(*  Title:      HOL/Codatatype/Tools/bnf_fp_sugar_tactics.ML

    Author:     Jasmin Blanchette, TU Muenchen

    Copyright   2012

Tactics for datatype and codatatype sugar.

*)

signature BNF_FP_SUGAR_TACTICS =

sig

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

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

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

  val mk_fld_iff_unf_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm ->

    tactic

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

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

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

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

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

end;

structure BNF_FP_Sugar_Tactics : BNF_FP_SUGAR_TACTICS =

struct

open BNF_Tactics

open BNF_Util

open BNF_FP_Util

val meta_mp = @{thm meta_mp};

val meta_spec = @{thm meta_spec};

fun inst_spurious_fs lthy thm =

  let

    val fs =

      Term.add_vars (prop_of thm) []

      |> filter (fn (_, Type (@{type_name fun}, [_, T'])) => T' <> HOLogic.boolT | _ => false);

    val cfs =

      map (fn f as (_, T) => (certify lthy (Var f), certify lthy (id_abs (domain_type T)))) fs;

  in

    Drule.cterm_instantiate cfs thm

  end;

val inst_spurious_fs_tac = PRIMITIVE o inst_spurious_fs;

fun mk_case_tac ctxt n k m case_def ctr_def unf_fld =

  Local_Defs.unfold_tac ctxt [case_def, ctr_def, unf_fld] THEN

  (rtac (mk_sum_casesN_balanced n k RS ssubst) THEN'

   REPEAT_DETERM_N (Int.max (0, m - 1)) o rtac (@{thm split} RS ssubst) THEN'

   rtac refl) 1;

fun mk_exhaust_tac ctxt n ctr_defs fld_iff_unf sumEN' =

  Local_Defs.unfold_tac ctxt (fld_iff_unf :: ctr_defs) THEN rtac sumEN' 1 THEN

  Local_Defs.unfold_tac ctxt @{thms all_prod_eq} THEN

  EVERY' (maps (fn k => [select_prem_tac n (rotate_tac 1) k, REPEAT_DETERM o dtac meta_spec,

    etac meta_mp, atac]) (1 upto n)) 1;

fun mk_fld_iff_unf_tac ctxt cTs cfld cunf fld_unf unf_fld =

  (rtac iffI THEN'

   EVERY' (map3 (fn cTs => fn cx => fn th =>

     dtac (Drule.instantiate' cTs [NONE, NONE, SOME cx] arg_cong) THEN'

     SELECT_GOAL (Local_Defs.unfold_tac ctxt [th]) THEN'

     atac) [rev cTs, cTs] [cunf, cfld] [unf_fld, fld_unf])) 1;

fun mk_half_distinct_tac ctxt fld_inject ctr_defs =

  Local_Defs.unfold_tac ctxt (fld_inject :: @{thms sum.inject} @ ctr_defs) THEN

  rtac @{thm sum.distinct(1)} 1;

fun mk_inject_tac ctxt ctr_def fld_inject =

  Local_Defs.unfold_tac ctxt [ctr_def] THEN rtac (fld_inject RS ssubst) 1 THEN

  Local_Defs.unfold_tac ctxt @{thms sum.inject Pair_eq conj_assoc} THEN rtac refl 1;

val iter_like_thms =

  @{thms case_unit comp_def convol_def id_apply map_pair_def sum.simps(5,6) sum_map.simps

      split_conv};

fun mk_iter_like_tac pre_map_defs map_ids iter_like_defs fld_iter_like ctr_def ctxt =

  Local_Defs.unfold_tac ctxt (ctr_def :: fld_iter_like :: iter_like_defs @ pre_map_defs @ map_ids @

    iter_like_thms) THEN Local_Defs.unfold_tac ctxt @{thms id_def} THEN rtac refl 1;

val coiter_like_ss = ss_only @{thms if_True if_False};

val coiter_like_thms = @{thms id_apply map_pair_def sum_map.simps prod.cases};

fun mk_coiter_like_tac coiter_like_defs map_ids fld_unf_coiter_like pre_map_def ctr_def ctxt =

  Local_Defs.unfold_tac ctxt (ctr_def :: coiter_like_defs) THEN

  subst_tac ctxt [fld_unf_coiter_like] 1 THEN asm_simp_tac coiter_like_ss 1 THEN

  Local_Defs.unfold_tac ctxt (pre_map_def :: coiter_like_thms @ map_ids) THEN

  Local_Defs.unfold_tac ctxt @{thms id_def} THEN

  TRY ((rtac refl ORELSE' subst_tac ctxt @{thms unit_eq} THEN' rtac refl) 1);

val maybe_singletonI_tac = atac ORELSE' rtac @{thm singletonI};

val solve_prem_prem_tac =

  REPEAT o (eresolve_tac @{thms bexE rev_bexI} ORELSE' rtac @{thm rev_bexI[OF UNIV_I]} ORELSE'

    hyp_subst_tac ORELSE' resolve_tac @{thms disjI1 disjI2}) THEN'

  (rtac refl ORELSE' atac ORELSE' rtac @{thm singletonI});

val induct_prem_prem_thms =

  @{thms SUP_empty Sup_empty Sup_insert UN_compreh_bex_eq_empty UN_compreh_bex_eq_singleton

      UN_insert Un_assoc Un_empty_left Un_empty_right Un_iff Union_Un_distrib collect_def[abs_def]

      eq_UN_compreh_Un fst_conv image_def o_apply snd_conv snd_prod_fun sum.cases sup_bot_right

      fst_map_pair map_pair_simp mem_Collect_eq mem_UN_compreh_eq prod_set_simps sum_map.simps

      sum_set_simps};

fun mk_induct_leverage_prem_prems_tac ctxt nn kks set_natural's pre_set_defs =

  EVERY' (maps (fn kk => [select_prem_tac nn (dtac meta_spec) kk, etac meta_mp,

     SELECT_GOAL (Local_Defs.unfold_tac ctxt

       (pre_set_defs @ set_natural's @ induct_prem_prem_thms)),

     solve_prem_prem_tac]) (rev kks)) 1;

fun mk_induct_discharge_prem_tac ctxt nn n set_natural's pre_set_defs m k kks =

  let val r = length kks in

    EVERY' [select_prem_tac n (rotate_tac 1) k, rotate_tac ~1, hyp_subst_tac,

      REPEAT_DETERM_N m o (dtac meta_spec THEN' rotate_tac ~1)] 1 THEN

    EVERY [REPEAT_DETERM_N r

        (rotate_tac ~1 1 THEN dtac meta_mp 1 THEN rotate_tac 1 1 THEN prefer_tac 2),

      if r > 0 then PRIMITIVE Raw_Simplifier.norm_hhf else all_tac, atac 1,

      mk_induct_leverage_prem_prems_tac ctxt nn kks set_natural's pre_set_defs]

  end;

fun mk_induct_tac ctxt ns mss kkss ctr_defs fld_induct' set_natural's pre_set_defss =

  let

    val nn = length ns;

    val n = Integer.sum ns;

  in

    Local_Defs.unfold_tac ctxt ctr_defs THEN rtac fld_induct' 1 THEN inst_spurious_fs_tac ctxt THEN

    EVERY (map4 (EVERY oooo map3 o mk_induct_discharge_prem_tac ctxt nn n set_natural's)

      pre_set_defss mss (unflat mss (1 upto n)) kkss)

  end;

end;