamma_1\vdash e_1\quad \cdots \quad\Gamma_n\vdash e_n}</span>
<a name="l00214"></a>00214 <span class="comment"> {\bigcup_{i=1}^n\Gamma_i\vdash \bigwedge_{i=1}^n e_i}</span>
<a name="l00215"></a>00215 <span class="comment"> \f]</span>
<a name="l00216"></a>00216 <span class="comment"> */</span>
<a name="l00217"></a>00217 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a4aa193bfeb969c96b63db39a70470015">andIntro</a>(<span class="keyword">const</span> std::vector<Theorem>& es) = 0;
<a name="l00218"></a>00218
<a name="l00219"></a>00219 <span class="comment">// G,a1,...,an |- phi</span>
<a name="l00220"></a>00220 <span class="comment">// -------------------------------------------------</span>
<a name="l00221"></a>00221 <span class="comment">// G |- (a1 & ... & an) -> phi</span><span class="comment"></span>
<a name="l00222"></a>00222 <span class="comment"> /*!</span>
<a name="l00223"></a>00223 <span class="comment"> * @brief Implication introduction rule:</span>
<a name="l00224"></a>00224 <span class="comment"> * \f[\frac{\Gamma,\,\alpha_1\,\ldots,\,\alpha_n\vdash\phi}</span>
<a name="l00225"></a>00225 <span class="comment"> * {\Gamma\vdash(\bigwedge_{i=1}^n\alpha_i)\to\phi}\f]</span>
<a name="l00226"></a>00226 <span class="comment"> *</span>
<a name="l00227"></a>00227 <span class="comment"> * \param phi is the formula \f$\phi\f$</span>
<a name="l00228"></a>00228 <span class="comment"> * \param assump is the vector of assumptions \f$\alpha_1\ldots\alpha_n\f$</span>
<a name="l00229"></a>00229 <span class="comment"> */</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_1CommonProofRules.html#a9292e13acd4b5ba2b215864022a22573" title="Implication introduction rule: .">implIntro</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& phi,
<a name="l00231"></a>00231 <span class="keyword">const</span> std::vector<Expr>& assump) = 0;
<a name="l00232"></a>00232 <span class="comment"></span>
<a name="l00233"></a>00233 <span class="comment"> //! e1 => e2 ==> ~e2 => ~e1</span>
<a name="l00234"></a>00234 <span class="comment"></span><span class="comment"> /*! \f[\frac{\Gamma\vdash e_1\Rightarrow e_2}</span>
<a name="l00235"></a>00235 <span class="comment"> * {\Gamma\vdash\sim e_2\Rightarrow\sim e_1}\f]</span>
<a name="l00236"></a>00236 <span class="comment"> * Where ~e is the <em>inverse</em> of e (that is, ~(!e') = e').</span>
<a name="l00237"></a>00237 <span class="comment"> */</span>
<a name="l00238"></a>00238 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a69da48e244e1674f6b501ac4ef168feb" title="e1 => e2 ==> ~e2 => ~e1">implContrapositive</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm) = 0;
<a name="l00239"></a>00239 <span class="comment"></span>
<a name="l00240"></a>00240 <span class="comment"> //! ==> ITE(TRUE, e1, e2) == e1</span>
<a name="l00241"></a>00241 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a0e770e47e947275a69b4c9f225f8beb6" title="==> ITE(TRUE, e1, e2) == e1">rewriteIteTrue</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;<span class="comment"></span>
<a name="l00242"></a>00242 <span class="comment"> //! ==> ITE(FALSE, e1, e2) == e2</span>
<a name="l00243"></a>00243 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a95af3ce5ccd4212b15bac9b249004c48" title="==> ITE(FALSE, e1, e2) == e2">rewriteIteFalse</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;<span class="comment"></span>
<a name="l00244"></a>00244 <span class="comment"> //! ==> ITE(c, e, e) == e</span>
<a name="l00245"></a>00245 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a6cb02a9489ef5ed4e548f49bbd07439f" title="==> ITE(c, e, e) == e">rewriteIteSame</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00246"></a>00246
<a name="l00247"></a>00247 <span class="comment">// NOT e ==> e IFF FALSE</span><span class="comment"></span>
<a name="l00248"></a>00248 <span class="comment"> //! \f[\frac{\vdash\neg e}{\vdash e\Leftrightarrow\mathrm{FALSE}}\f]</span>
<a name="l00249"></a>00249 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a34064eea86afa953b9229537b075a420">notToIff</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& not_e) = 0;
<a name="l00250"></a>00250
<a name="l00251"></a>00251 <span class="comment">// e1 XOR e2 ==> e1 IFF (NOT e2)</span><span class="comment"></span>
<a name="l00252"></a>00252 <span class="comment"> //! \f[\frac{\vdash e_1 XOR e_2}{\vdash e_1\Leftrightarrow(\neg e_2)}\f]</span>
<a name="l00253"></a>00253 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#ae25f68b7cceeeb25b41b1d2bcb1df8f3">xorToIff</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00254"></a>00254 <span class="comment"></span>
<a name="l00255"></a>00255 <span class="comment"> //! ==> (e1 <=> e2) <=> [simplified expr]</span>
<a name="l00256"></a>00256 <span class="comment"></span><span class="comment"> /*! Rewrite formulas like FALSE/TRUE <=> e, e <=> NOT e, etc. */</span>
<a name="l00257"></a>00257 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a5c50bf251b95dfc47ccfc6e8b51426c1" title="==> (e1 <=> e2) <=> [simplified expr]">rewriteIff</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00258"></a>00258
<a name="l00259"></a>00259 <span class="comment">// AND and OR rewrites check for TRUE and FALSE arguments and</span>
<a name="l00260"></a>00260 <span class="comment">// remove them or collapse the entire expression to TRUE and FALSE</span>
<a name="l00261"></a>00261 <span class="comment">// appropriately</span>
<a name="l00262"></a>00262 <span class="comment"></span>
<a name="l00263"></a>00263 <span class="comment"> //! ==> AND(e1,e2) IFF [simplified expr]</span>
<a name="l00264"></a>00264 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#afb2ae30738c04b088459281d259a6d3a" title="==> AND(e1,e2) IFF [simplified expr]">rewriteAnd</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00265"></a>00265 <span class="comment"></span>
<a name="l00266"></a>00266 <span class="comment"> //! ==> OR(e1,...,en) IFF [simplified expr]</span>
<a name="l00267"></a>00267 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#aa3cfb7d47a6d6bc84c85c7fa6a3e1242" title="==> OR(e1,...,en) IFF [simplified expr]">rewriteOr</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00268"></a>00268 <span class="comment"></span>
<a name="l00269"></a>00269 <span class="comment"> //! ==> NOT TRUE IFF FALSE</span>
<a name="l00270"></a>00270 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#ad55b11590196fbd73d24daa1d0d6eeb1" title="==> NOT TRUE IFF FALSE">rewriteNotTrue</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00271"></a>00271 <span class="comment"></span>
<a name="l00272"></a>00272 <span class="comment"> //! ==> NOT FALSE IFF TRUE</span>
<a name="l00273"></a>00273 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a30fa79637f4308e8e733015624293775" title="==> NOT FALSE IFF TRUE">rewriteNotFalse</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00274"></a>00274 <span class="comment"></span>
<a name="l00275"></a>00275 <span class="comment"> //! ==> NOT NOT e IFF e, takes !!e</span>
<a name="l00276"></a>00276 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a8a04ff29591a019d4d4cf073c0987316" title="==> NOT NOT e IFF e, takes !!e">rewriteNotNot</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00277"></a>00277 <span class="comment"></span>
<a name="l00278"></a>00278 <span class="comment"> //! ==> NOT FORALL (vars): e IFF EXISTS (vars) NOT e</span>
<a name="l00279"></a>00279 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#ad14f0ceb0d486ba3d78c2c3c6e47382a" title="==> NOT FORALL (vars): e IFF EXISTS (vars) NOT e">rewriteNotForall</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& forallExpr) = 0;
<a name="l00280"></a>00280 <span class="comment"></span>
<a name="l00281"></a>00281 <span class="comment"> //! ==> NOT EXISTS (vars): e IFF FORALL (vars) NOT e</span>
<a name="l00282"></a>00282 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a12d8ca9f5547fb3a3239d7dc6f53987c" title="==> NOT EXISTS (vars): e IFF FORALL (vars) NOT e">rewriteNotExists</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& existsExpr) = 0;
<a name="l00283"></a>00283
<a name="l00284"></a>00284 <span class="comment">//From expr EXISTS(x1: t1, ..., xn: tn) phi(x1,...,cn)</span>
<a name="l00285"></a>00285 <span class="comment">//we create phi(c1,...,cn) where ci is a skolem constant</span>
<a name="l00286"></a>00286 <span class="comment">//defined by the original expression and the index i.</span>
<a name="l00287"></a>00287 <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_1CommonProofRules.html#a015539886185195ba5d98c60cd7e8f66">skolemize</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00288"></a>00288 <span class="comment"></span>
<a name="l00289"></a>00289 <span class="comment"> /*! skolem rewrite rule: Introduces axiom |- Exists(x) phi(x) <=> phi(c)</span>
<a name="l00290"></a>00290 <span class="comment"> * where c is a constant defined by the expression Exists(x) phi(x)</span>
<a name="l00291"></a>00291 <span class="comment"> */</span>
<a name="l00292"></a>00292 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a8a2561e9e4763460c65dbebe10d2f281">skolemizeRewrite</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00293"></a>00293 <span class="comment"></span>
<a name="l00294"></a>00294 <span class="comment"> //! Special version of skolemizeRewrite for "EXISTS x. t = x"</span>
<a name="l00295"></a>00295 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a4013a795d82cebb8b60ed67c094a7cba" title="Special version of skolemizeRewrite for "EXISTS x. t = x".">skolemizeRewriteVar</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00296"></a>00296 <span class="comment"></span>
<a name="l00297"></a>00297 <span class="comment"> //! |- EXISTS x. e = x</span>
<a name="l00298"></a>00298 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#aab746efc9d013643bccc065affa82992" title="|- EXISTS x. e = x">varIntroRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00299"></a>00299 <span class="comment"></span>
<a name="l00300"></a>00300 <span class="comment"> /*! @brief If thm is (EXISTS x: phi(x)), create the Skolemized version</span>
<a name="l00301"></a>00301 <span class="comment"> and add it to the database. Otherwise returns just thm. */</span><span class="comment"></span>
<a name="l00302"></a>00302 <span class="comment"> /*!</span>
<a name="l00303"></a>00303 <span class="comment"> * \param thm is the Theorem(EXISTS x: phi(x))</span>
<a name="l00304"></a>00304 <span class="comment"> */</span>
<a name="l00305"></a>00305 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a015539886185195ba5d98c60cd7e8f66">skolemize</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm) = 0;
<a name="l00306"></a>00306 <span class="comment"></span>
<a name="l00307"></a>00307 <span class="comment"> //! Retrun a theorem "|- e = v" for a new Skolem constant v</span>
<a name="l00308"></a>00308 <span class="comment"></span><span class="comment"> /*!</span>
<a name="l00309"></a>00309 <span class="comment"> * This is equivalent to skolemize(d_core->varIntroRule(e)), only more</span>
<a name="l00310"></a>00310 <span class="comment"> * efficient.</span>
<a name="l00311"></a>00311 <span class="comment"> */</span>
<a name="l00312"></a>00312 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a10fa187373ec24079c10874d8e804ecb" title="Retrun a theorem "|- e = v" for a new Skolem constant v.">varIntroSkolem</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00313"></a>00313
<a name="l00314"></a>00314 <span class="comment">// Derived rules</span>
<a name="l00315"></a>00315 <span class="comment"></span>
<a name="l00316"></a>00316 <span class="comment"> //! ==> TRUE</span>
<a name="l00317"></a>00317 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a6e93694c76f7b567487bc8cae674ae5d" title="==> TRUE">trueTheorem</a>() = 0;
<a name="l00318"></a>00318 <span class="comment"></span>
<a name="l00319"></a>00319 <span class="comment"> //! AND(e1,e2) ==> [simplified expr]</span>
<a name="l00320"></a>00320 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#afb2ae30738c04b088459281d259a6d3a" title="==> AND(e1,e2) IFF [simplified expr]">rewriteAnd</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e) = 0;
<a name="l00321"></a>00321 <span class="comment"></span>
<a name="l00322"></a>00322 <span class="comment"> //! OR(e1,...,en) ==> [simplified expr]</span>
<a name="l00323"></a>00323 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#aa3cfb7d47a6d6bc84c85c7fa6a3e1242" title="==> OR(e1,...,en) IFF [simplified expr]">rewriteOr</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e) = 0;
<a name="l00324"></a>00324
<a name="l00325"></a>00325 <span class="comment">// TODO: do we really need this?</span>
<a name="l00326"></a>00326 <span class="keyword">virtual</span> std::vector<Theorem>& <a class="code" href="classCVC3_1_1CommonProofRules.html#ac773341edabcc5091ca25af74fcb7653">getSkolemAxioms</a>() = 0;
<a name="l00327"></a>00327
<a name="l00328"></a>00328 <span class="comment">//TODO: do we need this?</span>
<a name="l00329"></a>00329 <span class="keyword">virtual</span> <span class="keywordtype">void</span> <a class="code" href="classCVC3_1_1CommonProofRules.html#a6f8068606f30fe7b2c405ddf5ce1a53b">clearSkolemAxioms</a>() = 0;
<a name="l00330"></a>00330
<a name="l00331"></a>00331 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a484540b067da205d23b2fe263662cda2">ackermann</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) = 0;
<a name="l00332"></a>00332
<a name="l00333"></a>00333 <span class="comment">// Given a propositional atom containing embedded ite's, lifts first ite condition</span>
<a name="l00334"></a>00334 <span class="comment">// to form a Boolean ITE</span>
<a name="l00335"></a>00335 <span class="comment">// |- P(...ite(a,b,c)...) <=> ite(a,P(...b...),P(...c...))</span>
<a name="l00336"></a>00336 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CommonProofRules.html#a893a258d9f7d49acb5c8a8b5b8ec39b0">liftOneITE</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e) = 0;
<a name="l00337"></a>00337
<a name="l00338"></a>00338 }; <span class="comment">// end of class CommonProofRules</span>
<a name="l00339"></a>00339
<a name="l00340"></a>00340 } <span class="comment">// end of namespace CVC3</span>
<a name="l00341"></a>00341
<a name="l00342"></a>00342 <span class="preprocessor">#endif</span>
</pre></div></div>
</div>
<hr class="footer"/><address class="footer"><small>Generated on Wed Sep 7 2011 for CVC3 by 
<a href="http://www.doxygen.org/index.html">
<img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.7.4 </small></address>
</body>
</html>
