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

    Author:     Jasmin Blanchette, TU Muenchen

    Copyright   2012

Tactics for wrapping existing freely generated type's constructors.

*)

signature CTR_SUGAR_TACTICS =

sig

  val mk_alternate_disc_def_tac: Proof.context -> int -> thm -> thm -> thm -> tactic

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

  val mk_case_cong_tac: Proof.context -> thm -> thm list -> tactic

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

    thm list list -> tactic

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

  val mk_disc_exhaust_tac: int -> thm -> thm list -> tactic

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

    thm list list list -> thm list list list -> tactic

  val mk_half_disc_exclude_tac: Proof.context -> int -> thm -> thm -> tactic

  val mk_nchotomy_tac: int -> thm -> tactic

  val mk_other_half_disc_exclude_tac: thm -> tactic

  val mk_sel_exhaust_tac: int -> thm -> thm list -> tactic

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

    list list -> tactic

  val mk_split_asm_tac: Proof.context -> thm -> tactic

  val mk_unique_disc_def_tac: int -> thm -> tactic

end;

structure Ctr_Sugar_Tactics : CTR_SUGAR_TACTICS =

struct

open BNF_Util

open BNF_Tactics

val meta_mp = @{thm meta_mp};

fun if_P_or_not_P_OF pos thm = thm RS (if pos then @{thm if_P} else @{thm if_not_P});

fun mk_nchotomy_tac n exhaust =

  HEADGOAL (rtac allI THEN' rtac exhaust THEN'

   EVERY' (maps (fn k => [rtac (mk_disjIN n k), REPEAT_DETERM o rtac exI, atac]) (1 upto n)));

fun mk_unique_disc_def_tac m uexhaust =

  HEADGOAL (EVERY' [rtac iffI, rtac uexhaust, REPEAT_DETERM_N m o rtac exI, atac, rtac refl]);

fun mk_alternate_disc_def_tac ctxt k other_disc_def distinct uexhaust =

  HEADGOAL (EVERY' ([rtac (other_disc_def RS @{thm arg_cong[of _ _ Not]} RS trans),

    rtac @{thm iffI_np}, REPEAT_DETERM o etac exE,

    hyp_subst_tac ctxt, SELECT_GOAL (unfold_thms_tac ctxt [not_ex]), REPEAT_DETERM o rtac allI,

    rtac distinct, rtac uexhaust] @

    (([etac notE, REPEAT_DETERM o rtac exI, atac], [REPEAT_DETERM o rtac exI, atac])

     |> k = 1 ? swap |> op @)));

fun mk_half_disc_exclude_tac ctxt m discD disc' =

  HEADGOAL (dtac discD THEN' REPEAT_DETERM_N m o etac exE THEN' hyp_subst_tac ctxt THEN'

    rtac disc');

fun mk_other_half_disc_exclude_tac half = HEADGOAL (etac @{thm contrapos_pn} THEN' etac half);

fun mk_disc_or_sel_exhaust_tac n exhaust destIs =

  HEADGOAL (rtac exhaust THEN'

    EVERY' (map2 (fn k => fn destI => dtac destI THEN'

      select_prem_tac n (etac meta_mp) k THEN' atac) (1 upto n) destIs));

val mk_disc_exhaust_tac = mk_disc_or_sel_exhaust_tac;

fun mk_sel_exhaust_tac n disc_exhaust collapses =

  mk_disc_or_sel_exhaust_tac n disc_exhaust collapses ORELSE

  HEADGOAL (etac meta_mp THEN' resolve_tac collapses);

fun mk_collapse_tac ctxt m discD sels =

  HEADGOAL (dtac discD THEN'

    (if m = 0 then

       atac

     else

       REPEAT_DETERM_N m o etac exE THEN' hyp_subst_tac ctxt THEN'

       SELECT_GOAL (unfold_thms_tac ctxt sels) THEN' rtac refl));

fun mk_expand_tac ctxt n ms udisc_exhaust vdisc_exhaust uncollapses disc_excludesss

    disc_excludesss' =

  if ms = [0] then

    HEADGOAL (rtac (@{thm trans_sym} OF (replicate 2 (the_single uncollapses))) THEN'

      TRY o EVERY' [rtac udisc_exhaust, atac, rtac vdisc_exhaust, atac])

  else

    let val ks = 1 upto n in

      HEADGOAL (rtac udisc_exhaust THEN'

        EVERY' (map5 (fn k => fn m => fn disc_excludess => fn disc_excludess' =>

            fn uuncollapse =>

          EVERY' [rtac (uuncollapse RS trans) THEN' TRY o atac,

            rtac sym, rtac vdisc_exhaust,

            EVERY' (map4 (fn k' => fn disc_excludes => fn disc_excludes' => fn vuncollapse =>

              EVERY'

                (if k' = k then

                   [rtac (vuncollapse RS trans), TRY o atac] @

                   (if m = 0 then

                      [rtac refl]

                    else

                      [if n = 1 then K all_tac else EVERY' [dtac meta_mp, atac, dtac meta_mp, atac],

                       REPEAT_DETERM_N (Int.max (0, m - 1)) o etac conjE,

                       asm_simp_tac (ss_only [] ctxt)])

                 else

                   [dtac (the_single (if k = n then disc_excludes else disc_excludes')),

                    etac (if k = n then @{thm iff_contradict(1)} else @{thm iff_contradict(2)}),

                    atac, atac]))

              ks disc_excludess disc_excludess' uncollapses)])

          ks ms disc_excludesss disc_excludesss' uncollapses))

    end;

fun mk_case_same_ctr_tac ctxt injects =

  REPEAT_DETERM o etac exE THEN' etac conjE THEN'

    (case injects of

      [] => atac

    | [inject] => dtac (inject RS iffD1) THEN' REPEAT_DETERM o etac conjE THEN'

        hyp_subst_tac ctxt THEN' rtac refl);

fun mk_case_distinct_ctrs_tac ctxt distincts =

  REPEAT_DETERM o etac exE THEN' etac conjE THEN' full_simp_tac (ss_only distincts ctxt);

fun mk_case_tac ctxt n k case_def injects distinctss =

  let

    val case_def' = mk_unabs_def (n + 1) (case_def RS meta_eq_to_obj_eq);

    val ks = 1 upto n;

  in

    HEADGOAL (rtac (case_def' RS trans) THEN' rtac @{thm the_equality} THEN'

      rtac (mk_disjIN n k) THEN' REPEAT_DETERM o rtac exI THEN' rtac conjI THEN' rtac refl THEN'

      rtac refl THEN'

      EVERY' (map2 (fn k' => fn distincts =>

        (if k' < n then etac disjE else K all_tac) THEN'

        (if k' = k then mk_case_same_ctr_tac ctxt injects

         else mk_case_distinct_ctrs_tac ctxt distincts)) ks distinctss))

  end;

fun mk_case_conv_if_tac ctxt n uexhaust cases discss' selss =

  HEADGOAL (rtac uexhaust THEN'

    EVERY' (map3 (fn casex => fn if_discs => fn sels =>

        EVERY' [hyp_subst_tac ctxt, SELECT_GOAL (unfold_thms_tac ctxt (if_discs @ sels)),

          rtac casex])

      cases (map2 (seq_conds if_P_or_not_P_OF n) (1 upto n) discss') selss));

fun mk_case_cong_tac ctxt uexhaust cases =

  HEADGOAL (rtac uexhaust THEN'

    EVERY' (maps (fn casex => [dtac sym, asm_simp_tac (ss_only [casex] ctxt)]) cases));

fun mk_split_tac ctxt uexhaust cases selss injectss distinctsss =

  HEADGOAL (rtac uexhaust) THEN

  ALLGOALS (fn k => (hyp_subst_tac ctxt THEN'

     simp_tac (ss_only (@{thms simp_thms} @ cases @ nth selss (k - 1) @ nth injectss (k - 1) @

       flat (nth distinctsss (k - 1))) ctxt)) k) THEN

  ALLGOALS (blast_tac (put_claset (claset_of @{theory_context HOL}) ctxt));

val split_asm_thms = @{thms imp_conv_disj de_Morgan_conj de_Morgan_disj not_not not_ex};

fun mk_split_asm_tac ctxt split =

  HEADGOAL (rtac (split RS trans)) THEN unfold_thms_tac ctxt split_asm_thms THEN

  HEADGOAL (rtac refl);

end;