(*  Title:      HOL/BNF/Tools/bnf_fp_rec_sugar_tactics.ML

     Author:     Jasmin Blanchette, TU Muenchen

     Copyright   2013

 Tactics for recursor and corecursor sugar.

 *)

 signature BNF_FP_REC_SUGAR_TACTICS =

 sig

   val mk_primcorec_code_tac: Proof.context -> thm -> thm list -> tactic

   val mk_primcorec_code_of_ctr_tac: Proof.context -> int list -> thm list -> tactic

   val mk_primcorec_ctr_of_dtr_tac: Proof.context -> int -> thm -> thm -> thm list -> tactic

   val mk_primcorec_ctr_or_sel_tac: Proof.context -> thm list -> thm -> int -> int ->

     thm list list list -> thm list -> thm list -> thm list -> tactic

   val mk_primcorec_disc_tac: Proof.context -> thm list -> thm -> int -> int -> thm list list list ->

     tactic

   val mk_primcorec_assumption_tac: Proof.context -> tactic

   val mk_primrec_tac: Proof.context -> int -> thm list -> thm list -> thm list -> thm -> tactic

 end;

 structure BNF_FP_Rec_Sugar_Tactics : BNF_FP_REC_SUGAR_TACTICS =

 struct

 open BNF_Util

 open BNF_Tactics

 fun mk_primrec_tac ctxt num_extra_args map_idents map_comps fun_defs recx =

   unfold_thms_tac ctxt fun_defs THEN

   HEADGOAL (rtac (funpow num_extra_args (fn thm => thm RS fun_cong) recx RS trans)) THEN

   unfold_thms_tac ctxt (@{thms id_def split o_def fst_conv snd_conv} @ map_comps @ map_idents) THEN

   HEADGOAL (rtac refl);

 fun mk_primcorec_assumption_tac ctxt =

   HEADGOAL (blast_tac (put_claset (claset_of @{theory_context HOL}) ctxt));

 fun mk_primcorec_same_case_tac m =

   HEADGOAL (if m = 0 then rtac TrueI

     else REPEAT_DETERM_N (m - 1) o (rtac conjI THEN' atac) THEN' atac);

 fun mk_primcorec_different_case_tac ctxt excl =

   unfold_thms_tac ctxt @{thms not_not not_False_eq_True} THEN

   HEADGOAL (rtac excl THEN_ALL_NEW SELECT_GOAL (mk_primcorec_assumption_tac ctxt));

 fun mk_primcorec_cases_tac ctxt k m exclsss =

   let val n = length exclsss in

     EVERY (map (fn [] => if k = n then all_tac else mk_primcorec_same_case_tac m

         | [excl] => mk_primcorec_different_case_tac ctxt excl)

       (take k (nth exclsss (k - 1))))

   end;

 fun mk_primcorec_prelude ctxt defs thm =

   unfold_thms_tac ctxt defs THEN HEADGOAL (rtac thm) THEN unfold_thms_tac ctxt @{thms split};

 fun mk_primcorec_disc_tac ctxt defs disc k m exclsss =

   mk_primcorec_prelude ctxt defs disc THEN mk_primcorec_cases_tac ctxt k m exclsss;

 fun mk_primcorec_ctr_or_sel_tac ctxt defs eq_thm k m exclsss maps map_idents map_comps =

   mk_primcorec_prelude ctxt defs (eq_thm RS trans) THEN

   mk_primcorec_cases_tac ctxt k m exclsss THEN

   unfold_thms_tac ctxt (@{thms if_if_True if_if_False if_True if_False if_cancel[of _ True]

     if_cancel[of _ False] o_def split_def sum.cases} @ maps @ map_comps @ map_idents) THEN

   HEADGOAL (rtac refl);

 fun mk_primcorec_ctr_of_dtr_tac ctxt m collapse disc sels =

   HEADGOAL (rtac (collapse RS sym RS trans) THEN' rtac disc THEN' REPEAT_DETERM_N m o atac) THEN

   unfold_thms_tac ctxt sels THEN HEADGOAL (rtac refl);

 fun mk_primcorec_code_of_ctr_case_tac ctxt m ctr_thm =

   HEADGOAL (REPEAT o rtac @{thm eq_ifI}) THEN

   mk_primcorec_prelude ctxt [] (ctr_thm RS trans) THEN

   REPEAT_DETERM_N m (mk_primcorec_assumption_tac ctxt) THEN

   HEADGOAL (asm_simp_tac (ss_only @{thms if_True if_False not_False_eq_True} ctxt));

 fun mk_primcorec_code_of_ctr_tac ctxt ms ctr_thms =

   EVERY (map2 (mk_primcorec_code_of_ctr_case_tac ctxt) ms ctr_thms);

 fun mk_primcorec_code_tac ctxt raw collapses =

   HEADGOAL (rtac (raw RS trans)) THEN unfold_thms_tac ctxt @{thms split_ifs} THEN

   Method.intros_tac @{thms conjI impI} [] THEN

   REPEAT (HEADGOAL (rtac refl ORELSE' (etac notE THEN' atac) ORELSE'

     eresolve_tac (maps (fn thm => [thm, thm RS sym]) collapses)));

 end;