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

     Author:     Jasmin Blanchette, TU Muenchen

     Copyright   2013

 Tactics for corecursor sugar.

 *)

 signature BNF_GFP_REC_SUGAR_TACTICS =

 sig

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

   val mk_primcorec_code_of_raw_code_tac: Proof.context -> 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_raw_code_of_ctr_tac: Proof.context -> thm list -> thm list -> thm list ->

     thm list -> int list -> thm 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

 end;

 structure BNF_GFP_Rec_Sugar_Tactics : BNF_GFP_REC_SUGAR_TACTICS =

 struct

 open BNF_Util

 open BNF_Tactics

 val falseEs = @{thms not_TrueE FalseE};

 val Let_def = @{thm Let_def};

 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_primcorec_assumption_tac ctxt discIs =

   SELECT_GOAL (unfold_thms_tac ctxt

       @{thms not_not not_False_eq_True not_True_eq_False de_Morgan_conj de_Morgan_disj} THEN

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

     eresolve_tac falseEs 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 m excl =

   HEADGOAL (if m = 0 then mk_primcorec_assumption_tac ctxt []

     else dtac excl THEN' (REPEAT_DETERM_N (m - 1) o atac) THEN' 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 m 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

   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'

     etac notE THEN' atac ORELSE'

     (CHANGED o SELECT_GOAL (unfold_thms_tac ctxt

       (@{thms id_def o_def split_def sum.cases} @ maps @ map_comps @ map_idents)))));

 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 (Let_def :: sel_fs) THEN HEADGOAL (rtac refl);

 fun inst_split_eq ctxt split =

   (case prop_of split of

     @{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ (Var (_, Type (_, [T, _])) $ _) $ _) =>

     let

       val s = Name.uu;

       val eq = Abs (Name.uu, T, HOLogic.mk_eq (Free (s, T), Bound 0));

       val split' = Drule.instantiate' [] [SOME (certify ctxt eq)] split;

     in

       Thm.generalize ([], [s]) (Thm.maxidx_of split' + 1) split'

     end

   | _ => split);

 fun distinct_in_prems_tac distincts =

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

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

 fun mk_primcorec_raw_code_of_ctr_single_tac ctxt distincts discIs splits split_asms m f_ctr =

   let

     val splits' =

       map (fn th => th RS iffD2) (@{thm split_if_eq2} :: map (inst_split_eq ctxt) splits)

   in

     HEADGOAL (REPEAT o (resolve_tac (splits' @ split_connectI))) THEN

     mk_primcorec_prelude ctxt [] (f_ctr RS trans) THEN

     HEADGOAL ((REPEAT_DETERM_N m o mk_primcorec_assumption_tac ctxt discIs) THEN'

       SELECT_GOAL (SOLVE (HEADGOAL (REPEAT_DETERM o

       (rtac refl ORELSE' atac ORELSE'

        resolve_tac (@{thm Code.abort_def} :: split_connectI) ORELSE'

        Splitter.split_tac (split_if :: splits) ORELSE'

        Splitter.split_asm_tac (split_if_asm :: split_asms) ORELSE'

        mk_primcorec_assumption_tac ctxt discIs ORELSE'

        distinct_in_prems_tac distincts ORELSE'

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

   end;

 fun mk_primcorec_raw_code_of_ctr_tac ctxt distincts discIs splits split_asms ms f_ctrs =

   EVERY (map2 (mk_primcorec_raw_code_of_ctr_single_tac ctxt distincts discIs splits split_asms) ms

     f_ctrs) THEN

   IF_UNSOLVED (unfold_thms_tac ctxt @{thms Code.abort_def} THEN

     HEADGOAL (REPEAT_DETERM o resolve_tac (refl :: split_connectI)));

 fun mk_primcorec_code_of_raw_code_tac ctxt distincts splits raw =

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

     SELECT_GOAL (unfold_thms_tac ctxt [Let_def]) THEN' REPEAT_DETERM o

     (rtac refl ORELSE' atac ORELSE'

      resolve_tac split_connectI ORELSE'

      Splitter.split_tac (split_if :: splits) ORELSE'

      distinct_in_prems_tac distincts ORELSE'

      rtac sym THEN' atac ORELSE'

      etac notE THEN' atac));

 end;