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<a href="arith__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 arith_proof_rules.h</span>
<a name="l00004"></a>00004 <span class="comment"> * \brief 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_proof_rules_h_</span>
<a name="l00023"></a>00023 <span class="preprocessor"></span><span class="preprocessor">#define _cvc3__arith_proof_rules_h_</span>
<a name="l00024"></a>00024 <span class="preprocessor"></span>
<a name="l00025"></a>00025 <span class="preprocessor">#include <vector></span>
<a name="l00026"></a>00026
<a name="l00027"></a>00027 <span class="keyword">namespace </span>CVC3 {
<a name="l00028"></a>00028
<a name="l00029"></a>00029 <span class="keyword">class </span>Theorem;
<a name="l00030"></a>00030 <span class="keyword">class </span>Expr;
<a name="l00031"></a>00031 <span class="keyword">class </span>Rational;
<a name="l00032"></a>00032
<a name="l00033"></a><a class="code" href="classCVC3_1_1ArithProofRules.html">00033</a> <span class="keyword">class </span><a class="code" href="classCVC3_1_1ArithProofRules.html">ArithProofRules</a> {
<a name="l00034"></a>00034 <span class="keyword">public</span>:
<a name="l00035"></a>00035 <span class="comment">// Destructor</span>
<a name="l00036"></a><a class="code" href="classCVC3_1_1ArithProofRules.html#a410c697fc050feca9680a388397b0968">00036</a> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1ArithProofRules.html#a410c697fc050feca9680a388397b0968">~ArithProofRules</a>() { }
<a name="l00037"></a>00037 <span class="comment"></span>
<a name="l00038"></a>00038 <span class="comment"> ////////////////////////////////////////////////////////////////////</span>
<a name="l00039"></a>00039 <span class="comment"></span> <span class="comment">// Canonization rules</span><span class="comment"></span>
<a name="l00040"></a>00040 <span class="comment"> ////////////////////////////////////////////////////////////////////</span>
<a name="l00041"></a>00041 <span class="comment"></span><span class="comment"></span>
<a name="l00042"></a>00042 <span class="comment"> //! ==> e = 1 * e</span>
<a name="l00043"></a>00043 <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_1ArithProofRules.html#a8b8db5ad0a8d4968f429e98964db93c1" 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) = 0;
<a name="l00044"></a>00044 <span class="comment"></span>
<a name="l00045"></a>00045 <span class="comment"> //! ==> -(e) = (-1) * e</span>
<a name="l00046"></a>00046 <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_1ArithProofRules.html#aa95faca93e7b4a1cf21667ff88d390e4" 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) = 0;
<a name="l00047"></a>00047 <span class="comment"></span>
<a name="l00048"></a>00048 <span class="comment"> //! ==> x - y = x + (-1) * y</span>
<a name="l00049"></a>00049 <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_1ArithProofRules.html#a4319c532082c0f43794b34a2fb9df73f" 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) = 0;
<a name="l00050"></a>00050 <span class="comment"></span>
<a name="l00051"></a>00051 <span class="comment"> //! -(e) ==> e / (-1); takes 'e'</span>
<a name="l00052"></a>00052 <span class="comment"></span><span class="comment"> /*! Canon Rule for unary minus: it just converts it to division by</span>
<a name="l00053"></a>00053 <span class="comment"> * -1, the result is not yet canonical:</span>
<a name="l00054"></a>00054 <span class="comment"> */</span>
<a name="l00055"></a>00055 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a0053398d4a8fc49d9a2f8ede6949fc70">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) = 0;
<a name="l00056"></a>00056 <span class="comment"></span>
<a name="l00057"></a>00057 <span class="comment"> /**</span>
<a name="l00058"></a>00058 <span class="comment"> * Transform e = (SUM r t1 ... tn) @ 0 into (SUM t1 ... tn) @ -r. The first </span>
<a name="l00059"></a>00059 <span class="comment"> * sum term (r) must be a rational and t1 ... tn terms must be canonised.</span>
<a name="l00060"></a>00060 <span class="comment"> * </span>
<a name="l00061"></a>00061 <span class="comment"> * @param e the expression to transform</span>
<a name="l00062"></a>00062 <span class="comment"> * @return rewrite theorem representing the transformation </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_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a18e5970bc4f670a63ca5775750f099ab">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) = 0;
<a name="l00065"></a>00065 <span class="comment"></span>
<a name="l00066"></a>00066 <span class="comment"> //! (c) / d ==> (c/d), takes c and d</span>
<a name="l00067"></a>00067 <span class="comment"></span><span class="comment"> /*! Canon Rules for division by constant 'd' */</span>
<a name="l00068"></a>00068 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a79c759f2bb7dc41ed98c5962febef804" 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) = 0;<span class="comment"></span>
<a name="l00069"></a>00069 <span class="comment"> //! (c * x) / d ==> (c/d) * x, takes (c*x) and d</span>
<a name="l00070"></a>00070 <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_1ArithProofRules.html#aee487a2a1e8ce4c34075568eb70ea874" 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) = 0;<span class="comment"></span>
<a name="l00071"></a>00071 <span class="comment"> //! (+ c ...)/d ==> push division to all the coefficients.</span>
<a name="l00072"></a>00072 <span class="comment"></span><span class="comment"> /*! The result is not canonical, but canonizing the summands will</span>
<a name="l00073"></a>00073 <span class="comment"> * make it canonical.</span>
<a name="l00074"></a>00074 <span class="comment"> * Takes (+ c ...) and d</span>
<a name="l00075"></a>00075 <span class="comment"> */</span>
<a name="l00076"></a>00076 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a92846ee0cdab98d1759a13ff7e8d710d" 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) = 0;<span class="comment"></span>
<a name="l00077"></a>00077 <span class="comment"> //! x / d ==> (1/d) * x, takes x and d</span>
<a name="l00078"></a>00078 <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_1ArithProofRules.html#a4ab0351b340ecb82d6ced530e4f30510" 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>& e, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& d) = 0;
<a name="l00079"></a>00079
<a name="l00080"></a>00080 <span class="comment">// Canon Rules for multiplication</span>
<a name="l00081"></a>00081
<a name="l00082"></a>00082 <span class="comment">// TODO Deepak:</span>
<a name="l00083"></a>00083 <span class="comment">// e == t1 * t2 where t1 and t2 are canonized expressions, i.e. it can be a</span>
<a name="l00084"></a>00084 <span class="comment">// 1) Rational constant</span>
<a name="l00085"></a>00085 <span class="comment">// 2) Arithmetic Leaf (var or term from another theory)</span>
<a name="l00086"></a>00086 <span class="comment">// 3) (POW rational leaf)</span>
<a name="l00087"></a>00087 <span class="comment">// 4) (MULT rational mterm'_1 ...) where each mterm' is of type (2) or (3)</span>
<a name="l00088"></a>00088 <span class="comment">// 5) (PLUS rational sterm_1 sterm_2 ...) where each sterm is of </span>
<a name="l00089"></a>00089 <span class="comment">// type (2) or (3) or (4) </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_1ArithProofRules.html#aa38d5c06ebe0b672570641fe933cfedb">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) = 0;<span class="comment"></span>
<a name="l00091"></a>00091 <span class="comment"> //! Canonize (PLUS t1 ... tn)</span>
<a name="l00092"></a>00092 <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_1ArithProofRules.html#a225fe511e6f654f313048e86c1550510" 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) = 0;<span class="comment"></span>
<a name="l00093"></a>00093 <span class="comment"> //! Canonize (MULT t1 ... tn)</span>
<a name="l00094"></a>00094 <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_1ArithProofRules.html#aca910e6ff44389aac100b14b486c1942" title="Canonize (MULT t1 ... tn)">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) = 0;<span class="comment"></span>
<a name="l00095"></a>00095 <span class="comment"> //! ==> 1/e = e' where e' is canonical; takes e.</span>
<a name="l00096"></a>00096 <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_1ArithProofRules.html#a9a806d487932bbfa9a019d4d1eed1cea" 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) = 0;<span class="comment"></span>
<a name="l00097"></a>00097 <span class="comment"> //! Canonize t1/t2</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_1ArithProofRules.html#a198b0b44145b8e33555ffd212f43b7b3" title="Canonize t1/t2.">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) = 0;
<a name="l00099"></a>00099 <span class="comment"></span>
<a name="l00100"></a>00100 <span class="comment"> //! t*c ==> c*t, takes constant c and term t</span>
<a name="l00101"></a>00101 <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_1ArithProofRules.html#a11870b90dbfcc61d2b9a2820df7f6057" 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) = 0;<span class="comment"></span>
<a name="l00102"></a>00102 <span class="comment"> //! t1*t2 ==> Error, takes t1 and t2 where both are non-constants</span>
<a name="l00103"></a>00103 <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_1ArithProofRules.html#a8b9abf99f0b013714eaaa49e81a618b9" 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) = 0;<span class="comment"></span>
<a name="l00104"></a>00104 <span class="comment"> //! 0*t ==> 0, takes 0*t</span>
<a name="l00105"></a>00105 <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_1ArithProofRules.html#aae559b4d1558fecba5621c9ba27daa88" 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) = 0;<span class="comment"></span>
<a name="l00106"></a>00106 <span class="comment"> //! 1*t ==> t, takes 1*t</span>
<a name="l00107"></a>00107 <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_1ArithProofRules.html#a87f9a39ecb1bec46adff5187bc899726" 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) = 0;<span class="comment"></span>
<a name="l00108"></a>00108 <span class="comment"> //! c1*c2 ==> c', takes constant c1*c2 </span>
<a name="l00109"></a>00109 <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_1ArithProofRules.html#a71be38a9fa2d89e147ac4fde35c49e21" 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) = 0;<span class="comment"></span>
<a name="l00110"></a>00110 <span class="comment"> //! c1*(c2*t) ==> c'*t, takes c1 and c2 and t</span>
<a name="l00111"></a>00111 <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>
<a name="l00112"></a>00112 <a class="code" href="classCVC3_1_1ArithProofRules.html#a96b1cb83272cf80c2de663de429e6a15" 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) = 0;<span class="comment"></span>
<a name="l00113"></a>00113 <span class="comment"> //! c1*(+ c2 v1 ...) ==> (+ c' c1v1 ...), takes c1 and the sum</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_1ArithProofRules.html#a978068749de266dbbba2000d9e0c3d39" 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) = 0;<span class="comment"></span>
<a name="l00115"></a>00115 <span class="comment"> //! c^n = c' (compute the constant power expression)</span>
<a name="l00116"></a>00116 <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_1ArithProofRules.html#a999f13a6fa4a6d8cbe97f02f93fc9ed3" 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>) = 0;
<a name="l00117"></a>00117
<a name="l00118"></a>00118 <span class="comment">// Rules for addition</span><span class="comment"></span>
<a name="l00119"></a>00119 <span class="comment"> //! flattens the input. accepts a PLUS expr</span>
<a name="l00120"></a>00120 <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_1ArithProofRules.html#af0f4877d7326a53faec76bef54a3d400" 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) = 0;
<a name="l00121"></a>00121 <span class="comment"></span>
<a name="l00122"></a>00122 <span class="comment"> //! combine like terms. accepts a flattened PLUS expr</span>
<a name="l00123"></a>00123 <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_1ArithProofRules.html#a1da0c47c02ff2392ca3e0b6493ac4823" 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) = 0;
<a name="l00124"></a>00124
<a name="l00125"></a>00125 <span class="comment">// 0 = (* e1 e2 ...) <=> 0 = e1 OR 0 = e2 OR ...</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_1ArithProofRules.html#af8f4f59bd12fdd8f93d1fd49ae41279e">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) = 0;
<a name="l00127"></a>00127
<a name="l00128"></a>00128 <span class="comment">// 0 = (^ c x) <=> false if c <=0</span>
<a name="l00129"></a>00129 <span class="comment">// <=> 0 = x if c > 0</span>
<a name="l00130"></a>00130 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#af17a5dbf4ebbe9d7e46d63ad1284ddaf">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) = 0;
<a name="l00131"></a>00131
<a name="l00132"></a>00132 <span class="comment">// x^n = y^n <=> x = y (if n is odd)</span>
<a name="l00133"></a>00133 <span class="comment">// x^n = y^n <=> x = y OR x = -y (if n is even)</span>
<a name="l00134"></a>00134 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a0e6f19ba5333f667efa3a0e3d8787775">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) = 0;
<a name="l00135"></a>00135
<a name="l00136"></a>00136 <span class="comment">// x^n = c <=> x = root (if n is odd and root^n = c)</span>
<a name="l00137"></a>00137 <span class="comment">// x^n = c <=> x = root OR x = -root (if n is even and root^n = c)</span>
<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_1ArithProofRules.html#a0e240fba4eac33522b24be6581d98346">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) = 0;
<a name="l00139"></a>00139
<a name="l00140"></a>00140 <span class="comment">// x^n = c <=> false (if n is even and c is negative)</span>
<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_1ArithProofRules.html#a80f948f405f0b1a88283c97b70aab43e">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) = 0;
<a name="l00142"></a>00142
<a name="l00143"></a>00143 <span class="comment">// x^n = c <=> false (if x is an integer and c is not a perfect n power)</span>
<a name="l00144"></a>00144 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#aff57d78a7d743fffd21de7d4415df3e4">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>) = 0;
<a name="l00145"></a>00145 <span class="comment"></span>
<a name="l00146"></a>00146 <span class="comment"> //! e0 \@ e1 <==> true | false, where \@ is {=,<,<=,>,>=}</span>
<a name="l00147"></a>00147 <span class="comment"></span><span class="comment"> /*! \param e takes e is (e0\@e1) where e0 and e1 are constants</span>
<a name="l00148"></a>00148 <span class="comment"> */</span>
<a name="l00149"></a>00149 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a8dd6bb6fed9a4745469b0cad5ed4a139" 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) = 0;
<a name="l00150"></a>00150 <span class="comment"></span>
<a name="l00151"></a>00151 <span class="comment"> //! e[0] @ e[1] <==> 0 @ e[1] - e[0], where @ is {=,<,<=,>,>=}</span>
<a name="l00152"></a>00152 <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_1ArithProofRules.html#acde77bf4aa73ff6b9a079b372ed7cc51" 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) = 0;
<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] @ 0, where @ is {=,<,<=,>,>=}</span>
<a name="l00155"></a>00155 <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_1ArithProofRules.html#a0201544f06baaba23df9946f5da47978" 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) = 0;
<a name="l00156"></a>00156 <span class="comment"></span>
<a name="l00157"></a>00157 <span class="comment"> //! x @ y <==> x + z @ y + z, where @ is {=,<,<=,>,>=} (given as 'kind')</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_1ArithProofRules.html#a0fa920a2a5cfa4419dbde10b1d913687" 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="l00159"></a>00159 <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, <span class="keywordtype">int</span> kind) = 0;
<a name="l00160"></a>00160 <span class="comment"></span>
<a name="l00161"></a>00161 <span class="comment"> //! x = y <==> x * z = y * z, where z is a non-zero constant</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_1ArithProofRules.html#ad62d795eb10e67c655c608774881bde3" 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) = 0;
<a name="l00163"></a>00163
<a name="l00164"></a>00164 <span class="comment">// x = y <==> z=0 OR x * 1/z = y * 1/z</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_1ArithProofRules.html#a419dd84177b5ca1fda7a23f3052b6132">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) = 0;
<a name="l00166"></a>00166 <span class="comment"></span>
<a name="l00167"></a>00167 <span class="comment"> //! Multiplying inequation by a non-zero constant</span>
<a name="l00168"></a>00168 <span class="comment"></span><span class="comment"> /*!</span>
<a name="l00169"></a>00169 <span class="comment"> * z>0 ==> e[0] @ e[1] <==> e[0]*z @ e[1]*z</span>
<a name="l00170"></a>00170 <span class="comment"> *</span>
<a name="l00171"></a>00171 <span class="comment"> * z<0 ==> e[0] @ e[1] <==> e[1]*z @ e[0]*z</span>
<a name="l00172"></a>00172 <span class="comment"> *</span>
<a name="l00173"></a>00173 <span class="comment"> * for @ in {<,<=,>,>=}:</span>
<a name="l00174"></a>00174 <span class="comment"> */</span>
<a name="l00175"></a>00175 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a70e83cfbc207a5d15fedd4adde7e9e76" 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) = 0;
<a name="l00176"></a>00176 <span class="comment"></span>
<a name="l00177"></a>00177 <span class="comment"> //! x = y ==> x <= y and x >= y</span>
<a name="l00178"></a>00178 <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_1ArithProofRules.html#a646e312e12d5d23dca0c4db39d2c9fb9" 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) = 0;
<a name="l00179"></a>00179 <span class="comment"></span>
<a name="l00180"></a>00180 <span class="comment"> //! "op1 GE|GT op2" <==> op2 LE|LT op1</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_1ArithProofRules.html#aff4a01da77770b0b60089444c83c9cef" 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) = 0;
<a name="l00182"></a>00182 <span class="comment"></span>
<a name="l00183"></a>00183 <span class="comment"> //! Propagating negation over <,<=,>,>=</span>
<a name="l00184"></a>00184 <span class="comment"></span><span class="comment"> /*! NOT (op1 < op2) <==> (op1 >= op2)</span>
<a name="l00185"></a>00185 <span class="comment"> *</span>
<a name="l00186"></a>00186 <span class="comment"> * NOT (op1 <= op2) <==> (op1 > op2)</span>
<a name="l00187"></a>00187 <span class="comment"> *</span>
<a name="l00188"></a>00188 <span class="comment"> * NOT (op1 > op2) <==> (op1 <= op2)</span>
<a name="l00189"></a>00189 <span class="comment"> *</span>
<a name="l00190"></a>00190 <span class="comment"> * NOT (op1 >= op2) <==> (op1 < op2)</span>
<a name="l00191"></a>00191 <span class="comment"> */</span>
<a name="l00192"></a>00192 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#aee47bda46999143ea29d7d4ff0be89d4" 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) = 0;
<a name="l00193"></a>00193 <span class="comment"></span>
<a name="l00194"></a>00194 <span class="comment"> //! Real shadow: a <(=) t, t <(=) b ==> a <(=) b</span>
<a name="l00195"></a>00195 <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_1ArithProofRules.html#a203c7079289189cd4bf4f604c10645e5" 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,
<a name="l00196"></a>00196 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& tLTbeta) = 0;
<a name="l00197"></a>00197 <span class="comment"></span>
<a name="l00198"></a>00198 <span class="comment"> //! Projecting a tight inequality: alpha <= t <= alpha ==> t = alpha</span>
<a name="l00199"></a>00199 <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_1ArithProofRules.html#a08dfccc28787af2a4141ed0f5a66bc9d" title="Projecting a tight inequality: alpha <= t <= alpha ==> t = alpha.">realShadowEq</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& alphaLEt,
<a name="l00200"></a>00200 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& tLEalpha) = 0;
<a name="l00201"></a>00201 <span class="comment"></span>
<a name="l00202"></a>00202 <span class="comment"> //! Finite interval for integers: a <= t <= a + c ==> G(t, a, 0, c)</span>
<a name="l00203"></a>00203 <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_1ArithProofRules.html#a5d419e48b93820624e356ba33efef27c" 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,
<a name="l00204"></a>00204 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& tLEac,
<a name="l00205"></a>00205 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isInta,
<a name="l00206"></a>00206 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntt) = 0;
<a name="l00207"></a>00207 <span class="comment"></span>
<a name="l00208"></a>00208 <span class="comment"> //! Dark & Gray shadows when a <= b</span>
<a name="l00209"></a>00209 <span class="comment"></span><span class="comment"> /*! takes two integer ineqs (i.e. all vars are ints) </span>
<a name="l00210"></a>00210 <span class="comment"> * "|- beta <= b.x" and "|- a.x <= alpha" and checks if "1 <= a <= b"</span>
<a name="l00211"></a>00211 <span class="comment"> * and returns (D or G) and (!D or !G), where</span>
<a name="l00212"></a>00212 <span class="comment"> * D = Dark_Shadow(ab-1, b.alpha - a.beta),</span>
<a name="l00213"></a>00213 <span class="comment"> * G = Gray_Shadow(a.x, alpha, -(a-1), 0).</span>
<a name="l00214"></a>00214 <span class="comment"> */</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_1ArithProofRules.html#a37835b10dd0f73b5c4cf36c1eebf0d1f" 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="l00216"></a>00216 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& axLEalpha,
<a name="l00217"></a>00217 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntAlpha,
<a name="l00218"></a>00218 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntBeta,
<a name="l00219"></a>00219 <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>)=0;
<a name="l00220"></a>00220 <span class="comment"></span>
<a name="l00221"></a>00221 <span class="comment"> //! Dark & Gray shadows when b <= a</span>
<a name="l00222"></a>00222 <span class="comment"></span><span class="comment"> /*! takes two integer ineqs (i.e. all vars are ints) </span>
<a name="l00223"></a>00223 <span class="comment"> * "|- beta <= b.x" and "|- a.x <= alpha" and checks if "1 <= b < a"</span>
<a name="l00224"></a>00224 <span class="comment"> * and returns (D or G) and (!D or !G), where</span>
<a name="l00225"></a>00225 <span class="comment"> * D = Dark_Shadow(ab-1, b.alpha - a.beta),</span>
<a name="l00226"></a>00226 <span class="comment"> * G = Gray_Shadow(b.x, beta, 0, b-1).</span>
<a name="l00227"></a>00227 <span class="comment"> */</span>
<a name="l00228"></a>00228 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#ab17282c2e4de9965586f4821f17bf60d" 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="l00229"></a>00229 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& axLEalpha,
<a name="l00230"></a>00230 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntAlpha,
<a name="l00231"></a>00231 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntBeta,
<a name="l00232"></a>00232 <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>)=0;
<a name="l00233"></a>00233 <span class="comment"></span>
<a name="l00234"></a>00234 <span class="comment"> //! DARK_SHADOW(t1, t2) ==> t1 <= t2</span>
<a name="l00235"></a>00235 <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_1ArithProofRules.html#a94ffe313b29aa63c32d5c3facb3bc917" title="DARK_SHADOW(t1, t2) ==> t1 <= t2.">expandDarkShadow</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& darkShadow)=0;
<a name="l00236"></a>00236 <span class="comment"></span>
<a name="l00237"></a>00237 <span class="comment"> //! GRAY_SHADOW(v, e, c, c) ==> v=e+c.</span>
<a name="l00238"></a>00238 <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_1ArithProofRules.html#a32df170ed2ec7fb3d1c7541e6f3dda77" 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>& g)=0;
<a name="l00239"></a>00239
<a name="l00240"></a>00240 <span class="comment">// [used to be] GRAY_SHADOW(t1, t2, i) ==> t1 = t2+i OR</span>
<a name="l00241"></a>00241 <span class="comment">// GRAY_SHADOW(t1, t2, i+/-1)</span>
<a name="l00242"></a>00242 <span class="comment"></span>
<a name="l00243"></a>00243 <span class="comment"> //! G(x, e, c1, c2) ==> (G1 or G2) and (!G1 or !G2)</span>
<a name="l00244"></a>00244 <span class="comment"></span><span class="comment"> /*! Here G1 = G(x,e,c1,c),</span>
<a name="l00245"></a>00245 <span class="comment"> * G2 = G(x,e,c+1,c2),</span>
<a name="l00246"></a>00246 <span class="comment"> * and c = floor((c1+c2)/2).</span>
<a name="l00247"></a>00247 <span class="comment"> */</span>
<a name="l00248"></a>00248 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a4b6ef5b29b05bada6ea2df72873abea6" 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>& g)=0;
<a name="l00249"></a>00249
<a name="l00250"></a>00250
<a name="l00251"></a>00251 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#aa33975feef2a9cdd513e5d641f14dc7a">splitGrayShadowSmall</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& g)=0;
<a name="l00252"></a>00252 <span class="comment"></span>
<a name="l00253"></a>00253 <span class="comment"> //! G(x, e, c1, c2) ==> e+c1 <= x AND x <= e+c2</span>
<a name="l00254"></a>00254 <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_1ArithProofRules.html#af936b764ef75b0a6f63043d01a819044" 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>& g)=0;
<a name="l00255"></a>00255 <span class="comment"></span>
<a name="l00256"></a>00256 <span class="comment"> //! Optimized rules: GRAY_SHADOW(a*x, c, c1, c2) ==> [expansion]</span>
<a name="l00257"></a>00257 <span class="comment"></span><span class="comment"> /*! Implements three versions of the rule:</span>
<a name="l00258"></a>00258 <span class="comment"> *</span>
<a name="l00259"></a>00259 <span class="comment"> * \f[\frac{\mathrm{GRAY\_SHADOW}(ax,c,c1,c2)}</span>
<a name="l00260"></a>00260 <span class="comment"> * {ax = c + i - \mathrm{sign}(i)\cdot j(c,i,a)</span>
<a name="l00261"></a>00261 <span class="comment"> * \lor GRAY\_SHADOW(ax, c, i-\mathrm{sign}(i)\cdot (a+j(c,i,a)))}\f]</span>
<a name="l00262"></a>00262 <span class="comment"> *</span>
<a name="l00263"></a>00263 <span class="comment"> * where the conclusion may become FALSE or without the</span>
<a name="l00264"></a>00264 <span class="comment"> * GRAY_SHADOW part, depending on the values of a, c and i.</span>
<a name="l00265"></a>00265 <span class="comment"> */</span>
<a name="l00266"></a>00266 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a3083a3c5893123f2a3ec54ce31718e09" 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>& g)=0;<span class="comment"></span>
<a name="l00267"></a>00267 <span class="comment"> //! |- G(ax, c, c1, c2) ==> |- G(x, 0, ceil((c1+c)/a), floor((c2+c)/a))</span>
<a name="l00268"></a>00268 <span class="comment"></span><span class="comment"> /*! In the case the new c1 > c2, return |- FALSE */</span>
<a name="l00269"></a>00269 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a597adbe8879c33bffefae537a5bca7c0" 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)=0;
<a name="l00270"></a>00270 <span class="comment"></span>
<a name="l00271"></a>00271 <span class="comment"> //! a,b: INT; a < b ==> a <= b-1 [or a+1 <= b]</span>
<a name="l00272"></a>00272 <span class="comment"></span><span class="comment"> /*! Takes a Theorem(\\alpha < \\beta) and returns </span>
<a name="l00273"></a>00273 <span class="comment"> * Theorem(\\alpha < \\beta <==> \\alpha <= \\beta -1)</span>
<a name="l00274"></a>00274 <span class="comment"> * or Theorem(\\alpha < \\beta <==> \\alpha + 1 <= \\beta),</span>
<a name="l00275"></a>00275 <span class="comment"> * depending on which side must be changed (changeRight flag)</span>
<a name="l00276"></a>00276 <span class="comment"> */</span>
<a name="l00277"></a>00277 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a7a0dad5cb9c2815421457dabc25bc537" title="a,b: INT; a < b ==> a <= b-1 [or a+1 <= b]">lessThanToLE</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& less,
<a name="l00278"></a>00278 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntLHS,
<a name="l00279"></a>00279 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntRHS,
<a name="l00280"></a>00280 <span class="keywordtype">bool</span> changeRight)=0;
<a name="l00281"></a>00281
<a name="l00282"></a>00282 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#af5cfb693ee5ee6f3463e83f01196b31e">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="l00283"></a>00283 <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& isIntRHS, <span class="keywordtype">bool</span> changeRight) = 0;
<a name="l00284"></a>00284
<a name="l00285"></a>00285 <span class="comment"></span>
<a name="l00286"></a>00286 <span class="comment"> /*! \param eqn is an equation 0 = a.x or 0 = c + a.x, where x is integer</span>
<a name="l00287"></a>00287 <span class="comment"> * \param isIntx is a proof of IS_INTEGER(x)</span>
<a name="l00288"></a>00288 <span class="comment"> *</span>
<a name="l00289"></a>00289 <span class="comment"> * \return the theorem 0 = c + a.x <==> x=-c/a if -c/a is int else</span>
<a name="l00290"></a>00290 <span class="comment"> * return the theorem 0 = c + a.x <==> false.</span>
<a name="l00291"></a>00291 <span class="comment"> *</span>
<a name="l00292"></a>00292 <span class="comment"> * It also handles the special case of 0 = a.x <==> x = 0</span>
<a name="l00293"></a>00293 <span class="comment"> */</span>
<a name="l00294"></a>00294 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a62d76b2ccca8af5e1f28c5104ea2e313">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,
<a name="l00295"></a>00295 <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>) = 0;<span class="comment"></span>
<a name="l00296"></a>00296 <span class="comment"> /*! IS_INTEGER(x) <=> EXISTS (y : INT) y = x</span>
<a name="l00297"></a>00297 <span class="comment"> * where x is not already known to be an integer.</span>
<a name="l00298"></a>00298 <span class="comment"> */</span>
<a name="l00299"></a>00299 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a8c3d5fdc2b0c9c11291d41c3c20067e4">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>) = 0;
<a name="l00300"></a>00300 <span class="comment"></span>
<a name="l00301"></a>00301 <span class="comment"> /*! @brief Equality elimination rule for integers:</span>
<a name="l00302"></a>00302 <span class="comment"> * \f[\frac{\mathsf{int}(a\cdot x)\quad</span>
<a name="l00303"></a>00303 <span class="comment"> * \mathsf{int}(C+\sum_{i=1}^{n}a_{i}\cdot x_{i})}</span>
<a name="l00304"></a>00304 <span class="comment"> * {a\cdot x=C+\sum_{i=1}^{n}a_{i}\cdot x_{i}</span>
<a name="l00305"></a>00305 <span class="comment"> * \quad\equiv\quad x=t_{2}\wedge 0=t_{3}}</span>
<a name="l00306"></a>00306 <span class="comment"> * \f]</span>
<a name="l00307"></a>00307 <span class="comment"> * See the detailed description for explanations.</span>
<a name="l00308"></a>00308 <span class="comment"> * </span>
<a name="l00309"></a>00309 <span class="comment"> * This rule implements a step in the iterative algorithm for</span>
<a name="l00310"></a>00310 <span class="comment"> * eliminating integer equality. The terms in the rule are</span>
<a name="l00311"></a>00311 <span class="comment"> * defined as follows:</span>
<a name="l00312"></a>00312 <span class="comment"> *</span>
<a name="l00313"></a>00313 <span class="comment"> * \f[\begin{array}{rcl}</span>
<a name="l00314"></a>00314 <span class="comment"> * t_{2} & = & </span>
<a name="l00315"></a>00315 <span class="comment"> * -(C\ \mathbf{mod}\ m+\sum_{i=1}^{n}(a_{i}\ \mathbf{mod}\ m)</span>
<a name="l00316"></a>00316 <span class="comment"> * \cdot x_{i}-m\cdot\sigma(t))\\ & & \\</span>
<a name="l00317"></a>00317 <span class="comment"> * t_{3} & = & </span>
<a name="l00318"></a>00318 <span class="comment"> * \mathbf{f}(C,m)+\sum_{i=1}^{n}\mathbf{f}(a_{i},m)\cdot x_{i}</span>
<a name="l00319"></a>00319 <span class="comment"> * -a\cdot\sigma(t)\\ & & \\</span>
<a name="l00320"></a>00320 <span class="comment"> * t & = &</span>
<a name="l00321"></a>00321 <span class="comment"> * (C\ \mathbf{mod}\ m+\sum_{i=1}^{n}(a_{i}\ \mathbf{mod}\ m)</span>
<a name="l00322"></a>00322 <span class="comment"> * \cdot x_{i}+x)/m\\ & & \\</span>
<a name="l00323"></a>00323 <span class="comment"> * m & = & a+1\\ & & \\</span>
<a name="l00324"></a>00324 <span class="comment"> * \mathbf{f}(i,m) & = & \left\lfloor \frac{i}{m}</span>
<a name="l00325"></a>00325 <span class="comment"> * +\frac{1}{2}\right\rfloor +i\ \mathbf{mod}\ m\\ & & \\</span>
<a name="l00326"></a>00326 <span class="comment"> * i\ \mathbf{mod}\ m & = & i-m\left\lfloor\frac{i}{m}</span>
<a name="l00327"></a>00327 <span class="comment"> * +\frac{1}{2}\right\rfloor</span>
<a name="l00328"></a>00328 <span class="comment"> * \end{array}</span>
<a name="l00329"></a>00329 <span class="comment"> * \f]</span>
<a name="l00330"></a>00330 <span class="comment"> *</span>
<a name="l00331"></a>00331 <span class="comment"> * All the variables and coefficients are integer, and a >= 2.</span>
<a name="l00332"></a>00332 <span class="comment"> *</span>
<a name="l00333"></a>00333 <span class="comment"> * \param eqn is the equation</span>
<a name="l00334"></a>00334 <span class="comment"> * \f[a\cdot x = C + \sum_{i=1}^n a_i\cdot x_i.\f]</span>
<a name="l00335"></a>00335 <span class="comment"> * </span>
<a name="l00336"></a>00336 <span class="comment"> */</span>
<a name="l00337"></a>00337
<a name="l00338"></a>00338 <span class="comment">/*</span>
<a name="l00339"></a>00339 <span class="comment"> virtual Theorem eqElimIntRule(const Expr& eqn,</span>
<a name="l00340"></a>00340 <span class="comment"> const Theorem& isIntLHS,</span>
<a name="l00341"></a>00341 <span class="comment"> const Theorem& isIntRHS) = 0;</span><span class="comment"></span>
<a name="l00342"></a>00342 <span class="comment"> //! a <=> b ==> c AND a <=> c AND b. Takes "a <=> b" and "c".</span>
<a name="l00343"></a>00343 <span class="comment"></span> virtual Theorem cANDaIffcANDb(const Theorem& thm,
<a name="l00344"></a>00344 const Expr& solvedEq) = 0;
<a name="l00345"></a>00345 virtual Theorem substSolvedFormRule(const Expr& e1,
<a name="l00346"></a>00346 ExprMap<Expr>& eMap) = 0;
<a name="l00347"></a>00347 virtual Theorem aANDcIffbANDc(const Theorem& thm, const Expr& newEq) = 0;
<a name="l00348"></a>00348 */
<a name="l00349"></a>00349 <span class="comment"></span>
<a name="l00350"></a>00350 <span class="comment"> ///////////////////////////////////////////////////////////////////////</span>
<a name="l00351"></a>00351 <span class="comment"></span> <span class="comment">// Alternative implementation of integer equality elimination</span><span class="comment"></span>
<a name="l00352"></a>00352 <span class="comment"> ///////////////////////////////////////////////////////////////////////</span>
<a name="l00353"></a>00353 <span class="comment"></span><span class="comment"></span>
<a name="l00354"></a>00354 <span class="comment"> /*! @brief</span>
<a name="l00355"></a>00355 <span class="comment"> * \f[\frac{\Gamma\models ax=t\quad</span>
<a name="l00356"></a>00356 <span class="comment"> * \Gamma'\models\mathsf{int}(x)\quad</span>
<a name="l00357"></a>00357 <span class="comment"> * \{\Gamma_i\models\mathsf{int}(x_i) | x_i\mbox{ is var in }t\}}</span>
<a name="l00358"></a>00358 <span class="comment"> * {\Gamma,\Gamma',\bigcup_i\Gamma_i\models</span>
<a name="l00359"></a>00359 <span class="comment"> * \exists (y:\mathrm{int}).\ x=t_2(y)\wedge 0=t_3(y)}</span>
<a name="l00360"></a>00360 <span class="comment"> * \f]</span>
<a name="l00361"></a>00361 <span class="comment"> * See detailed docs for more information.</span>
<a name="l00362"></a>00362 <span class="comment"> *</span>
<a name="l00363"></a>00363 <span class="comment"> * This rule implements a step in the iterative algorithm for</span>
<a name="l00364"></a>00364 <span class="comment"> * eliminating integer equality. The terms in the rule are</span>
<a name="l00365"></a>00365 <span class="comment"> * defined as follows:</span>
<a name="l00366"></a>00366 <span class="comment"> *</span>
<a name="l00367"></a>00367 <span class="comment"> * \f[\begin{array}{rcl}</span>
<a name="l00368"></a>00368 <span class="comment"> * t & = & C+\sum_{i=1}^na_{i}\cdot x_{i}\\</span>
<a name="l00369"></a>00369 <span class="comment"> * t_{2}(y) & = & </span>
<a name="l00370"></a>00370 <span class="comment"> * -(C\ \mathbf{mod}\ m+\sum_{i=1}^{n}(a_{i}\ \mathbf{mod}\ m)</span>
<a name="l00371"></a>00371 <span class="comment"> * \cdot x_{i}-m\cdot y)\\ & & \\</span>
<a name="l00372"></a>00372 <span class="comment"> * t_{3}(y) & = & </span>
<a name="l00373"></a>00373 <span class="comment"> * \mathbf{f}(C,m)+\sum_{i=1}^{n}\mathbf{f}(a_{i},m)\cdot x_{i}</span>
<a name="l00374"></a>00374 <span class="comment"> * -a\cdot y\\ & & \\</span>
<a name="l00375"></a>00375 <span class="comment"> * m & = & a+1\\ & & \\</span>
<a name="l00376"></a>00376 <span class="comment"> * \mathbf{f}(i,m) & = & \left\lfloor \frac{i}{m}</span>
<a name="l00377"></a>00377 <span class="comment"> * +\frac{1}{2}\right\rfloor +i\ \mathbf{mod}\ m\\ & & \\</span>
<a name="l00378"></a>00378 <span class="comment"> * i\ \mathbf{mod}\ m & = & i-m\left\lfloor\frac{i}{m}</span>
<a name="l00379"></a>00379 <span class="comment"> * +\frac{1}{2}\right\rfloor</span>
<a name="l00380"></a>00380 <span class="comment"> * \end{array}</span>
<a name="l00381"></a>00381 <span class="comment"> * \f]</span>
<a name="l00382"></a>00382 <span class="comment"> *</span>
<a name="l00383"></a>00383 <span class="comment"> * All the variables and coefficients are integer, and a >= 2.</span>
<a name="l00384"></a>00384 <span class="comment"> *</span>
<a name="l00385"></a>00385 <span class="comment"> * \param eqn is the equation ax=t:</span>
<a name="l00386"></a>00386 <span class="comment"> * \f[a\cdot x = C + \sum_{i=1}^n a_i\cdot x_i.\f]</span>
<a name="l00387"></a>00387 <span class="comment"> *</span>
<a name="l00388"></a>00388 <span class="comment"> * \param isIntx is a Theorem deriving the integrality of the</span>
<a name="l00389"></a>00389 <span class="comment"> * LHS variable: IS_INTEGER(x)</span>
<a name="l00390"></a>00390 <span class="comment"> *</span>
<a name="l00391"></a>00391 <span class="comment"> * \param isIntVars is a vector of Theorems deriving the</span>
<a name="l00392"></a>00392 <span class="comment"> * integrality of all variables on the RHS</span>
<a name="l00393"></a>00393 <span class="comment"> */</span>
<a name="l00394"></a>00394 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a08b14a730bbc6b4ca28bb808e6f6dc85" 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,
<a name="l00395"></a>00395 <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="l00396"></a>00396 <span class="keyword">const</span> std::vector<Theorem>& isIntVars) = 0;
<a name="l00397"></a>00397 <span class="comment"></span>
<a name="l00398"></a>00398 <span class="comment"> /*!</span>
<a name="l00399"></a>00399 <span class="comment"> * @brief return e <=> TRUE/FALSE for e == IS_INTEGER(c), where c</span>
<a name="l00400"></a>00400 <span class="comment"> * is a constant</span>
<a name="l00401"></a>00401 <span class="comment"> *</span>
<a name="l00402"></a>00402 <span class="comment"> * \param e is a predicate IS_INTEGER(c) where c is a rational constant</span>
<a name="l00403"></a>00403 <span class="comment"> */</span>
<a name="l00404"></a>00404 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a5e9bccd77000156ab34b0b42d3e3bb18" 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) = 0;
<a name="l00405"></a>00405
<a name="l00406"></a>00406 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#ac05fd3606540a5222ebaa68f9091345b">equalLeaves1</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm) = 0;
<a name="l00407"></a>00407 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a5052c783af25243987424ef66e2bf5fc">equalLeaves2</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm) = 0;
<a name="l00408"></a>00408 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a893c86f0404789d229540f7a0a00df89">equalLeaves3</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm) = 0;
<a name="l00409"></a>00409 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#aa9018c4d16d3d0a2d8f1614f8e7cae23">equalLeaves4</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm) = 0;
<a name="l00410"></a>00410 <span class="comment"></span>
<a name="l00411"></a>00411 <span class="comment"> //! x /= y ==> (x < y) OR (x > y)</span>
<a name="l00412"></a>00412 <span class="comment"></span><span class="comment"> /*! Used in concrete model generation */</span>
<a name="l00413"></a>00413 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#af180898d9f1d255ef3a2f528ecd8ac65" 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) = 0;
<a name="l00414"></a>00414
<a name="l00415"></a>00415 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a24ea340651805e648d7180debad17225">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) = 0;
<a name="l00416"></a>00416
<a name="l00417"></a>00417 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a1ebae10d65430ab1a3a14c866af93de6">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) = 0;
<a name="l00418"></a>00418
<a name="l00419"></a>00419 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#ad0b23fb01a7adea349c8958059b9f7fd">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) = 0;
<a name="l00420"></a>00420
<a name="l00421"></a>00421 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#ac06dd83948d0f3e474f073ecac592343">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) = 0;
<a name="l00422"></a>00422 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#ac06dd83948d0f3e474f073ecac592343">addInequalities</a>(<span class="keyword">const</span> std::vector<Theorem>& thms) = 0;
<a name="l00423"></a>00423
<a name="l00424"></a>00424 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a9abe85f95b61d94fa308a0b15f2b2ef8">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) = 0;
<a name="l00425"></a>00425
<a name="l00426"></a>00426 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a5eaf4d106f7ce86227ab1d96ffc66b55">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) = 0;
<a name="l00427"></a>00427
<a name="l00428"></a>00428 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a0090e0d4065efbf936ec92f0e99935e9">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) = 0;
<a name="l00429"></a>00429
<a name="l00430"></a>00430 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a11976de555ee2e88236575893f2ed766">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) = 0;
<a name="l00431"></a>00431
<a name="l00432"></a>00432 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a4b61e3ea9d5ac911806de95241cf35de">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) = 0;
<a name="l00433"></a>00433
<a name="l00434"></a>00434 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a95bc88d9e126e6b9c938691ce92985aa">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) = 0;
<a name="l00435"></a>00435
<a name="l00436"></a>00436 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a93489420e882a93eb308c7d99c27dc1e">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) = 0;
<a name="l00437"></a>00437
<a name="l00438"></a>00438 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a5a544980652c3f6793057b16cbc43cf9">cycleConflict</a>(<span class="keyword">const</span> std::vector<Theorem>& inequalitites) = 0;
<a name="l00439"></a>00439
<a name="l00440"></a>00440 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a5b475214a53d70298e55f4ac5f3db71f">implyEqualities</a>(<span class="keyword">const</span> std::vector<Theorem>& inequalities) = 0;
<a name="l00441"></a>00441
<a name="l00442"></a>00442 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#aafc12b4bdf180f3475ecf4eaa40648d9">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) = 0;
<a name="l00443"></a>00443
<a name="l00444"></a>00444 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a61ecf1cfc7219c010519cd90cb31d465">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) = 0;
<a name="l00445"></a>00445
<a name="l00446"></a>00446 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#ac48d6f8b2ad8e8f8fefac775d33825b5">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) = 0;
<a name="l00447"></a>00447
<a name="l00448"></a>00448 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a98020e790bcb60c9c2cc5a7e406f500f">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) = 0;
<a name="l00449"></a>00449
<a name="l00450"></a>00450 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#aa6874fa9f5b02db0adb8149af9664b05">nonLinearIneqSignSplit</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& ineqThm) = 0;
<a name="l00451"></a>00451
<a name="l00452"></a>00452 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#af80ad28bb01d8a37e32f29c746d22dbc">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="l00453"></a>00453 std::vector<Theorem>& x_le_c2, <a class="code" href="classCVC3_1_1Rational.html">Rational</a> c2) = 0;
<a name="l00454"></a>00454
<a name="l00455"></a>00455 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#ad3dee93f4078a4fc79ccacef33f05119">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) = 0;
<a name="l00456"></a>00456
<a name="l00457"></a>00457 <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArithProofRules.html#a81d9ea1e5c2d42c2b60a893c879145bd">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="l00458"></a>00458
<a name="l00459"></a>00459 }; <span class="comment">// end of class ArithProofRules</span>
<a name="l00460"></a>00460 } <span class="comment">// end of namespace CVC3</span>
<a name="l00461"></a>00461
<a name="l00462"></a>00462 <span class="preprocessor">#endif</span>
</pre></div></div>
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