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<a href="bitvector__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 bitvector_proof_rules.h</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * \brief Arithmetic proof rules</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: Vijay Ganesh.</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 May 5 15:47:28 PST 2004</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__bitvector_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__bitvector_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 <string></span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include <vector></span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> </div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">namespace </span>CVC3 {</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">class </span>Expr;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keyword">class </span>Theorem;</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> </div>
<div class="line"><a name="l00033"></a><span class="lineno"><a class="code" href="classCVC3_1_1BitvectorProofRules.html"> 33</a></span>  <span class="keyword">class </span><a class="code" href="classCVC3_1_1BitvectorProofRules.html">BitvectorProofRules</a> {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="comment">// Destructor</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"><a class="code" href="classCVC3_1_1BitvectorProofRules.html#a7b9613e9ffdee59c9f70bd06e1a6f29e"> 36</a></span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a7b9613e9ffdee59c9f70bd06e1a6f29e">~BitvectorProofRules</a>() { }</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="comment"></span></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"></span> <span class="comment">// Bitblasting rules for equations</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"></span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="comment"> /*! \param thm input theorem: (e1[i]<=>e2[i])<=>false</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"> * \result (e1=e2)<=>false</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a6536981ca57bbf915b88a818ad56a1f3">bitvectorFalseRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm) = 0;</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment"></span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment"> /*! \param thm input theorem: (~e1[i]<=>e2[i])<=>true</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="comment"> * \result (e1!=e2)<=>true</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a27a79309cbbf8554394d32c9773472cc">bitvectorTrueRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm) = 0;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> </div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> <span class="comment"></span></div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment"> //! t1=t2 ==> AND_i(t1[i:i] = t2[i:i])</span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="comment"></span><span class="comment"> /*!</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="comment"> * \param e is a Expr(t1=t2)</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> <span class="comment"> * \param f is the resulting expression AND_i(t1[i:i] = t2[i:i])</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> <span class="comment"> * is passed to the rule for efficiency.</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="comment"> */</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_1BitvectorProofRules.html#a596c0779b2f39d41816ff658eef9203b" title="t1=t2 ==> AND_i(t1[i:i] = t2[i:i])">bitBlastEqnRule</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>& f) = 0;<span class="comment"></span></div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment"> //! t1/=t2 ==> OR_i(NOT t1[i]<=>t2[i])</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="comment"></span><span class="comment"> /*!</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment"> * \param e is a Theorem(t1/=t2)</span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> <span class="comment"> * \param f is the resulting expression OR_i(NOT t1[i]<=>t2[i]),</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> <span class="comment"> * passed to the rule for efficiency.</span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#aefb184e963398f43e9dd7a0799563350" title="t1/=t2 ==> OR_i(NOT t1[i]<=>t2[i])">bitBlastDisEqnRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e, <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& f) = 0;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> </div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="comment"></span></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"></span> <span class="comment">// Bitblasting and rewrite rules for Inequations</span><span class="comment"></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"></span><span class="comment"></span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"> //! sign extend the input SX(e) appropriately</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_1BitvectorProofRules.html#a06405edfaf820f9b2940ce7bf406615f" title="sign extend the input SX(e) appropriately">signExtendRule</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="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"> //! Pad the kids of BVLT/BVLE to make their length equal</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</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_1BitvectorProofRules.html#a5ca10099b3728f472fc70efbe03fce11" title="Pad the kids of BVLT/BVLE to make their length equal.">padBVLTRule</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> len) = 0;</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment"></span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="comment"> //! Sign Extend the kids of BVSLT/BVSLE to make their length equal</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_1BitvectorProofRules.html#a9a4fef11fae7f9d9b281876569c3ecaf" title="Sign Extend the kids of BVSLT/BVSLE to make their length equal.">padBVSLTRule</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> len) = 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"> /*! input: e0 <=(s) e1. output depends on whether the topbits(MSB) of</span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment"> * e0 and e1 are constants. If they are constants then optimizations</span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span> <span class="comment"> * are done, otherwise the following rule is implemented.</span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="comment"> * e0 <=(s) e1 <==> (e0[n-1] AND NOT e1[n-1]) OR</span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> <span class="comment"> * (e0[n-1] AND e1[n-1] AND e1[n-2:0] <= e0[n-2:0]) OR</span></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span> <span class="comment"> * (NOT e0[n-1] AND NOT e1[n-1] AND e0[n-2:0] <= e1[n-2:0])</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> <span class="comment"> */</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_1BitvectorProofRules.html#af472ab5f550394b03c264675181ac1c9">signBVLTRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e,</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& topBit0,</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& topBit1) = 0;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> <span class="comment"></span></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span> <span class="comment"> /*! NOT(e[0][0] = e[0][1]) <==> e[0][0] = ~e[0][1]</span></div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a7fdf91656d5a4d1b9278e8a974a2578e">notBVEQ1Rule</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="l00101"></a><span class="lineno"> 101</span> <span class="comment"></span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> <span class="comment"> /*! NOT(e[0][0] < e[0][1]) <==> (e[0][1] <= e[0][0]),</span></div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span> <span class="comment"> * NOT(e[0][0] <= e[0][1]) <==> (e[0][1] < e[0][0])</span></div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a328733af3be6889566b4ab81c7dd4759">notBVLTRule</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="l00106"></a><span class="lineno"> 106</span> <span class="comment"></span></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> <span class="comment"> //! if(lhs==rhs) then we have (lhs < rhs <==> false),(lhs <= rhs <==> true)</span></div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</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_1BitvectorProofRules.html#a4be7745b6e05010590d15b0ae9f87212" title="if(lhs==rhs) then we have (lhs < rhs <==> false),(lhs <= rhs <==> true)">lhsEqRhsIneqn</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> kind) = 0;</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> </div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> </div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a7536abc5b7725abfec2d93987cf86a6b">zeroLeq</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="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_1BitvectorProofRules.html#a3ce4fc360b44dec2f89d8d597244c305">bvConstIneqn</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> kind) = 0;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a666ed19d6d57236061243c0951ee6228">generalIneqn</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e,</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e0,</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e1, <span class="keywordtype">int</span> kind) = 0;</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> </div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> <span class="comment"></span></div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="comment"> ////////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="comment"></span> <span class="comment">// Bitblast rules for terms</span><span class="comment"></span></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="comment"> ////////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <span class="comment"></span></div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="comment">// Input: |- BOOLEXTRACT(a,0) <=> bc_0, ... BOOLEXTRACT(a,n-1) <=> bc_(n-1)</span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="comment">// where each bc_0 is TRUE or FALSE</span></div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="comment">// Output: |- a = c</span></div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="comment">// where c is an n-bit constant made from the values bc_0..bc_(n-1)</span></div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ad63871213ec8c864a622bb3d2248b043">bitExtractAllToConstEq</a>(std::vector<Theorem>& thms) = 0;</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> <span class="comment"></span></div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span> <span class="comment"> //! t[i] ==> t[i:i] = 0bin1 or NOT t[i] ==> t[i:i] = 0bin0</span></div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="comment"></span><span class="comment"> /*! \param thm is a Theorem(t[i]) or Theorem(NOT t[i]), where t[i]</span></div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment"> * is BOOLEXTRACT(t, i).</span></div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a77c82c6fccba740e2df14739edb40a02" title="t[i] ==> t[i:i] = 0bin1 or NOT t[i] ==> t[i:i] = 0bin0">bitExtractToExtract</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& thm) = 0;</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span> <span class="comment"></span></div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span> <span class="comment"> //! t[i] <=> t[i:i][0] (to use rewriter for simplifying t[i:i])</span></div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</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_1BitvectorProofRules.html#a79a44f95f79735f733cd75f289887da9" title="t[i] <=> t[i:i][0] (to use rewriter for simplifying t[i:i])">bitExtractRewrite</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;</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> <span class="comment"></span></div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> <span class="comment"> /*! \param x is bitvector constant</span></div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> <span class="comment"> * \param i is extracted bitposition</span></div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span> <span class="comment"> * \result \f[ \frac{}{\mathrm{BOOLEXTRACT(x,i)} \iff</span></div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> <span class="comment"> * \mathrm{TRUE}} \f], if bitposition has a 1; \f[</span></div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span> <span class="comment"> * \frac{}{\mathrm{BOOLEXTRACT(x,i)} \iff \mathrm{FALSE}} \f], if</span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span> <span class="comment"> * the bitposition has a 0</span></div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ace62b8eacaad88c90231099943a49090">bitExtractConstant</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="keywordtype">int</span> i)= 0;</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="comment"></span></div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span> <span class="comment"> /*! \param x is bitvector binary concatenation</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="comment"> * \param i is extracted bitposition</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> <span class="comment"> * \result \f[ \frac{}{(t_{[m]}@q_{[n]})[i] \iff (q_{[n]})[i]}</span></div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span> <span class="comment"> * \f], where \f[ 0 \geq i \geq n-1 \f], another case of</span></div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span> <span class="comment"> * boolextract over concatenation is:</span></div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span> <span class="comment"> * \f[\frac{}{(t_{[m]}@q_{[n]})[i] \iff (t_{[m]})[i-n]} \f],</span></div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span> <span class="comment"> * where \f[ n \geq i \geq m+n-1 \f]</span></div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a14d171b56b3318b1a070fc2c0798f038">bitExtractConcatenation</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & x,</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordtype">int</span> i)= 0;</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> <span class="comment"></span></div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="comment"> /*! \param t is bitvector binary BVMULT. x[0] must be BVCONST</span></div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span> <span class="comment"> * \param i is extracted bitposition</span></div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span> <span class="comment"> * \result bitblast of BVMULT</span></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a14a48b5e0170be003c5a52585654fa6c">bitExtractConstBVMult</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t, <span class="keywordtype">int</span> i)= 0;</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span> <span class="comment"></span></div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> <span class="comment"> /*! \param t : input1 is bitvector binary BVMULT. t[0] must not be BVCONST</span></div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span> <span class="comment"> * \param i : input2 is extracted bitposition</span></div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> <span class="comment"> * \result bitblast of BVMULT</span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ac473ab04bc4692de3ff7f19940d4a3a2">bitExtractBVMult</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& t, <span class="keywordtype">int</span> i) = 0;</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> <span class="comment"></span></div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span> <span class="comment"> /*! \param x is bitvector extraction e[k:j]</span></div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment"> * \param i is extracted bitposition</span></div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment"> * \result \f[ \frac{}{(t_{[n]}[k:j])[i] \iff (t_{[n]})[i+j]}</span></div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span> <span class="comment"> * \f], where \f[ 0 \geq j \geq k < n, 0 \geq i < k-j \f]</span></div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ae46b941cbb7c67aec7a96a45b33e73ab">bitExtractExtraction</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="keywordtype">int</span> i)= 0;</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="comment"></span></div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span> <span class="comment"> /*! \param t1 is vector of bitblasts of t, from bit i-1 to 0</span></div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> <span class="comment"> * \param t2 is vector of bitblasts of q, from bit i-1 to 0</span></div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="comment"> * \param bvPlusTerm is BVPLUS term: BVPLUS(n,t,q)</span></div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="comment"> * \param i is extracted bitposition</span></div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="comment"> * \result The base case is: \f[</span></div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="comment"> * \frac{}{(\mathrm{BVPLUS}(n,t,q))[0] \iff t[0] \oplus q[0]}</span></div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="comment"> * \f], when \f[ 0 < i \leq n-1 \f], we have \f[</span></div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span> <span class="comment"> * \frac{}{(\mathrm{BVPLUS}(n,t,q))[i] \iff t[i] \oplus q[i]</span></div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="comment"> * \oplus c(t,q,i)} \f], where c(t,q,i) is the carry generated</span></div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span> <span class="comment"> * by the addition of bits from 0 to i-1</span></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ab60522e7672d31bcf2957d1cbd118208">bitExtractBVPlus</a>(<span class="keyword">const</span> std::vector<Theorem>& t1,</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keyword">const</span> std::vector<Theorem>& t2,</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& bvPlusTerm, <span class="keywordtype">int</span> i) = 0;</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> </div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span> </div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ab521ae872e2a877f5e30ec9f1b8ded8f">bitExtractBVPlusPreComputed</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& t1_i,</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& t2_i,</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& bvPlusTerm,</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keywordtype">int</span> bitPos,</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keywordtype">int</span> precomputed) = 0;</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span> </div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> <span class="comment"></span></div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="comment"> /*! \param bvPlusTerm : input1 is bvPlusTerm, a BVPLUS term with</span></div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> <span class="comment"> * arity > 2</span></div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="comment"> * \result : output is iff-Theorem: bvPlusTerm <==> outputTerm,</span></div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span> <span class="comment"> * where outputTerm is an equivalent BINARY bvplus.</span></div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a0836ea2282578bd221ade4a06d0abc2e">bvPlusAssociativityRule</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& bvPlusTerm)= 0;</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> <span class="comment"></span></div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="comment"> /*! \param x : input1 is bitwise NEGATION</span></div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="comment"> * \param i : input2 is extracted bitposition</span></div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="comment"> * \result \f[ \frac{}{(\sim t_{[n]})[i] \iff \neg (t_{[n]}[i])}</span></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="comment"> * \f]</span></div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a40fd98cf00aa03114e7bdf0e164abe69">bitExtractNot</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="keywordtype">int</span> i)= 0;</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span> <span class="comment"></span></div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span> <span class="comment"> //! Extract from bitwise AND, OR, or XOR</span></div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</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_1BitvectorProofRules.html#a9f09c5a49fd132f26a01ec7d96168e42" title="Extract from bitwise AND, OR, or XOR.">bitExtractBitwise</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="keywordtype">int</span> i, <span class="keywordtype">int</span> kind)= 0;</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span> <span class="comment"></span></div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span> <span class="comment"> /*! \param x : input1 is bitvector FIXED SHIFT \f[ e_{[n]} \ll k \f]</span></div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span> <span class="comment"> * \param i : input2 is extracted bitposition</span></div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span> <span class="comment"> * \result \f[\frac{}{(e_{[n]} \ll k)[i] \iff \mathrm{FALSE}}</span></div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span> <span class="comment"> * \f], if 0 <= i < k. however, if k <= i < n then, result is</span></div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span> <span class="comment"> * \f[\frac{}{(e_{[n]} \ll k)[i] \iff e_{[n]}[i]} \f]</span></div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a3c7217656c1f4bdd8ab08e415ef3dc7d">bitExtractFixedLeftShift</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & x,</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keywordtype">int</span> i)= 0;</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span> </div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a8671b7ed4e5e09402cf5a732fb13a373">bitExtractFixedRightShift</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a> & x,</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keywordtype">int</span> i)= 0;</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="comment">// BOOLEXTRACT(bvshl(t,s),i) <=> ((s = 0) AND BOOLEXTRACT(t,i)) OR</span></div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="comment">// ((s = 1) AND BOOLEXTRACT(t,i-1)) OR ...</span></div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="comment">// ((s = i) AND BOOLEXTRACT(t,0))</span></div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#afcd3c4de329e1b2912d83853be46130a">bitExtractBVSHL</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="keywordtype">int</span> i) = 0;</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span> </div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="comment">// BOOLEXTRACT(bvlshr(t,s),i) <=> ((s = 0) AND BOOLEXTRACT(t,i)) OR</span></div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="comment">// ((s = 1) AND BOOLEXTRACT(t,i+1)) OR ...</span></div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="comment">// ((s = n-1-i) AND BOOLEXTRACT(t,n-1))</span></div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#aebe59090c69f529aa1450a64f2d80538">bitExtractBVLSHR</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="keywordtype">int</span> i) = 0;</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span> </div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="comment">// BOOLEXTRACT(bvashr(t,s),i) <=> ((s = 0) AND BOOLEXTRACT(t,i)) OR</span></div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="comment">// ((s = 1) AND BOOLEXTRACT(t,i+1)) OR ...</span></div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="comment">// ((s >= n-1-i) AND BOOLEXTRACT(t,n-1))</span></div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a95f41581d03d993ec02541ec78fbd655">bitExtractBVASHR</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="keywordtype">int</span> i) = 0;</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="comment"></span></div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span> <span class="comment"> /*! \param e : input1 is bitvector term</span></div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span> <span class="comment"> * \param r : input2 is extracted bitposition</span></div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="comment"> * \result we check if r > bvlength(e). if yes, then return</span></div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span> <span class="comment"> * BOOLEXTRACT(e,r) <==> FALSE; else raise soundness</span></div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="comment"> * exception. (Note: this rule is used in BVPLUS bitblast</span></div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span> <span class="comment"> * function)</span></div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ae806df67b545215d677ccd81b68c9b16">zeroPaddingRule</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> r)= 0;</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span> </div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span> </div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a0520e4a3cf5ce89aaa0cf24c1cf5dd9a">bitExtractSXRule</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> i) = 0;</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span> <span class="comment"></span></div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span> <span class="comment"> ///////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span> <span class="comment"> ///// Special case rewrite rules</span></div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span> <span class="comment"> ///////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span> <span class="comment"></span><span class="comment"></span></div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span> <span class="comment"> //! c1=c2 <=> TRUE/FALSE (equality of constant bitvectors)</span></div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</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_1BitvectorProofRules.html#ad88adf2f899f5eab5c0de7c09892178f" title="c1=c2 <=> TRUE/FALSE (equality of constant bitvectors)">eqConst</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="l00271"></a><span class="lineno"> 271</span> <span class="comment"> //! |- c1=c2 ==> |- AND(c1[i:i] = c2[i:i]) - expanding equalities into bits</span></div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</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_1BitvectorProofRules.html#a72537952b59dbed6451fe20803e565a6" title="|- c1=c2 ==> |- AND(c1[i:i] = c2[i:i]) - expanding equalities into bits">eqToBits</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& eq) = 0;<span class="comment"></span></div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span> <span class="comment"> //! t<<n = c @ 0bin00...00, takes e == (t<<n)</span></div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</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_1BitvectorProofRules.html#a2944e9810307f39e543f8fa6b973f0a8" title="t<<n = c @ 0bin00...00, takes e == (t<<n)">leftShiftToConcat</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="l00275"></a><span class="lineno"> 275</span> <span class="comment"> //! t<<n = c @ 0bin00...00, takes e == (t<<n)</span></div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</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_1BitvectorProofRules.html#aaf79659bd7a160d20c3d27d7746d9ca3" title="t<<n = c @ 0bin00...00, takes e == (t<<n)">constWidthLeftShiftToConcat</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="l00277"></a><span class="lineno"> 277</span> <span class="comment"> //! t>>m = 0bin00...00 @ t[bvlength-1:m], takes e == (t>>n)</span></div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</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_1BitvectorProofRules.html#ab2d4f1d9f2f71845d0e2efb2e9ab0f02" title="t>>m = 0bin00...00 @ t[bvlength-1:m], takes e == (t>>n)">rightShiftToConcat</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="l00279"></a><span class="lineno"> 279</span> <span class="comment"> //! BVSHL(t,c) = t[n-c,0] @ 0bin00...00</span></div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</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_1BitvectorProofRules.html#aa665d97eb8067ae68741a6e25135e307" title="BVSHL(t,c) = t[n-c,0] @ 0bin00...00.">bvshlToConcat</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="l00281"></a><span class="lineno"> 281</span> <span class="comment"> //! BVSHL(t,c) = IF (c = 0) THEN t ELSE IF (c = 1) ...</span></div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</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_1BitvectorProofRules.html#ab3a7d61a6e1627433906f527f89e300b" title="BVSHL(t,c) = IF (c = 0) THEN t ELSE IF (c = 1) ...">bvshlSplit</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="l00283"></a><span class="lineno"> 283</span> <span class="comment"> //! BVLSHR(t,c) = 0bin00...00 @ t[n-1,c]</span></div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</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_1BitvectorProofRules.html#a994aa73b02c523cd2e9e76a4880a167b" title="BVLSHR(t,c) = 0bin00...00 @ t[n-1,c].">bvlshrToConcat</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="l00285"></a><span class="lineno"> 285</span> <span class="comment"> //! Any shift over a zero = 0</span></div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</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_1BitvectorProofRules.html#a52acdd1024ed2ab0737c7747102fa7fe" title="Any shift over a zero = 0.">bvShiftZero</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="l00287"></a><span class="lineno"> 287</span> <span class="comment"> //! BVASHR(t,c) = SX(t[n-1,c], n-1)</span></div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</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_1BitvectorProofRules.html#a42639e0098377ce718308a2ae833430b" title="BVASHR(t,c) = SX(t[n-1,c], n-1)">bvashrToConcat</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="l00289"></a><span class="lineno"> 289</span> <span class="comment"> //! a XNOR b <=> (~a & ~b) | (a & b)</span></div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</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_1BitvectorProofRules.html#af126175b4dbb92231ec44c14f32d8b21" title="a XNOR b <=> (~a & ~b) | (a & b)">rewriteXNOR</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="l00291"></a><span class="lineno"> 291</span> <span class="comment"> //! a NAND b <=> ~(a & b)</span></div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</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_1BitvectorProofRules.html#a53c8279d20f7d229437790ce6c0da2da" title="a NAND b <=> ~(a & b)">rewriteNAND</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="l00293"></a><span class="lineno"> 293</span> <span class="comment"> //! a NOR b <=> ~(a | b)</span></div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</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_1BitvectorProofRules.html#a8e2d34a4c387bd5eace8b7e6237bd936" title="a NOR b <=> ~(a | b)">rewriteNOR</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="l00295"></a><span class="lineno"> 295</span> <span class="comment"> //! BVCOMP(a,b) <=> ITE(a=b,0bin1,0bin0)</span></div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</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_1BitvectorProofRules.html#acccc78337e0a0143b9635e1cd49ac657" title="BVCOMP(a,b) <=> ITE(a=b,0bin1,0bin0)">rewriteBVCOMP</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="l00297"></a><span class="lineno"> 297</span> <span class="comment"> //! a - b <=> a + (-b)</span></div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</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_1BitvectorProofRules.html#a693f8801e36967bf64a0fef0290cad5a" title="a - b <=> a + (-b)">rewriteBVSub</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="l00299"></a><span class="lineno"> 299</span> <span class="comment"> //! k*t = BVPLUS(n, <sum of shifts of t>) -- translation of k*t to BVPLUS</span></div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span> <span class="comment"></span><span class="comment"> /*! If k = 2^m, return k*t = t\@0...0 */</span></div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ac132cce6c99ee7626ee4696010e77aa6" title="k*t = BVPLUS(n, <sum of shifts of t>) – translation of k*t to BVPLUS">constMultToPlus</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="l00302"></a><span class="lineno"> 302</span> <span class="comment"> //! 0bin0...0 @ BVPLUS(n, args) = BVPLUS(n+k, args)</span></div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span> <span class="comment"></span><span class="comment"> /*! provided that m+ceil(log2(l)) <= n, where k is the size of the</span></div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span> <span class="comment"> * 0bin0...0, m is the max. length of each argument, and l is the</span></div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span> <span class="comment"> * number of arguments.</span></div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a425296e1ac48c9698802b9a7513745d5" title="0bin0...0 @ BVPLUS(n, args) = BVPLUS(n+k, args)">bvplusZeroConcatRule</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="l00308"></a><span class="lineno"> 308</span> </div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span> <span class="comment"></span></div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span> <span class="comment"> ///////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span> <span class="comment"> ///// Bvplus Normal Form rules</span></div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span> <span class="comment"> ///////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</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_1BitvectorProofRules.html#a0dacf60fcac4bbbcc45019a5c58d576c">zeroCoeffBVMult</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="l00314"></a><span class="lineno"> 314</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a99efc60c900f6818e718eaa76634f82d">oneCoeffBVMult</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="l00315"></a><span class="lineno"> 315</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ae17fc2f1a86046cc389e4f828ce6043c">flipBVMult</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="l00316"></a><span class="lineno"> 316</span> <span class="comment"> //! Make args the same length as the result (zero-extend)</span></div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</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_1BitvectorProofRules.html#a534b8599309b8a1f04355f974450eb44" title="Make args the same length as the result (zero-extend)">padBVPlus</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="l00318"></a><span class="lineno"> 318</span> <span class="comment"> //! Make args the same length as the result (zero-extend)</span></div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</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_1BitvectorProofRules.html#a185de05a96896134fb0c204bfa2b701f" title="Make args the same length as the result (zero-extend)">padBVMult</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="l00320"></a><span class="lineno"> 320</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a47645c759c4c43b1336d6aa8ea4bef24">bvConstMultAssocRule</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="l00321"></a><span class="lineno"> 321</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a06eb338d6dbad205f7ce886b94866e01">bvMultAssocRule</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="l00322"></a><span class="lineno"> 322</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a0a00757ccf2b0b5115003629085752f5">bvMultDistRule</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="l00323"></a><span class="lineno"> 323</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a5c1a3b38a87b8cdf2fe7674b0c50c8ed">flattenBVPlus</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="l00324"></a><span class="lineno"> 324</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a88dbf100f26bd80ac71b976513cf5ed0">combineLikeTermsRule</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="l00325"></a><span class="lineno"> 325</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ad7df7b16e4ba8d0a84163dac7a3fd29d">lhsMinusRhsRule</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="l00326"></a><span class="lineno"> 326</span> <span class="comment"> //! (x *[n] y)[m:k] = (x *[m+1] y)[m:k], where m < n</span></div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</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_1BitvectorProofRules.html#aa3c6172968875b9189228eb7f8c50187" title="(x *[n] y)[m:k] = (x *[m+1] y)[m:k], where m < n">extractBVMult</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="l00328"></a><span class="lineno"> 328</span> <span class="comment"> //! (x +[n] y)[m:k] = (x +[m+1] y)[m:k], where m < n</span></div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</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_1BitvectorProofRules.html#a144383710caebde013be9b2cefce5a4c" title="(x +[n] y)[m:k] = (x +[m+1] y)[m:k], where m < n">extractBVPlus</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="l00330"></a><span class="lineno"> 330</span> <span class="comment"> //! ite(c,t1,t2)[i:j] <=> ite(c,t1[i:j],t2[i:j])</span></div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</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_1BitvectorProofRules.html#adabf3a32d5a2444ca64e2f66a414f185" title="ite(c,t1,t2)[i:j] <=> ite(c,t1[i:j],t2[i:j])">iteExtractRule</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="l00332"></a><span class="lineno"> 332</span> <span class="comment"> //! ~ite(c,t1,t2) <=> ite(c,~t1,~t2)</span></div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</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_1BitvectorProofRules.html#ae25244a21bbc10ad069c9c98ac49590e" title="~ite(c,t1,t2) <=> ite(c,~t1,~t2)">iteBVnegRule</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="l00334"></a><span class="lineno"> 334</span> </div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#afb6657218e31843d4f9fb55494133a51">bvuminusBVConst</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="l00336"></a><span class="lineno"> 336</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ae96c6008f1ded31a7d8985264594cbbc">bvuminusBVMult</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="l00337"></a><span class="lineno"> 337</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a331e5974d6b4cf1458501aba9c4a2556">bvuminusBVUminus</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="l00338"></a><span class="lineno"> 338</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#aaa564090b043862b11ce47d777a9c959">bvuminusVar</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="l00339"></a><span class="lineno"> 339</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a63c42dbedb2f04af9dd61d6b104c42f0">bvmultBVUminus</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="l00340"></a><span class="lineno"> 340</span> <span class="comment"> //! -t <==> ~t+1</span></div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</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_1BitvectorProofRules.html#ab7d869044d0d907fb1066e706039ca68" title="-t <==> ~t+1">bvuminusToBVPlus</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="l00342"></a><span class="lineno"> 342</span> <span class="comment"> //! -(c1*t1+...+cn*tn) <==> (-(c1*t1)+...+-(cn*tn))</span></div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</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_1BitvectorProofRules.html#ac77eea8dcc7f833bb3f426fd3f021a93" title="-(c1*t1+...+cn*tn) <==> (-(c1*t1)+...+-(cn*tn))">bvuminusBVPlus</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="l00344"></a><span class="lineno"> 344</span> </div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span> </div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="comment"></span></div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="comment"> ///////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span> <span class="comment"> ///// Concatenation Normal Form rules</span></div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span> <span class="comment"> ///////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span> <span class="comment"></span></div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <span class="comment">// Extraction rules</span></div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span> <span class="comment"></span></div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span> <span class="comment"> //! c1[i:j] = c (extraction from a constant bitvector)</span></div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</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_1BitvectorProofRules.html#a56770462de38c0c8eed61d1f33c77d6c" title="c1[i:j] = c (extraction from a constant bitvector)">extractConst</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="l00355"></a><span class="lineno"> 355</span> <span class="comment"> //! t[n-1:0] = t for n-bit t</span></div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</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_1BitvectorProofRules.html#ae9d9e1338cf24b20f8eb713fbd9b0219" title="t[n-1:0] = t for n-bit t">extractWhole</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="l00357"></a><span class="lineno"> 357</span> <span class="comment"> //! t[i:j][k:l] = t[k+j:l+j] (eliminate double extraction)</span></div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</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_1BitvectorProofRules.html#a7fc72894f97ec709bf1558254e40903e" title="t[i:j][k:l] = t[k+j:l+j] (eliminate double extraction)">extractExtract</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="l00359"></a><span class="lineno"> 359</span> <span class="comment"> //! (t1 @ t2)[i:j] = t1[...] @ t2[...] (push extraction through concat)</span></div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</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_1BitvectorProofRules.html#a483af962d2b2c8390207e94bd2ae6dc1" title="(t1 @ t2)[i:j] = t1[...] @ t2[...] (push extraction through concat)">extractConcat</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="l00361"></a><span class="lineno"> 361</span> <span class="comment"> //! (t1 & t2)[i:j] = t1[i:j] & t2[i:j] (push extraction through OR)</span></div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</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_1BitvectorProofRules.html#a9c8be2deedd7168a29b288737cd050a8" title="(t1 & t2)[i:j] = t1[i:j] & t2[i:j] (push extraction through OR)">extractAnd</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="l00363"></a><span class="lineno"> 363</span> <span class="comment"> //! (t1 | t2)[i:j] = t1[i:j] | t2[i:j] (push extraction through AND)</span></div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</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_1BitvectorProofRules.html#a7cdfdc4ac2ed578d2c584549b8a374a7" title="(t1 | t2)[i:j] = t1[i:j] | t2[i:j] (push extraction through AND)">extractOr</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="l00365"></a><span class="lineno"> 365</span> <span class="comment"> //! (~t)[i:j] = ~(t[i:j]) (push extraction through NEG)</span></div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</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_1BitvectorProofRules.html#ac258a650188de30470eae5c53116abfd" title="(~t)[i:j] = ~(t[i:j]) (push extraction through NEG)">extractNeg</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="l00367"></a><span class="lineno"> 367</span> <span class="comment"> //! Auxiliary function: (t1 op t2)[i:j] = t1[i:j] op t2[i:j]</span></div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</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_1BitvectorProofRules.html#a548cc7ab83b3d604226f09235d2097bf" title="Auxiliary function: (t1 op t2)[i:j] = t1[i:j] op t2[i:j].">extractBitwise</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e,</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="keywordtype">int</span> kind, <span class="keyword">const</span> std::string& name) = 0;</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span> </div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <span class="comment">// Negation rules</span></div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span> <span class="comment"></span></div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span> <span class="comment"> //! ~c1 = c (bit-wise negation of a constant bitvector)</span></div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</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_1BitvectorProofRules.html#a76151013db10b5faa12ba32ad2374fc6" title="~c1 = c (bit-wise negation of a constant bitvector)">negConst</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="l00375"></a><span class="lineno"> 375</span> <span class="comment"> //! ~(t1\@...\@tn) = (~t1)\@...\@(~tn) -- push negation through concat</span></div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</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_1BitvectorProofRules.html#a9c4a53c0c1961951e3d847394bfa1b20" title="~(t1@...@tn) = (~t1)@...@(~tn) – push negation through concat">negConcat</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="l00377"></a><span class="lineno"> 377</span> <span class="comment"> //! ~(~t) = t -- eliminate double negation</span></div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</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_1BitvectorProofRules.html#ac6cbc581e757d482483d62366e84afb9" title="~(~t) = t – eliminate double negation">negNeg</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="l00379"></a><span class="lineno"> 379</span> <span class="comment"> //! ~t = -1*t + 1 -- eliminate negation</span></div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</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_1BitvectorProofRules.html#a13eeb7dac6de93650d885b61eb72e0ad" title="~t = -1*t + 1 – eliminate negation">negElim</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="l00381"></a><span class="lineno"> 381</span> <span class="comment"> //! ~(t1 & t2) <=> ~t1 | ~t2 -- DeMorgan's Laws</span></div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</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_1BitvectorProofRules.html#a4fb78e904f25388d54eb0ba54ced536d" title="~(t1 & t2) <=> ~t1 | ~t2 – DeMorgan's Laws">negBVand</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="l00383"></a><span class="lineno"> 383</span> <span class="comment"> //! ~(t1 | t2) <=> ~t1 & ~t2 -- DeMorgan's Laws</span></div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</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_1BitvectorProofRules.html#a5763889eb6cd07ab04d4c98686db01cf" title="~(t1 | t2) <=> ~t1 & ~t2 – DeMorgan's Laws">negBVor</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="l00385"></a><span class="lineno"> 385</span> <span class="comment"> //! ~(t1 xor t2) = ~t1 xor t2</span></div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</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_1BitvectorProofRules.html#a2b4170a86c6978a77c338dbf832929ad" title="~(t1 xor t2) = ~t1 xor t2">negBVxor</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="l00387"></a><span class="lineno"> 387</span> <span class="comment"> //! ~(t1 xnor t2) = t1 xor t2</span></div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</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_1BitvectorProofRules.html#accade48c8a792079d97d49d92dc2abee" title="~(t1 xnor t2) = t1 xor t2">negBVxnor</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="l00389"></a><span class="lineno"> 389</span> <span class="comment"></span></div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span> <span class="comment"> //! Combine constants in bitwise AND, OR, XOR</span></div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</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_1BitvectorProofRules.html#abc8792717d3f194aa05f279f63033ec1" title="Combine constants in bitwise AND, OR, XOR.">bitwiseConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& e,</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  <span class="keyword">const</span> std::vector<int>& idxs,</div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  <span class="keywordtype">int</span> kind) = 0;<span class="comment"></span></div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span> <span class="comment"> //! Lifts concatenation above bitwise operators.</span></div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</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_1BitvectorProofRules.html#a29d3cce157edf35040c7c237570e37c9" title="Lifts concatenation above bitwise operators.">bitwiseConcat</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> kind) = 0;<span class="comment"></span></div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span> <span class="comment"> //! Flatten bitwise operation</span></div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</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_1BitvectorProofRules.html#a78d58f8b598713266bad87dcfba0d93b" title="Flatten bitwise operation.">bitwiseFlatten</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> kind) = 0;<span class="comment"></span></div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span> <span class="comment"> //! Simplify bitwise operator containing a constant child</span></div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span> <span class="comment"></span><span class="comment"> /*! \param e is the bit-wise expr</span></div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span> <span class="comment"> * \param idx is the index of the constant bitvector</span></div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span> <span class="comment"> * \param kind is the kind of e</span></div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ab67de0bd797585c3a5cfa3d80a4bfa42" title="Simplify bitwise operator containing a constant child.">bitwiseConstElim</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, <span class="keywordtype">int</span> kind) = 0;</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span> </div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  <span class="comment">// Concatenation rules</span></div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span> <span class="comment"></span></div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="comment"> //! c1\@c2\@...\@cn = c (concatenation of constant bitvectors)</span></div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</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_1BitvectorProofRules.html#a067fc47b8a688b6a08b94c5044d2faf5" title="c1@c2@...@cn = c (concatenation of constant bitvectors)">concatConst</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="l00409"></a><span class="lineno"> 409</span> <span class="comment"> //! Flatten one level of nested concatenation, e.g.: x\@(y\@z)\@w = x\@y\@z\@w</span></div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</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_1BitvectorProofRules.html#a06461d9c64f09ce1dc9acf6cb0628977" title="Flatten one level of nested concatenation, e.g.: x@(y@z)@w = x@y@z@w.">concatFlatten</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="l00411"></a><span class="lineno"> 411</span> <span class="comment"> //! Merge n-ary concat. of adjacent extractions: x[15:8]\@x[7:0] = x[15:0]</span></div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</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_1BitvectorProofRules.html#adec7f3c93376d5e5c0abb20fc3b44eb9" title="Merge n-ary concat. of adjacent extractions: x[15:8]@x[7:0] = x[15:0].">concatMergeExtract</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="l00413"></a><span class="lineno"> 413</span> <span class="comment"></span></div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span> <span class="comment"> ///////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span> <span class="comment"> ///// Modulo arithmetic rules</span></div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span> <span class="comment"> ///////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span> <span class="comment"></span><span class="comment"></span></div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span> <span class="comment"> //! BVPLUS(n, c1,c2,...,cn) = c (bit-vector plus of constant bitvectors)</span></div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</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_1BitvectorProofRules.html#a70ff8e2477ef2d049bd33d1a4bab482e" title="BVPLUS(n, c1,c2,...,cn) = c (bit-vector plus of constant bitvectors)">bvplusConst</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="l00420"></a><span class="lineno"> 420</span> <span class="comment"> /*! @brief n*c1 = c, where n >= 0 (multiplication of a constant</span></div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span> <span class="comment"> * bitvector by a non-negative constant) */</span></div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ae0c8cdf3fade0ff0824c6112f4bdec0c" title="n*c1 = c, where n >= 0 (multiplication of a constant bitvector by a non-negative constant)">bvmultConst</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="l00423"></a><span class="lineno"> 423</span> <span class="comment"></span></div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span> <span class="comment"> ///////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span> <span class="comment"> ///// Type predicate rules</span></div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span> <span class="comment"> ///////////////////////////////////////////////////////////////////</span></div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span> <span class="comment"></span><span class="comment"></span></div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span> <span class="comment"> //! |- t=0 OR t=1 for any 1-bit bitvector t</span></div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</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_1BitvectorProofRules.html#a2096bde76317290227a520452a3ab4c4" title="|- t=0 OR t=1 for any 1-bit bitvector t">typePredBit</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="l00430"></a><span class="lineno"> 430</span> <span class="comment"> //! Expand the type predicate wrapper (compute the actual type predicate)</span></div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</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_1BitvectorProofRules.html#acff4dd7561fb19a337f76edfa024c1aa" title="Expand the type predicate wrapper (compute the actual type predicate)">expandTypePred</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& tp) = 0;</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span> </div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  <span class="comment">/*Beginning of Lorenzo PLatania's methods*/</span></div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span> </div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  <span class="comment">// virtual Theorem multiply_coeff( Rational mult_inv, const Expr& e)=0;</span></div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span> <span class="comment"></span></div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span> <span class="comment"> //! isolate a variable with coefficient = 1 on the Lhs of an</span></div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span> <span class="comment"></span> <span class="comment">//equality expression</span></div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#aef8e88512f778d081ade97e6304f1d18" title="isolate a variable with coefficient = 1 on the Lhs of an">isolate_var</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="l00440"></a><span class="lineno"> 440</span> </div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  <span class="comment">// BVPLUS(N, a@b, y) = BVPLUS(N-n,a,BVPLUS(N,b,y)[N-1:n])@BVPLUS(n,b,y)</span></div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  <span class="comment">// where n = BVSize(b), a != 0</span></div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a17c15204dfec661af091bb07f44c4f51">liftConcatBVMult</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="l00444"></a><span class="lineno"> 444</span> <span class="comment"></span></div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span> <span class="comment"> //! canonize BVMult expressions in order to get one coefficient</span></div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span> <span class="comment"></span> <span class="comment">//multiplying the variable(s) in the expression</span></div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a74f5018affcab70b831029b390692552" title="canonize BVMult expressions in order to get one coefficient">canonBVMult</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="l00448"></a><span class="lineno"> 448</span> </div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <span class="comment">// BVPLUS(N, a@b, y) = BVPLUS(N-n,a,BVPLUS(N,b,y)[N-1:n])@BVPLUS(n,b,y)</span></div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  <span class="comment">// where n = BVSize(b)</span></div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#affb1cdfd198f4140f1943f9296b1b97c">liftConcatBVPlus</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="l00452"></a><span class="lineno"> 452</span> <span class="comment"></span></div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span> <span class="comment"> //! canonize BVPlus expressions in order to get just one</span></div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span> <span class="comment"></span> <span class="comment">//coefficient multiplying each variable in the expression</span></div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a07f756438b45b15b493497341944bbb4" title="canonize BVPlus expressions in order to get just one">canonBVPlus</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="l00456"></a><span class="lineno"> 456</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#acb966a104436262e81299cea86bc21bb">canonBVUMinus</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="l00457"></a><span class="lineno"> 457</span>  <span class="comment">// Input: t[hi:lo] = rhs</span></div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="comment">// if t appears as leaf in rhs, then:</span></div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <span class="comment">// t[hi:lo] = rhs |- Exists x,y,z. (t = x @ y @ z AND y = rhs), solvedForm = false</span></div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  <span class="comment">// else</span></div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  <span class="comment">// t[hi:lo] = rhs |- Exists x,y,z. (t = x @ rhs @ z AND y = rhs), solvedForm = true</span></div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ac018d05ae792d761195fbcc9731017d0">processExtract</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a>& e, <span class="keywordtype">bool</span>& solvedForm)=0;</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  <span class="comment">// normalizes equation</span></div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a04f65b94c6a9ca2b84a6063aac0d082f">canonBVEQ</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> maxEffort = 3 )=0;</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span> <span class="comment"></span></div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span> <span class="comment"> //! apply the distributive rule on the BVMULT expression e</span></div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</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_1BitvectorProofRules.html#a11422aabc07aa0721cf17b2297a97b40" title="apply the distributive rule on the BVMULT expression e">distributive_rule</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="l00468"></a><span class="lineno"> 468</span>  <span class="comment">// virtual Theorem BVMultConstTerm( const Expr& e1, const Expr& e2)=0;</span></div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  <span class="comment">// recursively reorder subterms in a BVMULT term</span></div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#aaeb132de41aad56b3bbb5a0c9fcede80">BVMult_order_subterms</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="l00471"></a><span class="lineno"> 471</span>  <span class="comment">// rewrites the equation in the form 0 = Expr</span></div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  <span class="comment">// this is needed for TheoryBitvector::solve</span></div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a02032b49999aa3913265a22cac129045">MarkNonSolvableEq</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="l00474"></a><span class="lineno"> 474</span>  <span class="comment">/*End of Lorenzo PLatania's methods*/</span></div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span> </div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  <span class="comment">// rewrite BVZEROEXTEND into CONCAT</span></div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a0e4bd4a89095a5c275cc898b624b9346">zeroExtendRule</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="l00478"></a><span class="lineno"> 478</span>  <span class="comment">// rewrite BVREPEAT into CONCAT</span></div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#aed9f65e2eed1299d80b6ec63274568a4">repeatRule</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="l00480"></a><span class="lineno"> 480</span>  <span class="comment">// rewrite BVROTL into CONCAT</span></div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a9a9c214170ee9595f2eb0b0552b6130f">rotlRule</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="l00482"></a><span class="lineno"> 482</span>  <span class="comment">// rewrite BVROTR into CONCAT</span></div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#aca310d258dd22e4e50b19274047c6528">rotrRule</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="l00484"></a><span class="lineno"> 484</span> <span class="comment"></span></div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span> <span class="comment"> * Divide a with b unsigned and return the bit-vector constant result</span></div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a95920e0fd327bc9630d41784449bae0a">bvUDivConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& divExpr) = 0;</div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span> <span class="comment"></span></div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span> <span class="comment"> * Rewrite a/b with a fresh variable d and add the constraints to make it be a divider.</span></div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#ab1b7fd737bbf85300e149a0ca1dce266">bvUDivTheorem</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& divExpr) = 0;</div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span> <span class="comment"></span></div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span> <span class="comment"> * Divide a with b unsigned and return the bit-vector constant result</span></div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a3cf92f9619244e27a40a6b218887cad0">bvURemConst</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& remExpr) = 0;</div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span> <span class="comment"></span></div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span> <span class="comment"> * Rewrite a%b in terms of a/b, i.e. a - a/b</span></div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a0e0a89d5b866cb77e50cc24c20f5d053">bvURemRewrite</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& divExpr) = 0;</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span> <span class="comment"></span></div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span> <span class="comment"> * Rewrite the signed divide in terms of the unsigned one.</span></div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a8737b8dee3cf693cba13dd073b132294">bvSDivRewrite</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& sDivExpr) = 0;</div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span> <span class="comment"></span></div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span> <span class="comment"> * Rewrite the signed remainder in terms of the unsigned one.</span></div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a41766b9dbe8dd7e8ebf5cf0349cf2e9e">bvSRemRewrite</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& sRemExpr) = 0;</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span> <span class="comment"></span></div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span> <span class="comment"> * Rewrite the signed mod in terms of the unsigned one.</span></div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#af8734beba48ae58dd465efd808f73117">bvSModRewrite</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& sModExpr) = 0;</div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span> <span class="comment"></span></div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span> <span class="comment"> * Bit-blast the multiplication a_times_b given the bits in a_bits and b_bits.</span></div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span> <span class="comment"> * The resulting output bits will be in the vector output_bits. The return value</span></div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span> <span class="comment"> * is a theorem saying there is no overflow for this multiplication. (TODO, it's</span></div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span> <span class="comment"> * just an empty theorem for now).</span></div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a05dd94575cc5674452e2ff63106e2a40">bitblastBVMult</a>(<span class="keyword">const</span> std::vector<Theorem>& a_bits,</div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  <span class="keyword">const</span> std::vector<Theorem>& b_bits,</div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& a_times_b,</div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  std::vector<Theorem>& output_bits) = 0;</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span> <span class="comment"></span></div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span> <span class="comment"> * Bit-blast the sum a_times_b given the bits in a_bits and b_bits.</span></div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span> <span class="comment"> * The resulting output bits will be in the vector output_bits. The return value</span></div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span> <span class="comment"> * is a theorem saying there is no overflow for this sum. (TODO, it's</span></div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span> <span class="comment"> * just an empty theorem for now).</span></div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a613cf0998893c8b66e40acf63b40a825">bitblastBVPlus</a>(<span class="keyword">const</span> std::vector<Theorem>& a_bits,</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  <span class="keyword">const</span> std::vector<Theorem>& b_bits,</div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  <span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& a_plus_b,</div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  std::vector<Theorem>& output_bits) = 0;</div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span> <span class="comment"></span></div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span> <span class="comment"> * Rewrite \f[x_1 \vee x_2 \vee \ldots \vee x_n = 0\f] into</span></div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span> <span class="comment"> * \f[x_1 = 0 \wedge x_2 = 0 \wedge \ldots \wedge x_n = 0\f].</span></div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a91229b0364c30d73cfdb5eba138ba712">zeroBVOR</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& orEqZero) = 0;</div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span> <span class="comment"></span></div>
<div class="line"><a name="l00548"></a><span class="lineno"> 548</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00549"></a><span class="lineno"> 549</span> <span class="comment"> * Rewrite \f[x_1 \wedge x_2 \wedge \ldots \wedge x_n = 1^n\f] into</span></div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span> <span class="comment"> * \f[x_1 = 1^n \wedge x_2 = 1^n \wedge \ldots \wedge x_n = 1^n\f].</span></div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a94e717097d7f4156e647893dd506b91d">oneBVAND</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& andEqOne) = 0;</div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span> <span class="comment"></span></div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span> <span class="comment"> * Equalities over constants go to true/false.</span></div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a30e4cf2ef646b5fbc1e0b2b6fb88115a">constEq</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& eq) = 0;</div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span> <span class="comment"></span></div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span> <span class="comment"> * Returns true if equation is of the form x[i:j] = x[k:l], where the</span></div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span> <span class="comment"> * extracted segments overlap, i.e. i > j >= k > l or k > i >= l > j.</span></div>
<div class="line"><a name="l00562"></a><span class="lineno"> 562</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  <span class="keyword">virtual</span> <span class="keywordtype">bool</span> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a3b3ae2372cab5026feec302b6bdaa7d6">solveExtractOverlapApplies</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& eq) = 0;</div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span> <span class="comment"></span></div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span> <span class="comment"> /**</span></div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span> <span class="comment"> * Returns the theorem that simplifies the equality of two overlapping</span></div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span> <span class="comment"> * extracts over the same term.</span></div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  <span class="keyword">virtual</span> <a class="code" href="classCVC3_1_1Theorem.html">Theorem</a> <a class="code" href="classCVC3_1_1BitvectorProofRules.html#a4e491d1c488cb38d6e22ec21ac894f46">solveExtractOverlap</a>(<span class="keyword">const</span> <a class="code" href="classCVC3_1_1Expr.html" title="Data structure of expressions in CVC3.">Expr</a>& eq) = 0;</div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span> </div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  }; <span class="comment">// end of class BitvectorProofRules</span></div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span> } <span class="comment">// end of name-space CVC3</span></div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span> </div>
<div class="line"><a name="l00574"></a><span class="lineno"> 574</span> <span class="preprocessor">#endif</span></div>
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