(*  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 -> thm 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_taut_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_taut_tac ctxt =

  HEADGOAL (etac FalseE) ORELSE

  unfold_thms_tac ctxt @{thms de_Morgan_conj de_Morgan_disj not_not not_False_eq_True} THEN

  HEADGOAL (SOLVE o REPEAT o (atac ORELSE' resolve_tac @{thms disjI1 disjI2 conjI TrueI}));

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_taut_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 defs ctr_thm =

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

  mk_primcorec_prelude ctxt defs (ctr_thm RS trans) THEN

  REPEAT_DETERM_N 2 (HEADGOAL

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

fun mk_primcorec_code_of_ctr_tac ctxt defs ctr_thms =

  unfold_thms_tac ctxt defs THEN

  EVERY (map (mk_primcorec_code_of_ctr_case_tac ctxt []) 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;