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1 (* Title: TFL/rules |
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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 |
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10 structure Rules : Rules_sig = |
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11 struct |
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12 |
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13 open Utils; |
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14 |
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15 structure USyntax = USyntax; |
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16 structure S = USyntax; |
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17 structure U = Utils; |
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18 structure D = Dcterm; |
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19 |
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20 |
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21 fun RULES_ERR{func,mesg} = Utils.ERR{module = "Rules",func=func,mesg=mesg}; |
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22 |
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23 |
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24 fun cconcl thm = D.drop_prop(#prop(crep_thm thm)); |
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25 fun chyps thm = map D.drop_prop(#hyps(crep_thm thm)); |
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26 |
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27 fun dest_thm thm = |
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28 let val {prop,hyps,...} = rep_thm thm |
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29 in (map HOLogic.dest_Trueprop hyps, HOLogic.dest_Trueprop prop) |
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30 end; |
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31 |
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32 |
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33 |
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34 (* Inference rules *) |
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35 |
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36 (*--------------------------------------------------------------------------- |
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37 * Equality (one step) |
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38 *---------------------------------------------------------------------------*) |
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39 fun REFL tm = Thm.reflexive tm RS meta_eq_to_obj_eq; |
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40 fun SYM thm = thm RS sym; |
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41 |
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42 fun ALPHA thm ctm1 = |
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43 let val ctm2 = cprop_of thm |
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44 val ctm2_eq = reflexive ctm2 |
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45 val ctm1_eq = reflexive ctm1 |
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46 in equal_elim (transitive ctm2_eq ctm1_eq) thm |
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47 end; |
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48 |
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49 |
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50 (*---------------------------------------------------------------------------- |
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51 * typ instantiation |
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52 *---------------------------------------------------------------------------*) |
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53 fun INST_TYPE blist thm = |
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54 let val {sign,...} = rep_thm thm |
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55 val blist' = map (fn (TVar(idx,_), B) => (idx, ctyp_of sign B)) blist |
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56 in Thm.instantiate (blist',[]) thm |
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57 end |
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58 handle _ => raise RULES_ERR{func = "INST_TYPE", mesg = ""}; |
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59 |
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60 |
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61 (*---------------------------------------------------------------------------- |
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62 * Implication and the assumption list |
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63 * |
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64 * Assumptions get stuck on the meta-language assumption list. Implications |
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65 * are in the object language, so discharging an assumption "A" from theorem |
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66 * "B" results in something that looks like "A --> B". |
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67 *---------------------------------------------------------------------------*) |
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68 fun ASSUME ctm = Thm.assume (D.mk_prop ctm); |
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69 |
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70 |
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71 (*--------------------------------------------------------------------------- |
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72 * Implication in TFL is -->. Meta-language implication (==>) is only used |
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73 * in the implementation of some of the inference rules below. |
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74 *---------------------------------------------------------------------------*) |
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75 fun MP th1 th2 = th2 RS (th1 RS mp); |
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76 |
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77 (*forces the first argument to be a proposition if necessary*) |
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78 fun DISCH tm thm = Thm.implies_intr (D.mk_prop tm) thm COMP impI; |
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79 |
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80 fun DISCH_ALL thm = Utils.itlist DISCH (#hyps (crep_thm thm)) thm; |
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81 |
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82 |
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83 fun FILTER_DISCH_ALL P thm = |
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84 let fun check tm = U.holds P (#t(rep_cterm tm)) |
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85 in foldr (fn (tm,th) => if (check tm) then DISCH tm th else th) |
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86 (chyps thm, thm) |
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87 end; |
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88 |
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89 (* freezeT expensive! *) |
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90 fun UNDISCH thm = |
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91 let val tm = D.mk_prop(#1(D.dest_imp(cconcl (freezeT thm)))) |
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92 in implies_elim (thm RS mp) (ASSUME tm) |
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93 end |
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94 handle _ => raise RULES_ERR{func = "UNDISCH", mesg = ""}; |
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95 |
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96 fun PROVE_HYP ath bth = MP (DISCH (cconcl ath) bth) ath; |
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97 |
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98 local val [p1,p2] = goal HOL.thy "(A-->B) ==> (B --> C) ==> (A-->C)" |
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99 val dummy = by (rtac impI 1) |
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100 val dummy = by (rtac (p2 RS mp) 1) |
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101 val dummy = by (rtac (p1 RS mp) 1) |
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102 val dummy = by (assume_tac 1) |
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103 val imp_trans = result() |
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104 in |
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105 fun IMP_TRANS th1 th2 = th2 RS (th1 RS imp_trans) |
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106 end; |
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107 |
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108 (*---------------------------------------------------------------------------- |
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109 * Conjunction |
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110 *---------------------------------------------------------------------------*) |
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111 fun CONJUNCT1 thm = (thm RS conjunct1) |
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112 fun CONJUNCT2 thm = (thm RS conjunct2); |
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113 fun CONJUNCTS th = (CONJUNCTS (CONJUNCT1 th) @ CONJUNCTS (CONJUNCT2 th)) |
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114 handle _ => [th]; |
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115 |
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116 fun LIST_CONJ [] = raise RULES_ERR{func = "LIST_CONJ", mesg = "empty list"} |
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117 | LIST_CONJ [th] = th |
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118 | LIST_CONJ (th::rst) = MP(MP(conjI COMP (impI RS impI)) th) (LIST_CONJ rst); |
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119 |
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120 |
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121 (*---------------------------------------------------------------------------- |
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122 * Disjunction |
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123 *---------------------------------------------------------------------------*) |
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124 local val {prop,sign,...} = rep_thm disjI1 |
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125 val [P,Q] = term_vars prop |
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126 val disj1 = forall_intr (cterm_of sign Q) disjI1 |
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127 in |
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128 fun DISJ1 thm tm = thm RS (forall_elim (D.drop_prop tm) disj1) |
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129 end; |
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130 |
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131 local val {prop,sign,...} = rep_thm disjI2 |
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132 val [P,Q] = term_vars prop |
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133 val disj2 = forall_intr (cterm_of sign P) disjI2 |
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134 in |
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135 fun DISJ2 tm thm = thm RS (forall_elim (D.drop_prop tm) disj2) |
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136 end; |
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137 |
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138 |
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139 (*---------------------------------------------------------------------------- |
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140 * |
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141 * A1 |- M1, ..., An |- Mn |
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142 * --------------------------------------------------- |
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143 * [A1 |- M1 \/ ... \/ Mn, ..., An |- M1 \/ ... \/ Mn] |
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144 * |
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145 *---------------------------------------------------------------------------*) |
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146 |
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147 |
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148 fun EVEN_ORS thms = |
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149 let fun blue ldisjs [] _ = [] |
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150 | blue ldisjs (th::rst) rdisjs = |
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151 let val tail = tl rdisjs |
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152 val rdisj_tl = D.list_mk_disj tail |
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153 in itlist DISJ2 ldisjs (DISJ1 th rdisj_tl) |
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154 :: blue (ldisjs@[cconcl th]) rst tail |
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155 end handle _ => [itlist DISJ2 ldisjs th] |
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156 in |
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157 blue [] thms (map cconcl thms) |
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158 end; |
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159 |
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160 |
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161 (*---------------------------------------------------------------------------- |
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162 * |
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163 * A |- P \/ Q B,P |- R C,Q |- R |
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164 * --------------------------------------------------- |
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165 * A U B U C |- R |
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166 * |
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167 *---------------------------------------------------------------------------*) |
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168 local val [p1,p2,p3] = goal HOL.thy "(P | Q) ==> (P --> R) ==> (Q --> R) ==> R" |
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169 val dummy = by (rtac (p1 RS disjE) 1) |
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170 val dummy = by (rtac (p2 RS mp) 1) |
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171 val dummy = by (assume_tac 1) |
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172 val dummy = by (rtac (p3 RS mp) 1) |
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173 val dummy = by (assume_tac 1) |
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174 val tfl_exE = result() |
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175 in |
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176 fun DISJ_CASES th1 th2 th3 = |
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177 let val c = D.drop_prop(cconcl th1) |
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178 val (disj1,disj2) = D.dest_disj c |
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179 val th2' = DISCH disj1 th2 |
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180 val th3' = DISCH disj2 th3 |
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181 in |
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182 th3' RS (th2' RS (th1 RS tfl_exE)) |
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183 end |
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184 end; |
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185 |
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186 |
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187 (*----------------------------------------------------------------------------- |
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188 * |
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189 * |- A1 \/ ... \/ An [A1 |- M, ..., An |- M] |
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190 * --------------------------------------------------- |
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191 * |- M |
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192 * |
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193 * Note. The list of theorems may be all jumbled up, so we have to |
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194 * first organize it to align with the first argument (the disjunctive |
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195 * theorem). |
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196 *---------------------------------------------------------------------------*) |
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197 |
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198 fun organize eq = (* a bit slow - analogous to insertion sort *) |
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199 let fun extract a alist = |
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200 let fun ex (_,[]) = raise RULES_ERR{func = "organize", |
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201 mesg = "not a permutation.1"} |
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202 | ex(left,h::t) = if (eq h a) then (h,rev left@t) else ex(h::left,t) |
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203 in ex ([],alist) |
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204 end |
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205 fun place [] [] = [] |
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206 | place (a::rst) alist = |
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207 let val (item,next) = extract a alist |
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208 in item::place rst next |
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209 end |
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210 | place _ _ = raise RULES_ERR{func = "organize", |
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211 mesg = "not a permutation.2"} |
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212 in place |
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213 end; |
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214 (* freezeT expensive! *) |
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215 fun DISJ_CASESL disjth thl = |
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216 let val c = cconcl disjth |
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217 fun eq th atm = exists (fn t => HOLogic.dest_Trueprop t |
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218 aconv term_of atm) |
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219 (#hyps(rep_thm th)) |
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220 val tml = D.strip_disj c |
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221 fun DL th [] = raise RULES_ERR{func="DISJ_CASESL",mesg="no cases"} |
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222 | DL th [th1] = PROVE_HYP th th1 |
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223 | DL th [th1,th2] = DISJ_CASES th th1 th2 |
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224 | DL th (th1::rst) = |
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225 let val tm = #2(D.dest_disj(D.drop_prop(cconcl th))) |
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226 in DISJ_CASES th th1 (DL (ASSUME tm) rst) end |
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227 in DL (freezeT disjth) (organize eq tml thl) |
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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 * Universals |
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233 *---------------------------------------------------------------------------*) |
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234 local (* this is fragile *) |
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235 val {prop,sign,...} = rep_thm spec |
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236 val x = hd (tl (term_vars prop)) |
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237 val (TVar (indx,_)) = type_of x |
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238 val gspec = forall_intr (cterm_of sign x) spec |
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239 in |
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240 fun SPEC tm thm = |
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241 let val {sign,T,...} = rep_cterm tm |
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242 val gspec' = instantiate([(indx,ctyp_of sign T)],[]) gspec |
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243 in |
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244 thm RS (forall_elim tm gspec') |
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245 end |
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246 end; |
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247 |
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248 fun SPEC_ALL thm = rev_itlist SPEC (#1(D.strip_forall(cconcl thm))) thm; |
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249 |
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250 val ISPEC = SPEC |
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251 val ISPECL = rev_itlist ISPEC; |
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252 |
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253 (* Not optimized! Too complicated. *) |
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254 local val {prop,sign,...} = rep_thm allI |
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255 val [P] = add_term_vars (prop, []) |
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256 fun cty_theta s = map (fn (i,ty) => (i, ctyp_of s ty)) |
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257 fun ctm_theta s = map (fn (i,tm2) => |
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258 let val ctm2 = cterm_of s tm2 |
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259 in (cterm_of s (Var(i,#T(rep_cterm ctm2))), ctm2) |
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260 end) |
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261 fun certify s (ty_theta,tm_theta) = (cty_theta s ty_theta, |
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262 ctm_theta s tm_theta) |
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263 in |
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264 fun GEN v th = |
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265 let val gth = forall_intr v th |
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266 val {prop=Const("all",_)$Abs(x,ty,rst),sign,...} = rep_thm gth |
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267 val P' = Abs(x,ty, HOLogic.dest_Trueprop rst) (* get rid of trueprop *) |
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268 val tsig = #tsig(Sign.rep_sg sign) |
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269 val theta = Pattern.match tsig (P,P') |
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270 val allI2 = instantiate (certify sign theta) allI |
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271 val thm = implies_elim allI2 gth |
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272 val {prop = tp $ (A $ Abs(_,_,M)),sign,...} = rep_thm thm |
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273 val prop' = tp $ (A $ Abs(x,ty,M)) |
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274 in ALPHA thm (cterm_of sign prop') |
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275 end |
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276 end; |
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277 |
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278 val GENL = itlist GEN; |
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279 |
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280 fun GEN_ALL thm = |
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281 let val {prop,sign,...} = rep_thm thm |
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282 val tycheck = cterm_of sign |
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283 val vlist = map tycheck (add_term_vars (prop, [])) |
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284 in GENL vlist thm |
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285 end; |
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286 |
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287 |
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288 fun MATCH_MP th1 th2 = |
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289 if (D.is_forall (D.drop_prop(cconcl th1))) |
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290 then MATCH_MP (th1 RS spec) th2 |
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291 else MP th1 th2; |
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292 |
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293 |
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294 (*---------------------------------------------------------------------------- |
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295 * Existentials |
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296 *---------------------------------------------------------------------------*) |
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297 |
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298 |
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299 |
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300 (*--------------------------------------------------------------------------- |
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301 * Existential elimination |
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302 * |
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303 * A1 |- ?x.t[x] , A2, "t[v]" |- t' |
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304 * ------------------------------------ (variable v occurs nowhere) |
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305 * A1 u A2 |- t' |
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306 * |
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307 *---------------------------------------------------------------------------*) |
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308 |
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309 local val [p1,p2] = goal HOL.thy "(? x. P x) ==> (!x. P x --> Q) ==> Q" |
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310 val dummy = by (rtac (p1 RS exE) 1) |
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311 val dummy = by (rtac ((p2 RS allE) RS mp) 1) |
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312 val dummy = by (assume_tac 2) |
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313 val dummy = by (assume_tac 1) |
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314 val choose_thm = result() |
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315 in |
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316 fun CHOOSE(fvar,exth) fact = |
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317 let val lam = #2(dest_comb(D.drop_prop(cconcl exth))) |
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318 val redex = capply lam fvar |
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319 val {sign, t = t$u,...} = rep_cterm redex |
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320 val residue = cterm_of sign (betapply(t,u)) |
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321 in GEN fvar (DISCH residue fact) RS (exth RS choose_thm) |
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322 end |
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323 end; |
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324 |
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325 |
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326 local val {prop,sign,...} = rep_thm exI |
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327 val [P,x] = term_vars prop |
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328 in |
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329 fun EXISTS (template,witness) thm = |
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330 let val {prop,sign,...} = rep_thm thm |
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331 val P' = cterm_of sign P |
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332 val x' = cterm_of sign x |
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333 val abstr = #2(dest_comb template) |
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334 in |
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335 thm RS (cterm_instantiate[(P',abstr), (x',witness)] exI) |
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336 end |
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337 end; |
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338 |
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339 (*---------------------------------------------------------------------------- |
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340 * |
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341 * A |- M |
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342 * ------------------- [v_1,...,v_n] |
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343 * A |- ?v1...v_n. M |
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344 * |
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345 *---------------------------------------------------------------------------*) |
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346 |
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347 fun EXISTL vlist th = |
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348 U.itlist (fn v => fn thm => EXISTS(D.mk_exists(v,cconcl thm), v) thm) |
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349 vlist th; |
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350 |
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351 |
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352 (*---------------------------------------------------------------------------- |
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353 * |
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354 * A |- M[x_1,...,x_n] |
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355 * ---------------------------- [(x |-> y)_1,...,(x |-> y)_n] |
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356 * A |- ?y_1...y_n. M |
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357 * |
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358 *---------------------------------------------------------------------------*) |
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359 (* Could be improved, but needs "subst_free" for certified terms *) |
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360 |
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361 fun IT_EXISTS blist th = |
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362 let val {sign,...} = rep_thm th |
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363 val tych = cterm_of sign |
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364 val detype = #t o rep_cterm |
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365 val blist' = map (fn (x,y) => (detype x, detype y)) blist |
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366 fun ?v M = cterm_of sign (S.mk_exists{Bvar=v,Body = M}) |
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367 |
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368 in |
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369 U.itlist (fn (b as (r1,r2)) => fn thm => |
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370 EXISTS(?r2(subst_free[b] |
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371 (HOLogic.dest_Trueprop(#prop(rep_thm thm)))), tych r1) |
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372 thm) |
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373 blist' th |
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374 end; |
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375 |
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376 (*--------------------------------------------------------------------------- |
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377 * Faster version, that fails for some as yet unknown reason |
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378 * fun IT_EXISTS blist th = |
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379 * let val {sign,...} = rep_thm th |
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380 * val tych = cterm_of sign |
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381 * fun detype (x,y) = ((#t o rep_cterm) x, (#t o rep_cterm) y) |
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382 * in |
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383 * fold (fn (b as (r1,r2), thm) => |
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384 * EXISTS(D.mk_exists(r2, tych(subst_free[detype b](#t(rep_cterm(cconcl thm))))), |
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385 * r1) thm) blist th |
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386 * end; |
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387 *---------------------------------------------------------------------------*) |
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388 |
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389 (*---------------------------------------------------------------------------- |
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390 * Rewriting |
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391 *---------------------------------------------------------------------------*) |
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392 |
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393 fun SUBS thl = |
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394 rewrite_rule (map (fn th => (th RS eq_reflection) handle _ => th) thl); |
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395 |
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396 local fun rew_conv mss = Thm.rewrite_cterm (true,false,false) mss (K(K None)) |
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397 in |
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398 fun simpl_conv ss thl ctm = |
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399 rew_conv (Thm.mss_of (#simps (Thm.dest_mss (#mss (rep_ss ss))) @ thl)) ctm |
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400 RS meta_eq_to_obj_eq |
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401 end; |
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402 |
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403 local fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]) |
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404 in |
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405 val RIGHT_ASSOC = rewrite_rule [prover"((a|b)|c) = (a|(b|c))" RS eq_reflection] |
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406 val ASM = refl RS iffD1 |
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407 end; |
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408 |
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409 |
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410 |
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411 |
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412 (*--------------------------------------------------------------------------- |
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413 * TERMINATION CONDITION EXTRACTION |
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414 *---------------------------------------------------------------------------*) |
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415 |
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416 |
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417 (* Object language quantifier, i.e., "!" *) |
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418 fun Forall v M = S.mk_forall{Bvar=v, Body=M}; |
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419 |
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420 |
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421 (* Fragile: it's a cong if it is not "R y x ==> cut f R x y = f y" *) |
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422 fun is_cong thm = |
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423 let val {prop, ...} = rep_thm thm |
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424 in case prop |
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425 of (Const("==>",_)$(Const("Trueprop",_)$ _) $ |
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426 (Const("==",_) $ (Const ("cut",_) $ f $ R $ a $ x) $ _)) => false |
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427 | _ => true |
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428 end; |
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429 |
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430 |
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431 |
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432 fun dest_equal(Const ("==",_) $ |
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433 (Const ("Trueprop",_) $ lhs) |
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434 $ (Const ("Trueprop",_) $ rhs)) = {lhs=lhs, rhs=rhs} |
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435 | dest_equal(Const ("==",_) $ lhs $ rhs) = {lhs=lhs, rhs=rhs} |
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436 | dest_equal tm = S.dest_eq tm; |
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437 |
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438 fun get_lhs tm = #lhs(dest_equal (HOLogic.dest_Trueprop tm)); |
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439 |
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440 fun dest_all(Const("all",_) $ (a as Abs _)) = S.dest_abs a |
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441 | dest_all _ = raise RULES_ERR{func = "dest_all", mesg = "not a !!"}; |
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442 |
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443 val is_all = Utils.can dest_all; |
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444 |
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445 fun strip_all fm = |
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446 if (is_all fm) |
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447 then let val {Bvar,Body} = dest_all fm |
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448 val (bvs,core) = strip_all Body |
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449 in ((Bvar::bvs), core) |
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450 end |
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451 else ([],fm); |
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452 |
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453 fun break_all(Const("all",_) $ Abs (_,_,body)) = body |
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454 | break_all _ = raise RULES_ERR{func = "break_all", mesg = "not a !!"}; |
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455 |
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456 fun list_break_all(Const("all",_) $ Abs (s,ty,body)) = |
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457 let val (L,core) = list_break_all body |
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458 in ((s,ty)::L, core) |
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459 end |
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460 | list_break_all tm = ([],tm); |
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461 |
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462 (*--------------------------------------------------------------------------- |
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463 * Rename a term of the form |
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464 * |
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465 * !!x1 ...xn. x1=M1 ==> ... ==> xn=Mn |
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466 * ==> ((%v1...vn. Q) x1 ... xn = g x1 ... xn. |
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467 * to one of |
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468 * |
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469 * !!v1 ... vn. v1=M1 ==> ... ==> vn=Mn |
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470 * ==> ((%v1...vn. Q) v1 ... vn = g v1 ... vn. |
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471 * |
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472 * This prevents name problems in extraction, and helps the result to read |
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473 * better. There is a problem with varstructs, since they can introduce more |
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474 * than n variables, and some extra reasoning needs to be done. |
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475 *---------------------------------------------------------------------------*) |
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476 |
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477 fun get ([],_,L) = rev L |
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478 | get (ant::rst,n,L) = |
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479 case (list_break_all ant) |
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480 of ([],_) => get (rst, n+1,L) |
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481 | (vlist,body) => |
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482 let val eq = Logic.strip_imp_concl body |
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483 val (f,args) = S.strip_comb (get_lhs eq) |
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484 val (vstrl,_) = S.strip_abs f |
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485 val names = variantlist (map (#1 o dest_Free) vstrl, |
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486 add_term_names(body, [])) |
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487 in get (rst, n+1, (names,n)::L) |
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488 end handle _ => get (rst, n+1, L); |
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489 |
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490 (* Note: rename_params_rule counts from 1, not 0 *) |
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491 fun rename thm = |
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492 let val {prop,sign,...} = rep_thm thm |
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493 val tych = cterm_of sign |
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494 val ants = Logic.strip_imp_prems prop |
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495 val news = get (ants,1,[]) |
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496 in |
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497 U.rev_itlist rename_params_rule news thm |
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498 end; |
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499 |
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500 |
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501 (*--------------------------------------------------------------------------- |
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502 * Beta-conversion to the rhs of an equation (taken from hol90/drule.sml) |
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503 *---------------------------------------------------------------------------*) |
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504 |
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505 fun list_beta_conv tm = |
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506 let fun rbeta th = transitive th (beta_conversion(#2(D.dest_eq(cconcl th)))) |
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507 fun iter [] = reflexive tm |
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508 | iter (v::rst) = rbeta (combination(iter rst) (reflexive v)) |
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509 in iter end; |
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510 |
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511 |
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512 (*--------------------------------------------------------------------------- |
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513 * Trace information for the rewriter |
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514 *---------------------------------------------------------------------------*) |
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515 val term_ref = ref[] : term list ref |
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516 val mss_ref = ref [] : meta_simpset list ref; |
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517 val thm_ref = ref [] : thm list ref; |
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518 val tracing = ref false; |
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519 |
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520 fun say s = if !tracing then writeln s else (); |
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521 |
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522 fun print_thms s L = |
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523 say (cat_lines (s :: map string_of_thm L)); |
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524 |
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525 fun print_cterms s L = |
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526 say (cat_lines (s :: map string_of_cterm L)); |
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527 |
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528 |
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529 (*--------------------------------------------------------------------------- |
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530 * General abstraction handlers, should probably go in USyntax. |
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531 *---------------------------------------------------------------------------*) |
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532 fun mk_aabs(vstr,body) = S.mk_abs{Bvar=vstr,Body=body} |
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533 handle _ => S.mk_pabs{varstruct = vstr, body = body}; |
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534 |
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535 fun list_mk_aabs (vstrl,tm) = |
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536 U.itlist (fn vstr => fn tm => mk_aabs(vstr,tm)) vstrl tm; |
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537 |
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538 fun dest_aabs tm = |
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539 let val {Bvar,Body} = S.dest_abs tm |
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540 in (Bvar,Body) |
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541 end handle _ => let val {varstruct,body} = S.dest_pabs tm |
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542 in (varstruct,body) |
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543 end; |
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544 |
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545 fun strip_aabs tm = |
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546 let val (vstr,body) = dest_aabs tm |
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547 val (bvs, core) = strip_aabs body |
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548 in (vstr::bvs, core) |
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549 end |
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550 handle _ => ([],tm); |
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551 |
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552 fun dest_combn tm 0 = (tm,[]) |
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553 | dest_combn tm n = |
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554 let val {Rator,Rand} = S.dest_comb tm |
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555 val (f,rands) = dest_combn Rator (n-1) |
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556 in (f,Rand::rands) |
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557 end; |
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558 |
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559 |
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560 |
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561 |
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562 local fun dest_pair M = let val {fst,snd} = S.dest_pair M in (fst,snd) end |
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563 fun mk_fst tm = |
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564 let val ty as Type("*", [fty,sty]) = type_of tm |
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565 in Const ("fst", ty --> fty) $ tm end |
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566 fun mk_snd tm = |
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567 let val ty as Type("*", [fty,sty]) = type_of tm |
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568 in Const ("snd", ty --> sty) $ tm end |
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569 in |
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570 fun XFILL tych x vstruct = |
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571 let fun traverse p xocc L = |
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572 if (is_Free p) |
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573 then tych xocc::L |
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574 else let val (p1,p2) = dest_pair p |
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575 in traverse p1 (mk_fst xocc) (traverse p2 (mk_snd xocc) L) |
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576 end |
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577 in |
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578 traverse vstruct x [] |
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579 end end; |
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580 |
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581 (*--------------------------------------------------------------------------- |
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582 * Replace a free tuple (vstr) by a universally quantified variable (a). |
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583 * Note that the notion of "freeness" for a tuple is different than for a |
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584 * variable: if variables in the tuple also occur in any other place than |
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585 * an occurrences of the tuple, they aren't "free" (which is thus probably |
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586 * the wrong word to use). |
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587 *---------------------------------------------------------------------------*) |
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588 |
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589 fun VSTRUCT_ELIM tych a vstr th = |
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590 let val L = S.free_vars_lr vstr |
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591 val bind1 = tych (HOLogic.mk_Trueprop (HOLogic.mk_eq(a,vstr))) |
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592 val thm1 = implies_intr bind1 (SUBS [SYM(assume bind1)] th) |
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593 val thm2 = forall_intr_list (map tych L) thm1 |
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594 val thm3 = forall_elim_list (XFILL tych a vstr) thm2 |
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595 in refl RS |
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596 rewrite_rule[symmetric (surjective_pairing RS eq_reflection)] thm3 |
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597 end; |
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598 |
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599 fun PGEN tych a vstr th = |
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600 let val a1 = tych a |
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601 val vstr1 = tych vstr |
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602 in |
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603 forall_intr a1 |
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604 (if (is_Free vstr) |
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605 then cterm_instantiate [(vstr1,a1)] th |
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606 else VSTRUCT_ELIM tych a vstr th) |
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607 end; |
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608 |
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609 |
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610 (*--------------------------------------------------------------------------- |
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611 * Takes apart a paired beta-redex, looking like "(\(x,y).N) vstr", into |
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612 * |
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613 * (([x,y],N),vstr) |
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614 *---------------------------------------------------------------------------*) |
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615 fun dest_pbeta_redex M n = |
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616 let val (f,args) = dest_combn M n |
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617 val dummy = dest_aabs f |
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618 in (strip_aabs f,args) |
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619 end; |
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620 |
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621 fun pbeta_redex M n = U.can (U.C dest_pbeta_redex n) M; |
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622 |
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623 fun dest_impl tm = |
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624 let val ants = Logic.strip_imp_prems tm |
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625 val eq = Logic.strip_imp_concl tm |
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626 in (ants,get_lhs eq) |
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627 end; |
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628 |
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629 fun restricted t = is_some (S.find_term |
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630 (fn (Const("cut",_)) =>true | _ => false) |
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631 t) |
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632 |
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633 fun CONTEXT_REWRITE_RULE (func, G, cut_lemma, congs) th = |
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634 let val globals = func::G |
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635 val pbeta_reduce = simpl_conv empty_ss [split RS eq_reflection]; |
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636 val tc_list = ref[]: term list ref |
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637 val dummy = term_ref := [] |
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638 val dummy = thm_ref := [] |
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639 val dummy = mss_ref := [] |
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640 val cut_lemma' = cut_lemma RS eq_reflection |
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641 fun prover mss thm = |
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642 let fun cong_prover mss thm = |
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643 let val dummy = say "cong_prover:" |
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644 val cntxt = prems_of_mss mss |
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645 val dummy = print_thms "cntxt:" cntxt |
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646 val dummy = say "cong rule:" |
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647 val dummy = say (string_of_thm thm) |
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648 val dummy = thm_ref := (thm :: !thm_ref) |
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649 val dummy = mss_ref := (mss :: !mss_ref) |
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650 (* Unquantified eliminate *) |
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651 fun uq_eliminate (thm,imp,sign) = |
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652 let val tych = cterm_of sign |
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653 val dummy = print_cterms "To eliminate:" [tych imp] |
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654 val ants = map tych (Logic.strip_imp_prems imp) |
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655 val eq = Logic.strip_imp_concl imp |
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656 val lhs = tych(get_lhs eq) |
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657 val mss' = add_prems(mss, map ASSUME ants) |
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658 val lhs_eq_lhs1 = Thm.rewrite_cterm(false,true,false)mss' prover lhs |
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659 handle _ => reflexive lhs |
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660 val dummy = print_thms "proven:" [lhs_eq_lhs1] |
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661 val lhs_eq_lhs2 = implies_intr_list ants lhs_eq_lhs1 |
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662 val lhs_eeq_lhs2 = lhs_eq_lhs2 RS meta_eq_to_obj_eq |
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663 in |
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664 lhs_eeq_lhs2 COMP thm |
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665 end |
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666 fun pq_eliminate (thm,sign,vlist,imp_body,lhs_eq) = |
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667 let val ((vstrl,_),args) = dest_pbeta_redex lhs_eq(length vlist) |
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668 val dummy = assert (forall (op aconv) |
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669 (ListPair.zip (vlist, args))) |
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670 "assertion failed in CONTEXT_REWRITE_RULE" |
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671 val imp_body1 = subst_free (ListPair.zip (args, vstrl)) |
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672 imp_body |
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673 val tych = cterm_of sign |
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674 val ants1 = map tych (Logic.strip_imp_prems imp_body1) |
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675 val eq1 = Logic.strip_imp_concl imp_body1 |
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676 val Q = get_lhs eq1 |
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677 val QeqQ1 = pbeta_reduce (tych Q) |
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678 val Q1 = #2(D.dest_eq(cconcl QeqQ1)) |
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679 val mss' = add_prems(mss, map ASSUME ants1) |
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680 val Q1eeqQ2 = Thm.rewrite_cterm (false,true,false) mss' prover Q1 |
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681 handle _ => reflexive Q1 |
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682 val Q2 = #2 (Logic.dest_equals (#prop(rep_thm Q1eeqQ2))) |
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683 val Q3 = tych(list_comb(list_mk_aabs(vstrl,Q2),vstrl)) |
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684 val Q2eeqQ3 = symmetric(pbeta_reduce Q3 RS eq_reflection) |
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685 val thA = transitive(QeqQ1 RS eq_reflection) Q1eeqQ2 |
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686 val QeeqQ3 = transitive thA Q2eeqQ3 handle _ => |
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687 ((Q2eeqQ3 RS meta_eq_to_obj_eq) |
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688 RS ((thA RS meta_eq_to_obj_eq) RS trans)) |
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689 RS eq_reflection |
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690 val impth = implies_intr_list ants1 QeeqQ3 |
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691 val impth1 = impth RS meta_eq_to_obj_eq |
|
692 (* Need to abstract *) |
|
693 val ant_th = U.itlist2 (PGEN tych) args vstrl impth1 |
|
694 in ant_th COMP thm |
|
695 end |
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696 fun q_eliminate (thm,imp,sign) = |
|
697 let val (vlist,imp_body) = strip_all imp |
|
698 val (ants,Q) = dest_impl imp_body |
|
699 in if (pbeta_redex Q) (length vlist) |
|
700 then pq_eliminate (thm,sign,vlist,imp_body,Q) |
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701 else |
|
702 let val tych = cterm_of sign |
|
703 val ants1 = map tych ants |
|
704 val mss' = add_prems(mss, map ASSUME ants1) |
|
705 val Q_eeq_Q1 = Thm.rewrite_cterm(false,true,false) mss' |
|
706 prover (tych Q) |
|
707 handle _ => reflexive (tych Q) |
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708 val lhs_eeq_lhs2 = implies_intr_list ants1 Q_eeq_Q1 |
|
709 val lhs_eq_lhs2 = lhs_eeq_lhs2 RS meta_eq_to_obj_eq |
|
710 val ant_th = forall_intr_list(map tych vlist)lhs_eq_lhs2 |
|
711 in |
|
712 ant_th COMP thm |
|
713 end end |
|
714 |
|
715 fun eliminate thm = |
|
716 case (rep_thm thm) |
|
717 of {prop = (Const("==>",_) $ imp $ _), sign, ...} => |
|
718 eliminate |
|
719 (if not(is_all imp) |
|
720 then uq_eliminate (thm,imp,sign) |
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721 else q_eliminate (thm,imp,sign)) |
|
722 (* Assume that the leading constant is ==, *) |
|
723 | _ => thm (* if it is not a ==> *) |
|
724 in Some(eliminate (rename thm)) |
|
725 end handle _ => None |
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726 |
|
727 fun restrict_prover mss thm = |
|
728 let val dummy = say "restrict_prover:" |
|
729 val cntxt = rev(prems_of_mss mss) |
|
730 val dummy = print_thms "cntxt:" cntxt |
|
731 val {prop = Const("==>",_) $ (Const("Trueprop",_) $ A) $ _, |
|
732 sign,...} = rep_thm thm |
|
733 fun genl tm = let val vlist = gen_rems (op aconv) |
|
734 (add_term_frees(tm,[]), globals) |
|
735 in U.itlist Forall vlist tm |
|
736 end |
|
737 (*-------------------------------------------------------------- |
|
738 * This actually isn't quite right, since it will think that |
|
739 * not-fully applied occs. of "f" in the context mean that the |
|
740 * current call is nested. The real solution is to pass in a |
|
741 * term "f v1..vn" which is a pattern that any full application |
|
742 * of "f" will match. |
|
743 *-------------------------------------------------------------*) |
|
744 val func_name = #1(dest_Const func) |
|
745 fun is_func (Const (name,_)) = (name = func_name) |
|
746 | is_func _ = false |
|
747 val rcontext = rev cntxt |
|
748 val cncl = HOLogic.dest_Trueprop o #prop o rep_thm |
|
749 val antl = case rcontext of [] => [] |
|
750 | _ => [S.list_mk_conj(map cncl rcontext)] |
|
751 val TC = genl(S.list_mk_imp(antl, A)) |
|
752 val dummy = print_cterms "func:" [cterm_of sign func] |
|
753 val dummy = print_cterms "TC:" |
|
754 [cterm_of sign (HOLogic.mk_Trueprop TC)] |
|
755 val dummy = tc_list := (TC :: !tc_list) |
|
756 val nestedp = is_some (S.find_term is_func TC) |
|
757 val dummy = if nestedp then say "nested" else say "not_nested" |
|
758 val dummy = term_ref := ([func,TC]@(!term_ref)) |
|
759 val th' = if nestedp then raise RULES_ERR{func = "solver", |
|
760 mesg = "nested function"} |
|
761 else let val cTC = cterm_of sign |
|
762 (HOLogic.mk_Trueprop TC) |
|
763 in case rcontext of |
|
764 [] => SPEC_ALL(ASSUME cTC) |
|
765 | _ => MP (SPEC_ALL (ASSUME cTC)) |
|
766 (LIST_CONJ rcontext) |
|
767 end |
|
768 val th'' = th' RS thm |
|
769 in Some (th'') |
|
770 end handle _ => None |
|
771 in |
|
772 (if (is_cong thm) then cong_prover else restrict_prover) mss thm |
|
773 end |
|
774 val ctm = cprop_of th |
|
775 val th1 = Thm.rewrite_cterm(false,true,false) (add_congs(mss_of [cut_lemma'], congs)) |
|
776 prover ctm |
|
777 val th2 = equal_elim th1 th |
|
778 in |
|
779 (th2, filter (not o restricted) (!tc_list)) |
|
780 end; |
|
781 |
|
782 |
|
783 |
|
784 fun prove (ptm,tac) = |
|
785 #1 (freeze_thaw (prove_goalw_cterm [] ptm (fn _ => [tac]))); |
|
786 |
|
787 |
|
788 end; (* Rules *) |