1 (* Title: HOL/Codatatype/Tools/bnf_fp_sugar_tactics.ML
2 Author: Jasmin Blanchette, TU Muenchen
5 Tactics for the LFP/GFP sugar.
8 signature BNF_FP_SUGAR_TACTICS =
10 val mk_case_tac: Proof.context -> int -> int -> int -> thm -> thm -> thm -> tactic
11 val mk_coiter_like_tac: thm list -> thm list -> thm -> thm -> thm -> Proof.context -> tactic
12 val mk_exhaust_tac: Proof.context -> int -> thm list -> thm -> thm -> tactic
13 val mk_fld_iff_unf_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm ->
15 val mk_half_distinct_tac: Proof.context -> thm -> thm list -> tactic
16 val mk_induct_tac: Proof.context -> int list -> int list list ->
17 ((int * int) * (int * int)) list list list -> thm list -> thm -> thm list -> thm list list ->
19 val mk_inject_tac: Proof.context -> thm -> thm -> tactic
20 val mk_iter_like_tac: thm list -> thm list -> thm list -> thm -> thm -> Proof.context -> tactic
23 structure BNF_FP_Sugar_Tactics : BNF_FP_SUGAR_TACTICS =
30 val meta_mp = @{thm meta_mp};
31 val meta_spec = @{thm meta_spec};
33 fun smash_spurious_fs lthy thm =
36 Term.add_vars (prop_of thm) []
37 |> filter (fn (_, Type (@{type_name fun}, [_, T'])) => T' <> HOLogic.boolT | _ => false);
39 map (fn s as (_, T) =>
40 (certify lthy (Var s), certify lthy (id_abs (domain_type T)))) spurious_fs;
42 Drule.cterm_instantiate cxs thm
45 val smash_spurious_fs_tac = PRIMITIVE o smash_spurious_fs;
47 fun mk_case_tac ctxt n k m case_def ctr_def unf_fld =
48 Local_Defs.unfold_tac ctxt [case_def, ctr_def, unf_fld] THEN
49 (rtac (mk_sum_casesN_balanced n k RS ssubst) THEN'
50 REPEAT_DETERM_N (Int.max (0, m - 1)) o rtac (@{thm split} RS ssubst) THEN'
53 fun mk_exhaust_tac ctxt n ctr_defs fld_iff_unf sumEN' =
54 Local_Defs.unfold_tac ctxt (fld_iff_unf :: ctr_defs) THEN rtac sumEN' 1 THEN
55 Local_Defs.unfold_tac ctxt @{thms all_prod_eq} THEN
56 EVERY' (maps (fn k => [select_prem_tac n (rotate_tac 1) k, REPEAT_DETERM o dtac meta_spec,
57 etac meta_mp, atac]) (1 upto n)) 1;
59 fun mk_fld_iff_unf_tac ctxt cTs cfld cunf fld_unf unf_fld =
61 EVERY' (map3 (fn cTs => fn cx => fn th =>
62 dtac (Drule.instantiate' cTs [NONE, NONE, SOME cx] arg_cong) THEN'
63 SELECT_GOAL (Local_Defs.unfold_tac ctxt [th]) THEN'
64 atac) [rev cTs, cTs] [cunf, cfld] [unf_fld, fld_unf])) 1;
66 fun mk_half_distinct_tac ctxt fld_inject ctr_defs =
67 Local_Defs.unfold_tac ctxt (fld_inject :: @{thms sum.inject} @ ctr_defs) THEN
68 rtac @{thm sum.distinct(1)} 1;
70 fun mk_inject_tac ctxt ctr_def fld_inject =
71 Local_Defs.unfold_tac ctxt [ctr_def] THEN rtac (fld_inject RS ssubst) 1 THEN
72 Local_Defs.unfold_tac ctxt @{thms sum.inject Pair_eq conj_assoc} THEN rtac refl 1;
75 @{thms case_unit comp_def convol_def id_apply map_pair_def sum.simps(5,6) sum_map.simps
78 fun mk_iter_like_tac pre_map_defs map_ids iter_like_defs fld_iter_like ctr_def ctxt =
79 Local_Defs.unfold_tac ctxt (ctr_def :: fld_iter_like :: iter_like_defs @ pre_map_defs @ map_ids @
80 iter_like_thms) THEN Local_Defs.unfold_tac ctxt @{thms id_def} THEN rtac refl 1;
82 val coiter_like_ss = ss_only @{thms if_True if_False};
83 val coiter_like_thms = @{thms id_apply map_pair_def sum_map.simps prod.cases};
85 fun mk_coiter_like_tac coiter_like_defs map_ids fld_unf_coiter_like pre_map_def ctr_def ctxt =
86 Local_Defs.unfold_tac ctxt (ctr_def :: coiter_like_defs) THEN
87 subst_tac ctxt [fld_unf_coiter_like] 1 THEN asm_simp_tac coiter_like_ss 1 THEN
88 Local_Defs.unfold_tac ctxt (pre_map_def :: coiter_like_thms @ map_ids) THEN
89 Local_Defs.unfold_tac ctxt @{thms id_def} THEN
90 TRY ((rtac refl ORELSE' subst_tac ctxt @{thms unit_eq} THEN' rtac refl) 1);
92 fun mk_induct_prelude_tac ctxt ctr_defs fld_induct' =
93 Local_Defs.unfold_tac ctxt ctr_defs THEN rtac fld_induct' 1 THEN smash_spurious_fs_tac ctxt;
95 fun mk_induct_prepare_prem_tac n m k =
96 EVERY' [select_prem_tac n (rotate_tac 1) k, rotate_tac ~1, hyp_subst_tac,
97 REPEAT_DETERM_N m o (dtac meta_spec THEN' rotate_tac ~1)] 1;
99 (* FIXME: why not in "Pure"? *)
100 fun prefer_tac i = defer_tac i THEN PRIMITIVE (Thm.permute_prems 0 ~1);
102 fun mk_induct_prepare_prem_prems_tac r =
103 REPEAT_DETERM_N r (rotate_tac ~1 1 THEN dtac meta_mp 1 THEN rotate_tac 1 1 THEN prefer_tac 2) THEN
104 PRIMITIVE Raw_Simplifier.norm_hhf;
106 val induct_prem_prem_thms =
107 @{thms SUP_empty Sup_empty Sup_insert UN_compreh_bex UN_insert Un_assoc[symmetric] Un_empty_left
108 Un_empty_right Union_Un_distrib collect_def[abs_def] fst_conv image_def o_apply snd_conv
109 snd_prod_fun sum.cases sup_bot_right fst_map_pair map_pair_simp sum_map.simps};
111 (* These rules interfere with the "set_natural'" properties of "sum" and "prod", so we explicitly
113 val induct_prem_prem_thms_delayed =
114 @{thms fsts_def[abs_def] snds_def[abs_def] sum_setl_def[abs_def] sum_setr_def[abs_def]};
116 (* TODO: Get rid of the "auto_tac" (or at least use a naked context) *)
117 fun mk_induct_prem_prem_endgame_tac _ 0 = atac ORELSE' rtac @{thm singletonI}
118 | mk_induct_prem_prem_endgame_tac ctxt qq =
120 (SELECT_GOAL (Local_Defs.unfold_tac ctxt @{thms Union_iff bex_simps(6)}) THEN'
121 etac @{thm induct_set_step}) THEN'
122 atac ORELSE' SELECT_GOAL (auto_tac ctxt);
124 fun mk_induct_discharge_prem_prems_tac ctxt nn ixs set_natural's pre_set_defs =
125 EVERY' (maps (fn ((pp, jj), (qq, kk)) =>
126 [select_prem_tac nn (dtac meta_spec) kk, rotate_tac ~1 (*FIXME: needed?*), etac meta_mp,
127 SELECT_GOAL (Local_Defs.unfold_tac ctxt pre_set_defs), (* FIXME: ### why on a line of its own? *)
128 SELECT_GOAL (Local_Defs.unfold_tac ctxt (set_natural's @ induct_prem_prem_thms)),
129 SELECT_GOAL (Local_Defs.unfold_tac ctxt
130 (induct_prem_prem_thms_delayed @ induct_prem_prem_thms)),
131 rtac (mk_UnIN pp jj) THEN' mk_induct_prem_prem_endgame_tac ctxt qq ORELSE'
132 SELECT_GOAL (auto_tac ctxt)])
135 fun mk_induct_discharge_prem_tac ctxt nn n set_natural's pre_set_defs m k ixs =
136 EVERY [mk_induct_prepare_prem_tac n m k,
137 mk_induct_prepare_prem_prems_tac (length ixs), atac 1,
138 mk_induct_discharge_prem_prems_tac ctxt nn ixs set_natural's pre_set_defs];
140 fun mk_induct_tac ctxt ns mss ixsss ctr_defs fld_induct' set_natural's pre_set_defss =
143 val n = Integer.sum ns;
145 mk_induct_prelude_tac ctxt ctr_defs fld_induct' THEN
146 EVERY (map4 (EVERY oooo map3 o mk_induct_discharge_prem_tac ctxt nn n set_natural's)
147 pre_set_defss mss (unflat mss (1 upto n)) ixsss)