1 (* Title: HOL/Codatatype/Tools/bnf_fp_sugar_tactics.ML
2 Author: Jasmin Blanchette, TU Muenchen
5 Tactics for the LFP/GFP sugar.
8 signature BNF_FP_SUGAR_TACTICS =
10 val mk_case_tac: Proof.context -> int -> int -> int -> thm -> thm -> thm -> tactic
11 val mk_coiter_like_tac: thm list -> thm list -> thm -> thm -> thm -> Proof.context -> tactic
12 val mk_exhaust_tac: Proof.context -> int -> thm list -> thm -> thm -> tactic
13 val mk_fld_iff_unf_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm
15 val mk_half_distinct_tac: Proof.context -> thm -> thm list -> tactic
16 val mk_inject_tac: Proof.context -> thm -> thm -> tactic
17 val mk_iter_like_tac: thm list -> thm list -> thm list -> thm -> thm -> Proof.context -> tactic
20 structure BNF_FP_Sugar_Tactics : BNF_FP_SUGAR_TACTICS =
26 fun mk_case_tac ctxt n k m case_def ctr_def unf_fld =
27 Local_Defs.unfold_tac ctxt [case_def, ctr_def, unf_fld] THEN
28 (rtac (BNF_FP_Util.mk_sum_casesN n k RS ssubst) THEN'
29 REPEAT_DETERM_N (Int.max (0, m - 1)) o rtac (@{thm split} RS ssubst) THEN'
32 fun mk_exhaust_tac ctxt n ctr_defs fld_iff_unf sumEN' =
33 Local_Defs.unfold_tac ctxt (fld_iff_unf :: ctr_defs) THEN rtac sumEN' 1 THEN
34 Local_Defs.unfold_tac ctxt @{thms all_prod_eq} THEN
35 EVERY' (maps (fn k => [select_prem_tac n (rotate_tac 1) k, REPEAT_DETERM o dtac @{thm meta_spec},
36 etac @{thm meta_mp}, atac]) (1 upto n)) 1;
38 fun mk_fld_iff_unf_tac ctxt cTs cfld cunf fld_unf unf_fld =
40 EVERY' (map3 (fn cTs => fn cx => fn th =>
41 dtac (Drule.instantiate' cTs [NONE, NONE, SOME cx] arg_cong) THEN'
42 SELECT_GOAL (Local_Defs.unfold_tac ctxt [th]) THEN'
43 atac) [rev cTs, cTs] [cunf, cfld] [unf_fld, fld_unf])) 1;
45 fun mk_half_distinct_tac ctxt fld_inject ctr_defs =
46 Local_Defs.unfold_tac ctxt (fld_inject :: @{thms sum.inject} @ ctr_defs) THEN
47 rtac @{thm sum.distinct(1)} 1;
49 fun mk_inject_tac ctxt ctr_def fld_inject =
50 Local_Defs.unfold_tac ctxt [ctr_def] THEN rtac (fld_inject RS ssubst) 1 THEN
51 Local_Defs.unfold_tac ctxt @{thms sum.inject Pair_eq conj_assoc} THEN rtac refl 1;
54 @{thms case_unit comp_def convol_def id_apply map_pair_def sum.simps(5,6) sum_map.simps
57 fun mk_iter_like_tac pre_map_defs map_id's iter_like_defs fld_iter_like ctr_def ctxt =
58 Local_Defs.unfold_tac ctxt (ctr_def :: fld_iter_like :: iter_like_defs @ pre_map_defs @ map_id's @
59 iter_like_thms) THEN rtac refl 1;
61 val coiter_like_ss = ss_only @{thms if_True if_False};
62 val coiter_like_thms = @{thms id_apply map_pair_def sum_map.simps prod.cases};
64 fun mk_coiter_like_tac coiter_like_defs map_id's fld_unf_coiter_like pre_map_def ctr_def ctxt =
65 Local_Defs.unfold_tac ctxt (ctr_def :: coiter_like_defs) THEN
66 subst_tac ctxt [fld_unf_coiter_like] 1 THEN asm_simp_tac coiter_like_ss 1 THEN
67 Local_Defs.unfold_tac ctxt (pre_map_def :: coiter_like_thms @ map_id's) THEN rtac refl 1;