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Quellcode-Bibliothek© Kompilation durch diese Firma[Weder Korrektheit noch Funktionsfähigkeit der Software werden zugesichert.]Datei: bnf_fp_def_sugar_tactics.ML Sprache: SMLOriginal von: Isabelle© |
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(* Title: HOL/Tools/BNF/bnf_fp_def_sugar_tactics.ML
Author: Jasmin Blanchette, TU Muenchen Author: Martin Desharnais, TU Muenchen Copyright 2012, 2013, 2014 Tactics for datatype and codatatype sugar. *) signature BNF_FP_DEF_SUGAR_TACTICS = sig val sumprod_thms_rel: thm list val co_induct_inst_as_projs_tac: Proof.context -> int -> tactic val mk_case_transfer_tac: Proof.context -> thm -> thm list -> tactic val mk_coinduct_discharge_prem_tac: Proof.context -> thm list -> thm list -> int -> int -> int -> thm -> thm -> thm -> thm -> thm -> thm list -> thm list list -> thm list list -> int -> tactic val mk_coinduct_tac: Proof.context -> thm list -> int -> int list -> thm -> thm list -> thm list -> thm list -> thm list -> thm list -> thm list list -> thm list list list -> thm list list list -> tactic val mk_corec_tac: thm list -> thm list -> thm -> thm -> thm -> thm -> Proof.context -> tactic val mk_corec_disc_iff_tac: thm list -> thm list -> thm list -> Proof.context -> tactic val mk_co_rec_o_map_tac: Proof.context -> thm -> thm list -> thm list -> thm list -> thm -> thm -> thm Seq.seq val mk_corec_transfer_tac: Proof.context -> cterm list -> cterm list -> thm list -> thm list -> thm list -> thm list -> thm list -> ''a list -> ''a list list -> ''a list list list list -> ''a list list list list -> tactic val mk_ctor_iff_dtor_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm -> tactic val mk_ctr_transfer_tac: Proof.context -> thm list -> thm list -> tactic val mk_disc_transfer_tac: Proof.context -> thm -> thm -> thm list -> tactic val mk_exhaust_tac: Proof.context -> int -> thm list -> thm -> thm -> tactic val mk_half_distinct_tac: Proof.context -> thm -> thm -> thm list -> tactic val mk_induct_discharge_prem_tac: Proof.context -> int -> int -> thm list -> thm list -> thm list -> thm list -> int -> int -> int list -> tactic val mk_induct_tac: Proof.context -> int -> int list -> int list list -> int list list list -> thm list -> thm -> thm list -> thm list -> thm list -> thm list list -> tactic val mk_inject_tac: Proof.context -> thm -> thm -> thm -> tactic val mk_map_tac: Proof.context -> thm list -> thm -> thm -> thm list -> thm list -> thm list -> tactic val mk_map_disc_iff_tac: Proof.context -> cterm -> thm -> thm list -> thm list -> tactic val mk_map_sel_tac: Proof.context -> cterm -> thm -> thm list -> thm list -> thm list -> thm list -> tactic val mk_rec_tac: thm list -> thm list -> thm list -> thm -> thm -> thm -> thm -> Proof.context -> tactic val mk_rec_transfer_tac: Proof.context -> int -> int list -> cterm list -> cterm list -> term list list list list -> thm list -> thm list -> thm list -> thm list -> tactic val mk_rel_tac: Proof.context -> thm list -> thm -> thm -> thm list -> thm list -> thm list -> tactic val mk_rel_case_tac: Proof.context -> cterm -> cterm -> thm -> thm list -> thm list -> thm list -> thm list -> thm list -> tactic val mk_rel_coinduct0_tac: Proof.context -> thm -> cterm list -> thm list -> thm list -> thm list list -> thm list list -> thm list list -> thm list -> thm list -> thm list -> thm list -> thm list -> thm list -> tactic val mk_rel_induct0_tac: Proof.context -> thm -> thm list -> cterm list -> thm list -> thm list list -> thm list -> thm list -> thm list -> thm list -> tactic val mk_rel_sel_tac: Proof.context -> cterm -> cterm -> thm -> thm list -> thm list -> thm list -> thm list -> thm list -> thm list -> tactic val mk_sel_transfer_tac: Proof.context -> int -> thm list -> thm -> tactic val mk_set0_tac: Proof.context -> thm list -> thm list -> thm -> thm list -> thm list -> thm list -> thm list -> thm list -> tactic val mk_set_cases_tac: Proof.context -> cterm -> thm list -> thm -> thm list -> tactic val mk_set_induct0_tac: Proof.context -> cterm list -> thm list -> thm list -> thm list -> thm list -> thm list -> thm list -> thm list -> tactic val mk_set_intros_tac: Proof.context -> thm list -> tactic val mk_set_sel_tac: Proof.context -> cterm -> thm -> thm list -> thm list -> thm list -> tactic end; structure BNF_FP_Def_Sugar_Tactics : BNF_FP_DEF_SUGAR_TACTICS = struct open Ctr_Sugar_Util open BNF_Tactics open BNF_Util open BNF_FP_Util val case_sum_transfer = @{thm case_sum_transfer}; val case_sum_transfer_eq = @{thm case_sum_transfer[of "(=)" _ "(=)", simplified sum.rel_e val case_prod_transfer = @{thm case_prod_transfer}; val case_prod_transfer_eq = @{thm case_prod_transfer[of "(=)" "(=)", simplified prod.rel val basic_simp_thms = @{thms simp_thms(7,8,12,14,22,24)}; val more_simp_thms = basic_simp_thms @ @{thms simp_thms(11,15,16,21)}; val simp_thms' = @{thms simp_thms(6,7,8,11,12,15,16,22,24)}; val sumprod_thms_map = @{thms id_apply map_prod_simp prod.case sum.case map_sum.simps}; val sumprod_thms_rel = @{thms rel_sum_simps rel_prod_inject prod.inject id_apply conj_as val basic_sumprod_thms_set = @{thms UN_empty UN_insert UN_iff Un_empty_left Un_empty_right Un_iff Union_Un_distrib o_ map_prod_simp mem_Collect_eq prod_set_simps map_sum.simps sum_set_simps}; val sumprod_thms_set = @{thms UN_simps(10) image_iff} @ basic_sumprod_thms_set; fun is_def_looping def = (case Thm.prop_of def of Const (\<^const_name>\<open>Pure.eq\<close>, _) $ lhs $ rhs => Term.exists_subterm (curry (op acon | _ => false); fun hhf_concl_conv cv ctxt ct = (case Thm.term_of ct of Const (\<^const_name>\<open>Pure.all\<close>, _) $ Abs _ => Conv.arg_conv (Conv.abs_conv (hhf_concl_conv cv o snd) ctxt) ct | _ => Conv.concl_conv ~1 cv ct); fun co_induct_inst_as_projs ctxt k thm = let val fs = Term.add_vars (Thm.prop_of thm) [] |> filter (fn (_, Type (\<^type_name>\<open>fun\<close>, [_, T'])) => T' <> HOLogic.boolT | _ => false) fun mk_inst (xi, T) = (xi, Thm.cterm_of ctxt (mk_proj T (num_binder_types T) k)); in infer_instantiate ctxt (map mk_inst fs) thm end; val co_induct_inst_as_projs_tac = PRIMITIVE oo co_induct_inst_as_projs; fun mk_case_transfer_tac ctxt rel_case cases = let val n = length (tl (Thm.prems_of rel_case)) in REPEAT_DETERM (HEADGOAL (rtac ctxt rel_funI)) THEN HEADGOAL (etac ctxt rel_case) THEN ALLGOALS (hyp_subst_tac ctxt) THEN unfold_thms_tac ctxt cases THEN ALLGOALS (fn k => (select_prem_tac ctxt n (dtac ctxt asm_rl) k) k) THEN ALLGOALS (REPEAT_DETERM o (rotate_tac ~1 THEN' dtac ctxt rel_funD THEN' (assume_tac ctxt THEN' etac ctxt thin_rl ORELSE' rtac ctxt refl)) THEN' assume_tac ctx end; fun mk_ctr_transfer_tac ctxt rel_intros rel_eqs = HEADGOAL Goal.conjunction_tac THEN ALLGOALS (REPEAT o (resolve_tac ctxt (rel_funI :: rel_intros) THEN' TRY o (REPEAT_DETERM1 o (SELECT_GOAL (unfold_thms_tac ctxt rel_eqs) THEN' (assume_tac ctxt ORELSE' hyp_subst_tac ctxt THEN' rtac ctxt refl))))); fun mk_disc_transfer_tac ctxt rel_sel exhaust_disc distinct_disc = let fun last_disc_tac iffD = HEADGOAL (rtac ctxt (rotate_prems ~1 exhaust_disc) THEN' assume_tac ctxt THEN' REPEAT_DETERM o (rotate_tac ~1 THEN' dtac ctxt (rotate_prems 1 iffD) THEN' assume_tac ctxt THEN' rotate_tac ~1 THEN' etac ctxt (rotate_prems 1 notE) THEN' eresolve_tac ctxt distinct_disc)); in HEADGOAL Goal.conjunction_tac THEN REPEAT_DETERM (HEADGOAL (rtac ctxt rel_funI THEN' dtac ctxt (rel_sel RS iffD1) THEN' REPEAT_DETERM o (etac ctxt conjE) THEN' (assume_tac ctxt ORELSE' rtac ctxt iffI))) THEN TRY (last_disc_tac iffD2) THEN TRY (last_disc_tac iffD1) end; fun mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor sumEN' = unfold_thms_tac ctxt (ctor_iff_dtor :: ctr_defs) THEN HEADGOAL (rtac ctxt sumEN') THEN HEADGOAL (EVERY' (maps (fn k => [select_prem_tac ctxt n (rotate_tac 1) k, REPEAT_DETERM o dtac ctxt meta_spec, etac ctxt meta_mp, assume_tac ctxt]) (1 upto n))); fun mk_ctor_iff_dtor_tac ctxt cTs cctor cdtor ctor_dtor dtor_ctor = HEADGOAL (rtac ctxt iffI THEN' EVERY' (@{map 3} (fn cTs => fn cx => fn th => dtac ctxt (Thm.instantiate' cTs [NONE, NONE, SOME cx] arg_cong) THEN' SELECT_GOAL (unfold_thms_tac ctxt [th]) THEN' assume_tac ctxt) [rev cTs, cTs] [cdtor, cctor] [dtor_ctor, ctor_dtor])); fun mk_half_distinct_tac ctxt ctor_inject abs_inject ctr_defs = unfold_thms_tac ctxt (ctor_inject :: abs_inject :: @{thms sum.inject} @ ctr_defs) THEN HEADGOAL (rtac ctxt @{thm sum.distinct(1)}); fun mk_inject_tac ctxt ctr_def ctor_inject abs_inject = unfold_thms_tac ctxt [ctr_def] THEN HEADGOAL (rtac ctxt (ctor_inject RS ssubst)) THEN unfold_thms_tac ctxt (abs_inject :: @{thms sum.inject prod.inject conj_assoc}) THEN HEADGOAL (rtac ctxt refl); val rec_unfold_thms = @{thms comp_def convol_def fst_conv id_def case_prod_Pair_iden snd_conv split_conv case_unit_Unity} @ sumprod_thms_map; fun mk_co_rec_o_map_tac ctxt co_rec_def pre_map_defs map_ident0s abs_inverses xtor_co_r let val rec_o_map_simps = @{thms o_def[abs_def] id_def case_prod_app case_sum_map_sum map_su case_prod_map_prod id_bnf_def map_prod_simp map_sum_if_distrib_then map_sum_if_distr if_distrib[THEN sym]}; in HEADGOAL (subst_tac ctxt (SOME [1, 2]) [co_rec_def] THEN' rtac ctxt (xtor_co_rec_o_map RS trans) THEN' CONVERSION Thm.eta_long_conversion THEN' asm_simp_tac (ss_only (pre_map_defs @ distinct Thm.eq_thm_prop (map_ident0s @ abs_invers rec_o_map_simps) ctxt)) end; fun mk_rec_tac pre_map_defs map_ident0s rec_defs ctor_rec pre_abs_inverse abs_inverse ct HEADGOAL ((if is_def_looping ctr_def then subst_tac ctxt NONE else SELECT_GOAL o unfold_thms_tac ctxt) [ctr_def]) THEN unfold_thms_tac ctxt (ctor_rec :: pre_abs_inverse :: abs_inverse :: rec_defs @ pre_map_defs @ map_ident0s @ rec_unfold_thms) THEN HEADGOAL (rtac ctxt refl); fun mk_rec_transfer_tac ctxt nn ns actives passives xssss rec_defs ctor_rec_transfers rel_ rel_eqs = let val ctor_rec_transfers' = map (infer_instantiate' ctxt (map SOME (passives @ actives))) ctor_rec_transfers; val total_n = Integer.sum ns; val True = \<^term>\<open>True\<close>; in HEADGOAL Goal.conjunction_tac THEN EVERY (map (fn ctor_rec_transfer => REPEAT_DETERM (HEADGOAL (rtac ctxt rel_funI)) THEN unfold_thms_tac ctxt rec_defs THEN HEADGOAL (etac ctxt (mk_rel_funDN_rotated (nn + 1) ctor_rec_transfer)) THEN unfold_thms_tac ctxt rel_pre_T_defs THEN EVERY (fst (@{fold_map 2} (fn k => fn xsss => fn acc => rpair (k + acc) (HEADGOAL (rtac ctxt (mk_rel_funDN_rotated 2 @{thm comp_transfer})) THEN HEADGOAL (rtac ctxt @{thm vimage2p_rel_fun}) THEN unfold_thms_tac ctxt rel_eqs THEN EVERY (@{map 2} (fn n => fn xss => REPEAT_DETERM (HEADGOAL (resolve_tac ctxt [mk_rel_funDN 2 case_sum_transfer_eq, mk_rel_funDN 2 case_sum_transfer])) THEN HEADGOAL (select_prem_tac ctxt total_n (dtac ctxt asm_rl) (acc + n)) THEN HEADGOAL (SELECT_GOAL (HEADGOAL (REPEAT_DETERM o (assume_tac ctxt ORELSE' resolve_tac ctxt [mk_rel_funDN 1 case_prod_transfer_eq, mk_rel_funDN 1 case_prod_transfer, rel_funI]) THEN_ALL_NEW (Subgoal.FOCUS (fn {prems, ...} => let val thm = prems |> permute_like (op =) (True :: flat xss) (True :: flat_rec_arg_args xss) |> Library.foldl1 (fn (acc, elem) => elem RS (acc RS rel_funD)) in HEADGOAL (rtac ctxt thm) end) ctxt))))) (1 upto k) xsss))) ns xssss 0))) ctor_rec_transfers') end; val corec_unfold_thms = @{thms id_def} @ sumprod_thms_map; fun mk_corec_tac corec_defs map_ident0s ctor_dtor_corec pre_map_def abs_inverse ctr_def let val ss = ss_only (pre_map_def :: abs_inverse :: map_ident0s @ corec_unfold_thms @ @{thms o_apply vimage2p_def if_True if_False}) ctxt; in unfold_thms_tac ctxt (ctr_def :: corec_defs) THEN HEADGOAL (rtac ctxt (ctor_dtor_corec RS trans) THEN' asm_simp_tac ss) THEN_MAYBE HEADGOAL (rtac ctxt refl ORELSE' rtac ctxt (@{thm unit_eq} RS arg_cong)) end; fun mk_corec_disc_iff_tac case_splits' corecs discs ctxt = EVERY (@{map 3} (fn case_split_tac => fn corec_thm => fn disc => HEADGOAL case_split_tac THEN unfold_thms_tac ctxt [corec_thm] THEN HEADGOAL (asm_simp_tac (ss_only basic_simp_thms ctxt)) THEN (if is_refl disc then all_tac else HEADGOAL (rtac ctxt disc))) (map (rtac ctxt) case_splits' @ [K all_tac]) corecs discs); fun mk_corec_transfer_tac ctxt actives passives type_definitions corec_defs dtor_corec_ rel_pre_T_defs rel_eqs pgs pss qssss gssss = let val num_pgs = length pgs; fun prem_no_of x = 1 + find_index (curry (op =) x) pgs; val Inl_Inr_Pair_tac = REPEAT_DETERM o (resolve_tac ctxt [mk_rel_funDN 1 @{thm Inl_transfer}, mk_rel_funDN 1 @{thm Inl_transfer[of "(=)" "(=)", simplified sum.rel_eq]}, mk_rel_funDN 1 @{thm Inr_transfer}, mk_rel_funDN 1 @{thm Inr_transfer[of "(=)" "(=)", simplified sum.rel_eq]}, mk_rel_funDN 2 @{thm Pair_transfer}, mk_rel_funDN 2 @{thm Pair_transfer[of "(=)" "(=)", simplified prod.rel_eq]}]); fun mk_unfold_If_tac total pos = HEADGOAL (Inl_Inr_Pair_tac THEN' rtac ctxt (mk_rel_funDN 3 @{thm If_transfer}) THEN' select_prem_tac ctxt total (dtac ctxt asm_rl) pos THEN' dtac ctxt rel_funD THEN' assume_tac ctxt THEN' assume_tac ctxt); fun mk_unfold_Inl_Inr_Pair_tac total pos = HEADGOAL (Inl_Inr_Pair_tac THEN' select_prem_tac ctxt total (dtac ctxt asm_rl) pos THEN' dtac ctxt rel_funD THEN' assume_tac ctxt THEN' assume_tac ctxt); fun mk_unfold_arg_tac qs gs = EVERY (map (mk_unfold_If_tac num_pgs o prem_no_of) qs) THEN EVERY (map (mk_unfold_Inl_Inr_Pair_tac num_pgs o prem_no_of) gs); fun mk_unfold_ctr_tac type_definition qss gss = HEADGOAL (rtac ctxt (mk_rel_funDN 1 (@{thm Abs_transfer} OF [type_definition, type_definition])) THEN' Inl_Inr_Pair_tac) THEN (case (qss, gss) of ([], []) => HEADGOAL (rtac ctxt refl) | _ => EVERY (map2 mk_unfold_arg_tac qss gss)); fun mk_unfold_type_tac type_definition ps qsss gsss = let val p_tacs = map (mk_unfold_If_tac num_pgs o prem_no_of) ps; val qg_tacs = map2 (mk_unfold_ctr_tac type_definition) qsss gsss; fun mk_unfold_ty [] [qg_tac] = qg_tac | mk_unfold_ty (p_tac :: p_tacs) (qg_tac :: qg_tacs) = p_tac THEN qg_tac THEN mk_unfold_ty p_tacs qg_tacs in HEADGOAL (rtac ctxt rel_funI) THEN mk_unfold_ty p_tacs qg_tacs end; fun mk_unfold_corec_type_tac dtor_corec_transfer corec_def = let val active :: actives' = actives; val dtor_corec_transfer' = infer_instantiate' ctxt (SOME active :: map SOME passives @ map SOME actives') dtor_corec_transfer; in HEADGOAL Goal.conjunction_tac THEN REPEAT_DETERM (HEADGOAL (rtac ctxt rel_funI)) THEN unfold_thms_tac ctxt [corec_def] THEN HEADGOAL (etac ctxt (mk_rel_funDN_rotated (1 + length actives) dtor_corec_transfer')) TH unfold_thms_tac ctxt (rel_pre_T_defs @ rel_eqs) end; fun mk_unfold_prop_tac dtor_corec_transfer corec_def = mk_unfold_corec_type_tac dtor_corec_transfer corec_def THEN EVERY (@{map 4} mk_unfold_type_tac type_definitions pss qssss gssss); in HEADGOAL Goal.conjunction_tac THEN EVERY (map2 mk_unfold_prop_tac dtor_corec_transfers corec_defs) end; fun solve_prem_prem_tac ctxt = REPEAT o (eresolve_tac ctxt @{thms bexE rev_bexI} ORELSE' rtac ctxt @{thm rev_bexI[OF UNIV_I]} ORELSE' hyp_subst_tac ctxt ORELSE' resolve_tac ctxt @{thms disjI1 disjI2}) THEN' (rtac ctxt refl ORELSE' assume_tac ctxt ORELSE' rtac ctxt @{thm singletonI}); fun mk_induct_leverage_prem_prems_tac ctxt nn kks pre_abs_inverses abs_inverses set_map pre_set_defs = HEADGOAL (EVERY' (maps (fn kk => [select_prem_tac ctxt nn (dtac ctxt meta_spec) k etac ctxt meta_mp, SELECT_GOAL (unfold_thms_tac ctxt (pre_set_defs @ pre_abs_inverses @ abs_inverses @ set_m sumprod_thms_set)), solve_prem_prem_tac ctxt]) (rev kks))); fun mk_induct_discharge_prem_tac ctxt nn n pre_abs_inverses abs_inverses set_maps pre_se kks = let val r = length kks in HEADGOAL (EVERY' [select_prem_tac ctxt n (rotate_tac 1) k, rotate_tac ~1, hyp_sub REPEAT_DETERM_N m o (dtac ctxt meta_spec THEN' rotate_tac ~1)]) THEN EVERY [REPEAT_DETERM_N r (HEADGOAL (rotate_tac ~1 THEN' dtac ctxt meta_mp THEN' rotate_tac 1) THEN prefer_tac 2), if r > 0 then ALLGOALS (Goal.norm_hhf_tac ctxt) else all_tac, HEADGOAL (assume_tac ctxt), mk_induct_leverage_prem_prems_tac ctxt nn kks pre_abs_inverses abs_inverses set_maps pre_set_defs] end; fun mk_induct_tac ctxt nn ns mss kksss ctr_defs ctor_induct' pre_abs_inverses abs_invers pre_set_defss = let val n = Integer.sum ns in (if exists is_def_looping ctr_defs then EVERY (map (fn def => HEADGOAL (subst_asm_tac ctxt NONE [def])) ctr_defs) else unfold_thms_tac ctxt ctr_defs) THEN HEADGOAL (rtac ctxt ctor_induct') THEN co_induct_inst_as_projs_tac ctxt 0 THEN EVERY (@{map 4} (EVERY oooo @{map 3} o mk_induct_discharge_prem_tac ctxt nn n pre_abs_inverses abs_inverses set_maps) pre_set_defss mss (unflat mss (1 upto n)) kksss) end; fun mk_coinduct_same_ctr_tac ctxt rel_eqs pre_rel_def pre_abs_inverse abs_inverse dtor_ discs sels extra_unfolds = hyp_subst_tac ctxt THEN' CONVERSION (hhf_concl_conv (Conv.top_conv (K (Conv.try_conv (Conv.rewr_conv ctr_def))) ctxt) ctxt) THEN' SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: dtor_ctor :: sels)) THEN' SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: pre_abs_inverse :: abs_inverse :: dtor_ sels @ sumprod_thms_rel @ extra_unfolds @ @{thms o_apply vimage2p_def})) THEN' (assume_tac ctxt ORELSE' REPEAT o etac ctxt conjE THEN' full_simp_tac (ss_only (no_refl discs @ rel_eqs @ more_simp_thms) ctxt) THEN' REPEAT o etac ctxt conjE THEN_MAYBE' REPEAT o hyp_subst_tac ctxt THEN' REPEAT o (resolve_tac ctxt [refl, conjI] ORELSE' assume_tac ctxt)); fun mk_coinduct_distinct_ctrs_tac ctxt discs discs' = let val discs'' = map (perhaps (try (fn th => th RS @{thm notnotD}))) (discs @ discs') |> distinct Thm.eq_thm_prop; in hyp_subst_tac ctxt THEN' REPEAT o etac ctxt conjE THEN' full_simp_tac (ss_only (refl :: no_refl discs'' @ basic_simp_thms) ctxt) end; fun mk_coinduct_discharge_prem_tac ctxt extra_unfolds rel_eqs' nn kk n pre_rel_def p abs_inverse dtor_ctor exhaust ctr_defs discss selss = let val ks = 1 upto n in EVERY' ([rtac ctxt allI, rtac ctxt allI, rtac ctxt impI, select_prem_tac ctxt nn (dtac ctxt meta_spec) kk, dtac ctxt meta_spec, dtac ctxt meta_mp, assume_tac ctxt, rtac ctxt exhaust, K (co_induct_inst_as_projs_tac ctxt 0), hyp_subst_tac ctxt] @ @{map 4} (fn k => fn ctr_def => fn discs => fn sels => EVERY' ([rtac ctxt exhaust, K (co_induct_inst_as_projs_tac ctxt 1)] @ map2 (fn k' => fn discs' => if k' = k then mk_coinduct_same_ctr_tac ctxt rel_eqs' pre_rel_def pre_abs_inverse abs_inverse dtor_ctor ctr_def discs sels extra_unfolds else mk_coinduct_distinct_ctrs_tac ctxt discs discs') ks discss)) ks ctr_defs discss sel end; fun mk_coinduct_tac ctxt rel_eqs' nn ns dtor_coinduct' pre_rel_defs pre_abs_inverses a dtor_ctors exhausts ctr_defss discsss selsss = HEADGOAL (rtac ctxt dtor_coinduct' THEN' EVERY' (@{map 10} (mk_coinduct_discharge_prem_tac ctxt [] rel_eqs' nn) (1 upto nn) ns pre_rel_defs pre_abs_inverses abs_inverses dtor_ctors exhausts ctr_defss discsss selsss)); fun mk_map_tac ctxt abs_inverses pre_map_def map_ctor live_nesting_map_id0s ctr_defs' extra_unfolds = TRYALL Goal.conjunction_tac THEN unfold_thms_tac ctxt (pre_map_def :: map_ctor :: abs_inverses @ live_nesting_map_id0s @ ctr_defs' @ extra_unfolds @ sumprod_thms_map @ @{thms o_apply id_apply id_o o_id}) THEN ALLGOALS (rtac ctxt refl); fun mk_map_disc_iff_tac ctxt ct exhaust discs maps = TRYALL Goal.conjunction_tac THEN ALLGOALS (rtac ctxt (infer_instantiate' ctxt [SOME ct] exhaust) THEN_ALL_NEW REPEAT_DETERM o hyp_subst_tac ctxt) THEN unfold_thms_tac ctxt maps THEN unfold_thms_tac ctxt (map (fn thm => thm RS eqFalseI handle THM _ => thm RS eqTrueI) discs) THEN ALLGOALS (rtac ctxt refl ORELSE' rtac ctxt TrueI); fun mk_map_sel_tac ctxt ct exhaust discs maps sels map_id0s = TRYALL Goal.conjunction_tac THEN ALLGOALS (rtac ctxt (infer_instantiate' ctxt [SOME ct] exhaust) THEN_ALL_NEW REPEAT_DETERM o hyp_subst_tac ctxt) THEN unfold_thms_tac ctxt ((discs RL [eqTrueI, eqFalseI]) @ @{thms not_True_eq_False not_False_eq_True}) THEN TRYALL (etac ctxt FalseE ORELSE' etac ctxt @{thm TrueE}) THEN unfold_thms_tac ctxt (@{thm id_apply} :: maps @ sels @ map_id0s) THEN ALLGOALS (rtac ctxt refl); fun mk_rel_tac ctxt abs_inverses pre_rel_def rel_ctor live_nesting_rel_eqs ctr_defs' ex TRYALL Goal.conjunction_tac THEN unfold_thms_tac ctxt (pre_rel_def :: rel_ctor :: abs_inverses @ live_nesting_rel_eqs @ ctr extra_unfolds @ sumprod_thms_rel @ @{thms vimage2p_def o_apply sum.inject sum.distinct(1)[THEN eq_False[THEN iffD2]] not_False_eq_True}) THEN ALLGOALS (resolve_tac ctxt [TrueI, refl]); fun mk_rel_case_tac ctxt ct1 ct2 exhaust injects rel_injects distincts rel_distincts rel_e HEADGOAL (rtac ctxt (infer_instantiate' ctxt [SOME ct1] exhaust) THEN_ALL_NEW rtac ctxt (infer_instantiate' ctxt [SOME ct2] exhaust) THEN_ALL_NEW hyp_subst_tac ctxt) THEN unfold_thms_tac ctxt (rel_eqs @ injects @ rel_injects @ @{thms conj_imp_eq_imp_imp simp_thms(6) True_implies_equals} @ map (fn thm => thm RS eqFalseI) (distincts @ rel_distincts) @ map (fn thm => thm RS eqTrueI) rel_injects) THEN TRYALL (assume_tac ctxt ORELSE' etac ctxt FalseE ORELSE' (REPEAT_DETERM o dtac ctxt meta_spec THEN' TRY o filter_prems_tac ctxt (forall (curry (op <>) (HOLogic.mk_Trueprop \<^term>\<open>False\<close>)) o Logic.strip_imp_pr REPEAT_DETERM o (dtac ctxt meta_mp THEN' rtac ctxt refl) THEN' (assume_tac ctxt ORELSE' Goal.assume_rule_tac ctxt))); fun mk_rel_coinduct0_tac ctxt dtor_rel_coinduct cts assms exhausts discss selss ctor_defs dtor_ctors ctor_injects abs_injects rel_pre_defs abs_inverses nesting_rel_eqs = rtac ctxt dtor_rel_coinduct 1 THEN EVERY (@{map 11} (fn ct => fn assm => fn exhaust => fn discs => fn sels => fn ctor_defs => fn dtor_ctor => fn ctor_inject => fn abs_inject => fn rel_pre_def => fn abs_inverse => (rtac ctxt exhaust THEN_ALL_NEW (rtac ctxt exhaust THEN_ALL_NEW (dtac ctxt (rotate_prems ~1 (infer_instantiate' ctxt [NONE, NONE, NONE, NONE, SOME c @{thm arg_cong2} RS iffD1)) THEN' assume_tac ctxt THEN' assume_tac ctxt THEN' hyp_subst_tac ctxt THEN' dtac ctxt assm T REPEAT_DETERM o etac ctxt conjE))) 1 THEN unfold_thms_tac ctxt ((discs RL [eqTrueI, eqFalseI]) @ sels @ simp_thms') THEN unfold_thms_tac ctxt (dtor_ctor :: rel_pre_def :: abs_inverse :: ctor_inject :: abs_inject :: ctor_defs @ nesting_rel_eqs @ simp_thms' @ @{thms id_bnf_def rel_sum_simps rel_prod_inject vimage2p_def Inl_Inr_False iffD2[OF eq_False Inr_not_Inl] sum.inject prod.inject}) THEN REPEAT_DETERM (HEADGOAL ((REPEAT_DETERM o etac ctxt conjE) THEN' (REPEAT_DETERM o rtac ctxt conjI) THEN' (rtac ctxt refl ORELSE' assume_tac ctxt)))) cts assms exhausts discss selss ctor_defss dtor_ctors ctor_injects abs_injects rel_pre_de abs_inverses); fun mk_rel_induct0_tac ctxt ctor_rel_induct assms cterms exhausts ctor_defss ctor_inject rel_pre_list_defs Abs_inverses nesting_rel_eqs = rtac ctxt ctor_rel_induct 1 THEN EVERY (@{map 6} (fn cterm => fn exhaust => fn ctor_defs => fn ctor_inject => fn rel_pre_list_def => fn Abs_inverse => HEADGOAL (rtac ctxt exhaust THEN_ALL_NEW (rtac ctxt exhaust THEN_ALL_NEW (rtac ctxt (infer_instantiate' ctxt (replicate 4 NONE @ [SOME cterm]) @{thm arg_co RS iffD2) THEN' assume_tac ctxt THEN' assume_tac ctxt THEN' TRY o resolve_tac ctxt assms))) T unfold_thms_tac ctxt (ctor_inject :: rel_pre_list_def :: ctor_defs @ nesting_rel_eqs @ @{thms id_bnf_def vimage2p_def}) THEN TRYALL (hyp_subst_tac ctxt) THEN unfold_thms_tac ctxt (Abs_inverse :: @{thms rel_sum_simps rel_prod_inject Inl_Inr_False Inr_Inl_False sum.inject prod.inject}) THEN TRYALL (rtac ctxt refl ORELSE' etac ctxt FalseE ORELSE' (REPEAT_DETERM o etac ctxt conjE) THEN' assume_tac ctxt)) cterms exhausts ctor_defss ctor_injects rel_pre_list_defs Abs_inverses); fun mk_rel_sel_tac ctxt ct1 ct2 exhaust discs sels rel_injects distincts rel_distincts rel_ HEADGOAL (rtac ctxt (infer_instantiate' ctxt [SOME ct1] exhaust) THEN_ALL_NEW rtac ctxt (infer_instantiate' ctxt [SOME ct2] exhaust) THEN_ALL_NEW hyp_subst_tac unfold_thms_tac ctxt (sels @ rel_injects @ rel_eqs @ @{thms simp_thms(6,7,8,11,12,15,16,21,22,24)} @ ((discs @ distincts) RL [eqTrueI, eqFals (rel_injects RL [eqTrueI]) @ (rel_distincts RL [eqFalseI])) THEN TRYALL (resolve_tac ctxt [TrueI, refl]); fun mk_sel_transfer_tac ctxt n sel_defs case_transfer = TRYALL Goal.conjunction_tac THEN unfold_thms_tac ctxt (map (Local_Defs.abs_def_rule ctxt) sel_defs) THEN ALLGOALS (rtac ctxt (mk_rel_funDN n case_transfer) THEN_ALL_NEW REPEAT_DETERM o (assume_tac ctxt ORELSE' rtac ctxt rel_funI)); fun mk_set0_tac ctxt abs_inverses pre_set_defs dtor_ctor fp_sets fp_nesting_set_maps live_nesting_set_maps ctr_defs' extra_unfolds = TRYALL Goal.conjunction_tac THEN unfold_thms_tac ctxt ctr_defs' THEN ALLGOALS (subst_tac ctxt NONE fp_sets) THEN unfold_thms_tac ctxt (dtor_ctor :: abs_inverses @ pre_set_defs @ fp_nesting_set_maps @ live_nesting_set_maps @ extra_unfolds @ basic_sumprod_thms_set @ @{thms UN_UN_flatten UN_Un_distrib UN_Un sup_assoc[THEN sym]}) THEN ALLGOALS (rtac ctxt @{thm set_eqI[OF iffI]}) THEN ALLGOALS (REPEAT_DETERM o etac ctxt UnE) THEN ALLGOALS (REPEAT o resolve_tac ctxt @{thms UnI1 UnI2} THEN' assume_tac ctxt); fun mk_set_sel_tac ctxt ct exhaust discs sels sets = TRYALL Goal.conjunction_tac THEN ALLGOALS (rtac ctxt (infer_instantiate' ctxt [SOME ct] exhaust) THEN_ALL_NEW REPEAT_DETERM o hyp_subst_tac ctxt) THEN unfold_thms_tac ctxt ((discs RL [eqTrueI, eqFalseI]) @ @{thms not_True_eq_False not_False_eq_True}) THEN TRYALL (etac ctxt FalseE ORELSE' etac ctxt @{thm TrueE}) THEN unfold_thms_tac ctxt (sels @ sets) THEN ALLGOALS (REPEAT o (resolve_tac ctxt @{thms UnI1 UnI2 imageI} ORELSE' eresolve_tac ctxt @{thms UN_I UN_I[rotated] imageE} ORELSE' hyp_subst_tac ctxt) THEN' (rtac ctxt @{thm singletonI} ORELSE' assume_tac ctxt)); fun mk_set_cases_tac ctxt ct assms exhaust sets = HEADGOAL (rtac ctxt (infer_instantiate' ctxt [SOME ct] exhaust) THEN_ALL_NEW hyp_subst_tac ctxt) THEN unfold_thms_tac ctxt sets THEN REPEAT_DETERM (HEADGOAL (eresolve_tac ctxt @{thms FalseE emptyE singletonE UnE UN_E insertE} ORELSE' hyp_subst_tac ctxt ORELSE' SELECT_GOAL (SOLVE (HEADGOAL (eresolve_tac ctxt assms THEN' REPEAT_DETERM o assume_tac ctxt))))); fun mk_set_intros_tac ctxt sets = TRYALL Goal.conjunction_tac THEN unfold_thms_tac ctxt sets THEN TRYALL (REPEAT o (resolve_tac ctxt @{thms UnI1 UnI2} ORELSE' eresolve_tac ctxt @{thms UN_I UN_I[rotated]}) THEN' (rtac ctxt @{thm singletonI} ORELSE' assume_tac ctxt)); fun mk_set_induct0_tac ctxt cts assms dtor_set_inducts exhausts set_pre_defs ctor_defs dt Abs_pre_inverses = let val assms_tac = let val assms' = map (unfold_thms ctxt (@{thm id_bnf_def} :: ctor_defs)) assms in fold (curry (op ORELSE')) (map (fn thm => funpow (length (Thm.prems_of thm)) (fn tac => tac THEN' assume_tac ctxt) (rtac ctxt thm)) assms') (etac ctxt FalseE) end; val exhausts' = map (fn thm => thm RS @{thm asm_rl[of "P x y" for P x y]}) exhaus |> map2 (fn ct => infer_instantiate' ctxt [NONE, SOME ct]) cts; in ALLGOALS (resolve_tac ctxt dtor_set_inducts) THEN TRYALL (resolve_tac ctxt exhausts' THEN_ALL_NEW (resolve_tac ctxt (map (fn ct => refl RS infer_instantiate' ctxt (replicate 4 NONE @ [SOME ct]) @{thm arg_cong2} RS iffD2 THEN' assume_tac ctxt THEN' hyp_subst_tac ctxt)) THEN unfold_thms_tac ctxt (Abs_pre_inverses @ dtor_ctors @ set_pre_defs @ ctor_defs @ @{thms id_bnf_def o_apply sum_set_simps prod_set_simps UN_empty UN_insert Un_empty_left Un_empty_right empty_iff singleton_iff}) THEN REPEAT (HEADGOAL (hyp_subst_tac ctxt ORELSE' eresolve_tac ctxt @{thms UN_E UnE singletonE} ORELSE' assms_tac)) end; end; ¤ Dauer der Verarbeitung: 0.23 Sekunden (vorverarbeitet) ¤ |
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