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1 (* Title: HOL/Tools/TFL/rules.ML |
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2 ID: $Id$ |
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3 Author: Konrad Slind, Cambridge University Computer Laboratory |
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4 Copyright 1997 University of Cambridge |
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5 |
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6 Emulation of HOL inference rules for TFL |
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7 *) |
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8 |
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9 signature RULES = |
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10 sig |
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11 val dest_thm: thm -> term list * term |
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12 |
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13 (* Inference rules *) |
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14 val REFL: cterm -> thm |
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15 val ASSUME: cterm -> thm |
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16 val MP: thm -> thm -> thm |
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17 val MATCH_MP: thm -> thm -> thm |
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18 val CONJUNCT1: thm -> thm |
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19 val CONJUNCT2: thm -> thm |
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20 val CONJUNCTS: thm -> thm list |
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21 val DISCH: cterm -> thm -> thm |
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22 val UNDISCH: thm -> thm |
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23 val SPEC: cterm -> thm -> thm |
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24 val ISPEC: cterm -> thm -> thm |
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25 val ISPECL: cterm list -> thm -> thm |
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26 val GEN: cterm -> thm -> thm |
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27 val GENL: cterm list -> thm -> thm |
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28 val LIST_CONJ: thm list -> thm |
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29 |
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30 val SYM: thm -> thm |
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31 val DISCH_ALL: thm -> thm |
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32 val FILTER_DISCH_ALL: (term -> bool) -> thm -> thm |
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33 val SPEC_ALL: thm -> thm |
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34 val GEN_ALL: thm -> thm |
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35 val IMP_TRANS: thm -> thm -> thm |
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36 val PROVE_HYP: thm -> thm -> thm |
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37 |
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38 val CHOOSE: cterm * thm -> thm -> thm |
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39 val EXISTS: cterm * cterm -> thm -> thm |
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40 val EXISTL: cterm list -> thm -> thm |
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41 val IT_EXISTS: (cterm*cterm) list -> thm -> thm |
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42 |
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43 val EVEN_ORS: thm list -> thm list |
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44 val DISJ_CASESL: thm -> thm list -> thm |
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45 |
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46 val list_beta_conv: cterm -> cterm list -> thm |
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47 val SUBS: thm list -> thm -> thm |
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48 val simpl_conv: simpset -> thm list -> cterm -> thm |
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49 |
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50 val rbeta: thm -> thm |
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51 (* For debugging my isabelle solver in the conditional rewriter *) |
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52 val term_ref: term list ref |
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53 val thm_ref: thm list ref |
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54 val ss_ref: simpset list ref |
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55 val tracing: bool ref |
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56 val CONTEXT_REWRITE_RULE: term * term list * thm * thm list |
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57 -> thm -> thm * term list |
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58 val RIGHT_ASSOC: thm -> thm |
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59 |
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60 val prove: bool -> cterm * tactic -> thm |
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61 end; |
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62 |
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63 structure Rules: RULES = |
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64 struct |
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65 |
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66 structure S = USyntax; |
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67 structure U = Utils; |
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68 structure D = Dcterm; |
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69 |
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70 |
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71 fun RULES_ERR func mesg = U.ERR {module = "Rules", func = func, mesg = mesg}; |
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72 |
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73 |
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74 fun cconcl thm = D.drop_prop (#prop (Thm.crep_thm thm)); |
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75 fun chyps thm = map D.drop_prop (#hyps (Thm.crep_thm thm)); |
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76 |
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77 fun dest_thm thm = |
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78 let val {prop,hyps,...} = Thm.rep_thm thm |
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79 in (map HOLogic.dest_Trueprop hyps, HOLogic.dest_Trueprop prop) end |
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80 handle TERM _ => raise RULES_ERR "dest_thm" "missing Trueprop"; |
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81 |
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82 |
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83 (* Inference rules *) |
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84 |
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85 (*--------------------------------------------------------------------------- |
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86 * Equality (one step) |
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87 *---------------------------------------------------------------------------*) |
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88 |
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89 fun REFL tm = Thm.reflexive tm RS meta_eq_to_obj_eq |
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90 handle THM (msg, _, _) => raise RULES_ERR "REFL" msg; |
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91 |
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92 fun SYM thm = thm RS sym |
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93 handle THM (msg, _, _) => raise RULES_ERR "SYM" msg; |
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94 |
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95 fun ALPHA thm ctm1 = |
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96 let |
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97 val ctm2 = Thm.cprop_of thm; |
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98 val ctm2_eq = Thm.reflexive ctm2; |
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99 val ctm1_eq = Thm.reflexive ctm1; |
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100 in Thm.equal_elim (Thm.transitive ctm2_eq ctm1_eq) thm end |
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101 handle THM (msg, _, _) => raise RULES_ERR "ALPHA" msg; |
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102 |
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103 fun rbeta th = |
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104 (case D.strip_comb (cconcl th) of |
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105 (_, [l, r]) => Thm.transitive th (Thm.beta_conversion false r) |
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106 | _ => raise RULES_ERR "rbeta" ""); |
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107 |
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108 |
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109 (*---------------------------------------------------------------------------- |
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110 * Implication and the assumption list |
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111 * |
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112 * Assumptions get stuck on the meta-language assumption list. Implications |
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113 * are in the object language, so discharging an assumption "A" from theorem |
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114 * "B" results in something that looks like "A --> B". |
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115 *---------------------------------------------------------------------------*) |
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116 |
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117 fun ASSUME ctm = Thm.assume (D.mk_prop ctm); |
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118 |
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119 |
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120 (*--------------------------------------------------------------------------- |
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121 * Implication in TFL is -->. Meta-language implication (==>) is only used |
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122 * in the implementation of some of the inference rules below. |
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123 *---------------------------------------------------------------------------*) |
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124 fun MP th1 th2 = th2 RS (th1 RS mp) |
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125 handle THM (msg, _, _) => raise RULES_ERR "MP" msg; |
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126 |
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127 (*forces the first argument to be a proposition if necessary*) |
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128 fun DISCH tm thm = Thm.implies_intr (D.mk_prop tm) thm COMP impI |
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129 handle THM (msg, _, _) => raise RULES_ERR "DISCH" msg; |
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130 |
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131 fun DISCH_ALL thm = fold_rev DISCH (#hyps (Thm.crep_thm thm)) thm; |
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132 |
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133 |
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134 fun FILTER_DISCH_ALL P thm = |
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135 let fun check tm = P (#t (Thm.rep_cterm tm)) |
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136 in foldr (fn (tm,th) => if check tm then DISCH tm th else th) |
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137 thm (chyps thm) |
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138 end; |
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139 |
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140 (* freezeT expensive! *) |
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141 fun UNDISCH thm = |
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142 let val tm = D.mk_prop (#1 (D.dest_imp (cconcl (Thm.freezeT thm)))) |
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143 in Thm.implies_elim (thm RS mp) (ASSUME tm) end |
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144 handle U.ERR _ => raise RULES_ERR "UNDISCH" "" |
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145 | THM _ => raise RULES_ERR "UNDISCH" ""; |
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146 |
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147 fun PROVE_HYP ath bth = MP (DISCH (cconcl ath) bth) ath; |
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148 |
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149 fun IMP_TRANS th1 th2 = th2 RS (th1 RS Thms.imp_trans) |
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150 handle THM (msg, _, _) => raise RULES_ERR "IMP_TRANS" msg; |
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151 |
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152 |
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153 (*---------------------------------------------------------------------------- |
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154 * Conjunction |
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155 *---------------------------------------------------------------------------*) |
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156 |
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157 fun CONJUNCT1 thm = thm RS conjunct1 |
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158 handle THM (msg, _, _) => raise RULES_ERR "CONJUNCT1" msg; |
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159 |
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160 fun CONJUNCT2 thm = thm RS conjunct2 |
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161 handle THM (msg, _, _) => raise RULES_ERR "CONJUNCT2" msg; |
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162 |
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163 fun CONJUNCTS th = CONJUNCTS (CONJUNCT1 th) @ CONJUNCTS (CONJUNCT2 th) handle U.ERR _ => [th]; |
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164 |
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165 fun LIST_CONJ [] = raise RULES_ERR "LIST_CONJ" "empty list" |
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166 | LIST_CONJ [th] = th |
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167 | LIST_CONJ (th :: rst) = MP (MP (conjI COMP (impI RS impI)) th) (LIST_CONJ rst) |
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168 handle THM (msg, _, _) => raise RULES_ERR "LIST_CONJ" msg; |
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169 |
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170 |
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171 (*---------------------------------------------------------------------------- |
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172 * Disjunction |
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173 *---------------------------------------------------------------------------*) |
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174 local val {prop,thy,...} = rep_thm disjI1 |
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175 val [P,Q] = term_vars prop |
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176 val disj1 = Thm.forall_intr (Thm.cterm_of thy Q) disjI1 |
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177 in |
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178 fun DISJ1 thm tm = thm RS (forall_elim (D.drop_prop tm) disj1) |
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179 handle THM (msg, _, _) => raise RULES_ERR "DISJ1" msg; |
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180 end; |
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181 |
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182 local val {prop,thy,...} = rep_thm disjI2 |
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183 val [P,Q] = term_vars prop |
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184 val disj2 = Thm.forall_intr (Thm.cterm_of thy P) disjI2 |
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185 in |
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186 fun DISJ2 tm thm = thm RS (forall_elim (D.drop_prop tm) disj2) |
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187 handle THM (msg, _, _) => raise RULES_ERR "DISJ2" msg; |
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188 end; |
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189 |
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190 |
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191 (*---------------------------------------------------------------------------- |
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192 * |
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193 * A1 |- M1, ..., An |- Mn |
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194 * --------------------------------------------------- |
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195 * [A1 |- M1 \/ ... \/ Mn, ..., An |- M1 \/ ... \/ Mn] |
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196 * |
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197 *---------------------------------------------------------------------------*) |
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198 |
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199 |
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200 fun EVEN_ORS thms = |
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201 let fun blue ldisjs [] _ = [] |
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202 | blue ldisjs (th::rst) rdisjs = |
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203 let val tail = tl rdisjs |
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204 val rdisj_tl = D.list_mk_disj tail |
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205 in fold_rev DISJ2 ldisjs (DISJ1 th rdisj_tl) |
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206 :: blue (ldisjs @ [cconcl th]) rst tail |
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207 end handle U.ERR _ => [fold_rev DISJ2 ldisjs th] |
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208 in blue [] thms (map cconcl thms) end; |
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209 |
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210 |
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211 (*---------------------------------------------------------------------------- |
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212 * |
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213 * A |- P \/ Q B,P |- R C,Q |- R |
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214 * --------------------------------------------------- |
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215 * A U B U C |- R |
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216 * |
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217 *---------------------------------------------------------------------------*) |
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218 |
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219 fun DISJ_CASES th1 th2 th3 = |
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220 let |
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221 val c = D.drop_prop (cconcl th1); |
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222 val (disj1, disj2) = D.dest_disj c; |
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223 val th2' = DISCH disj1 th2; |
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224 val th3' = DISCH disj2 th3; |
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225 in |
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226 th3' RS (th2' RS (th1 RS Thms.tfl_disjE)) |
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227 handle THM (msg, _, _) => raise RULES_ERR "DISJ_CASES" msg |
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228 end; |
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229 |
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230 |
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231 (*----------------------------------------------------------------------------- |
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232 * |
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233 * |- A1 \/ ... \/ An [A1 |- M, ..., An |- M] |
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234 * --------------------------------------------------- |
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235 * |- M |
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236 * |
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237 * Note. The list of theorems may be all jumbled up, so we have to |
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238 * first organize it to align with the first argument (the disjunctive |
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239 * theorem). |
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240 *---------------------------------------------------------------------------*) |
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241 |
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242 fun organize eq = (* a bit slow - analogous to insertion sort *) |
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243 let fun extract a alist = |
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244 let fun ex (_,[]) = raise RULES_ERR "organize" "not a permutation.1" |
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245 | ex(left,h::t) = if (eq h a) then (h,rev left@t) else ex(h::left,t) |
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246 in ex ([],alist) |
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247 end |
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248 fun place [] [] = [] |
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249 | place (a::rst) alist = |
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250 let val (item,next) = extract a alist |
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251 in item::place rst next |
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252 end |
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253 | place _ _ = raise RULES_ERR "organize" "not a permutation.2" |
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254 in place |
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255 end; |
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256 (* freezeT expensive! *) |
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257 fun DISJ_CASESL disjth thl = |
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258 let val c = cconcl disjth |
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259 fun eq th atm = exists (fn t => HOLogic.dest_Trueprop t |
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260 aconv term_of atm) |
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261 (#hyps(rep_thm th)) |
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262 val tml = D.strip_disj c |
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263 fun DL th [] = raise RULES_ERR "DISJ_CASESL" "no cases" |
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264 | DL th [th1] = PROVE_HYP th th1 |
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265 | DL th [th1,th2] = DISJ_CASES th th1 th2 |
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266 | DL th (th1::rst) = |
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267 let val tm = #2(D.dest_disj(D.drop_prop(cconcl th))) |
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268 in DISJ_CASES th th1 (DL (ASSUME tm) rst) end |
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269 in DL (Thm.freezeT disjth) (organize eq tml thl) |
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270 end; |
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271 |
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272 |
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273 (*---------------------------------------------------------------------------- |
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274 * Universals |
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275 *---------------------------------------------------------------------------*) |
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276 local (* this is fragile *) |
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277 val {prop,thy,...} = rep_thm spec |
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278 val x = hd (tl (term_vars prop)) |
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279 val cTV = ctyp_of thy (type_of x) |
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280 val gspec = forall_intr (cterm_of thy x) spec |
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281 in |
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282 fun SPEC tm thm = |
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283 let val {thy,T,...} = rep_cterm tm |
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284 val gspec' = instantiate ([(cTV, ctyp_of thy T)], []) gspec |
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285 in |
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286 thm RS (forall_elim tm gspec') |
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287 end |
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288 end; |
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289 |
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290 fun SPEC_ALL thm = fold SPEC (#1(D.strip_forall(cconcl thm))) thm; |
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291 |
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292 val ISPEC = SPEC |
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293 val ISPECL = fold ISPEC; |
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294 |
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295 (* Not optimized! Too complicated. *) |
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296 local val {prop,thy,...} = rep_thm allI |
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297 val [P] = add_term_vars (prop, []) |
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298 fun cty_theta s = map (fn (i, (S, ty)) => (ctyp_of s (TVar (i, S)), ctyp_of s ty)) |
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299 fun ctm_theta s = map (fn (i, (_, tm2)) => |
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300 let val ctm2 = cterm_of s tm2 |
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301 in (cterm_of s (Var(i,#T(rep_cterm ctm2))), ctm2) |
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302 end) |
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303 fun certify s (ty_theta,tm_theta) = |
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304 (cty_theta s (Vartab.dest ty_theta), |
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305 ctm_theta s (Vartab.dest tm_theta)) |
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306 in |
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307 fun GEN v th = |
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308 let val gth = forall_intr v th |
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309 val {prop=Const("all",_)$Abs(x,ty,rst),thy,...} = rep_thm gth |
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310 val P' = Abs(x,ty, HOLogic.dest_Trueprop rst) (* get rid of trueprop *) |
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311 val theta = Pattern.match thy (P,P') (Vartab.empty, Vartab.empty); |
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312 val allI2 = instantiate (certify thy theta) allI |
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313 val thm = Thm.implies_elim allI2 gth |
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314 val {prop = tp $ (A $ Abs(_,_,M)),thy,...} = rep_thm thm |
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315 val prop' = tp $ (A $ Abs(x,ty,M)) |
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316 in ALPHA thm (cterm_of thy prop') |
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317 end |
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318 end; |
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319 |
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320 val GENL = fold_rev GEN; |
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321 |
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322 fun GEN_ALL thm = |
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323 let val {prop,thy,...} = rep_thm thm |
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324 val tycheck = cterm_of thy |
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325 val vlist = map tycheck (add_term_vars (prop, [])) |
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326 in GENL vlist thm |
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327 end; |
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328 |
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329 |
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330 fun MATCH_MP th1 th2 = |
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331 if (D.is_forall (D.drop_prop(cconcl th1))) |
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332 then MATCH_MP (th1 RS spec) th2 |
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333 else MP th1 th2; |
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334 |
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335 |
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336 (*---------------------------------------------------------------------------- |
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337 * Existentials |
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338 *---------------------------------------------------------------------------*) |
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339 |
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340 |
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341 |
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342 (*--------------------------------------------------------------------------- |
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343 * Existential elimination |
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344 * |
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345 * A1 |- ?x.t[x] , A2, "t[v]" |- t' |
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346 * ------------------------------------ (variable v occurs nowhere) |
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347 * A1 u A2 |- t' |
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348 * |
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349 *---------------------------------------------------------------------------*) |
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350 |
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351 fun CHOOSE (fvar, exth) fact = |
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352 let |
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353 val lam = #2 (D.dest_comb (D.drop_prop (cconcl exth))) |
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354 val redex = D.capply lam fvar |
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355 val {thy, t = t$u,...} = Thm.rep_cterm redex |
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356 val residue = Thm.cterm_of thy (Term.betapply (t, u)) |
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357 in |
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358 GEN fvar (DISCH residue fact) RS (exth RS Thms.choose_thm) |
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359 handle THM (msg, _, _) => raise RULES_ERR "CHOOSE" msg |
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360 end; |
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361 |
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362 local val {prop,thy,...} = rep_thm exI |
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363 val [P,x] = term_vars prop |
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364 in |
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365 fun EXISTS (template,witness) thm = |
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366 let val {prop,thy,...} = rep_thm thm |
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367 val P' = cterm_of thy P |
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368 val x' = cterm_of thy x |
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369 val abstr = #2 (D.dest_comb template) |
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370 in |
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371 thm RS (cterm_instantiate[(P',abstr), (x',witness)] exI) |
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372 handle THM (msg, _, _) => raise RULES_ERR "EXISTS" msg |
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373 end |
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374 end; |
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375 |
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376 (*---------------------------------------------------------------------------- |
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377 * |
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378 * A |- M |
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379 * ------------------- [v_1,...,v_n] |
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380 * A |- ?v1...v_n. M |
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381 * |
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382 *---------------------------------------------------------------------------*) |
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383 |
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384 fun EXISTL vlist th = |
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385 fold_rev (fn v => fn thm => EXISTS(D.mk_exists(v,cconcl thm), v) thm) |
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386 vlist th; |
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387 |
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388 |
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389 (*---------------------------------------------------------------------------- |
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390 * |
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391 * A |- M[x_1,...,x_n] |
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392 * ---------------------------- [(x |-> y)_1,...,(x |-> y)_n] |
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393 * A |- ?y_1...y_n. M |
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394 * |
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395 *---------------------------------------------------------------------------*) |
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396 (* Could be improved, but needs "subst_free" for certified terms *) |
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397 |
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398 fun IT_EXISTS blist th = |
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399 let val {thy,...} = rep_thm th |
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400 val tych = cterm_of thy |
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401 val detype = #t o rep_cterm |
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402 val blist' = map (fn (x,y) => (detype x, detype y)) blist |
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403 fun ex v M = cterm_of thy (S.mk_exists{Bvar=v,Body = M}) |
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404 |
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405 in |
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406 fold_rev (fn (b as (r1,r2)) => fn thm => |
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407 EXISTS(ex r2 (subst_free [b] |
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408 (HOLogic.dest_Trueprop(#prop(rep_thm thm)))), tych r1) |
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409 thm) |
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410 blist' th |
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411 end; |
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412 |
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413 (*--------------------------------------------------------------------------- |
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414 * Faster version, that fails for some as yet unknown reason |
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415 * fun IT_EXISTS blist th = |
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416 * let val {thy,...} = rep_thm th |
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417 * val tych = cterm_of thy |
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418 * fun detype (x,y) = ((#t o rep_cterm) x, (#t o rep_cterm) y) |
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419 * in |
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420 * fold (fn (b as (r1,r2), thm) => |
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421 * EXISTS(D.mk_exists(r2, tych(subst_free[detype b](#t(rep_cterm(cconcl thm))))), |
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422 * r1) thm) blist th |
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423 * end; |
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424 *---------------------------------------------------------------------------*) |
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425 |
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426 (*---------------------------------------------------------------------------- |
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427 * Rewriting |
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428 *---------------------------------------------------------------------------*) |
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429 |
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430 fun SUBS thl = |
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431 rewrite_rule (map (fn th => th RS eq_reflection handle THM _ => th) thl); |
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432 |
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433 val rew_conv = MetaSimplifier.rewrite_cterm (true, false, false) (K (K NONE)); |
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434 |
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435 fun simpl_conv ss thl ctm = |
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436 rew_conv (ss addsimps thl) ctm RS meta_eq_to_obj_eq; |
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437 |
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438 |
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439 val RIGHT_ASSOC = rewrite_rule [Thms.disj_assoc]; |
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440 |
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441 |
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442 |
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443 (*--------------------------------------------------------------------------- |
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444 * TERMINATION CONDITION EXTRACTION |
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445 *---------------------------------------------------------------------------*) |
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446 |
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447 |
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448 (* Object language quantifier, i.e., "!" *) |
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449 fun Forall v M = S.mk_forall{Bvar=v, Body=M}; |
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450 |
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451 |
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452 (* Fragile: it's a cong if it is not "R y x ==> cut f R x y = f y" *) |
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453 fun is_cong thm = |
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454 let val {prop, ...} = rep_thm thm |
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455 in case prop |
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456 of (Const("==>",_)$(Const("Trueprop",_)$ _) $ |
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457 (Const("==",_) $ (Const ("Wellfounded_Recursion.cut",_) $ f $ R $ a $ x) $ _)) => false |
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458 | _ => true |
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459 end; |
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460 |
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461 |
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462 |
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463 fun dest_equal(Const ("==",_) $ |
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464 (Const ("Trueprop",_) $ lhs) |
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465 $ (Const ("Trueprop",_) $ rhs)) = {lhs=lhs, rhs=rhs} |
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466 | dest_equal(Const ("==",_) $ lhs $ rhs) = {lhs=lhs, rhs=rhs} |
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467 | dest_equal tm = S.dest_eq tm; |
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468 |
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469 fun get_lhs tm = #lhs(dest_equal (HOLogic.dest_Trueprop tm)); |
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470 |
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471 fun dest_all used (Const("all",_) $ (a as Abs _)) = S.dest_abs used a |
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472 | dest_all _ _ = raise RULES_ERR "dest_all" "not a !!"; |
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473 |
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474 val is_all = can (dest_all []); |
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475 |
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476 fun strip_all used fm = |
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477 if (is_all fm) |
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478 then let val ({Bvar, Body}, used') = dest_all used fm |
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479 val (bvs, core, used'') = strip_all used' Body |
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480 in ((Bvar::bvs), core, used'') |
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481 end |
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482 else ([], fm, used); |
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483 |
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484 fun break_all(Const("all",_) $ Abs (_,_,body)) = body |
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485 | break_all _ = raise RULES_ERR "break_all" "not a !!"; |
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486 |
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487 fun list_break_all(Const("all",_) $ Abs (s,ty,body)) = |
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488 let val (L,core) = list_break_all body |
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489 in ((s,ty)::L, core) |
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490 end |
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491 | list_break_all tm = ([],tm); |
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492 |
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493 (*--------------------------------------------------------------------------- |
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494 * Rename a term of the form |
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495 * |
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496 * !!x1 ...xn. x1=M1 ==> ... ==> xn=Mn |
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497 * ==> ((%v1...vn. Q) x1 ... xn = g x1 ... xn. |
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498 * to one of |
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499 * |
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500 * !!v1 ... vn. v1=M1 ==> ... ==> vn=Mn |
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501 * ==> ((%v1...vn. Q) v1 ... vn = g v1 ... vn. |
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502 * |
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503 * This prevents name problems in extraction, and helps the result to read |
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504 * better. There is a problem with varstructs, since they can introduce more |
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505 * than n variables, and some extra reasoning needs to be done. |
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506 *---------------------------------------------------------------------------*) |
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507 |
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508 fun get ([],_,L) = rev L |
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509 | get (ant::rst,n,L) = |
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510 case (list_break_all ant) |
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511 of ([],_) => get (rst, n+1,L) |
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512 | (vlist,body) => |
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513 let val eq = Logic.strip_imp_concl body |
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514 val (f,args) = S.strip_comb (get_lhs eq) |
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515 val (vstrl,_) = S.strip_abs f |
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516 val names = |
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517 Name.variant_list (add_term_names(body, [])) (map (#1 o dest_Free) vstrl) |
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518 in get (rst, n+1, (names,n)::L) end |
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519 handle TERM _ => get (rst, n+1, L) |
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520 | U.ERR _ => get (rst, n+1, L); |
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521 |
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522 (* Note: rename_params_rule counts from 1, not 0 *) |
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523 fun rename thm = |
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524 let val {prop,thy,...} = rep_thm thm |
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525 val tych = cterm_of thy |
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526 val ants = Logic.strip_imp_prems prop |
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527 val news = get (ants,1,[]) |
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528 in |
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529 fold rename_params_rule news thm |
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530 end; |
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531 |
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532 |
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533 (*--------------------------------------------------------------------------- |
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534 * Beta-conversion to the rhs of an equation (taken from hol90/drule.sml) |
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535 *---------------------------------------------------------------------------*) |
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536 |
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537 fun list_beta_conv tm = |
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538 let fun rbeta th = Thm.transitive th (beta_conversion false (#2(D.dest_eq(cconcl th)))) |
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539 fun iter [] = Thm.reflexive tm |
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540 | iter (v::rst) = rbeta (combination(iter rst) (Thm.reflexive v)) |
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541 in iter end; |
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542 |
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543 |
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544 (*--------------------------------------------------------------------------- |
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545 * Trace information for the rewriter |
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546 *---------------------------------------------------------------------------*) |
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547 val term_ref = ref[] : term list ref |
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548 val ss_ref = ref [] : simpset list ref; |
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549 val thm_ref = ref [] : thm list ref; |
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550 val tracing = ref false; |
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551 |
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552 fun say s = if !tracing then writeln s else (); |
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553 |
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554 fun print_thms s L = |
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555 say (cat_lines (s :: map string_of_thm L)); |
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556 |
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557 fun print_cterms s L = |
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558 say (cat_lines (s :: map string_of_cterm L)); |
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559 |
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560 |
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561 (*--------------------------------------------------------------------------- |
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562 * General abstraction handlers, should probably go in USyntax. |
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563 *---------------------------------------------------------------------------*) |
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564 fun mk_aabs (vstr, body) = |
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565 S.mk_abs {Bvar = vstr, Body = body} |
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566 handle U.ERR _ => S.mk_pabs {varstruct = vstr, body = body}; |
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567 |
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568 fun list_mk_aabs (vstrl,tm) = |
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569 fold_rev (fn vstr => fn tm => mk_aabs(vstr,tm)) vstrl tm; |
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570 |
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571 fun dest_aabs used tm = |
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572 let val ({Bvar,Body}, used') = S.dest_abs used tm |
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573 in (Bvar, Body, used') end |
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574 handle U.ERR _ => |
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575 let val {varstruct, body, used} = S.dest_pabs used tm |
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576 in (varstruct, body, used) end; |
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577 |
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578 fun strip_aabs used tm = |
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579 let val (vstr, body, used') = dest_aabs used tm |
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580 val (bvs, core, used'') = strip_aabs used' body |
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581 in (vstr::bvs, core, used'') end |
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582 handle U.ERR _ => ([], tm, used); |
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583 |
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584 fun dest_combn tm 0 = (tm,[]) |
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585 | dest_combn tm n = |
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586 let val {Rator,Rand} = S.dest_comb tm |
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587 val (f,rands) = dest_combn Rator (n-1) |
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588 in (f,Rand::rands) |
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589 end; |
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590 |
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591 |
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592 |
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593 |
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594 local fun dest_pair M = let val {fst,snd} = S.dest_pair M in (fst,snd) end |
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595 fun mk_fst tm = |
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596 let val ty as Type("*", [fty,sty]) = type_of tm |
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597 in Const ("fst", ty --> fty) $ tm end |
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598 fun mk_snd tm = |
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599 let val ty as Type("*", [fty,sty]) = type_of tm |
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600 in Const ("snd", ty --> sty) $ tm end |
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601 in |
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602 fun XFILL tych x vstruct = |
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603 let fun traverse p xocc L = |
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604 if (is_Free p) |
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605 then tych xocc::L |
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606 else let val (p1,p2) = dest_pair p |
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607 in traverse p1 (mk_fst xocc) (traverse p2 (mk_snd xocc) L) |
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608 end |
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609 in |
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610 traverse vstruct x [] |
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611 end end; |
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612 |
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613 (*--------------------------------------------------------------------------- |
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614 * Replace a free tuple (vstr) by a universally quantified variable (a). |
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615 * Note that the notion of "freeness" for a tuple is different than for a |
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616 * variable: if variables in the tuple also occur in any other place than |
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617 * an occurrences of the tuple, they aren't "free" (which is thus probably |
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618 * the wrong word to use). |
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619 *---------------------------------------------------------------------------*) |
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620 |
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621 fun VSTRUCT_ELIM tych a vstr th = |
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622 let val L = S.free_vars_lr vstr |
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623 val bind1 = tych (HOLogic.mk_Trueprop (HOLogic.mk_eq(a,vstr))) |
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624 val thm1 = implies_intr bind1 (SUBS [SYM(assume bind1)] th) |
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625 val thm2 = forall_intr_list (map tych L) thm1 |
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626 val thm3 = forall_elim_list (XFILL tych a vstr) thm2 |
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627 in refl RS |
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628 rewrite_rule [Thm.symmetric (surjective_pairing RS eq_reflection)] thm3 |
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629 end; |
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630 |
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631 fun PGEN tych a vstr th = |
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632 let val a1 = tych a |
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633 val vstr1 = tych vstr |
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634 in |
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635 forall_intr a1 |
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636 (if (is_Free vstr) |
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637 then cterm_instantiate [(vstr1,a1)] th |
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638 else VSTRUCT_ELIM tych a vstr th) |
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639 end; |
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640 |
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641 |
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642 (*--------------------------------------------------------------------------- |
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643 * Takes apart a paired beta-redex, looking like "(\(x,y).N) vstr", into |
|
644 * |
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645 * (([x,y],N),vstr) |
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646 *---------------------------------------------------------------------------*) |
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647 fun dest_pbeta_redex used M n = |
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648 let val (f,args) = dest_combn M n |
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649 val dummy = dest_aabs used f |
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650 in (strip_aabs used f,args) |
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651 end; |
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652 |
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653 fun pbeta_redex M n = can (U.C (dest_pbeta_redex []) n) M; |
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654 |
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655 fun dest_impl tm = |
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656 let val ants = Logic.strip_imp_prems tm |
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657 val eq = Logic.strip_imp_concl tm |
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658 in (ants,get_lhs eq) |
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659 end; |
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660 |
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661 fun restricted t = isSome (S.find_term |
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662 (fn (Const("Wellfounded_Recursion.cut",_)) =>true | _ => false) |
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663 t) |
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664 |
|
665 fun CONTEXT_REWRITE_RULE (func, G, cut_lemma, congs) th = |
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666 let val globals = func::G |
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667 val ss0 = Simplifier.theory_context (Thm.theory_of_thm th) empty_ss |
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668 val pbeta_reduce = simpl_conv ss0 [split_conv RS eq_reflection]; |
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669 val tc_list = ref[]: term list ref |
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670 val dummy = term_ref := [] |
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671 val dummy = thm_ref := [] |
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672 val dummy = ss_ref := [] |
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673 val cut_lemma' = cut_lemma RS eq_reflection |
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674 fun prover used ss thm = |
|
675 let fun cong_prover ss thm = |
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676 let val dummy = say "cong_prover:" |
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677 val cntxt = MetaSimplifier.prems_of_ss ss |
|
678 val dummy = print_thms "cntxt:" cntxt |
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679 val dummy = say "cong rule:" |
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680 val dummy = say (string_of_thm thm) |
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681 val dummy = thm_ref := (thm :: !thm_ref) |
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682 val dummy = ss_ref := (ss :: !ss_ref) |
|
683 (* Unquantified eliminate *) |
|
684 fun uq_eliminate (thm,imp,thy) = |
|
685 let val tych = cterm_of thy |
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686 val dummy = print_cterms "To eliminate:" [tych imp] |
|
687 val ants = map tych (Logic.strip_imp_prems imp) |
|
688 val eq = Logic.strip_imp_concl imp |
|
689 val lhs = tych(get_lhs eq) |
|
690 val ss' = MetaSimplifier.add_prems (map ASSUME ants) ss |
|
691 val lhs_eq_lhs1 = MetaSimplifier.rewrite_cterm (false,true,false) (prover used) ss' lhs |
|
692 handle U.ERR _ => Thm.reflexive lhs |
|
693 val dummy = print_thms "proven:" [lhs_eq_lhs1] |
|
694 val lhs_eq_lhs2 = implies_intr_list ants lhs_eq_lhs1 |
|
695 val lhs_eeq_lhs2 = lhs_eq_lhs2 RS meta_eq_to_obj_eq |
|
696 in |
|
697 lhs_eeq_lhs2 COMP thm |
|
698 end |
|
699 fun pq_eliminate (thm,thy,vlist,imp_body,lhs_eq) = |
|
700 let val ((vstrl, _, used'), args) = dest_pbeta_redex used lhs_eq (length vlist) |
|
701 val dummy = forall (op aconv) (ListPair.zip (vlist, args)) |
|
702 orelse error "assertion failed in CONTEXT_REWRITE_RULE" |
|
703 val imp_body1 = subst_free (ListPair.zip (args, vstrl)) |
|
704 imp_body |
|
705 val tych = cterm_of thy |
|
706 val ants1 = map tych (Logic.strip_imp_prems imp_body1) |
|
707 val eq1 = Logic.strip_imp_concl imp_body1 |
|
708 val Q = get_lhs eq1 |
|
709 val QeqQ1 = pbeta_reduce (tych Q) |
|
710 val Q1 = #2(D.dest_eq(cconcl QeqQ1)) |
|
711 val ss' = MetaSimplifier.add_prems (map ASSUME ants1) ss |
|
712 val Q1eeqQ2 = MetaSimplifier.rewrite_cterm (false,true,false) (prover used') ss' Q1 |
|
713 handle U.ERR _ => Thm.reflexive Q1 |
|
714 val Q2 = #2 (Logic.dest_equals (Thm.prop_of Q1eeqQ2)) |
|
715 val Q3 = tych(list_comb(list_mk_aabs(vstrl,Q2),vstrl)) |
|
716 val Q2eeqQ3 = Thm.symmetric(pbeta_reduce Q3 RS eq_reflection) |
|
717 val thA = Thm.transitive(QeqQ1 RS eq_reflection) Q1eeqQ2 |
|
718 val QeeqQ3 = Thm.transitive thA Q2eeqQ3 handle THM _ => |
|
719 ((Q2eeqQ3 RS meta_eq_to_obj_eq) |
|
720 RS ((thA RS meta_eq_to_obj_eq) RS trans)) |
|
721 RS eq_reflection |
|
722 val impth = implies_intr_list ants1 QeeqQ3 |
|
723 val impth1 = impth RS meta_eq_to_obj_eq |
|
724 (* Need to abstract *) |
|
725 val ant_th = U.itlist2 (PGEN tych) args vstrl impth1 |
|
726 in ant_th COMP thm |
|
727 end |
|
728 fun q_eliminate (thm,imp,thy) = |
|
729 let val (vlist, imp_body, used') = strip_all used imp |
|
730 val (ants,Q) = dest_impl imp_body |
|
731 in if (pbeta_redex Q) (length vlist) |
|
732 then pq_eliminate (thm,thy,vlist,imp_body,Q) |
|
733 else |
|
734 let val tych = cterm_of thy |
|
735 val ants1 = map tych ants |
|
736 val ss' = MetaSimplifier.add_prems (map ASSUME ants1) ss |
|
737 val Q_eeq_Q1 = MetaSimplifier.rewrite_cterm |
|
738 (false,true,false) (prover used') ss' (tych Q) |
|
739 handle U.ERR _ => Thm.reflexive (tych Q) |
|
740 val lhs_eeq_lhs2 = implies_intr_list ants1 Q_eeq_Q1 |
|
741 val lhs_eq_lhs2 = lhs_eeq_lhs2 RS meta_eq_to_obj_eq |
|
742 val ant_th = forall_intr_list(map tych vlist)lhs_eq_lhs2 |
|
743 in |
|
744 ant_th COMP thm |
|
745 end end |
|
746 |
|
747 fun eliminate thm = |
|
748 case (rep_thm thm) |
|
749 of {prop = (Const("==>",_) $ imp $ _), thy, ...} => |
|
750 eliminate |
|
751 (if not(is_all imp) |
|
752 then uq_eliminate (thm,imp,thy) |
|
753 else q_eliminate (thm,imp,thy)) |
|
754 (* Assume that the leading constant is ==, *) |
|
755 | _ => thm (* if it is not a ==> *) |
|
756 in SOME(eliminate (rename thm)) end |
|
757 handle U.ERR _ => NONE (* FIXME handle THM as well?? *) |
|
758 |
|
759 fun restrict_prover ss thm = |
|
760 let val dummy = say "restrict_prover:" |
|
761 val cntxt = rev(MetaSimplifier.prems_of_ss ss) |
|
762 val dummy = print_thms "cntxt:" cntxt |
|
763 val {prop = Const("==>",_) $ (Const("Trueprop",_) $ A) $ _, |
|
764 thy,...} = rep_thm thm |
|
765 fun genl tm = let val vlist = subtract (op aconv) globals |
|
766 (add_term_frees(tm,[])) |
|
767 in fold_rev Forall vlist tm |
|
768 end |
|
769 (*-------------------------------------------------------------- |
|
770 * This actually isn't quite right, since it will think that |
|
771 * not-fully applied occs. of "f" in the context mean that the |
|
772 * current call is nested. The real solution is to pass in a |
|
773 * term "f v1..vn" which is a pattern that any full application |
|
774 * of "f" will match. |
|
775 *-------------------------------------------------------------*) |
|
776 val func_name = #1(dest_Const func) |
|
777 fun is_func (Const (name,_)) = (name = func_name) |
|
778 | is_func _ = false |
|
779 val rcontext = rev cntxt |
|
780 val cncl = HOLogic.dest_Trueprop o Thm.prop_of |
|
781 val antl = case rcontext of [] => [] |
|
782 | _ => [S.list_mk_conj(map cncl rcontext)] |
|
783 val TC = genl(S.list_mk_imp(antl, A)) |
|
784 val dummy = print_cterms "func:" [cterm_of thy func] |
|
785 val dummy = print_cterms "TC:" |
|
786 [cterm_of thy (HOLogic.mk_Trueprop TC)] |
|
787 val dummy = tc_list := (TC :: !tc_list) |
|
788 val nestedp = isSome (S.find_term is_func TC) |
|
789 val dummy = if nestedp then say "nested" else say "not_nested" |
|
790 val dummy = term_ref := ([func,TC]@(!term_ref)) |
|
791 val th' = if nestedp then raise RULES_ERR "solver" "nested function" |
|
792 else let val cTC = cterm_of thy |
|
793 (HOLogic.mk_Trueprop TC) |
|
794 in case rcontext of |
|
795 [] => SPEC_ALL(ASSUME cTC) |
|
796 | _ => MP (SPEC_ALL (ASSUME cTC)) |
|
797 (LIST_CONJ rcontext) |
|
798 end |
|
799 val th'' = th' RS thm |
|
800 in SOME (th'') |
|
801 end handle U.ERR _ => NONE (* FIXME handle THM as well?? *) |
|
802 in |
|
803 (if (is_cong thm) then cong_prover else restrict_prover) ss thm |
|
804 end |
|
805 val ctm = cprop_of th |
|
806 val names = add_term_names (term_of ctm, []) |
|
807 val th1 = MetaSimplifier.rewrite_cterm(false,true,false) |
|
808 (prover names) (ss0 addsimps [cut_lemma'] addeqcongs congs) ctm |
|
809 val th2 = equal_elim th1 th |
|
810 in |
|
811 (th2, List.filter (not o restricted) (!tc_list)) |
|
812 end; |
|
813 |
|
814 |
|
815 fun prove strict (ptm, tac) = |
|
816 let |
|
817 val {thy, t, ...} = Thm.rep_cterm ptm; |
|
818 val ctxt = ProofContext.init thy |> Variable.auto_fixes t; |
|
819 in |
|
820 if strict then Goal.prove ctxt [] [] t (K tac) |
|
821 else Goal.prove ctxt [] [] t (K tac) |
|
822 handle ERROR msg => (warning msg; raise RULES_ERR "prove" msg) |
|
823 end; |
|
824 |
|
825 end; |