1 (* Title: HOL/BNF/Tools/bnf_fp_rec_sugar_tactics.ML |
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2 Author: Jasmin Blanchette, TU Muenchen |
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3 Copyright 2013 |
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4 |
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5 Tactics for recursor and corecursor sugar. |
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6 *) |
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7 |
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8 signature BNF_FP_REC_SUGAR_TACTICS = |
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9 sig |
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10 val mk_primcorec_assumption_tac: Proof.context -> thm list -> int -> tactic |
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11 val mk_primcorec_code_of_raw_code_tac: Proof.context -> thm list -> thm list -> thm -> tactic |
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12 val mk_primcorec_ctr_of_dtr_tac: Proof.context -> int -> thm -> thm option -> thm list -> tactic |
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13 val mk_primcorec_disc_tac: Proof.context -> thm list -> thm -> int -> int -> thm list list list -> |
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14 tactic |
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15 val mk_primcorec_raw_code_of_ctr_tac: Proof.context -> thm list -> thm list -> thm list -> |
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16 thm list -> int list -> thm list -> tactic |
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17 val mk_primcorec_sel_tac: Proof.context -> thm list -> thm list -> thm list -> thm list -> |
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18 thm list -> thm list -> thm list -> thm -> int -> int -> thm list list list -> tactic |
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19 val mk_primrec_tac: Proof.context -> int -> thm list -> thm list -> thm list -> thm -> tactic |
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20 end; |
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21 |
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22 structure BNF_FP_Rec_Sugar_Tactics : BNF_FP_REC_SUGAR_TACTICS = |
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23 struct |
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24 |
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25 open BNF_Util |
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26 open BNF_Tactics |
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27 |
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28 val falseEs = @{thms not_TrueE FalseE}; |
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29 val Let_def = @{thm Let_def}; |
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30 val neq_eq_eq_contradict = @{thm neq_eq_eq_contradict}; |
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31 val split_if = @{thm split_if}; |
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32 val split_if_asm = @{thm split_if_asm}; |
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33 val split_connectI = @{thms allI impI conjI}; |
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34 |
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35 fun mk_primrec_tac ctxt num_extra_args map_idents map_comps fun_defs recx = |
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36 unfold_thms_tac ctxt fun_defs THEN |
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37 HEADGOAL (rtac (funpow num_extra_args (fn thm => thm RS fun_cong) recx RS trans)) THEN |
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38 unfold_thms_tac ctxt (@{thms id_def split o_def fst_conv snd_conv} @ map_comps @ map_idents) THEN |
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39 HEADGOAL (rtac refl); |
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40 |
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41 fun mk_primcorec_assumption_tac ctxt discIs = |
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42 SELECT_GOAL (unfold_thms_tac ctxt |
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43 @{thms not_not not_False_eq_True not_True_eq_False de_Morgan_conj de_Morgan_disj} THEN |
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44 SOLVE (HEADGOAL (REPEAT o (rtac refl ORELSE' atac ORELSE' etac conjE ORELSE' |
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45 eresolve_tac falseEs ORELSE' |
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46 resolve_tac @{thms TrueI conjI disjI1 disjI2} ORELSE' |
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47 dresolve_tac discIs THEN' atac ORELSE' |
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48 etac notE THEN' atac ORELSE' |
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49 etac disjE)))); |
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50 |
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51 fun mk_primcorec_same_case_tac m = |
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52 HEADGOAL (if m = 0 then rtac TrueI |
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53 else REPEAT_DETERM_N (m - 1) o (rtac conjI THEN' atac) THEN' atac); |
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54 |
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55 fun mk_primcorec_different_case_tac ctxt m excl = |
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56 HEADGOAL (if m = 0 then mk_primcorec_assumption_tac ctxt [] |
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57 else dtac excl THEN' (REPEAT_DETERM_N (m - 1) o atac) THEN' mk_primcorec_assumption_tac ctxt []); |
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58 |
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59 fun mk_primcorec_cases_tac ctxt k m exclsss = |
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60 let val n = length exclsss in |
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61 EVERY (map (fn [] => if k = n then all_tac else mk_primcorec_same_case_tac m |
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62 | [excl] => mk_primcorec_different_case_tac ctxt m excl) |
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63 (take k (nth exclsss (k - 1)))) |
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64 end; |
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65 |
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66 fun mk_primcorec_prelude ctxt defs thm = |
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67 unfold_thms_tac ctxt defs THEN HEADGOAL (rtac thm) THEN |
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68 unfold_thms_tac ctxt @{thms Let_def split}; |
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69 |
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70 fun mk_primcorec_disc_tac ctxt defs disc_corec k m exclsss = |
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71 mk_primcorec_prelude ctxt defs disc_corec THEN mk_primcorec_cases_tac ctxt k m exclsss; |
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72 |
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73 fun mk_primcorec_sel_tac ctxt defs distincts splits split_asms maps map_idents map_comps f_sel k m |
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74 exclsss = |
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75 mk_primcorec_prelude ctxt defs (f_sel RS trans) THEN |
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76 mk_primcorec_cases_tac ctxt k m exclsss THEN |
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77 HEADGOAL (REPEAT_DETERM o (rtac refl ORELSE' rtac ext ORELSE' |
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78 eresolve_tac falseEs ORELSE' |
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79 resolve_tac split_connectI ORELSE' |
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80 Splitter.split_asm_tac (split_if_asm :: split_asms) ORELSE' |
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81 Splitter.split_tac (split_if :: splits) ORELSE' |
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82 eresolve_tac (map (fn thm => thm RS neq_eq_eq_contradict) distincts) THEN' atac ORELSE' |
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83 etac notE THEN' atac ORELSE' |
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84 (CHANGED o SELECT_GOAL (unfold_thms_tac ctxt |
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85 (@{thms id_def o_def split_def sum.cases} @ maps @ map_comps @ map_idents))))); |
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86 |
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87 fun mk_primcorec_ctr_of_dtr_tac ctxt m collapse maybe_disc_f sel_fs = |
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88 HEADGOAL (rtac ((if null sel_fs then collapse else collapse RS sym) RS trans) THEN' |
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89 (the_default (K all_tac) (Option.map rtac maybe_disc_f)) THEN' REPEAT_DETERM_N m o atac) THEN |
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90 unfold_thms_tac ctxt (Let_def :: sel_fs) THEN HEADGOAL (rtac refl); |
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91 |
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92 fun inst_split_eq ctxt split = |
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93 (case prop_of split of |
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94 @{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ (Var (_, Type (_, [T, _])) $ _) $ _) => |
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95 let |
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96 val s = Name.uu; |
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97 val eq = Abs (Name.uu, T, HOLogic.mk_eq (Free (s, T), Bound 0)); |
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98 val split' = Drule.instantiate' [] [SOME (certify ctxt eq)] split; |
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99 in |
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100 Thm.generalize ([], [s]) (Thm.maxidx_of split' + 1) split' |
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101 end |
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102 | _ => split); |
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103 |
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104 fun distinct_in_prems_tac distincts = |
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105 eresolve_tac (map (fn thm => thm RS neq_eq_eq_contradict) distincts) THEN' atac; |
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106 |
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107 (* TODO: reduce code duplication with selector tactic above *) |
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108 fun mk_primcorec_raw_code_of_ctr_single_tac ctxt distincts discIs splits split_asms m f_ctr = |
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109 let |
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110 val splits' = |
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111 map (fn th => th RS iffD2) (@{thm split_if_eq2} :: map (inst_split_eq ctxt) splits) |
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112 in |
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113 HEADGOAL (REPEAT o (resolve_tac (splits' @ split_connectI))) THEN |
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114 mk_primcorec_prelude ctxt [] (f_ctr RS trans) THEN |
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115 HEADGOAL ((REPEAT_DETERM_N m o mk_primcorec_assumption_tac ctxt discIs) THEN' |
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116 SELECT_GOAL (SOLVE (HEADGOAL (REPEAT_DETERM o |
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117 (rtac refl ORELSE' atac ORELSE' |
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118 resolve_tac (@{thm Code.abort_def} :: split_connectI) ORELSE' |
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119 Splitter.split_tac (split_if :: splits) ORELSE' |
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120 Splitter.split_asm_tac (split_if_asm :: split_asms) ORELSE' |
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121 mk_primcorec_assumption_tac ctxt discIs ORELSE' |
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122 distinct_in_prems_tac distincts ORELSE' |
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123 (TRY o dresolve_tac discIs) THEN' etac notE THEN' atac))))) |
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124 end; |
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125 |
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126 fun mk_primcorec_raw_code_of_ctr_tac ctxt distincts discIs splits split_asms ms f_ctrs = |
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127 EVERY (map2 (mk_primcorec_raw_code_of_ctr_single_tac ctxt distincts discIs splits split_asms) ms |
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128 f_ctrs) THEN |
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129 IF_UNSOLVED (unfold_thms_tac ctxt @{thms Code.abort_def} THEN |
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130 HEADGOAL (REPEAT_DETERM o resolve_tac (refl :: split_connectI))); |
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131 |
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132 fun mk_primcorec_code_of_raw_code_tac ctxt distincts splits raw = |
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133 HEADGOAL (rtac raw ORELSE' rtac (raw RS trans) THEN' |
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134 SELECT_GOAL (unfold_thms_tac ctxt [Let_def]) THEN' REPEAT_DETERM o |
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135 (rtac refl ORELSE' atac ORELSE' |
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136 resolve_tac split_connectI ORELSE' |
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137 Splitter.split_tac (split_if :: splits) ORELSE' |
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138 distinct_in_prems_tac distincts ORELSE' |
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139 rtac sym THEN' atac ORELSE' |
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140 etac notE THEN' atac)); |
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141 |
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142 end; |
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