made tactic more flexible w.r.t. case expressions and such
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 -> tactic
11 val mk_primcorec_code_tac: thm list -> thm list -> thm -> thm list -> tactic
12 val mk_primcorec_code_of_ctr_tac: Proof.context -> thm list -> int list -> thm list -> tactic
13 val mk_primcorec_ctr_of_dtr_tac: Proof.context -> int -> thm -> thm option -> thm list -> tactic
14 val mk_primcorec_ctr_or_sel_tac: Proof.context -> thm list -> thm -> int -> int ->
15 thm list list list -> thm list -> thm list -> thm list -> thm list -> thm list ->tactic
16 val mk_primcorec_disc_of_ctr_tac: thm -> thm -> tactic;
17 val mk_primcorec_disc_tac: Proof.context -> thm list -> thm -> int -> int -> thm list list list ->
19 val mk_primcorec_sel_of_ctr_tac: thm -> thm -> tactic;
20 val mk_primrec_tac: Proof.context -> int -> thm list -> thm list -> thm list -> thm -> tactic
23 structure BNF_FP_Rec_Sugar_Tactics : BNF_FP_REC_SUGAR_TACTICS =
29 fun mk_primrec_tac ctxt num_extra_args map_idents map_comps fun_defs recx =
30 unfold_thms_tac ctxt fun_defs THEN
31 HEADGOAL (rtac (funpow num_extra_args (fn thm => thm RS fun_cong) recx RS trans)) THEN
32 unfold_thms_tac ctxt (@{thms id_def split o_def fst_conv snd_conv} @ map_comps @ map_idents) THEN
35 fun mk_primcorec_assumption_tac ctxt =
36 HEADGOAL (blast_tac (put_claset (claset_of @{theory_context HOL}) ctxt));
38 fun mk_primcorec_same_case_tac m =
39 HEADGOAL (if m = 0 then rtac TrueI
40 else REPEAT_DETERM_N (m - 1) o (rtac conjI THEN' atac) THEN' atac);
42 fun mk_primcorec_different_case_tac ctxt excl =
43 unfold_thms_tac ctxt @{thms not_not not_False_eq_True} THEN
44 HEADGOAL (rtac excl THEN_ALL_NEW SELECT_GOAL (mk_primcorec_assumption_tac ctxt));
46 fun mk_primcorec_cases_tac ctxt k m exclsss =
47 let val n = length exclsss in
48 EVERY (map (fn [] => if k = n then all_tac else mk_primcorec_same_case_tac m
49 | [excl] => mk_primcorec_different_case_tac ctxt excl)
50 (take k (nth exclsss (k - 1))))
53 fun mk_primcorec_prelude ctxt defs thm =
54 unfold_thms_tac ctxt defs THEN HEADGOAL (rtac thm) THEN unfold_thms_tac ctxt @{thms split};
56 fun mk_primcorec_disc_tac ctxt defs disc_corec k m exclsss =
57 mk_primcorec_prelude ctxt defs disc_corec THEN mk_primcorec_cases_tac ctxt k m exclsss;
59 fun mk_primcorec_ctr_or_sel_tac ctxt defs f_eq k m exclsss maps map_idents map_comps splits
61 mk_primcorec_prelude ctxt defs (f_eq RS trans) THEN
62 mk_primcorec_cases_tac ctxt k m exclsss THEN
63 unfold_thms_tac ctxt (@{thms o_def split_def sum.cases} @ maps @ map_comps @ map_idents) THEN
64 HEADGOAL (REPEAT_DETERM o (rtac refl ORELSE'
65 eresolve_tac @{thms not_TrueE FalseE} ORELSE'
66 resolve_tac @{thms allI impI conjI} ORELSE'
67 Splitter.split_asm_tac (@{thm split_if_asm} :: split_asms) ORELSE'
68 Splitter.split_tac (@{thm split_if} :: splits) ORELSE'
69 etac notE THEN' atac));
71 fun mk_primcorec_ctr_of_dtr_tac ctxt m collapse maybe_disc_f sel_fs =
72 HEADGOAL (rtac ((if null sel_fs then collapse else collapse RS sym) RS trans) THEN'
73 (the_default (K all_tac) (Option.map rtac maybe_disc_f)) THEN' REPEAT_DETERM_N m o atac) THEN
74 unfold_thms_tac ctxt sel_fs THEN HEADGOAL (rtac refl);
76 fun mk_primcorec_disc_of_ctr_tac discI f_ctr =
77 HEADGOAL (rtac discI THEN' rtac f_ctr) THEN ALLGOALS atac;
79 fun mk_primcorec_sel_of_ctr_tac sel f_ctr =
80 HEADGOAL (etac (f_ctr RS arg_cong RS trans) THEN' rtac sel);
82 fun mk_primcorec_code_of_ctr_case_tac ctxt eq_caseIs m f_ctr =
83 HEADGOAL (REPEAT o resolve_tac (@{thm eq_ifI} :: eq_caseIs)) THEN
84 mk_primcorec_prelude ctxt [] (f_ctr RS trans) THEN
85 REPEAT_DETERM_N m (mk_primcorec_assumption_tac ctxt) THEN
86 (* FIXME: Something like (ss_only @{thms if_True if_False not_False_eq_True simp_thms} ctxt) *)
87 HEADGOAL (asm_simp_tac ctxt);
89 fun mk_primcorec_code_of_ctr_tac ctxt eq_caseIs ms ctr_thms =
90 EVERY (map2 (mk_primcorec_code_of_ctr_case_tac ctxt eq_caseIs) ms ctr_thms);
92 fun mk_primcorec_code_tac eq_caseIs disc_excludes raw collapses =
93 HEADGOAL (rtac raw ORELSE' rtac (raw RS trans) THEN' REPEAT o
94 (resolve_tac (maps (fn thm => [thm, thm RS sym]) (@{thm eq_ifI} :: eq_caseIs)) ORELSE'
95 rtac refl ORELSE' etac notE THEN' atac ORELSE'
96 dresolve_tac disc_excludes THEN' etac notE THEN' atac ORELSE'
97 eresolve_tac (maps (fn thm => [thm, thm RS sym]) collapses)));