1 (* Title: HOL/BNF/Tools/bnf_fp_rec_sugar_tactics.ML
2 Author: Jasmin Blanchette, TU Muenchen
5 Tactics for recursor and corecursor sugar.
8 signature BNF_FP_REC_SUGAR_TACTICS =
10 val mk_primcorec_assumption_tac: Proof.context -> thm list -> tactic
11 val mk_primcorec_code_of_ctr_tac: Proof.context -> thm list -> thm list -> thm list -> thm list ->
12 thm list -> int list -> thm list -> tactic
13 val mk_primcorec_code_of_raw_tac: thm list -> thm list -> thm -> thm list -> tactic
14 val mk_primcorec_ctr_of_dtr_tac: Proof.context -> int -> thm -> thm option -> thm list -> tactic
15 val mk_primcorec_disc_tac: Proof.context -> thm list -> thm -> int -> int -> thm list list list ->
17 val mk_primcorec_sel_tac: Proof.context -> thm list -> thm -> int -> int ->
18 thm list list list -> thm list -> thm list -> thm list -> thm list -> thm list ->tactic
19 val mk_primrec_tac: Proof.context -> int -> thm list -> thm list -> thm list -> thm -> tactic
22 structure BNF_FP_Rec_Sugar_Tactics : BNF_FP_REC_SUGAR_TACTICS =
28 val falseEs = @{thms not_TrueE FalseE};
29 val split_if = @{thm split_if};
30 val split_if_asm = @{thm split_if_asm};
31 val split_connectI = @{thms allI impI conjI};
33 fun mk_primrec_tac ctxt num_extra_args map_idents map_comps fun_defs recx =
34 unfold_thms_tac ctxt fun_defs THEN
35 HEADGOAL (rtac (funpow num_extra_args (fn thm => thm RS fun_cong) recx RS trans)) THEN
36 unfold_thms_tac ctxt (@{thms id_def split o_def fst_conv snd_conv} @ map_comps @ map_idents) THEN
39 fun mk_primcorec_assumption_tac ctxt discIs =
40 HEADGOAL (SELECT_GOAL (unfold_thms_tac ctxt
41 @{thms not_not not_False_eq_True de_Morgan_conj de_Morgan_disj} THEN
42 SOLVE (HEADGOAL (REPEAT o (rtac refl ORELSE' atac ORELSE'
43 resolve_tac @{thms TrueI conjI disjI1 disjI2} ORELSE'
44 dresolve_tac discIs THEN' atac)))));
46 fun mk_primcorec_same_case_tac m =
47 HEADGOAL (if m = 0 then rtac TrueI
48 else REPEAT_DETERM_N (m - 1) o (rtac conjI THEN' atac) THEN' atac);
50 fun mk_primcorec_different_case_tac ctxt excl =
51 unfold_thms_tac ctxt @{thms not_not not_False_eq_True} THEN
52 HEADGOAL (rtac excl THEN_ALL_NEW SELECT_GOAL (mk_primcorec_assumption_tac ctxt []));
54 fun mk_primcorec_cases_tac ctxt k m exclsss =
55 let val n = length exclsss in
56 EVERY (map (fn [] => if k = n then all_tac else mk_primcorec_same_case_tac m
57 | [excl] => mk_primcorec_different_case_tac ctxt excl)
58 (take k (nth exclsss (k - 1))))
61 fun mk_primcorec_prelude ctxt defs thm =
62 unfold_thms_tac ctxt defs THEN HEADGOAL (rtac thm) THEN unfold_thms_tac ctxt @{thms split};
64 fun mk_primcorec_disc_tac ctxt defs disc_corec k m exclsss =
65 mk_primcorec_prelude ctxt defs disc_corec THEN mk_primcorec_cases_tac ctxt k m exclsss;
67 fun mk_primcorec_sel_tac ctxt defs f_sel k m exclsss maps map_idents map_comps splits split_asms =
68 mk_primcorec_prelude ctxt defs (f_sel RS trans) THEN
69 mk_primcorec_cases_tac ctxt k m exclsss THEN
70 unfold_thms_tac ctxt (@{thms o_def split_def sum.cases} @ maps @ map_comps @ map_idents) THEN
71 HEADGOAL (REPEAT_DETERM o (rtac refl ORELSE'
72 eresolve_tac falseEs ORELSE'
73 resolve_tac split_connectI ORELSE'
74 Splitter.split_asm_tac (split_if_asm :: split_asms) ORELSE'
75 Splitter.split_tac (split_if :: splits) ORELSE'
76 etac notE THEN' atac));
78 fun mk_primcorec_ctr_of_dtr_tac ctxt m collapse maybe_disc_f sel_fs =
79 HEADGOAL (rtac ((if null sel_fs then collapse else collapse RS sym) RS trans) THEN'
80 (the_default (K all_tac) (Option.map rtac maybe_disc_f)) THEN' REPEAT_DETERM_N m o atac) THEN
81 unfold_thms_tac ctxt sel_fs THEN HEADGOAL (rtac refl);
83 fun mk_primcorec_code_of_ctr_single_tac ctxt distincts discIs collapses splits split_asms m f_ctr =
84 HEADGOAL (REPEAT o (resolve_tac split_connectI ORELSE' split_tac (split_if :: splits))) THEN
85 mk_primcorec_prelude ctxt [] (f_ctr RS trans) THEN
86 REPEAT_DETERM_N m (mk_primcorec_assumption_tac ctxt discIs) THEN
87 HEADGOAL (SELECT_GOAL (HEADGOAL (REPEAT_DETERM o
88 (rtac refl ORELSE' atac ORELSE'
89 eresolve_tac (falseEs @ map (fn thm => thm RS trans) collapses) ORELSE'
90 resolve_tac split_connectI ORELSE'
91 Splitter.split_asm_tac (split_if_asm :: split_asms) ORELSE'
92 Splitter.split_tac (split_if :: splits) ORELSE'
93 eresolve_tac (map (fn thm => thm RS @{thm neq_eq_eq_contradict}) distincts) THEN' atac ORELSE'
94 (TRY o dresolve_tac discIs) THEN' etac notE THEN' atac))));
96 fun mk_primcorec_code_of_ctr_tac ctxt distincts discIs collapses splits split_asms ms ctr_thms =
97 EVERY (map2 (mk_primcorec_code_of_ctr_single_tac ctxt distincts discIs collapses splits
98 split_asms) ms ctr_thms);
100 fun mk_primcorec_code_of_raw_tac splits disc_excludes raw collapses =
101 HEADGOAL (rtac raw ORELSE' rtac (raw RS trans) THEN' REPEAT_DETERM o
103 (TRY o rtac sym) THEN' atac ORELSE'
104 resolve_tac split_connectI ORELSE'
105 Splitter.split_tac (split_if :: splits) ORELSE'
106 etac notE THEN' atac ORELSE'
107 dresolve_tac disc_excludes THEN' etac notE THEN' atac ORELSE'
108 eresolve_tac (maps (fn thm => [thm, thm RS sym]) collapses)));