author | traytel |
Mon, 15 Jul 2013 14:23:51 +0200 | |
changeset 52659 | 58b87aa4dc3b |
parent 52349 | 07fd21c01e93 |
child 52966 | 3777ba39c660 |
permissions | -rw-r--r-- |
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(* Title: HOL/BNF/Tools/bnf_fp_def_sugar_tactics.ML |
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Author: Jasmin Blanchette, TU Muenchen |
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Copyright 2012 |
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Tactics for datatype and codatatype sugar. |
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*) |
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signature BNF_FP_DEF_SUGAR_TACTICS = |
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sig |
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val sum_prod_thms_map: thm list |
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val sum_prod_thms_set: thm list |
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val sum_prod_thms_rel: thm list |
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|
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val mk_case_tac: Proof.context -> int -> int -> int -> thm -> thm -> thm -> tactic |
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val mk_coinduct_tac: Proof.context -> thm list -> int -> int list -> thm -> thm list -> |
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thm list -> thm list -> thm list list -> thm list list list -> thm list list list -> tactic |
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val mk_coiter_tac: thm list -> thm list -> thm -> thm -> thm -> Proof.context -> tactic |
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val mk_ctor_iff_dtor_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm -> |
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tactic |
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val mk_disc_coiter_iff_tac: thm list -> thm list -> thm list -> 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_half_distinct_tac: Proof.context -> thm -> thm list -> tactic |
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val mk_induct_tac: Proof.context -> int -> int list -> int list list -> int list list list -> |
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thm list -> thm -> thm list -> thm list list -> tactic |
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val mk_inject_tac: Proof.context -> thm -> thm -> tactic |
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val mk_iter_tac: thm list -> thm list -> thm list -> thm -> thm -> Proof.context -> tactic |
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end; |
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structure BNF_FP_Def_Sugar_Tactics : BNF_FP_DEF_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 basic_simp_thms = @{thms simp_thms(7,8,12,14,22,24)}; |
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val more_simp_thms = basic_simp_thms @ @{thms simp_thms(11,15,16,21)}; |
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val sum_prod_thms_map = @{thms id_apply map_pair_simp prod.cases sum.cases sum_map.simps}; |
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val sum_prod_thms_set0 = |
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@{thms SUP_empty Sup_empty Sup_insert UN_insert Un_empty_left Un_empty_right Un_iff |
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Union_Un_distrib collect_def[abs_def] image_def o_apply map_pair_simp |
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mem_Collect_eq mem_UN_compreh_eq prod_set_simps sum_map.simps sum_set_simps}; |
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val sum_prod_thms_set = @{thms UN_compreh_eq_eq} @ sum_prod_thms_set0; |
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val sum_prod_thms_rel = @{thms prod_rel_simp sum_rel_simps id_apply}; |
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val ss_if_True_False = simpset_of (ss_only @{thms if_True if_False} @{context}); |
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fun mk_proj T k = |
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let val binders = binder_types T in |
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fold_rev (fn T => fn t => Abs (Name.uu, T, t)) binders (Bound (length binders - k)) |
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end; |
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||
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fun hhf_concl_conv cv ctxt ct = |
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(case Thm.term_of ct of |
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Const (@{const_name all}, _) $ Abs _ => |
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Conv.arg_conv (Conv.abs_conv (hhf_concl_conv cv o snd) ctxt) ct |
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| _ => Conv.concl_conv ~1 cv ct); |
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fun inst_as_projs ctxt k 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 ctxt (Var f), certify ctxt (mk_proj T k))) 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_as_projs_tac = PRIMITIVE oo inst_as_projs; |
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fun mk_case_tac ctxt n k m case_def ctr_def dtor_ctor = |
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unfold_thms_tac ctxt [case_def, ctr_def, dtor_ctor] THEN |
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HEADGOAL (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); |
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fun mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor sumEN' = |
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unfold_thms_tac ctxt (ctor_iff_dtor :: ctr_defs) THEN HEADGOAL (rtac sumEN') THEN |
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unfold_thms_tac ctxt @{thms split_paired_all} THEN |
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HEADGOAL (EVERY' (maps (fn k => [select_prem_tac n (rotate_tac 1) k, |
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REPEAT_DETERM o dtac meta_spec, etac meta_mp, atac]) (1 upto n))); |
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fun mk_ctor_iff_dtor_tac ctxt cTs cctor cdtor ctor_dtor dtor_ctor = |
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HEADGOAL (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 (unfold_thms_tac ctxt [th]) THEN' |
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atac) [rev cTs, cTs] [cdtor, cctor] [dtor_ctor, ctor_dtor])); |
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fun mk_half_distinct_tac ctxt ctor_inject ctr_defs = |
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unfold_thms_tac ctxt (ctor_inject :: @{thms sum.inject} @ ctr_defs) THEN |
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HEADGOAL (rtac @{thm sum.distinct(1)}); |
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fun mk_inject_tac ctxt ctr_def ctor_inject = |
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unfold_thms_tac ctxt [ctr_def] THEN HEADGOAL (rtac (ctor_inject RS ssubst)) THEN |
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unfold_thms_tac ctxt @{thms sum.inject Pair_eq conj_assoc} THEN HEADGOAL (rtac refl); |
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val iter_unfold_thms = |
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@{thms comp_def convol_def fst_conv id_def prod_case_Pair_iden snd_conv |
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split_conv unit_case_Unity} @ sum_prod_thms_map; |
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fun mk_iter_tac pre_map_defs map_ids'' iter_defs ctor_iter ctr_def ctxt = |
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unfold_thms_tac ctxt (ctr_def :: ctor_iter :: iter_defs @ pre_map_defs @ map_ids'' @ |
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iter_unfold_thms) THEN HEADGOAL (rtac refl); |
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val coiter_unfold_thms = @{thms id_def} @ sum_prod_thms_map; |
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fun mk_coiter_tac coiter_defs map_ids'' ctor_dtor_coiter pre_map_def ctr_def ctxt = |
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unfold_thms_tac ctxt (ctr_def :: coiter_defs) THEN |
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HEADGOAL (rtac (ctor_dtor_coiter RS trans) THEN' |
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asm_simp_tac (put_simpset ss_if_True_False ctxt)) THEN_MAYBE |
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(unfold_thms_tac ctxt (pre_map_def :: map_ids'' @ coiter_unfold_thms) THEN |
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HEADGOAL (rtac refl ORELSE' rtac (@{thm unit_eq} RS arg_cong))); |
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fun mk_disc_coiter_iff_tac case_splits' coiters discs ctxt = |
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EVERY (map3 (fn case_split_tac => fn coiter_thm => fn disc => |
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HEADGOAL case_split_tac THEN unfold_thms_tac ctxt [coiter_thm] THEN |
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HEADGOAL (asm_simp_tac (ss_only basic_simp_thms ctxt)) THEN |
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(if is_refl disc then all_tac else HEADGOAL (rtac disc))) |
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(map rtac case_splits' @ [K all_tac]) coiters discs); |
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fun solve_prem_prem_tac ctxt = |
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REPEAT o (eresolve_tac @{thms bexE rev_bexI} ORELSE' rtac @{thm rev_bexI[OF UNIV_I]} ORELSE' |
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hyp_subst_tac ctxt ORELSE' resolve_tac @{thms disjI1 disjI2}) THEN' |
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(rtac refl ORELSE' atac ORELSE' rtac @{thm singletonI}); |
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fun mk_induct_leverage_prem_prems_tac ctxt nn kks set_map's pre_set_defs = |
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HEADGOAL (EVERY' (maps (fn kk => [select_prem_tac nn (dtac meta_spec) kk, etac meta_mp, |
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SELECT_GOAL (unfold_thms_tac ctxt (pre_set_defs @ set_map's @ sum_prod_thms_set0)), |
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solve_prem_prem_tac ctxt]) (rev kks))); |
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fun mk_induct_discharge_prem_tac ctxt nn n set_map's pre_set_defs m k kks = |
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let val r = length kks in |
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HEADGOAL (EVERY' [select_prem_tac n (rotate_tac 1) k, rotate_tac ~1, hyp_subst_tac ctxt, |
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REPEAT_DETERM_N m o (dtac meta_spec THEN' rotate_tac ~1)]) THEN |
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EVERY [REPEAT_DETERM_N r |
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(HEADGOAL (rotate_tac ~1 THEN' dtac meta_mp THEN' rotate_tac 1) THEN prefer_tac 2), |
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if r > 0 then ALLGOALS Goal.norm_hhf_tac else all_tac, HEADGOAL atac, |
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mk_induct_leverage_prem_prems_tac ctxt nn kks set_map's pre_set_defs] |
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end; |
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fun mk_induct_tac ctxt nn ns mss kkss ctr_defs ctor_induct' set_map's pre_set_defss = |
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let val n = Integer.sum ns in |
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unfold_thms_tac ctxt ctr_defs THEN |
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HEADGOAL (rtac ctor_induct' THEN' inst_as_projs_tac ctxt) THEN |
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EVERY (map4 (EVERY oooo map3 o mk_induct_discharge_prem_tac ctxt nn n set_map's) pre_set_defss |
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mss (unflat mss (1 upto n)) kkss) |
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end; |
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fun mk_coinduct_same_ctr ctxt rel_eqs pre_rel_def dtor_ctor ctr_def discs sels = |
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hyp_subst_tac ctxt THEN' |
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CONVERSION (hhf_concl_conv |
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(Conv.top_conv (K (Conv.try_conv (Conv.rewr_conv ctr_def))) ctxt) ctxt) THEN' |
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SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: dtor_ctor :: sels)) THEN' |
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SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: dtor_ctor :: sels @ sum_prod_thms_rel)) THEN' |
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(atac ORELSE' REPEAT o etac conjE THEN' |
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full_simp_tac |
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(ss_only (@{thm prod.inject} :: no_refl discs @ rel_eqs @ more_simp_thms) ctxt) THEN' |
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REPEAT o etac conjE THEN_MAYBE' REPEAT o hyp_subst_tac ctxt THEN' REPEAT o rtac conjI THEN' |
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REPEAT o rtac refl); |
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fun mk_coinduct_distinct_ctrs ctxt discs discs' = |
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hyp_subst_tac ctxt THEN' REPEAT o etac conjE THEN' |
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full_simp_tac (ss_only (refl :: no_refl (discs @ discs') @ basic_simp_thms) ctxt); |
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fun mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn kk n pre_rel_def dtor_ctor exhaust ctr_defs |
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discss selss = |
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let val ks = 1 upto n in |
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EVERY' ([rtac allI, rtac allI, rtac impI, select_prem_tac nn (dtac meta_spec) kk, dtac |
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meta_spec, dtac meta_mp, atac, rtac exhaust, K (HEADGOAL (inst_as_projs_tac ctxt)), |
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hyp_subst_tac ctxt] @ |
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map4 (fn k => fn ctr_def => fn discs => fn sels => |
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EVERY' ([rtac exhaust, K (inst_as_projs_tac ctxt 2)] @ |
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map2 (fn k' => fn discs' => |
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if k' = k then |
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mk_coinduct_same_ctr ctxt rel_eqs' pre_rel_def dtor_ctor ctr_def discs sels |
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else |
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simplifier uses proper Proof.context instead of historic type simpset;
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mk_coinduct_distinct_ctrs ctxt discs discs') ks discss)) ks ctr_defs discss selss) |
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end; |
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fun mk_coinduct_tac ctxt rel_eqs' nn ns dtor_coinduct' pre_rel_defs dtor_ctors exhausts ctr_defss |
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discsss selsss = |
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HEADGOAL (rtac dtor_coinduct' THEN' |
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EVERY' (map8 (mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn) |
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(1 upto nn) ns pre_rel_defs dtor_ctors exhausts ctr_defss discsss selsss)); |
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end; |