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1 structure Tfl |
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2 :sig |
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3 structure Prim : TFL_sig |
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4 |
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5 val tgoalw : theory -> thm list -> thm -> thm list |
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6 val tgoal: theory -> thm -> thm list |
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7 |
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8 val WF_TAC : thm list -> tactic |
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9 |
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10 val simplifier : thm -> thm |
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11 val std_postprocessor : theory |
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12 -> {induction:thm, rules:thm, TCs:term list list} |
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13 -> {induction:thm, rules:thm, nested_tcs:thm list} |
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14 |
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15 val rfunction : theory |
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16 -> (thm list -> thm -> thm) |
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17 -> term -> term |
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18 -> {induction:thm, rules:thm, |
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19 tcs:term list, theory:theory} |
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20 |
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21 val Rfunction : theory -> term -> term |
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22 -> {induction:thm, rules:thm, |
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23 theory:theory, tcs:term list} |
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24 |
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25 val function : theory -> term -> {theory:theory, eq_ind : thm} |
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26 val lazyR_def : theory -> term -> {theory:theory, eqns : thm} |
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27 |
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28 val tflcongs : theory -> thm list |
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29 |
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30 end = |
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31 struct |
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32 structure Prim = Prim |
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33 |
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34 fun tgoalw thy defs thm = |
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35 let val L = Prim.termination_goals thm |
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36 open USyntax |
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37 val g = cterm_of (sign_of thy) (mk_prop(list_mk_conj L)) |
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38 in goalw_cterm defs g |
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39 end; |
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40 |
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41 val tgoal = Utils.C tgoalw []; |
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42 |
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43 fun WF_TAC thms = REPEAT(FIRST1(map rtac thms)) |
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44 val WFtac = WF_TAC[wf_measure, wf_inv_image, wf_lex_prod, |
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45 wf_pred_nat, wf_pred_list, wf_trancl]; |
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46 |
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47 val terminator = simp_tac(HOL_ss addsimps[pred_nat_def,pred_list_def, |
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48 fst_conv,snd_conv, |
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49 mem_Collect_eq,lessI]) 1 |
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50 THEN TRY(fast_tac set_cs 1); |
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51 |
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52 val simpls = [less_eq RS eq_reflection, |
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53 lex_prod_def, measure_def, inv_image_def, |
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54 fst_conv RS eq_reflection, snd_conv RS eq_reflection, |
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55 mem_Collect_eq RS eq_reflection(*, length_Cons RS eq_reflection*)]; |
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56 |
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57 val std_postprocessor = Prim.postprocess{WFtac = WFtac, |
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58 terminator = terminator, |
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59 simplifier = Prim.Rules.simpl_conv simpls}; |
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60 |
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61 val simplifier = rewrite_rule (simpls @ #simps(rep_ss HOL_ss) @ |
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62 [pred_nat_def,pred_list_def]); |
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63 fun tflcongs thy = Prim.Context.read() @ (#case_congs(Thry.extract_info thy)); |
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64 |
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65 |
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66 local structure S = Prim.USyntax |
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67 in |
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68 fun func_of_cond_eqn tm = |
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69 #1(S.strip_comb(#lhs(S.dest_eq(#2(S.strip_forall(#2(S.strip_imp tm))))))) |
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70 end; |
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71 |
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72 |
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73 val concl = #2 o Prim.Rules.dest_thm; |
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74 |
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75 (*--------------------------------------------------------------------------- |
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76 * Defining a function with an associated termination relation. Lots of |
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77 * postprocessing takes place. |
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78 *---------------------------------------------------------------------------*) |
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79 local |
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80 structure S = Prim.USyntax |
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81 structure R = Prim.Rules |
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82 structure U = Utils |
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83 |
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84 val solved = not o U.can S.dest_eq o #2 o S.strip_forall o concl |
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85 |
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86 fun id_thm th = |
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87 let val {lhs,rhs} = S.dest_eq(#2(S.strip_forall(#2 (R.dest_thm th)))) |
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88 in S.aconv lhs rhs |
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89 end handle _ => false |
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90 |
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91 fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]); |
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92 val P_imp_P_iff_True = prover "P --> (P= True)" RS mp; |
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93 val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection; |
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94 fun mk_meta_eq r = case concl_of r of |
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95 Const("==",_)$_$_ => r |
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96 | _$(Const("op =",_)$_$_) => r RS eq_reflection |
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97 | _ => r RS P_imp_P_eq_True |
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98 fun rewrite L = rewrite_rule (map mk_meta_eq (Utils.filter(not o id_thm) L)) |
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99 |
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100 fun join_assums th = |
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101 let val {sign,...} = rep_thm th |
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102 val tych = cterm_of sign |
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103 val {lhs,rhs} = S.dest_eq(#2 (S.strip_forall (concl th))) |
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104 val cntxtl = (#1 o S.strip_imp) lhs (* cntxtl should = cntxtr *) |
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105 val cntxtr = (#1 o S.strip_imp) rhs (* but union is solider *) |
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106 val cntxt = U.union S.aconv cntxtl cntxtr |
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107 in |
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108 R.GEN_ALL |
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109 (R.DISCH_ALL |
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110 (rewrite (map (R.ASSUME o tych) cntxt) (R.SPEC_ALL th))) |
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111 end |
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112 val gen_all = S.gen_all |
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113 in |
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114 fun rfunction theory reducer R eqs = |
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115 let val _ = output(std_out, "Making definition.. ") |
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116 val _ = flush_out std_out |
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117 val {rules,theory, full_pats_TCs, |
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118 TCs,...} = Prim.gen_wfrec_definition theory {R=R,eqs=eqs} |
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119 val f = func_of_cond_eqn(concl(R.CONJUNCT1 rules handle _ => rules)) |
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120 val _ = output(std_out, "Definition made.\n") |
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121 val _ = output(std_out, "Proving induction theorem.. ") |
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122 val _ = flush_out std_out |
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123 val ind = Prim.mk_induction theory f R full_pats_TCs |
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124 val _ = output(std_out, "Proved induction theorem.\n") |
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125 val pp = std_postprocessor theory |
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126 val _ = output(std_out, "Postprocessing.. ") |
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127 val _ = flush_out std_out |
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128 val {rules,induction,nested_tcs} = pp{rules=rules,induction=ind,TCs=TCs} |
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129 val normal_tcs = Prim.termination_goals rules |
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130 in |
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131 case nested_tcs |
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132 of [] => (output(std_out, "Postprocessing done.\n"); |
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133 {theory=theory, induction=induction, rules=rules,tcs=normal_tcs}) |
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134 | L => let val _ = output(std_out, "Simplifying nested TCs.. ") |
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135 val (solved,simplified,stubborn) = |
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136 U.itlist (fn th => fn (So,Si,St) => |
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137 if (id_thm th) then (So, Si, th::St) else |
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138 if (solved th) then (th::So, Si, St) |
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139 else (So, th::Si, St)) nested_tcs ([],[],[]) |
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140 val simplified' = map join_assums simplified |
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141 val induction' = reducer (solved@simplified') induction |
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142 val rules' = reducer (solved@simplified') rules |
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143 val _ = output(std_out, "Postprocessing done.\n") |
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144 in |
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145 {induction = induction', |
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146 rules = rules', |
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147 tcs = normal_tcs @ |
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148 map (gen_all o S.rhs o #2 o S.strip_forall o concl) |
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149 (simplified@stubborn), |
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150 theory = theory} |
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151 end |
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152 end |
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153 handle (e as Utils.ERR _) => Utils.Raise e |
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154 | e => print_exn e |
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155 |
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156 |
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157 fun Rfunction thry = |
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158 rfunction thry |
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159 (fn thl => rewrite (map standard thl @ #simps(rep_ss HOL_ss))); |
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160 |
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161 |
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162 end; |
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163 |
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164 |
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165 local structure R = Prim.Rules |
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166 in |
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167 fun function theory eqs = |
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168 let val _ = output(std_out, "Making definition.. ") |
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169 val {rules,R,theory,full_pats_TCs,...} = Prim.lazyR_def theory eqs |
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170 val f = func_of_cond_eqn (concl(R.CONJUNCT1 rules handle _ => rules)) |
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171 val _ = output(std_out, "Definition made.\n") |
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172 val _ = output(std_out, "Proving induction theorem.. ") |
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173 val induction = Prim.mk_induction theory f R full_pats_TCs |
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174 val _ = output(std_out, "Induction theorem proved.\n") |
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175 in {theory = theory, |
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176 eq_ind = standard (induction RS (rules RS conjI))} |
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177 end |
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178 handle (e as Utils.ERR _) => Utils.Raise e |
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179 | e => print_exn e |
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180 end; |
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181 |
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182 |
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183 fun lazyR_def theory eqs = |
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184 let val {rules,theory, ...} = Prim.lazyR_def theory eqs |
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185 in {eqns=rules, theory=theory} |
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186 end |
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187 handle (e as Utils.ERR _) => Utils.Raise e |
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188 | e => print_exn e; |
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189 |
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190 |
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191 val () = Prim.Context.write[Thms.LET_CONG, Thms.COND_CONG]; |
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192 |
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193 end; |