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 int list -> thm list -> tactic
13 val mk_primcorec_code_of_raw_tac: thm list -> thm list -> thm -> 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 list -> thm list -> thm list ->
18 thm list -> thm list -> thm list -> thm -> int -> int -> thm list list 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 neq_eq_eq_contradict = @{thm neq_eq_eq_contradict};
30 val split_if = @{thm split_if};
31 val split_if_asm = @{thm split_if_asm};
32 val split_connectI = @{thms allI impI conjI};
34 fun mk_primrec_tac ctxt num_extra_args map_idents map_comps fun_defs recx =
35 unfold_thms_tac ctxt fun_defs THEN
36 HEADGOAL (rtac (funpow num_extra_args (fn thm => thm RS fun_cong) recx RS trans)) THEN
37 unfold_thms_tac ctxt (@{thms id_def split o_def fst_conv snd_conv} @ map_comps @ map_idents) THEN
40 fun mk_primcorec_assumption_tac ctxt discIs =
41 HEADGOAL (SELECT_GOAL (unfold_thms_tac ctxt
42 @{thms not_not not_False_eq_True de_Morgan_conj de_Morgan_disj} THEN
43 SOLVE (HEADGOAL (REPEAT o (rtac refl ORELSE' atac ORELSE'
44 resolve_tac @{thms TrueI conjI disjI1 disjI2} ORELSE'
45 dresolve_tac discIs THEN' atac)))));
47 fun mk_primcorec_same_case_tac m =
48 HEADGOAL (if m = 0 then rtac TrueI
49 else REPEAT_DETERM_N (m - 1) o (rtac conjI THEN' atac) THEN' atac);
51 fun mk_primcorec_different_case_tac ctxt excl =
52 unfold_thms_tac ctxt @{thms not_not not_False_eq_True} THEN
53 HEADGOAL (rtac excl THEN_ALL_NEW SELECT_GOAL (mk_primcorec_assumption_tac ctxt []));
55 fun mk_primcorec_cases_tac ctxt k m exclsss =
56 let val n = length exclsss in
57 EVERY (map (fn [] => if k = n then all_tac else mk_primcorec_same_case_tac m
58 | [excl] => mk_primcorec_different_case_tac ctxt excl)
59 (take k (nth exclsss (k - 1))))
62 fun mk_primcorec_prelude ctxt defs thm =
63 unfold_thms_tac ctxt defs THEN HEADGOAL (rtac thm) THEN unfold_thms_tac ctxt @{thms split};
65 fun mk_primcorec_disc_tac ctxt defs disc_corec k m exclsss =
66 mk_primcorec_prelude ctxt defs disc_corec THEN mk_primcorec_cases_tac ctxt k m exclsss;
68 fun mk_primcorec_sel_tac ctxt defs distincts splits split_asms maps map_idents map_comps f_sel k m
70 mk_primcorec_prelude ctxt defs (f_sel RS trans) THEN
71 mk_primcorec_cases_tac ctxt k m exclsss THEN
72 unfold_thms_tac ctxt (@{thms o_def split_def sum.cases} @ maps @ map_comps @ map_idents) THEN
73 HEADGOAL (REPEAT_DETERM o (rtac refl ORELSE'
74 eresolve_tac falseEs ORELSE'
75 resolve_tac split_connectI ORELSE'
76 Splitter.split_asm_tac (split_if_asm :: split_asms) ORELSE'
77 Splitter.split_tac (split_if :: splits) ORELSE'
78 eresolve_tac (map (fn thm => thm RS neq_eq_eq_contradict) distincts) THEN' atac ORELSE'
79 etac notE THEN' atac));
81 fun mk_primcorec_ctr_of_dtr_tac ctxt m collapse maybe_disc_f sel_fs =
82 HEADGOAL (rtac ((if null sel_fs then collapse else collapse RS sym) RS trans) THEN'
83 (the_default (K all_tac) (Option.map rtac maybe_disc_f)) THEN' REPEAT_DETERM_N m o atac) THEN
84 unfold_thms_tac ctxt sel_fs THEN HEADGOAL (rtac refl);
86 (* TODO: reduce code duplication with selector tactic above *)
87 fun mk_primcorec_code_of_ctr_single_tac ctxt distincts discIs splits split_asms m f_ctr =
88 HEADGOAL (REPEAT o (resolve_tac split_connectI ORELSE' split_tac (split_if :: splits))) THEN
89 mk_primcorec_prelude ctxt [] (f_ctr RS trans) THEN
90 REPEAT_DETERM_N m (mk_primcorec_assumption_tac ctxt discIs) THEN
91 HEADGOAL (SELECT_GOAL (HEADGOAL (REPEAT_DETERM o
92 (rtac refl ORELSE' atac ORELSE'
93 resolve_tac split_connectI ORELSE'
94 Splitter.split_asm_tac (split_if_asm :: split_asms) ORELSE'
95 Splitter.split_tac (split_if :: splits) ORELSE'
96 eresolve_tac (map (fn thm => thm RS neq_eq_eq_contradict) distincts) THEN' atac ORELSE'
97 (TRY o dresolve_tac discIs) THEN' etac notE THEN' atac))));
99 fun mk_primcorec_code_of_ctr_tac ctxt distincts discIs splits split_asms ms ctr_thms =
100 EVERY (map2 (mk_primcorec_code_of_ctr_single_tac ctxt distincts discIs splits split_asms)
103 fun mk_primcorec_code_of_raw_tac splits disc_excludes raw =
104 HEADGOAL (rtac raw ORELSE' rtac (raw RS trans) THEN' REPEAT_DETERM o
106 (TRY o rtac sym) THEN' atac ORELSE'
107 resolve_tac split_connectI ORELSE'
108 Splitter.split_tac (split_if :: splits) ORELSE'
109 etac notE THEN' atac ORELSE'
110 (TRY o dresolve_tac disc_excludes) THEN' etac notE THEN' atac));