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_disc_tac: Proof.context -> thm list -> thm -> int -> int -> thm list list list ->
16 val mk_primcorec_sel_tac: Proof.context -> thm list -> thm -> int -> int ->
17 thm list list list -> thm list -> thm list -> thm list -> thm list -> thm list ->tactic
18 val mk_primrec_tac: Proof.context -> int -> thm list -> thm list -> thm list -> thm -> tactic
21 structure BNF_FP_Rec_Sugar_Tactics : BNF_FP_REC_SUGAR_TACTICS =
27 fun mk_primrec_tac ctxt num_extra_args map_idents map_comps fun_defs recx =
28 unfold_thms_tac ctxt fun_defs THEN
29 HEADGOAL (rtac (funpow num_extra_args (fn thm => thm RS fun_cong) recx RS trans)) THEN
30 unfold_thms_tac ctxt (@{thms id_def split o_def fst_conv snd_conv} @ map_comps @ map_idents) THEN
33 fun mk_primcorec_assumption_tac ctxt =
34 HEADGOAL (blast_tac (put_claset (claset_of @{theory_context HOL}) ctxt));
36 fun mk_primcorec_same_case_tac m =
37 HEADGOAL (if m = 0 then rtac TrueI
38 else REPEAT_DETERM_N (m - 1) o (rtac conjI THEN' atac) THEN' atac);
40 fun mk_primcorec_different_case_tac ctxt excl =
41 unfold_thms_tac ctxt @{thms not_not not_False_eq_True} THEN
42 HEADGOAL (rtac excl THEN_ALL_NEW SELECT_GOAL (mk_primcorec_assumption_tac ctxt));
44 fun mk_primcorec_cases_tac ctxt k m exclsss =
45 let val n = length exclsss in
46 EVERY (map (fn [] => if k = n then all_tac else mk_primcorec_same_case_tac m
47 | [excl] => mk_primcorec_different_case_tac ctxt excl)
48 (take k (nth exclsss (k - 1))))
51 fun mk_primcorec_prelude ctxt defs thm =
52 unfold_thms_tac ctxt defs THEN HEADGOAL (rtac thm) THEN unfold_thms_tac ctxt @{thms split};
54 fun mk_primcorec_disc_tac ctxt defs disc_corec k m exclsss =
55 mk_primcorec_prelude ctxt defs disc_corec THEN mk_primcorec_cases_tac ctxt k m exclsss;
57 fun mk_primcorec_sel_tac ctxt defs f_sel k m exclsss maps map_idents map_comps splits split_asms =
58 mk_primcorec_prelude ctxt defs (f_sel RS trans) THEN
59 mk_primcorec_cases_tac ctxt k m exclsss THEN
60 unfold_thms_tac ctxt (@{thms o_def split_def sum.cases} @ maps @ map_comps @ map_idents) THEN
61 HEADGOAL (REPEAT_DETERM o (rtac refl ORELSE'
62 eresolve_tac @{thms not_TrueE FalseE} ORELSE'
63 resolve_tac @{thms allI impI conjI} ORELSE'
64 Splitter.split_asm_tac (@{thm split_if_asm} :: split_asms) ORELSE'
65 Splitter.split_tac (@{thm split_if} :: splits) ORELSE'
66 etac notE THEN' atac));
68 fun mk_primcorec_ctr_of_dtr_tac ctxt m collapse maybe_disc_f sel_fs =
69 HEADGOAL (rtac ((if null sel_fs then collapse else collapse RS sym) RS trans) THEN'
70 (the_default (K all_tac) (Option.map rtac maybe_disc_f)) THEN' REPEAT_DETERM_N m o atac) THEN
71 unfold_thms_tac ctxt sel_fs THEN HEADGOAL (rtac refl);
73 fun mk_primcorec_code_of_ctr_case_tac ctxt eq_caseIs m f_ctr =
74 HEADGOAL (REPEAT o resolve_tac (@{thm eq_ifI} :: eq_caseIs)) THEN
75 mk_primcorec_prelude ctxt [] (f_ctr RS trans) THEN
76 REPEAT_DETERM_N m (mk_primcorec_assumption_tac ctxt) THEN
77 (* FIXME: Something like (ss_only @{thms if_True if_False not_False_eq_True simp_thms} ctxt) *)
78 HEADGOAL (asm_simp_tac ctxt);
80 fun mk_primcorec_code_of_ctr_tac ctxt eq_caseIs ms ctr_thms =
81 EVERY (map2 (mk_primcorec_code_of_ctr_case_tac ctxt eq_caseIs) ms ctr_thms);
83 fun mk_primcorec_code_tac eq_caseIs disc_excludes raw collapses =
84 HEADGOAL (rtac raw ORELSE' rtac (raw RS trans) THEN' REPEAT o
85 (resolve_tac (maps (fn thm => [thm, thm RS sym]) (@{thm eq_ifI} :: eq_caseIs)) ORELSE'
86 rtac refl ORELSE' etac notE THEN' atac ORELSE'
87 dresolve_tac disc_excludes THEN' etac notE THEN' atac ORELSE'
88 eresolve_tac (maps (fn thm => [thm, thm RS sym]) collapses)));