src/HOL/BNF/Tools/bnf_fp_rec_sugar_tactics.ML
author blanchet
Fri, 30 Aug 2013 14:17:19 +0200
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(*  Title:      HOL/BNF/Tools/bnf_fp_rec_sugar_tactics.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2013
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Tactics for recursor and corecursor sugar.
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*)
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signature BNF_FP_REC_SUGAR_TACTICS =
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sig
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  val mk_primcorec_taut_tac: Proof.context -> tactic
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  val mk_primcorec_disc_tac: Proof.context -> thm list -> thm -> int -> int -> thm list list list ->
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    tactic
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  val mk_primcorec_dtr_to_ctr_tac: Proof.context -> int -> thm -> thm -> thm list -> tactic
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  val mk_primcorec_eq_tac: Proof.context -> thm list -> thm -> int -> int -> thm list list list ->
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    thm list -> thm list -> thm list -> tactic
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  val mk_primrec_tac: Proof.context -> int -> thm list -> thm list -> thm list -> thm -> tactic
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end;
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structure BNF_FP_Rec_Sugar_Tactics : BNF_FP_REC_SUGAR_TACTICS =
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struct
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open BNF_Util
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open BNF_Tactics
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fun mk_primrec_tac ctxt num_extra_args map_idents map_comps fun_defs recx =
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  unfold_thms_tac ctxt fun_defs THEN
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  HEADGOAL (rtac (funpow num_extra_args (fn thm => thm RS fun_cong) recx RS trans)) THEN
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  unfold_thms_tac ctxt (@{thms id_def split o_def fst_conv snd_conv} @ map_comps @ map_idents) THEN
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  HEADGOAL (rtac refl);
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fun mk_primcorec_taut_tac ctxt =
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  HEADGOAL (etac FalseE) ORELSE
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  unfold_thms_tac ctxt @{thms de_Morgan_conj de_Morgan_disj not_not not_False_eq_True} THEN
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  HEADGOAL (SOLVE o REPEAT o (atac ORELSE' resolve_tac @{thms disjI1 disjI2 conjI TrueI}));
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fun mk_primcorec_same_case_tac m =
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  HEADGOAL (if m = 0 then rtac TrueI
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    else REPEAT_DETERM_N (m - 1) o (rtac conjI THEN' atac) THEN' atac);
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fun mk_primcorec_different_case_tac ctxt excl =
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  unfold_thms_tac ctxt @{thms not_not not_False_eq_True} THEN
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  HEADGOAL (rtac excl THEN_ALL_NEW SELECT_GOAL (mk_primcorec_taut_tac ctxt));
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fun mk_primcorec_cases_tac ctxt k m exclsss =
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  let val n = length exclsss in
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    EVERY (map (fn [] => if k = n then all_tac else mk_primcorec_same_case_tac m
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        | [excl] => mk_primcorec_different_case_tac ctxt excl)
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      (take k (nth exclsss (k - 1))))
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  end;
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fun mk_primcorec_prelude ctxt defs thm =
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  unfold_thms_tac ctxt defs THEN HEADGOAL (rtac thm) THEN unfold_thms_tac ctxt @{thms split};
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fun mk_primcorec_disc_tac ctxt defs disc k m exclsss =
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  mk_primcorec_prelude ctxt defs disc THEN mk_primcorec_cases_tac ctxt k m exclsss;
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fun mk_primcorec_eq_tac ctxt defs sel k m exclsss maps map_idents map_comps =
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  mk_primcorec_prelude ctxt defs (sel RS trans) THEN mk_primcorec_cases_tac ctxt k m exclsss THEN
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  unfold_thms_tac ctxt (@{thms if_if_True if_if_False if_True if_False o_def split_def sum.cases} @
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    maps @ map_comps @ map_idents) THEN HEADGOAL (rtac refl);
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fun mk_primcorec_dtr_to_ctr_tac ctxt m collapse disc sels =
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  HEADGOAL (rtac (collapse RS sym RS trans) THEN' rtac disc THEN' REPEAT_DETERM_N m o atac) THEN
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  unfold_thms_tac ctxt sels THEN HEADGOAL (rtac refl);
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end;