(*  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_exhaust_tac: Proof.context -> int -> int list -> 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_inject_tac: Proof.context -> thm -> thm -> tactic

 end;

 structure BNF_FP_Sugar_Tactics : BNF_FP_SUGAR_TACTICS =

 struct

 open BNF_Tactics

 open BNF_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 (BNF_FP_Util.mk_sum_casesN 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 ms 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' (map2 (fn k => fn m =>

      select_prem_tac n (REPEAT_DETERM_N m o dtac @{thm meta_spec} THEN' etac @{thm meta_mp}) k THEN'

      atac) (1 upto n) ms) 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;

 end;