author | blanchet |
Mon, 17 Sep 2012 21:13:30 +0200 | |
changeset 49426 | 6d05b8452cf3 |
parent 49391 | 3a96797fd53e |
child 49427 | b017e1dbc77c |
permissions | -rw-r--r-- |
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(* Title: HOL/Codatatype/Tools/bnf_fp_sugar_tactics.ML |
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Author: Jasmin Blanchette, TU Muenchen |
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Copyright 2012 |
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49389 | 5 |
Tactics for datatype and codatatype sugar. |
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*) |
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signature BNF_FP_SUGAR_TACTICS = |
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sig |
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val mk_case_tac: Proof.context -> int -> int -> int -> thm -> thm -> thm -> tactic |
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val mk_coiter_like_tac: thm list -> thm list -> thm -> thm -> thm -> Proof.context -> tactic |
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val mk_exhaust_tac: Proof.context -> int -> thm list -> thm -> thm -> tactic |
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val mk_fld_iff_unf_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm -> |
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tactic |
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val mk_half_distinct_tac: Proof.context -> thm -> thm list -> tactic |
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val mk_induct_tac: Proof.context -> int list -> int list list -> |
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((int * int) * (int * int)) list list list -> thm list -> thm -> thm list -> thm list list -> |
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tactic |
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val mk_inject_tac: Proof.context -> thm -> thm -> tactic |
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val mk_iter_like_tac: thm list -> thm list -> thm list -> thm -> thm -> Proof.context -> tactic |
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end; |
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structure BNF_FP_Sugar_Tactics : BNF_FP_SUGAR_TACTICS = |
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struct |
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open BNF_Tactics |
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open BNF_Util |
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open BNF_FP_Util |
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val meta_mp = @{thm meta_mp}; |
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val meta_spec = @{thm meta_spec}; |
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fun inst_spurious_fs lthy thm = |
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let |
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val fs = |
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Term.add_vars (prop_of thm) [] |
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|> filter (fn (_, Type (@{type_name fun}, [_, T'])) => T' <> HOLogic.boolT | _ => false); |
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val cfs = |
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map (fn f as (_, T) => (certify lthy (Var f), certify lthy (id_abs (domain_type T)))) fs; |
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in |
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Drule.cterm_instantiate cfs thm |
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end; |
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val inst_spurious_fs_tac = PRIMITIVE o inst_spurious_fs; |
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fun mk_case_tac ctxt n k m case_def ctr_def unf_fld = |
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Local_Defs.unfold_tac ctxt [case_def, ctr_def, unf_fld] THEN |
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(rtac (mk_sum_casesN_balanced n k RS ssubst) THEN' |
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REPEAT_DETERM_N (Int.max (0, m - 1)) o rtac (@{thm split} RS ssubst) THEN' |
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rtac refl) 1; |
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fun mk_exhaust_tac ctxt n ctr_defs fld_iff_unf sumEN' = |
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Local_Defs.unfold_tac ctxt (fld_iff_unf :: ctr_defs) THEN rtac sumEN' 1 THEN |
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Local_Defs.unfold_tac ctxt @{thms all_prod_eq} THEN |
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EVERY' (maps (fn k => [select_prem_tac n (rotate_tac 1) k, REPEAT_DETERM o dtac meta_spec, |
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etac meta_mp, atac]) (1 upto n)) 1; |
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fun mk_fld_iff_unf_tac ctxt cTs cfld cunf fld_unf unf_fld = |
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(rtac iffI THEN' |
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EVERY' (map3 (fn cTs => fn cx => fn th => |
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dtac (Drule.instantiate' cTs [NONE, NONE, SOME cx] arg_cong) THEN' |
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SELECT_GOAL (Local_Defs.unfold_tac ctxt [th]) THEN' |
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atac) [rev cTs, cTs] [cunf, cfld] [unf_fld, fld_unf])) 1; |
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fun mk_half_distinct_tac ctxt fld_inject ctr_defs = |
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Local_Defs.unfold_tac ctxt (fld_inject :: @{thms sum.inject} @ ctr_defs) THEN |
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rtac @{thm sum.distinct(1)} 1; |
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fun mk_inject_tac ctxt ctr_def fld_inject = |
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Local_Defs.unfold_tac ctxt [ctr_def] THEN rtac (fld_inject RS ssubst) 1 THEN |
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Local_Defs.unfold_tac ctxt @{thms sum.inject Pair_eq conj_assoc} THEN rtac refl 1; |
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val iter_like_thms = |
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@{thms case_unit comp_def convol_def id_apply map_pair_def sum.simps(5,6) sum_map.simps |
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split_conv}; |
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fun mk_iter_like_tac pre_map_defs map_ids iter_like_defs fld_iter_like ctr_def ctxt = |
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Local_Defs.unfold_tac ctxt (ctr_def :: fld_iter_like :: iter_like_defs @ pre_map_defs @ map_ids @ |
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iter_like_thms) THEN Local_Defs.unfold_tac ctxt @{thms id_def} THEN rtac refl 1; |
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val coiter_like_ss = ss_only @{thms if_True if_False}; |
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val coiter_like_thms = @{thms id_apply map_pair_def sum_map.simps prod.cases}; |
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fun mk_coiter_like_tac coiter_like_defs map_ids fld_unf_coiter_like pre_map_def ctr_def ctxt = |
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Local_Defs.unfold_tac ctxt (ctr_def :: coiter_like_defs) THEN |
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subst_tac ctxt [fld_unf_coiter_like] 1 THEN asm_simp_tac coiter_like_ss 1 THEN |
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Local_Defs.unfold_tac ctxt (pre_map_def :: coiter_like_thms @ map_ids) THEN |
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Local_Defs.unfold_tac ctxt @{thms id_def} THEN |
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TRY ((rtac refl ORELSE' subst_tac ctxt @{thms unit_eq} THEN' rtac refl) 1); |
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(* TODO: Get rid of "auto_tac" (or at least use a naked context) *) |
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fun mk_induct_prem_prem_endgame_tac _ 0 = atac ORELSE' rtac @{thm singletonI} |
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| mk_induct_prem_prem_endgame_tac ctxt qq = |
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REPEAT_DETERM_N qq o |
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(SELECT_GOAL (Local_Defs.unfold_tac ctxt @{thms Union_iff bex_simps(6)}) THEN' |
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etac @{thm induct_set_step}) THEN' |
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atac ORELSE' SELECT_GOAL (auto_tac ctxt); |
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fun gen_UN_comprehI_tac UnI = REPEAT_DETERM o resolve_tac @{thms mem_UN_comprehI} THEN' rtac UnI; |
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fun gen_UnIN_tac 1 1 = REPEAT_DETERM o resolve_tac @{thms mem_UN_comprehI'} |
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| gen_UnIN_tac _ 1 = gen_UN_comprehI_tac @{thm UnI1} THEN' gen_UnIN_tac 1 1 |
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| gen_UnIN_tac n k = gen_UN_comprehI_tac @{thm UnI2} THEN' gen_UnIN_tac (n - 1) (k - 1); |
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val induct_prem_prem_thms = |
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@{thms SUP_empty Sup_empty Sup_insert UN_compreh_bex_eq_empty UN_compreh_bex_eq_singleton |
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UN_insert Un_assoc Un_empty_left Un_empty_right Union_Un_distrib collect_def[abs_def] fst_conv |
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image_def o_apply snd_conv snd_prod_fun sum.cases sup_bot_right fst_map_pair map_pair_simp |
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sum_map.simps}; |
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(* These rules interfere with the "set_natural'" properties of "sum" and "prod", so we explicitly |
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delay them. *) |
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val induct_prem_prem_thms_delayed = |
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@{thms fsts_def[abs_def] snds_def[abs_def] sum_setl_def[abs_def] sum_setr_def[abs_def]}; |
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fun mk_induct_leverage_prem_prems_tac ctxt nn ppjjqqkks set_natural's pre_set_defs = |
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EVERY' (maps (fn ((pp, jj), (qq, kk)) => |
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[select_prem_tac nn (dtac meta_spec) kk, etac meta_mp, |
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SELECT_GOAL (Local_Defs.unfold_tac ctxt |
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(pre_set_defs @ set_natural's @ induct_prem_prem_thms)), |
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SELECT_GOAL (Local_Defs.unfold_tac ctxt |
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(induct_prem_prem_thms_delayed @ induct_prem_prem_thms)), |
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gen_UnIN_tac pp jj THEN' mk_induct_prem_prem_endgame_tac ctxt qq]) (rev ppjjqqkks)) 1; |
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fun mk_induct_discharge_prem_tac ctxt nn n set_natural's pre_set_defs m k ppjjqqkks = |
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let val r = length ppjjqqkks in |
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EVERY' [select_prem_tac n (rotate_tac 1) k, rotate_tac ~1, hyp_subst_tac, |
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REPEAT_DETERM_N m o (dtac meta_spec THEN' rotate_tac ~1)] 1 THEN |
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EVERY [REPEAT_DETERM_N r |
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(rotate_tac ~1 1 THEN dtac meta_mp 1 THEN rotate_tac 1 1 THEN prefer_tac 2), |
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if r > 0 then PRIMITIVE Raw_Simplifier.norm_hhf else all_tac, atac 1, |
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mk_induct_leverage_prem_prems_tac ctxt nn ppjjqqkks set_natural's pre_set_defs] |
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end; |
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fun mk_induct_tac ctxt ns mss ppjjqqkksss ctr_defs fld_induct' set_natural's pre_set_defss = |
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let |
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val nn = length ns; |
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val n = Integer.sum ns; |
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in |
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Local_Defs.unfold_tac ctxt ctr_defs THEN rtac fld_induct' 1 THEN inst_spurious_fs_tac ctxt THEN |
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EVERY (map4 (EVERY oooo map3 o mk_induct_discharge_prem_tac ctxt nn n set_natural's) |
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pre_set_defss mss (unflat mss (1 upto n)) ppjjqqkksss) |
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end; |
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end; |