(*  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;