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_exhaust_tac: Proof.context -> int -> int list -> thm list -> thm -> thm -> tactic
12 val mk_fld_iff_unf_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm
14 val mk_half_distinct_tac: Proof.context -> thm -> thm list -> tactic
15 val mk_inject_tac: Proof.context -> thm -> thm -> tactic
18 structure BNF_FP_Sugar_Tactics : BNF_FP_SUGAR_TACTICS =
24 fun mk_case_tac ctxt n k m case_def ctr_def unf_fld =
25 Local_Defs.unfold_tac ctxt [case_def, ctr_def, unf_fld] THEN
26 (rtac (BNF_FP_Util.mk_sum_casesN n k RS ssubst) THEN'
27 REPEAT_DETERM_N (Int.max (0, m - 1)) o rtac (@{thm split} RS ssubst) THEN'
30 fun mk_exhaust_tac ctxt n ms ctr_defs fld_iff_unf sumEN' =
31 Local_Defs.unfold_tac ctxt (fld_iff_unf :: ctr_defs) THEN rtac sumEN' 1 THEN
32 Local_Defs.unfold_tac ctxt @{thms all_prod_eq} THEN
33 EVERY' (map2 (fn k => fn m => select_prem_tac n (REPEAT_DETERM_N m o dtac @{thm meta_spec} THEN'
34 etac @{thm meta_mp}) k THEN' atac) (1 upto n) ms) 1;
36 fun mk_fld_iff_unf_tac ctxt cTs cfld cunf fld_unf unf_fld =
38 EVERY' (map3 (fn cTs => fn cx => fn th =>
39 dtac (Drule.instantiate' cTs [NONE, NONE, SOME cx] arg_cong) THEN'
40 SELECT_GOAL (Local_Defs.unfold_tac ctxt [th]) THEN'
41 atac) [rev cTs, cTs] [cunf, cfld] [unf_fld, fld_unf])) 1;
43 fun mk_half_distinct_tac ctxt fld_inject ctr_defs =
44 Local_Defs.unfold_tac ctxt (fld_inject :: @{thms sum.inject} @ ctr_defs) THEN
45 rtac @{thm sum.distinct(1)} 1;
47 fun mk_inject_tac ctxt ctr_def fld_inject =
48 Local_Defs.unfold_tac ctxt [ctr_def] THEN rtac (fld_inject RS ssubst) 1 THEN
49 Local_Defs.unfold_tac ctxt @{thms sum.inject Pair_eq conj_assoc} THEN rtac refl 1;