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<a href="array__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 array_proof_rules.h</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * Author: Clark Barrett 5/29/2003</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> * Created: May 29 19:16:33 GMT 2003</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> * <hr></span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> * License to use, copy, modify, sell and/or distribute this software</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment"> * and its documentation for any purpose is hereby granted without</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment"> * royalty, subject to the terms and conditions defined in the \ref</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment"> * LICENSE file provided with this distribution.</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> * <hr></span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> * </span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> * CLASS: ArrayProofRules</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> <span class="comment"> * Description: Array proof rules.</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">/*****************************************************************************/</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> </div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#ifndef _cvc3__theory_array__array_proof_rules_h_</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor"></span><span class="preprocessor">#define _cvc3__theory_array__array_proof_rules_h_</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include <vector></span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> </div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="keyword">namespace </span>CVC3 {</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> </div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <span class="keyword">class </span>Theorem;</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keyword">class </span>Expr;</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  </div>
<div class="line"><a name="l00035"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArrayProofRules.html"> 35</a></span>  <span class="keyword">class </span><a class="code" href="classCVC3_1_1ArrayProofRules.html">ArrayProofRules</a> {</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="comment">// Destructor</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"><a class="code" href="classCVC3_1_1ArrayProofRules.html#a33d0304f92256a794052280219b7c303"> 38</a></span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1ArrayProofRules.html#a33d0304f92256a794052280219b7c303">~ArrayProofRules</a>() { }</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="comment"></span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="comment"> ////////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="comment"></span> <span class="comment">// Proof rules</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></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">// write(store, index_0, v_0, index_1, v_1, ..., index_n, v_n) = store IFF</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="comment">//</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="comment">// read(store, index_n) = v_n &</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="comment">// index_{n-1} != index_n -> read(store, index_{n-1}) = v_{n-1} &</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="comment">// (index_{n-2} != index_{n-1} & index_{n-2} != index_n) -> read(store, index_{n-2}) = v_{n-2} &</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="comment">// ...</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="comment">// (index_1 != index_2 & ... & index_1 != index_n) -> read(store, index_1) = v_1</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">// (index_0 != index_1 & index_0 != index_2 & ... & index_0 != index_n) -> read(store, index_0) = v_0</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArrayProofRules.html#a972bcffba3fec45e0407b21eb337cc36">rewriteSameStore</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> n) = 0;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="comment">// ==> write(store, index, value) = write(...) IFF</span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="comment">// store = write(write(...), index, read(store, index)) &</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="comment">// value = read(write(...), index)</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArrayProofRules.html#a7bd90a2d883b5a0e9de8de61ae495be2">rewriteWriteWrite</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="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="comment">// ==> read(write(store, index1, value), index2) =</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="comment">// ite(index1 = index2, value, read(store, index2))</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArrayProofRules.html#a7cc5971eef4c841bd3b5c2dce8029b53">rewriteReadWrite</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="l00063"></a><span class="lineno"> 63</span> </div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="comment">// e = read(write(store, index1, value), index2):</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="comment">// ==> ite(index1 = index2,</span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="comment">// read(write(store, index1, value), index2) = value,</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="comment">// read(write(store, index1, value), index2) = read(store, index2))</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArrayProofRules.html#ae493f58a14d1ab904de9e24fab6f7c10">rewriteReadWrite2</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">// value = read(store, index) ==></span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="comment">// write(store, index, value) = store</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArrayProofRules.html#ad6a2685b58c198964d3e62b0cd9b7536">rewriteRedundantWrite1</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& v_eq_r,</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& write) = 0;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> </div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="comment">// ==></span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="comment">// write(write(store, index, v1), index, v2) = write(store, index, v2)</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArrayProofRules.html#a528af9ac1b1f4d43bbf14cad57f0cad7">rewriteRedundantWrite2</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="l00078"></a><span class="lineno"> 78</span> </div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="comment">// ==></span></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="comment">// write(write(store, index1, v1), index2, v2) =</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="comment">// write(write(store, index2, v2), index1, ite(index1 = index2, v2, v1))</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArrayProofRules.html#adecec86a93de04d1329f64d7426800d9">interchangeIndices</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"> //! Beta reduction of array literal: |- (array x. f(x))[arg] = f(arg)</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_1ArrayProofRules.html#aa5e52ae0cc9df232b4304421d0ed5e3c" title="Beta reduction of array literal: |- (array x. f(x))[arg] = f(arg)">readArrayLiteral</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="l00085"></a><span class="lineno"> 85</span> <span class="comment"></span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span> <span class="comment"> //! Lift ite over read</span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</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_1ArrayProofRules.html#a3fbe2484ae8a80bee72b432e26cfed6e" title="Lift ite over read.">liftReadIte</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="l00088"></a><span class="lineno"> 88</span> <span class="comment"></span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment"> //! a /= b |- exists i. a[i] /= b[i]</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</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_1ArrayProofRules.html#aeae33c2284acb4cdd65e8737afb58227" title="a /= b |- exists i. a[i] /= b[i]">arrayNotEq</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e) = 0;</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> </div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArrayProofRules.html#a894c9cfb8219f6607e9f653384d2076e">splitOnConstants</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& a, <span class="keyword">const</span> std::vector<Expr>& consts) = 0;</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> </div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1ArrayProofRules.html#ae9a9b93c9d3eb87eab3d17c007d4578f">propagateIndexDiseq</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& read1eqread2isFalse) = 0;</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  }; <span class="comment">// end of class ArrayProofRules</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> } <span class="comment">// end of namespace CVC3</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> </div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="preprocessor">#endif</span></div>
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