(* Title: HOL/Codatatype/Tools/bnf_fp_sugar_tactics.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2012
Tactics for the LFP/GFP sugar.
*)
signature BNF_FP_SUGAR_TACTICS =
sig
val mk_case_tac: Proof.context -> int -> int -> int -> thm -> thm -> thm -> tactic
val mk_coiter_like_tac: thm list -> thm list -> thm -> thm -> thm -> Proof.context -> tactic
val mk_exhaust_tac: Proof.context -> int -> thm list -> thm -> thm -> tactic
val mk_fld_iff_unf_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm
-> tactic
val mk_half_distinct_tac: Proof.context -> thm -> thm list -> tactic
val mk_induct_tac: Proof.context -> tactic
val mk_inject_tac: Proof.context -> thm -> thm -> tactic
val mk_iter_like_tac: thm list -> thm list -> thm list -> thm -> thm -> Proof.context -> tactic
end;
structure BNF_FP_Sugar_Tactics : BNF_FP_SUGAR_TACTICS =
struct
open BNF_Tactics
open BNF_Util
open BNF_FP_Util
fun mk_case_tac ctxt n k m case_def ctr_def unf_fld =
Local_Defs.unfold_tac ctxt [case_def, ctr_def, unf_fld] THEN
(rtac (mk_sum_casesN_balanced n k RS ssubst) THEN'
REPEAT_DETERM_N (Int.max (0, m - 1)) o rtac (@{thm split} RS ssubst) THEN'
rtac refl) 1;
fun mk_exhaust_tac ctxt n ctr_defs fld_iff_unf sumEN' =
Local_Defs.unfold_tac ctxt (fld_iff_unf :: ctr_defs) THEN rtac sumEN' 1 THEN
Local_Defs.unfold_tac ctxt @{thms all_prod_eq} THEN
EVERY' (maps (fn k => [select_prem_tac n (rotate_tac 1) k, REPEAT_DETERM o dtac @{thm meta_spec},
etac @{thm meta_mp}, atac]) (1 upto n)) 1;
fun mk_fld_iff_unf_tac ctxt cTs cfld cunf fld_unf unf_fld =
(rtac iffI THEN'
EVERY' (map3 (fn cTs => fn cx => fn th =>
dtac (Drule.instantiate' cTs [NONE, NONE, SOME cx] arg_cong) THEN'
SELECT_GOAL (Local_Defs.unfold_tac ctxt [th]) THEN'
atac) [rev cTs, cTs] [cunf, cfld] [unf_fld, fld_unf])) 1;
fun mk_half_distinct_tac ctxt fld_inject ctr_defs =
Local_Defs.unfold_tac ctxt (fld_inject :: @{thms sum.inject} @ ctr_defs) THEN
rtac @{thm sum.distinct(1)} 1;
fun mk_inject_tac ctxt ctr_def fld_inject =
Local_Defs.unfold_tac ctxt [ctr_def] THEN rtac (fld_inject RS ssubst) 1 THEN
Local_Defs.unfold_tac ctxt @{thms sum.inject Pair_eq conj_assoc} THEN rtac refl 1;
fun mk_induct_tac ctxt =
Skip_Proof.cheat_tac (Proof_Context.theory_of ctxt) (* FIXME: TODO *);
val iter_like_thms =
@{thms case_unit comp_def convol_def id_apply map_pair_def sum.simps(5,6) sum_map.simps
split_conv};
fun mk_iter_like_tac pre_map_defs map_ids iter_like_defs fld_iter_like ctr_def ctxt =
Local_Defs.unfold_tac ctxt (ctr_def :: fld_iter_like :: iter_like_defs @ pre_map_defs @ map_ids @
iter_like_thms) THEN Local_Defs.unfold_tac ctxt @{thms id_def} THEN rtac refl 1;
val coiter_like_ss = ss_only @{thms if_True if_False};
val coiter_like_thms = @{thms id_apply map_pair_def sum_map.simps prod.cases};
fun mk_coiter_like_tac coiter_like_defs map_ids fld_unf_coiter_like pre_map_def ctr_def ctxt =
Local_Defs.unfold_tac ctxt (ctr_def :: coiter_like_defs) THEN
subst_tac ctxt [fld_unf_coiter_like] 1 THEN asm_simp_tac coiter_like_ss 1 THEN
Local_Defs.unfold_tac ctxt (pre_map_def :: coiter_like_thms @ map_ids) THEN
Local_Defs.unfold_tac ctxt @{thms id_def} THEN
TRY ((rtac refl ORELSE' subst_tac ctxt @{thms unit_eq} THEN' rtac refl) 1);
end;