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1 (* Title: HOL/BNF/Tools/bnf_fp_sugar_tactics.ML |
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2 Author: Jasmin Blanchette, TU Muenchen |
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3 Copyright 2012 |
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4 |
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5 Tactics for datatype and codatatype sugar. |
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6 *) |
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7 |
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8 signature BNF_FP_SUGAR_TACTICS = |
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9 sig |
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10 val mk_case_tac: Proof.context -> int -> int -> int -> thm -> thm -> thm -> tactic |
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11 val mk_corec_like_tac: thm list -> thm list -> thm -> thm -> thm -> Proof.context -> tactic |
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12 val mk_ctor_iff_dtor_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm -> |
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13 tactic |
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14 val mk_disc_corec_like_iff_tac: thm list -> thm list -> thm list -> Proof.context -> tactic |
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15 val mk_exhaust_tac: Proof.context -> int -> thm list -> thm -> thm -> tactic |
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16 val mk_half_distinct_tac: Proof.context -> thm -> thm list -> tactic |
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17 val mk_induct_tac: Proof.context -> int list -> int list list -> int list list list -> thm list -> |
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18 thm -> thm list -> thm list list -> tactic |
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19 val mk_inject_tac: Proof.context -> thm -> thm -> tactic |
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20 val mk_rec_like_tac: thm list -> thm list -> thm list -> thm -> thm -> Proof.context -> tactic |
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21 end; |
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22 |
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23 structure BNF_FP_Sugar_Tactics : BNF_FP_SUGAR_TACTICS = |
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24 struct |
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25 |
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26 open BNF_Tactics |
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27 open BNF_Util |
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28 open BNF_FP |
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29 |
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30 val meta_mp = @{thm meta_mp}; |
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31 val meta_spec = @{thm meta_spec}; |
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32 |
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33 fun inst_spurious_fs lthy thm = |
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34 let |
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35 val fs = |
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36 Term.add_vars (prop_of thm) [] |
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37 |> filter (fn (_, Type (@{type_name fun}, [_, T'])) => T' <> HOLogic.boolT | _ => false); |
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38 val cfs = |
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39 map (fn f as (_, T) => (certify lthy (Var f), certify lthy (id_abs (domain_type T)))) fs; |
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40 in |
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41 Drule.cterm_instantiate cfs thm |
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42 end; |
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43 |
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44 val inst_spurious_fs_tac = PRIMITIVE o inst_spurious_fs; |
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45 |
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46 fun mk_case_tac ctxt n k m case_def ctr_def dtor_ctor = |
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47 unfold_thms_tac ctxt [case_def, ctr_def, dtor_ctor] THEN |
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48 (rtac (mk_sum_casesN_balanced n k RS ssubst) THEN' |
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49 REPEAT_DETERM_N (Int.max (0, m - 1)) o rtac (@{thm split} RS ssubst) THEN' |
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50 rtac refl) 1; |
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51 |
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52 fun mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor sumEN' = |
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53 unfold_thms_tac ctxt (ctor_iff_dtor :: ctr_defs) THEN rtac sumEN' 1 THEN |
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54 unfold_thms_tac ctxt @{thms all_prod_eq} THEN |
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55 EVERY' (maps (fn k => [select_prem_tac n (rotate_tac 1) k, REPEAT_DETERM o dtac meta_spec, |
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56 etac meta_mp, atac]) (1 upto n)) 1; |
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57 |
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58 fun mk_ctor_iff_dtor_tac ctxt cTs cctor cdtor ctor_dtor dtor_ctor = |
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59 (rtac iffI THEN' |
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60 EVERY' (map3 (fn cTs => fn cx => fn th => |
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61 dtac (Drule.instantiate' cTs [NONE, NONE, SOME cx] arg_cong) THEN' |
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62 SELECT_GOAL (unfold_thms_tac ctxt [th]) THEN' |
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63 atac) [rev cTs, cTs] [cdtor, cctor] [dtor_ctor, ctor_dtor])) 1; |
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64 |
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65 fun mk_half_distinct_tac ctxt ctor_inject ctr_defs = |
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66 unfold_thms_tac ctxt (ctor_inject :: @{thms sum.inject} @ ctr_defs) THEN |
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67 rtac @{thm sum.distinct(1)} 1; |
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68 |
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69 fun mk_inject_tac ctxt ctr_def ctor_inject = |
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70 unfold_thms_tac ctxt [ctr_def] THEN rtac (ctor_inject RS ssubst) 1 THEN |
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71 unfold_thms_tac ctxt @{thms sum.inject Pair_eq conj_assoc} THEN rtac refl 1; |
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72 |
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73 val rec_like_unfold_thms = |
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74 @{thms case_unit comp_def convol_def id_apply map_pair_def sum.simps(5,6) sum_map.simps |
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75 split_conv}; |
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76 |
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77 fun mk_rec_like_tac pre_map_defs map_ids rec_like_defs ctor_rec_like ctr_def ctxt = |
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78 unfold_thms_tac ctxt (ctr_def :: ctor_rec_like :: rec_like_defs @ pre_map_defs @ map_ids @ |
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79 rec_like_unfold_thms) THEN unfold_thms_tac ctxt @{thms id_def} THEN rtac refl 1; |
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80 |
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81 val corec_like_ss = ss_only @{thms if_True if_False}; |
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82 val corec_like_unfold_thms = @{thms id_apply map_pair_def sum_map.simps prod.cases}; |
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83 |
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84 fun mk_corec_like_tac corec_like_defs map_ids ctor_dtor_corec_like pre_map_def ctr_def ctxt = |
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85 unfold_thms_tac ctxt (ctr_def :: corec_like_defs) THEN |
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86 subst_tac ctxt [ctor_dtor_corec_like] 1 THEN asm_simp_tac corec_like_ss 1 THEN |
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87 unfold_thms_tac ctxt (pre_map_def :: corec_like_unfold_thms @ map_ids) THEN |
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88 unfold_thms_tac ctxt @{thms id_def} THEN |
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89 TRY ((rtac refl ORELSE' subst_tac ctxt @{thms unit_eq} THEN' rtac refl) 1); |
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90 |
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91 fun mk_disc_corec_like_iff_tac case_splits' corec_likes discs ctxt = |
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92 EVERY (map3 (fn case_split_tac => fn corec_like_thm => fn disc => |
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93 case_split_tac 1 THEN unfold_thms_tac ctxt [corec_like_thm] THEN |
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94 asm_simp_tac (ss_only @{thms simp_thms(7,8,12,14,22,24)}) 1 THEN |
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95 (if is_refl disc then all_tac else rtac disc 1)) |
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96 (map rtac case_splits' @ [K all_tac]) corec_likes discs); |
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97 |
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98 val solve_prem_prem_tac = |
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99 REPEAT o (eresolve_tac @{thms bexE rev_bexI} ORELSE' rtac @{thm rev_bexI[OF UNIV_I]} ORELSE' |
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100 hyp_subst_tac ORELSE' resolve_tac @{thms disjI1 disjI2}) THEN' |
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101 (rtac refl ORELSE' atac ORELSE' rtac @{thm singletonI}); |
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102 |
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103 val induct_prem_prem_thms = |
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104 @{thms SUP_empty Sup_empty Sup_insert UN_insert Un_empty_left Un_empty_right Un_iff |
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105 Union_Un_distrib collect_def[abs_def] image_def o_apply map_pair_simp |
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106 mem_Collect_eq mem_UN_compreh_eq prod_set_simps sum_map.simps sum_set_simps}; |
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107 |
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108 fun mk_induct_leverage_prem_prems_tac ctxt nn kks set_natural's pre_set_defs = |
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109 EVERY' (maps (fn kk => [select_prem_tac nn (dtac meta_spec) kk, etac meta_mp, |
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110 SELECT_GOAL (unfold_thms_tac ctxt (pre_set_defs @ set_natural's @ induct_prem_prem_thms)), |
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111 solve_prem_prem_tac]) (rev kks)) 1; |
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112 |
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113 fun mk_induct_discharge_prem_tac ctxt nn n set_natural's pre_set_defs m k kks = |
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114 let val r = length kks in |
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115 EVERY' [select_prem_tac n (rotate_tac 1) k, rotate_tac ~1, hyp_subst_tac, |
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116 REPEAT_DETERM_N m o (dtac meta_spec THEN' rotate_tac ~1)] 1 THEN |
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117 EVERY [REPEAT_DETERM_N r |
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118 (rotate_tac ~1 1 THEN dtac meta_mp 1 THEN rotate_tac 1 1 THEN prefer_tac 2), |
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119 if r > 0 then PRIMITIVE Raw_Simplifier.norm_hhf else all_tac, atac 1, |
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120 mk_induct_leverage_prem_prems_tac ctxt nn kks set_natural's pre_set_defs] |
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121 end; |
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122 |
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123 fun mk_induct_tac ctxt ns mss kkss ctr_defs ctor_induct' set_natural's pre_set_defss = |
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124 let |
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125 val nn = length ns; |
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126 val n = Integer.sum ns; |
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127 in |
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128 unfold_thms_tac ctxt ctr_defs THEN rtac ctor_induct' 1 THEN inst_spurious_fs_tac ctxt THEN |
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129 EVERY (map4 (EVERY oooo map3 o mk_induct_discharge_prem_tac ctxt nn n set_natural's) |
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130 pre_set_defss mss (unflat mss (1 upto n)) kkss) |
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131 end; |
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132 |
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133 end; |