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<a href="core__proof__rules_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/*****************************************************************************/</span><span class="comment"></span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">/*!</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> *\file core_proof_rules.h</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> *\brief Proof rules used by theory_core</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * Author: Clark Barrett</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> * Created: Wed Jan 11 15:48:35 2006</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> * <hr></span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> * License to use, copy, modify, sell and/or distribute this software</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"> * and its documentation for any purpose is hereby granted without</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> * royalty, subject to the terms and conditions defined in the \ref</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> * LICENSE file provided with this distribution.</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> * <hr></span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">/*****************************************************************************/</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> </div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor">#ifndef _cvc3__core_proof_rules_h_</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor"></span><span class="preprocessor">#define _cvc3__core_proof_rules_h_</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#include <vector></span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> </div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="keyword">namespace </span>CVC3 {</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> </div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keyword">class </span>Theorem;</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <span class="keyword">class </span>Theorem3;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keyword">class </span>Expr;</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <span class="keyword">class </span>Op;</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> </div>
<div class="line"><a name="l00034"></a><span class="lineno"><a class="code" href="classCVC3_1_1CoreProofRules.html"> 34</a></span>  <span class="keyword">class </span><a class="code" href="classCVC3_1_1CoreProofRules.html">CoreProofRules</a> {</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keyword">public</span>:<span class="comment"></span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> <span class="comment"> //! Destructor</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"><a class="code" href="classCVC3_1_1CoreProofRules.html#a04af291caa087f8dc1c2c8d346e4dffe"> 37</a></span> <span class="comment"></span> <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1CoreProofRules.html#a04af291caa087f8dc1c2c8d346e4dffe" title="Destructor.">~CoreProofRules</a>() { }</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="comment"></span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"> //! e: T ==> |- typePred_T(e) [deriving the type predicate of e]</span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <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_1CoreProofRules.html#ae4fcd08f795189bb93d76144f77a3862" title="e: T ==> |- typePred_T(e) [deriving the type predicate of e]">typePred</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;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment"></span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> ////////////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="comment"></span> <span class="comment">// Core rewrite rules</span><span class="comment"></span></div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="comment"> ////////////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment"></span><span class="comment"></span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> <span class="comment"> //! Replace LETDECL with its definition</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment"></span><span class="comment"> /*! Used only in TheoryCore */</span> </div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CoreProofRules.html#acad687c3e6faa5709961210637c260da" title="Replace LETDECL with its definition.">rewriteLetDecl</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></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment"> //! ==> NOT (AND e1 ... en) IFF (OR !e1 ... !en), takes (AND ...)</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <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_1CoreProofRules.html#ade3007866410b6565ee0ea1ff4c49a99" title="==> NOT (AND e1 ... en) IFF (OR !e1 ... !en), takes (AND ...)">rewriteNotAnd</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></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment"> //! ==> NOT (OR e1 ... en) IFF (AND !e1 ... !en), takes (OR ...)</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <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_1CoreProofRules.html#aea875ee7355ae6aab01b84c176dbccf6" title="==> NOT (OR e1 ... en) IFF (AND !e1 ... !en), takes (OR ...)">rewriteNotOr</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></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment"> //! ==> NOT IFF(e1,e2) IFF IFF(e1,NOT e2)</span></div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <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_1CoreProofRules.html#ae480ca62cb7a8656f01ea3f938fb97d8" title="==> NOT IFF(e1,e2) IFF IFF(e1,NOT e2)">rewriteNotIff</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></div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment"> //! ==> NOT ITE(a,b,c) IFF ITE(a,NOT b,NOT c)</span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <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_1CoreProofRules.html#ac68942cf0c21011f9429042e279b4a54" title="==> NOT ITE(a,b,c) IFF ITE(a,NOT b,NOT c)">rewriteNotIte</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></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment"> //! a |- b == d ==> ITE(a, b, c) == ITE(a, d, c)</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <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_1CoreProofRules.html#a8117a95eed02c35936f988d1c9c2bdab" title="a |- b == d ==> ITE(a, b, c) == ITE(a, d, c)">rewriteIteThen</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>& thenThm) = 0;<span class="comment"></span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment"> //! !a |- c == d ==> ITE(a, b, c) == ITE(a, b, d)</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <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_1CoreProofRules.html#a7912f66f5be7e05b0c85f15596747be4" title="!a |- c == d ==> ITE(a, b, c) == ITE(a, b, d)">rewriteIteElse</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>& elseThm) = 0;<span class="comment"></span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment"> //! ==> ITE(c, e1, e2) <=> (c => e1) AND (!c => e2)</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <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_1CoreProofRules.html#aa66c668de7d5a026297a6bc901a1f7c3" title="==> ITE(c, e1, e2) <=> (c => e1) AND (!c => e2)">rewriteIteBool</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& c,</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <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;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment"></span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment"> //! |= (A & B1) | (A & B2) | ... | (A & bn) <=> A & (B1 | B2 | ...| Bn)</span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <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_1CoreProofRules.html#ac86206cae475f12c9512e436c64656f0" title="|= (A & B1) | (A & B2) | ... | (A & bn) <=> A & (B1 | B2 | ...| Bn)">orDistributivityRule</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></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment"> //! |= (A | B1) & (A | B2) & ... & (A | bn) <=> A | (B1 & B2 & ...& Bn)</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <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_1CoreProofRules.html#aa3091e00758d1cb9e91f1cd3fca1e696" title="|= (A | B1) & (A | B2) & ... & (A | bn) <=> A | (B1 & B2 & ...& Bn)">andDistributivityRule</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;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment"></span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"> //! ==> IMPLIES(e1,e2) IFF OR(!e1, e2)</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <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_1CoreProofRules.html#a3389cd795acc4cee4b591c1488293963" title="==> IMPLIES(e1,e2) IFF OR(!e1, e2)">rewriteImplies</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;</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span> <span class="comment"></span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="comment"> //! ==> DISTINCT(e1,...,en) IFF AND 1 <= i < j <= n (e[i] /= e[j])</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <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_1CoreProofRules.html#ae429bb5ede0ce74b02cb85f8d0a372dd" title="==> DISTINCT(e1,...,en) IFF AND 1 <= i < j <= n (e[i] /= e[j])">rewriteDistinct</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;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment"></span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"> //! ==> NOT(e) == ITE(e, FALSE, TRUE)</span></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <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_1CoreProofRules.html#aa801f2fa243080def2ef1bff48fba3a9" title="==> NOT(e) == ITE(e, FALSE, TRUE)">NotToIte</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& not_e) = 0;<span class="comment"></span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"> //! ==> Or(e) == ITE(e[1], TRUE, e[0])</span></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <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_1CoreProofRules.html#a07be24cd846d62320aca4fb69645a1db" title="==> Or(e) == ITE(e[1], TRUE, e[0])">OrToIte</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></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment"> //! ==> And(e) == ITE(e[1], e[0], FALSE)</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <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_1CoreProofRules.html#a332e730ff085f109382a680847189a0d" title="==> And(e) == ITE(e[1], e[0], FALSE)">AndToIte</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></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment"> //! ==> IFF(a,b) == ITE(a, b, !b)</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <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_1CoreProofRules.html#ac0bd85a42727e1f5d41c7f4fb5366acf" title="==> IFF(a,b) == ITE(a, b, !b)">IffToIte</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></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment"> //! ==> IMPLIES(a,b) == ITE(a, b, TRUE)</span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <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_1CoreProofRules.html#a6639598cf87b9c51bc097bad578b0ac4" title="==> IMPLIES(a,b) == ITE(a, b, TRUE)">ImpToIte</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;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment"></span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment"> //! ==> ITE(e, FALSE, TRUE) IFF NOT(e)</span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <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_1CoreProofRules.html#a71c2aa506efd447f6c411159f44d5af0" title="==> ITE(e, FALSE, TRUE) IFF NOT(e)">rewriteIteToNot</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></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment"> //! ==> ITE(a, TRUE, b) IFF OR(a, b)</span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <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_1CoreProofRules.html#ab23828c9cc70a3805a0be7632e03163b" title="==> ITE(a, TRUE, b) IFF OR(a, b)">rewriteIteToOr</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></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment"> //! ==> ITE(a, b, FALSE) IFF AND(a, b)</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <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_1CoreProofRules.html#a3eb08bdf90ac80d5c372e4791120d894" title="==> ITE(a, b, FALSE) IFF AND(a, b)">rewriteIteToAnd</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></div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> <span class="comment"> //! ==> ITE(a, b, !b) IFF IFF(a, b)</span></div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <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_1CoreProofRules.html#a8a98457f410ab11e4b66adad150e1b67" title="==> ITE(a, b, !b) IFF IFF(a, b)">rewriteIteToIff</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></div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> <span class="comment"> //! ==> ITE(a, b, TRUE) IFF IMPLIES(a, b)</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <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_1CoreProofRules.html#a1d30881c6f1a902575da033dbbeb2aa9" title="==> ITE(a, b, TRUE) IFF IMPLIES(a, b)">rewriteIteToImp</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></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment"> //! ==> ITE(a, b(a), c(a)) IFF ITE(a, b(TRUE), c(FALSE))</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <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_1CoreProofRules.html#a03f8a74b8b1b6d90ff23a0a6150c49d6" title="==> ITE(a, b(a), c(a)) IFF ITE(a, b(TRUE), c(FALSE))">rewriteIteCond</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;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="comment"></span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="comment"> //! |- op(ITE(cond,a,b)) =/<=> ITE(cond,op(a),op(b))</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <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_1CoreProofRules.html#abbf1d27a8dba7669aac602a4a95f0b3f" title="|- op(ITE(cond,a,b)) =/<=> ITE(cond,op(a),op(b))">ifLiftUnaryRule</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></div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment"> //! ((a|b)<=>(a|c))<=>(a|(b<=>c)); takes ((a|b)<=>(a|c)) as 'iff'</span></div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <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_1CoreProofRules.html#a8fc33a9fbd44abba98547acf63322fc8" title="((a|b)<=>(a|c))<=>(a|(b<=>c)); takes ((a|b)<=>(a|c)) as 'iff'">iffOrDistrib</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& iff) = 0;<span class="comment"></span></div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> <span class="comment"> //! ((a&b)<=>(a&c))<=>(!a|(b<=>c)); takes ((a&b)<=>(a&c)) as 'iff'</span></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span> <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_1CoreProofRules.html#a0648f60b8e9b11dee35544c83512fa30" title="((a&b)<=>(a&c))<=>(!a|(b<=>c)); takes ((a&b)<=>(a&c)) as 'iff'">iffAndDistrib</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& iff) = 0;</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> </div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="comment">// Advanced Boolean transformations</span></div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment"></span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment"> //! (a & b) <=> a & b[a/true]; takes the index of a</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="comment"></span><span class="comment"> /*! and rewrites all the other conjuncts. */</span></div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CoreProofRules.html#a07d66271324bda72a66505bb427df156" title="(a & b) <=> a & b[a/true]; takes the index of a">rewriteAndSubterms</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="keywordtype">int</span> idx) = 0;<span class="comment"></span></div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> <span class="comment"> //! (a | b) <=> a | b[a/false]; takes the index of a</span></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span> <span class="comment"></span><span class="comment"> /*! and rewrites all the other disjuncts. */</span></div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1CoreProofRules.html#a0d589028239025d0e43c92c04b5d586a" title="(a | b) <=> a | b[a/false]; takes the index of a">rewriteOrSubterms</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="keywordtype">int</span> idx) = 0;</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="comment"></span></div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="comment"> //! Temporary cheat for building theorems</span></div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <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_1CoreProofRules.html#a9592705bbf82393b7f6500fa33ead252" title="Temporary cheat for building theorems.">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;</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> </div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  }; <span class="comment">// end of class CoreProofRules</span></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> </div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> } <span class="comment">// end of namespace CVC3</span></div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span> </div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> <span class="preprocessor">#endif</span></div>
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