(*  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_assumption_tac: Proof.context -> thm list -> tactic

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

    int list -> thm list -> tactic

  val mk_primcorec_code_of_raw_tac: thm list -> thm list -> thm -> tactic

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

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

    tactic

  val mk_primcorec_sel_tac: Proof.context -> thm list -> thm list -> thm list -> thm list ->

    thm list -> thm list -> thm list -> thm -> int -> int -> thm list list list -> 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

val falseEs = @{thms not_TrueE FalseE};

val neq_eq_eq_contradict = @{thm neq_eq_eq_contradict};

val split_if = @{thm split_if};

val split_if_asm = @{thm split_if_asm};

val split_connectI = @{thms allI impI conjI};

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 discIs =

  HEADGOAL (SELECT_GOAL (unfold_thms_tac ctxt

      @{thms not_not not_False_eq_True de_Morgan_conj de_Morgan_disj} THEN

    SOLVE (HEADGOAL (REPEAT o (rtac refl ORELSE' atac ORELSE' etac conjE ORELSE'

    resolve_tac @{thms TrueI conjI disjI1 disjI2} ORELSE'

    dresolve_tac discIs THEN' atac ORELSE'

    etac notE THEN' atac ORELSE'

    etac disjE)))));

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 not_True_eq_False} 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 Let_def split};

fun mk_primcorec_disc_tac ctxt defs disc_corec k m exclsss =

  mk_primcorec_prelude ctxt defs disc_corec THEN mk_primcorec_cases_tac ctxt k m exclsss;

fun mk_primcorec_sel_tac ctxt defs distincts splits split_asms maps map_idents map_comps f_sel k m

    exclsss =

  mk_primcorec_prelude ctxt defs (f_sel RS trans) THEN

  mk_primcorec_cases_tac ctxt k m exclsss THEN

  unfold_thms_tac ctxt (@{thms id_apply o_def split_def} @ maps @ map_comps @ map_idents) THEN

  HEADGOAL (REPEAT_DETERM o (rtac refl ORELSE' rtac ext ORELSE'

    eresolve_tac falseEs ORELSE'

    resolve_tac split_connectI ORELSE'

    Splitter.split_asm_tac (split_if_asm :: split_asms) ORELSE'

    Splitter.split_tac (split_if :: splits) ORELSE'

    eresolve_tac (map (fn thm => thm RS neq_eq_eq_contradict) distincts) THEN' atac ORELSE'

    (CHANGED o SELECT_GOAL (unfold_tac @{thms sum.cases} ctxt)) ORELSE'

    etac notE THEN' atac));

fun mk_primcorec_ctr_of_dtr_tac ctxt m collapse maybe_disc_f sel_fs =

  HEADGOAL (rtac ((if null sel_fs then collapse else collapse RS sym) RS trans) THEN'

    (the_default (K all_tac) (Option.map rtac maybe_disc_f)) THEN' REPEAT_DETERM_N m o atac) THEN

  unfold_thms_tac ctxt sel_fs THEN HEADGOAL (rtac refl);

(* TODO: reduce code duplication with selector tactic above *)

fun mk_primcorec_code_of_ctr_single_tac ctxt distincts discIs splits split_asms m f_ctr =

  HEADGOAL (REPEAT o (resolve_tac split_connectI ORELSE' split_tac (split_if :: splits))) THEN

  mk_primcorec_prelude ctxt [] (f_ctr RS trans) THEN

  REPEAT_DETERM_N m (mk_primcorec_assumption_tac ctxt discIs) THEN

  HEADGOAL (SELECT_GOAL (SOLVE (HEADGOAL (REPEAT_DETERM o

    (rtac refl ORELSE' atac ORELSE'

     resolve_tac split_connectI ORELSE'

     Splitter.split_asm_tac (split_if_asm :: split_asms) ORELSE'

     Splitter.split_tac (split_if :: splits) ORELSE'

     K (mk_primcorec_assumption_tac ctxt discIs) ORELSE'

     eresolve_tac (map (fn thm => thm RS neq_eq_eq_contradict) distincts) THEN' atac ORELSE'

     (TRY o dresolve_tac discIs) THEN' etac notE THEN' atac)))));

fun mk_primcorec_code_of_ctr_tac ctxt distincts discIs splits split_asms ms ctr_thms =

  EVERY (map2 (mk_primcorec_code_of_ctr_single_tac ctxt distincts discIs splits split_asms)

    ms ctr_thms);

fun mk_primcorec_code_of_raw_tac splits disc_excludes raw =

  HEADGOAL (rtac raw ORELSE' rtac (raw RS trans) THEN' REPEAT_DETERM o

    (rtac refl ORELSE'

     (TRY o rtac sym) THEN' atac ORELSE'

     resolve_tac split_connectI ORELSE'

     Splitter.split_tac (split_if :: splits) ORELSE'

     etac notE THEN' atac ORELSE'

     (TRY o dresolve_tac disc_excludes) THEN' etac notE THEN' atac));

end;