src/HOL/BNF/Tools/bnf_fp_rec_sugar_tactics.ML
author blanchet
Thu, 26 Sep 2013 02:25:33 +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_assumption_tac: Proof.context -> thm list -> tactic
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  val mk_primcorec_code_of_ctr_tac: Proof.context -> thm list -> thm list -> thm list -> thm list ->
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    thm list -> int list -> thm list -> tactic
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  val mk_primcorec_code_of_raw_tac: thm list -> thm list -> thm -> thm list -> tactic
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  val mk_primcorec_ctr_of_dtr_tac: Proof.context -> int -> thm -> thm option -> thm list -> 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_sel_tac: Proof.context -> thm list -> thm -> int -> int ->
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    thm list list list -> thm list -> thm list -> 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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val split_if = @{thm split_if};
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val split_if_asm = @{thm split_if_asm};
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val split_connectI = @{thms allI impI conjI};
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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_assumption_tac ctxt discIs =
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  HEADGOAL (SELECT_GOAL (unfold_thms_tac ctxt
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      @{thms not_not not_False_eq_True de_Morgan_conj de_Morgan_disj} THEN
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    SOLVE (HEADGOAL (REPEAT o (rtac refl ORELSE' atac ORELSE'
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    resolve_tac @{thms TrueI conjI disjI1 disjI2} ORELSE'
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    dresolve_tac discIs THEN' atac)))));
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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_assumption_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_corec k m exclsss =
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  mk_primcorec_prelude ctxt defs disc_corec THEN mk_primcorec_cases_tac ctxt k m exclsss;
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fun mk_primcorec_sel_tac ctxt defs f_sel k m exclsss maps map_idents map_comps splits split_asms =
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  mk_primcorec_prelude ctxt defs (f_sel RS trans) THEN
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  mk_primcorec_cases_tac ctxt k m exclsss THEN
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  unfold_thms_tac ctxt (@{thms o_def split_def sum.cases} @ maps @ map_comps @ map_idents) THEN
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  HEADGOAL (REPEAT_DETERM o (rtac refl ORELSE'
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    eresolve_tac @{thms not_TrueE FalseE} ORELSE'
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    resolve_tac split_connectI ORELSE'
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    Splitter.split_asm_tac (split_if_asm :: split_asms) ORELSE'
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    Splitter.split_tac (split_if :: splits) ORELSE'
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    etac notE THEN' atac));
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fun mk_primcorec_ctr_of_dtr_tac ctxt m collapse maybe_disc_f sel_fs =
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  HEADGOAL (rtac ((if null sel_fs then collapse else collapse RS sym) RS trans) THEN'
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    (the_default (K all_tac) (Option.map rtac maybe_disc_f)) THEN' REPEAT_DETERM_N m o atac) THEN
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  unfold_thms_tac ctxt sel_fs THEN HEADGOAL (rtac refl);
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fun mk_primcorec_split distincts discIs collapses splits split_asms =
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  HEADGOAL (SELECT_GOAL (HEADGOAL (REPEAT_DETERM o
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    (rtac refl ORELSE' atac ORELSE'
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     eresolve_tac (@{thms not_TrueE FalseE} @ map (fn thm => thm RS trans) collapses) ORELSE'
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     resolve_tac split_connectI ORELSE'
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     Splitter.split_asm_tac (split_if_asm :: split_asms) ORELSE'
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     Splitter.split_tac (split_if :: splits) ORELSE'
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     eresolve_tac (map (fn thm => thm RS @{thm neq_eq_eq_contradict}) distincts) THEN' atac ORELSE'
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     (TRY o dresolve_tac discIs) THEN' etac notE THEN' atac))));
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fun mk_primcorec_code_of_ctr_single_tac ctxt distincts discIs collapses splits split_asms m f_ctr =
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  HEADGOAL (REPEAT o (resolve_tac split_connectI ORELSE' split_tac (split_if :: splits))) THEN
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  mk_primcorec_prelude ctxt [] (f_ctr RS trans) THEN
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  REPEAT_DETERM_N m (mk_primcorec_assumption_tac ctxt discIs) THEN
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  mk_primcorec_split distincts discIs collapses splits split_asms;
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fun mk_primcorec_code_of_ctr_tac ctxt distincs discIs collapses splits split_asms ms ctr_thms =
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  EVERY (map2 (mk_primcorec_code_of_ctr_single_tac ctxt distincs discIs collapses splits split_asms)
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    ms ctr_thms);
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fun mk_primcorec_code_of_raw_tac splits disc_excludes raw collapses =
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  HEADGOAL (rtac raw ORELSE' rtac (raw RS trans) THEN' REPEAT_DETERM o
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    (rtac refl ORELSE'
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     (TRY o rtac sym) THEN' atac ORELSE'
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     resolve_tac split_connectI ORELSE'
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     Splitter.split_tac (split_if :: splits) ORELSE'
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     etac notE THEN' atac ORELSE'
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     dresolve_tac disc_excludes THEN' etac notE THEN' atac ORELSE'
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     eresolve_tac (maps (fn thm => [thm, thm RS sym]) collapses)));
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end;