blanchet@50138: (*  Title:      HOL/Codatatype/Tools/bnf_fp_sugar_tactics.ML
blanchet@50138:     Author:     Jasmin Blanchette, TU Muenchen
blanchet@50138:     Copyright   2012
blanchet@50138: 
blanchet@50404: Tactics for datatype and codatatype sugar.
blanchet@50138: *)
blanchet@50138: 
blanchet@50138: signature BNF_FP_SUGAR_TACTICS =
blanchet@50138: sig
blanchet@50145:   val mk_case_tac: Proof.context -> int -> int -> int -> thm -> thm -> thm -> tactic
blanchet@50241:   val mk_coiter_like_tac: thm list -> thm list -> thm -> thm -> thm -> Proof.context -> tactic
blanchet@50176:   val mk_exhaust_tac: Proof.context -> int -> thm list -> thm -> thm -> tactic
blanchet@50387:   val mk_fld_iff_unf_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm ->
blanchet@50387:     tactic
blanchet@50142:   val mk_half_distinct_tac: Proof.context -> thm -> thm list -> tactic
blanchet@50444:   val mk_induct_tac: Proof.context -> int list -> int list list -> int list list list -> thm list ->
blanchet@50444:     thm -> thm list -> thm list list -> tactic
blanchet@50141:   val mk_inject_tac: Proof.context -> thm -> thm -> tactic
blanchet@50241:   val mk_iter_like_tac: thm list -> thm list -> thm list -> thm -> thm -> Proof.context -> tactic
blanchet@50138: end;
blanchet@50138: 
blanchet@50138: structure BNF_FP_Sugar_Tactics : BNF_FP_SUGAR_TACTICS =
blanchet@50138: struct
blanchet@50138: 
blanchet@50140: open BNF_Tactics
blanchet@50138: open BNF_Util
blanchet@50279: open BNF_FP_Util
blanchet@50138: 
blanchet@50383: val meta_mp = @{thm meta_mp};
blanchet@50383: val meta_spec = @{thm meta_spec};
blanchet@50383: 
blanchet@50406: fun inst_spurious_fs lthy thm =
blanchet@50383:   let
blanchet@50399:     val fs =
blanchet@50383:       Term.add_vars (prop_of thm) []
blanchet@50383:       |> filter (fn (_, Type (@{type_name fun}, [_, T'])) => T' <> HOLogic.boolT | _ => false);
blanchet@50399:     val cfs =
blanchet@50399:       map (fn f as (_, T) => (certify lthy (Var f), certify lthy (id_abs (domain_type T)))) fs;
blanchet@50383:   in
blanchet@50399:     Drule.cterm_instantiate cfs thm
blanchet@50383:   end;
blanchet@50383: 
blanchet@50406: val inst_spurious_fs_tac = PRIMITIVE o inst_spurious_fs;
blanchet@50383: 
blanchet@50145: fun mk_case_tac ctxt n k m case_def ctr_def unf_fld =
blanchet@50145:   Local_Defs.unfold_tac ctxt [case_def, ctr_def, unf_fld] THEN
blanchet@50279:   (rtac (mk_sum_casesN_balanced n k RS ssubst) THEN'
blanchet@50145:    REPEAT_DETERM_N (Int.max (0, m - 1)) o rtac (@{thm split} RS ssubst) THEN'
blanchet@50145:    rtac refl) 1;
blanchet@50145: 
blanchet@50176: fun mk_exhaust_tac ctxt n ctr_defs fld_iff_unf sumEN' =
blanchet@50278:   Local_Defs.unfold_tac ctxt (fld_iff_unf :: ctr_defs) THEN rtac sumEN' 1 THEN
blanchet@50140:   Local_Defs.unfold_tac ctxt @{thms all_prod_eq} THEN
blanchet@50383:   EVERY' (maps (fn k => [select_prem_tac n (rotate_tac 1) k, REPEAT_DETERM o dtac meta_spec,
blanchet@50383:     etac meta_mp, atac]) (1 upto n)) 1;
blanchet@50140: 
blanchet@50138: fun mk_fld_iff_unf_tac ctxt cTs cfld cunf fld_unf unf_fld =
blanchet@50138:   (rtac iffI THEN'
blanchet@50138:    EVERY' (map3 (fn cTs => fn cx => fn th =>
blanchet@50138:      dtac (Drule.instantiate' cTs [NONE, NONE, SOME cx] arg_cong) THEN'
blanchet@50138:      SELECT_GOAL (Local_Defs.unfold_tac ctxt [th]) THEN'
blanchet@50138:      atac) [rev cTs, cTs] [cunf, cfld] [unf_fld, fld_unf])) 1;
blanchet@50138: 
blanchet@50142: fun mk_half_distinct_tac ctxt fld_inject ctr_defs =
blanchet@50142:   Local_Defs.unfold_tac ctxt (fld_inject :: @{thms sum.inject} @ ctr_defs) THEN
blanchet@50142:   rtac @{thm sum.distinct(1)} 1;
blanchet@50142: 
blanchet@50141: fun mk_inject_tac ctxt ctr_def fld_inject =
blanchet@50150:   Local_Defs.unfold_tac ctxt [ctr_def] THEN rtac (fld_inject RS ssubst) 1 THEN
blanchet@50150:   Local_Defs.unfold_tac ctxt @{thms sum.inject Pair_eq conj_assoc} THEN rtac refl 1;
blanchet@50141: 
blanchet@50226: val iter_like_thms =
blanchet@50248:   @{thms case_unit comp_def convol_def id_apply map_pair_def sum.simps(5,6) sum_map.simps
blanchet@50248:       split_conv};
blanchet@50220: 
blanchet@50244: fun mk_iter_like_tac pre_map_defs map_ids iter_like_defs fld_iter_like ctr_def ctxt =
blanchet@50244:   Local_Defs.unfold_tac ctxt (ctr_def :: fld_iter_like :: iter_like_defs @ pre_map_defs @ map_ids @
blanchet@50247:     iter_like_thms) THEN Local_Defs.unfold_tac ctxt @{thms id_def} THEN rtac refl 1;
blanchet@50220: 
blanchet@50228: val coiter_like_ss = ss_only @{thms if_True if_False};
blanchet@50291: val coiter_like_thms = @{thms id_apply map_pair_def sum_map.simps prod.cases};
blanchet@50228: 
blanchet@50244: fun mk_coiter_like_tac coiter_like_defs map_ids fld_unf_coiter_like pre_map_def ctr_def ctxt =
blanchet@50228:   Local_Defs.unfold_tac ctxt (ctr_def :: coiter_like_defs) THEN
blanchet@50241:   subst_tac ctxt [fld_unf_coiter_like] 1 THEN asm_simp_tac coiter_like_ss 1 THEN
blanchet@50247:   Local_Defs.unfold_tac ctxt (pre_map_def :: coiter_like_thms @ map_ids) THEN
blanchet@50250:   Local_Defs.unfold_tac ctxt @{thms id_def} THEN
blanchet@50377:   TRY ((rtac refl ORELSE' subst_tac ctxt @{thms unit_eq} THEN' rtac refl) 1);
blanchet@50228: 
blanchet@50442: val maybe_singletonI_tac = atac ORELSE' rtac @{thm singletonI};
blanchet@50383: 
blanchet@50444: val solve_prem_prem_tac =
blanchet@50444:   REPEAT o (eresolve_tac @{thms bexE rev_bexI} ORELSE' rtac @{thm rev_bexI[OF UNIV_I]} ORELSE'
blanchet@50444:     hyp_subst_tac ORELSE' resolve_tac @{thms disjI1 disjI2}) THEN'
blanchet@50444:   (rtac refl ORELSE' atac ORELSE' rtac @{thm singletonI});
blanchet@50441: 
blanchet@50383: val induct_prem_prem_thms =
blanchet@50441:   @{thms SUP_empty Sup_empty Sup_insert UN_compreh_bex_eq_empty UN_compreh_bex_eq_singleton
blanchet@50444:       UN_insert Un_assoc Un_empty_left Un_empty_right Un_iff Union_Un_distrib collect_def[abs_def]
blanchet@50444:       eq_UN_compreh_Un fst_conv image_def o_apply snd_conv snd_prod_fun sum.cases sup_bot_right
blanchet@50444:       fst_map_pair map_pair_simp mem_Collect_eq mem_UN_compreh_eq prod_set_simps sum_map.simps
blanchet@50444:       sum_set_simps};
blanchet@50383: 
blanchet@50444: fun mk_induct_leverage_prem_prems_tac ctxt nn kks set_natural's pre_set_defs =
blanchet@50444:   EVERY' (maps (fn kk => [select_prem_tac nn (dtac meta_spec) kk, etac meta_mp,
blanchet@50404:      SELECT_GOAL (Local_Defs.unfold_tac ctxt
blanchet@50404:        (pre_set_defs @ set_natural's @ induct_prem_prem_thms)),
blanchet@50444:      solve_prem_prem_tac]) (rev kks)) 1;
blanchet@50393: 
blanchet@50444: fun mk_induct_discharge_prem_tac ctxt nn n set_natural's pre_set_defs m k kks =
blanchet@50444:   let val r = length kks in
blanchet@50406:     EVERY' [select_prem_tac n (rotate_tac 1) k, rotate_tac ~1, hyp_subst_tac,
blanchet@50406:       REPEAT_DETERM_N m o (dtac meta_spec THEN' rotate_tac ~1)] 1 THEN
blanchet@50406:     EVERY [REPEAT_DETERM_N r
blanchet@50406:         (rotate_tac ~1 1 THEN dtac meta_mp 1 THEN rotate_tac 1 1 THEN prefer_tac 2),
blanchet@50406:       if r > 0 then PRIMITIVE Raw_Simplifier.norm_hhf else all_tac, atac 1,
blanchet@50444:       mk_induct_leverage_prem_prems_tac ctxt nn kks set_natural's pre_set_defs]
blanchet@50406:   end;
blanchet@50383: 
blanchet@50444: fun mk_induct_tac ctxt ns mss kkss ctr_defs fld_induct' set_natural's pre_set_defss =
blanchet@50391:   let
blanchet@50391:     val nn = length ns;
blanchet@50391:     val n = Integer.sum ns;
blanchet@50391:   in
blanchet@50406:     Local_Defs.unfold_tac ctxt ctr_defs THEN rtac fld_induct' 1 THEN inst_spurious_fs_tac ctxt THEN
blanchet@50391:     EVERY (map4 (EVERY oooo map3 o mk_induct_discharge_prem_tac ctxt nn n set_natural's)
blanchet@50444:       pre_set_defss mss (unflat mss (1 upto n)) kkss)
blanchet@50383:   end;
blanchet@50383: 
blanchet@50138: end;