author | desharna |
Mon, 06 Oct 2014 13:32:41 +0200 | |
changeset 58560 | ee502a9b38aa |
parent 58507 | ce0b9be06f85 |
child 58634 | 9f10d82e8188 |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/BNF/bnf_fp_def_sugar_tactics.ML |
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Author: Jasmin Blanchette, TU Muenchen |
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Author: Martin Desharnais, TU Muenchen |
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Copyright 2012, 2013, 2014 |
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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 sumprod_thms_map: thm list |
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val sumprod_thms_set: thm list |
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val basic_sumprod_thms_set: thm list |
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val sumprod_thms_rel: thm list |
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val mk_case_transfer_tac: Proof.context -> thm -> thm list -> 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 -> thm list -> thm list list -> thm list list list -> |
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thm list list list -> tactic |
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val mk_corec_tac: thm list -> thm list -> thm -> thm -> thm -> thm -> Proof.context -> tactic |
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val mk_corec_disc_iff_tac: thm list -> thm list -> thm list -> Proof.context -> tactic |
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val mk_corec_transfer_tac: Proof.context -> cterm list -> cterm list -> thm list -> thm list -> |
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thm list -> thm list -> thm list -> ''a list -> ''a list list -> ''a list list list list -> |
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''a list list list list -> 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_ctr_transfer_tac: Proof.context -> thm list -> thm list -> tactic |
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val mk_disc_transfer_tac: thm -> thm -> thm list -> 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 -> 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 -> thm list -> thm list list -> tactic |
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val mk_inject_tac: Proof.context -> thm -> thm -> thm -> tactic |
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val mk_map_disc_iff_tac: Proof.context -> cterm -> thm -> thm list -> thm list -> tactic |
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val mk_map_sel_tac: Proof.context -> cterm -> thm -> thm list -> thm list -> thm list -> |
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thm list -> tactic |
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val mk_rec_tac: thm list -> thm list -> thm list -> thm -> thm -> thm -> thm -> Proof.context -> |
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tactic |
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val mk_rec_transfer_tac: Proof.context -> int -> int list -> cterm list -> cterm list -> |
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thm list -> thm list -> thm list -> thm list -> tactic |
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val mk_rel_cases_tac: Proof.context -> cterm -> cterm -> thm -> thm list -> thm list -> |
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thm list -> thm list -> thm list -> tactic |
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val mk_rel_coinduct0_tac: Proof.context -> thm -> cterm list -> thm list -> thm list -> |
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thm list list -> thm list list -> thm list list -> thm list -> thm list -> thm list -> |
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thm list -> thm list -> thm list -> tactic |
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val mk_rel_induct0_tac: Proof.context -> thm -> thm list -> cterm list -> thm list -> |
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thm list list -> thm list -> thm list -> thm list -> thm list -> tactic |
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val mk_rel_sel_tac: Proof.context -> cterm -> cterm -> thm -> thm list -> thm list -> thm list -> |
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thm list -> thm list -> thm list -> tactic |
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val mk_set_cases_tac: Proof.context -> cterm -> thm list -> thm -> thm list -> tactic |
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val mk_set_induct0_tac: Proof.context -> cterm list -> thm list -> thm list -> thm list -> |
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thm list -> thm list -> thm list -> thm list -> tactic |
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val mk_set_intros_tac: Proof.context -> thm list -> tactic |
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val mk_set_sel_tac: Proof.context -> cterm -> thm -> thm list -> thm list -> thm list -> 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 Ctr_Sugar_Util |
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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 case_sum_transfer = @{thm case_sum_transfer}; |
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val case_sum_transfer_eq = @{thm case_sum_transfer[of "op =" _ "op =", unfolded sum.rel_eq]}; |
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val case_prod_transfer = @{thm case_prod_transfer}; |
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val case_prod_transfer_eq = @{thm case_prod_transfer[of "op =" "op =", unfolded prod.rel_eq]}; |
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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 simp_thms' = @{thms simp_thms(6,7,8,11,12,15,16,22,24)}; |
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val sumprod_thms_map = @{thms id_apply map_prod_simp prod.case sum.case map_sum.simps}; |
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val basic_sumprod_thms_set = |
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@{thms UN_empty UN_insert UN_iff Un_empty_left Un_empty_right Un_iff Union_Un_distrib |
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o_apply map_prod_simp mem_Collect_eq prod_set_simps map_sum.simps sum_set_simps}; |
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val sumprod_thms_set = @{thms UN_simps(10) image_iff} @ basic_sumprod_thms_set; |
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val sumprod_thms_rel = @{thms rel_sum_simps rel_prod_apply prod.inject id_apply conj_assoc}; |
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fun is_def_looping def = |
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(case Thm.prop_of def of |
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Const (@{const_name Pure.eq}, _) $ lhs $ rhs => Term.exists_subterm (curry (op =) lhs) rhs |
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| _ => false); |
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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 Pure.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 co_induct_inst_as_projs ctxt k thm = |
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let |
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val fs = 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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fun mk_cfp (f as (_, T)) = |
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(certify ctxt (Var f), certify ctxt (mk_proj T (num_binder_types T) k)); |
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val cfps = map mk_cfp fs; |
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in |
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Drule.cterm_instantiate cfps thm |
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end; |
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val co_induct_inst_as_projs_tac = PRIMITIVE oo co_induct_inst_as_projs; |
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fun mk_case_transfer_tac ctxt rel_cases cases = |
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let |
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val n = length (tl (prems_of rel_cases)); |
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in |
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REPEAT_DETERM (HEADGOAL (rtac rel_funI)) THEN |
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HEADGOAL (etac rel_cases) THEN |
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ALLGOALS (hyp_subst_tac ctxt) THEN |
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unfold_thms_tac ctxt cases THEN |
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ALLGOALS (fn k => (select_prem_tac n (dtac asm_rl) k) k) THEN |
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ALLGOALS (REPEAT_DETERM o (rotate_tac ~1 THEN' dtac @{thm rel_funD} THEN' |
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(atac THEN' etac thin_rl ORELSE' rtac refl)) THEN' atac) |
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end; |
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fun mk_ctr_transfer_tac ctxt rel_intros rel_eqs = |
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HEADGOAL Goal.conjunction_tac THEN |
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ALLGOALS (REPEAT o (resolve_tac (rel_funI :: rel_intros) THEN' |
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TRY o (REPEAT_DETERM1 o (atac ORELSE' |
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K (unfold_thms_tac ctxt rel_eqs) THEN' hyp_subst_tac ctxt THEN' rtac refl)))); |
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fun mk_disc_transfer_tac rel_sel exhaust_disc distinct_disc= |
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let |
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fun last_disc_tac iffD = |
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HEADGOAL (rtac (rotate_prems ~1 exhaust_disc) THEN' atac THEN' |
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REPEAT_DETERM o (rotate_tac ~1 THEN' dtac (rotate_prems 1 iffD) THEN' atac THEN' |
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rotate_tac ~1 THEN' etac (rotate_prems 1 notE) THEN' eresolve_tac distinct_disc)); |
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in |
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HEADGOAL Goal.conjunction_tac THEN |
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REPEAT_DETERM (HEADGOAL (rtac rel_funI THEN' dtac (rel_sel RS iffD1) THEN' |
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REPEAT_DETERM o (etac conjE) THEN' (atac ORELSE' rtac iffI))) THEN |
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TRY (last_disc_tac iffD2) THEN TRY (last_disc_tac iffD1) |
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end; |
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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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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 abs_inject ctr_defs = |
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unfold_thms_tac ctxt (ctor_inject :: abs_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 abs_inject = |
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unfold_thms_tac ctxt [ctr_def] THEN |
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HEADGOAL (rtac (ctor_inject RS ssubst)) THEN |
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unfold_thms_tac ctxt (abs_inject :: @{thms sum.inject prod.inject conj_assoc}) THEN |
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HEADGOAL (rtac refl); |
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val rec_unfold_thms = |
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@{thms comp_def convol_def fst_conv id_def case_prod_Pair_iden snd_conv split_conv |
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case_unit_Unity} @ sumprod_thms_map; |
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fun mk_rec_tac pre_map_defs map_ident0s rec_defs ctor_rec fp_abs_inverse abs_inverse ctr_def ctxt = |
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HEADGOAL ((if is_def_looping ctr_def then subst_tac ctxt NONE |
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else SELECT_GOAL o unfold_thms_tac ctxt) [ctr_def]) THEN |
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unfold_thms_tac ctxt (ctor_rec :: fp_abs_inverse :: abs_inverse :: rec_defs @ |
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pre_map_defs @ map_ident0s @ rec_unfold_thms) THEN HEADGOAL (rtac refl); |
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fun mk_rec_transfer_tac ctxt nn ns actives passives rec_defs ctor_rec_transfers rel_pre_T_defs |
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rel_eqs = |
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let |
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val ctor_rec_transfers' = |
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map (cterm_instantiate_pos (map SOME (passives @ actives))) ctor_rec_transfers; |
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val total_n = Integer.sum ns; |
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in |
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HEADGOAL Goal.conjunction_tac THEN |
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EVERY (map (fn ctor_rec_transfer => |
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REPEAT_DETERM (HEADGOAL (rtac rel_funI)) THEN |
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unfold_thms_tac ctxt rec_defs THEN |
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HEADGOAL (etac (mk_rel_funDN_rotated (nn + 1) ctor_rec_transfer)) THEN |
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unfold_thms_tac ctxt rel_pre_T_defs THEN |
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EVERY (fst (fold_map (fn k => fn acc => rpair (k + acc) |
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(HEADGOAL (rtac (mk_rel_funDN_rotated 2 @{thm comp_transfer})) THEN |
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HEADGOAL (rtac @{thm vimage2p_rel_fun}) THEN |
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unfold_thms_tac ctxt rel_eqs THEN |
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EVERY (map (fn n => |
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REPEAT_DETERM (HEADGOAL |
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(rtac (mk_rel_funDN 2 case_sum_transfer_eq) ORELSE' |
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rtac (mk_rel_funDN 2 case_sum_transfer))) THEN |
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HEADGOAL (select_prem_tac total_n (dtac asm_rl) (acc + n)) THEN |
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HEADGOAL (SELECT_GOAL (HEADGOAL |
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((REPEAT_DETERM o (atac ORELSE' |
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rtac (mk_rel_funDN 1 case_prod_transfer_eq) ORELSE' |
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rtac (mk_rel_funDN 1 case_prod_transfer) ORELSE' |
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rtac rel_funI)) THEN_ALL_NEW |
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(REPEAT_ALL_NEW (dtac rel_funD) THEN_ALL_NEW atac))))) |
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(1 upto k)))) |
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ns 0))) |
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ctor_rec_transfers') |
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end; |
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val corec_unfold_thms = @{thms id_def} @ sumprod_thms_map; |
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fun mk_corec_tac corec_defs map_ident0s ctor_dtor_corec pre_map_def abs_inverse ctr_def ctxt = |
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205 |
let |
57399 | 206 |
val ss = ss_only (pre_map_def :: abs_inverse :: map_ident0s @ corec_unfold_thms @ |
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207 |
@{thms o_apply vimage2p_def if_True if_False}) ctxt; |
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208 |
in |
55867 | 209 |
unfold_thms_tac ctxt (ctr_def :: corec_defs) THEN |
210 |
HEADGOAL (rtac (ctor_dtor_corec RS trans) THEN' asm_simp_tac ss) THEN_MAYBE |
|
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|
211 |
HEADGOAL (rtac refl ORELSE' rtac (@{thm unit_eq} RS arg_cong)) |
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212 |
end; |
49213 | 213 |
|
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|
214 |
fun mk_corec_disc_iff_tac case_splits' corecs discs ctxt = |
55867 | 215 |
EVERY (map3 (fn case_split_tac => fn corec_thm => fn disc => |
216 |
HEADGOAL case_split_tac THEN unfold_thms_tac ctxt [corec_thm] THEN |
|
52324 | 217 |
HEADGOAL (asm_simp_tac (ss_only basic_simp_thms ctxt)) THEN |
218 |
(if is_refl disc then all_tac else HEADGOAL (rtac disc))) |
|
55867 | 219 |
(map rtac case_splits' @ [K all_tac]) corecs discs); |
49482 | 220 |
|
58448 | 221 |
fun mk_corec_transfer_tac ctxt actives passives type_definitions corec_defs dtor_corec_transfers |
222 |
rel_pre_T_defs rel_eqs pgs pss qssss gssss = |
|
223 |
let |
|
224 |
val num_pgs = length pgs; |
|
225 |
fun prem_no_of x = 1 + find_index (curry (op =) x) pgs; |
|
226 |
||
227 |
val Inl_Inr_Pair_tac = REPEAT_DETERM o |
|
228 |
(rtac (mk_rel_funDN 1 @{thm Inl_transfer}) ORELSE' |
|
229 |
rtac (mk_rel_funDN 1 @{thm Inr_transfer}) ORELSE' |
|
230 |
rtac (mk_rel_funDN 2 @{thm Pair_transfer})); |
|
231 |
||
232 |
fun mk_unfold_If_tac total pos = |
|
233 |
HEADGOAL (Inl_Inr_Pair_tac THEN' |
|
234 |
rtac (mk_rel_funDN 3 @{thm If_transfer}) THEN' |
|
235 |
select_prem_tac total (dtac asm_rl) pos THEN' |
|
236 |
dtac rel_funD THEN' atac THEN' atac); |
|
237 |
||
238 |
fun mk_unfold_Inl_Inr_Pair_tac total pos = |
|
239 |
HEADGOAL (Inl_Inr_Pair_tac THEN' |
|
240 |
select_prem_tac total (dtac asm_rl) pos THEN' |
|
241 |
dtac rel_funD THEN' atac THEN' atac); |
|
242 |
||
243 |
fun mk_unfold_arg_tac qs gs = |
|
244 |
EVERY (map (mk_unfold_If_tac num_pgs o prem_no_of) qs) THEN |
|
245 |
EVERY (map (mk_unfold_Inl_Inr_Pair_tac num_pgs o prem_no_of) gs); |
|
246 |
||
247 |
fun mk_unfold_ctr_tac type_definition qss gss = |
|
248 |
HEADGOAL (rtac (mk_rel_funDN 1 (@{thm Abs_transfer} OF |
|
249 |
[type_definition, type_definition])) THEN' Inl_Inr_Pair_tac) THEN |
|
250 |
(case (qss, gss) of |
|
251 |
([], []) => HEADGOAL (rtac refl) |
|
252 |
| _ => EVERY (map2 mk_unfold_arg_tac qss gss)); |
|
253 |
||
254 |
fun mk_unfold_type_tac type_definition ps qsss gsss = |
|
255 |
let |
|
256 |
val p_tacs = map (mk_unfold_If_tac num_pgs o prem_no_of) ps; |
|
257 |
val qg_tacs = map2 (mk_unfold_ctr_tac type_definition) qsss gsss; |
|
258 |
fun mk_unfold_ty [] [qg_tac] = qg_tac |
|
259 |
| mk_unfold_ty (p_tac :: p_tacs) (qg_tac :: qg_tacs) = |
|
260 |
p_tac THEN qg_tac THEN mk_unfold_ty p_tacs qg_tacs |
|
261 |
in |
|
262 |
HEADGOAL (rtac rel_funI) THEN mk_unfold_ty p_tacs qg_tacs |
|
263 |
end; |
|
264 |
||
265 |
fun mk_unfold_corec_type_tac dtor_corec_transfer corec_def = |
|
266 |
let |
|
267 |
val active :: actives' = actives; |
|
268 |
val dtor_corec_transfer' = cterm_instantiate_pos |
|
269 |
(SOME active :: map SOME passives @ map SOME actives') dtor_corec_transfer; |
|
270 |
in |
|
271 |
HEADGOAL Goal.conjunction_tac THEN |
|
272 |
REPEAT_DETERM (HEADGOAL (rtac rel_funI)) THEN |
|
273 |
unfold_thms_tac ctxt [corec_def] THEN |
|
274 |
HEADGOAL (etac (mk_rel_funDN_rotated (1 + length actives) dtor_corec_transfer')) THEN |
|
275 |
unfold_thms_tac ctxt (rel_pre_T_defs @ rel_eqs) |
|
276 |
end; |
|
277 |
||
278 |
fun mk_unfold_prop_tac dtor_corec_transfer corec_def = |
|
279 |
mk_unfold_corec_type_tac dtor_corec_transfer corec_def THEN |
|
280 |
EVERY (map4 mk_unfold_type_tac type_definitions pss qssss gssss); |
|
281 |
in |
|
282 |
HEADGOAL Goal.conjunction_tac THEN |
|
283 |
EVERY (map2 mk_unfold_prop_tac dtor_corec_transfers corec_defs) |
|
284 |
end; |
|
285 |
||
51798 | 286 |
fun solve_prem_prem_tac ctxt = |
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|
287 |
REPEAT o (eresolve_tac @{thms bexE rev_bexI} ORELSE' rtac @{thm rev_bexI[OF UNIV_I]} ORELSE' |
51798 | 288 |
hyp_subst_tac ctxt ORELSE' resolve_tac @{thms disjI1 disjI2}) THEN' |
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changeset
|
289 |
(rtac refl ORELSE' atac ORELSE' rtac @{thm singletonI}); |
49426 | 290 |
|
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|
291 |
fun mk_induct_leverage_prem_prems_tac ctxt nn kks fp_abs_inverses abs_inverses set_maps |
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changeset
|
292 |
pre_set_defs = |
52324 | 293 |
HEADGOAL (EVERY' (maps (fn kk => [select_prem_tac nn (dtac meta_spec) kk, etac meta_mp, |
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changeset
|
294 |
SELECT_GOAL (unfold_thms_tac ctxt (pre_set_defs @ fp_abs_inverses @ abs_inverses @ set_maps @ |
55966 | 295 |
sumprod_thms_set)), |
52324 | 296 |
solve_prem_prem_tac ctxt]) (rev kks))); |
49368 | 297 |
|
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|
298 |
fun mk_induct_discharge_prem_tac ctxt nn n fp_abs_inverses abs_inverses set_maps pre_set_defs m k |
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|
299 |
kks = |
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changeset
|
300 |
let val r = length kks in |
52324 | 301 |
HEADGOAL (EVERY' [select_prem_tac n (rotate_tac 1) k, rotate_tac ~1, hyp_subst_tac ctxt, |
302 |
REPEAT_DETERM_N m o (dtac meta_spec THEN' rotate_tac ~1)]) THEN |
|
49391 | 303 |
EVERY [REPEAT_DETERM_N r |
52324 | 304 |
(HEADGOAL (rotate_tac ~1 THEN' dtac meta_mp THEN' rotate_tac 1) THEN prefer_tac 2), |
54742
7a86358a3c0b
proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
wenzelm
parents:
54241
diff
changeset
|
305 |
if r > 0 then ALLGOALS (Goal.norm_hhf_tac ctxt) else all_tac, HEADGOAL atac, |
55803
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parents:
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diff
changeset
|
306 |
mk_induct_leverage_prem_prems_tac ctxt nn kks fp_abs_inverses abs_inverses set_maps |
74d3fe9031d8
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parents:
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changeset
|
307 |
pre_set_defs] |
49391 | 308 |
end; |
49368 | 309 |
|
55803
74d3fe9031d8
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parents:
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diff
changeset
|
310 |
fun mk_induct_tac ctxt nn ns mss kkss ctr_defs ctor_induct' fp_abs_inverses abs_inverses set_maps |
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diff
changeset
|
311 |
pre_set_defss = |
49590 | 312 |
let val n = Integer.sum ns in |
58359
3782c7b0d1cc
avoid 'subst_tac' when possible (it is suspected of not helping 'HOL-Proofs')
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parents:
58353
diff
changeset
|
313 |
(if exists is_def_looping ctr_defs then |
3782c7b0d1cc
avoid 'subst_tac' when possible (it is suspected of not helping 'HOL-Proofs')
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parents:
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diff
changeset
|
314 |
EVERY (map (fn def => HEADGOAL (subst_asm_tac ctxt NONE [def])) ctr_defs) |
3782c7b0d1cc
avoid 'subst_tac' when possible (it is suspected of not helping 'HOL-Proofs')
blanchet
parents:
58353
diff
changeset
|
315 |
else |
3782c7b0d1cc
avoid 'subst_tac' when possible (it is suspected of not helping 'HOL-Proofs')
blanchet
parents:
58353
diff
changeset
|
316 |
unfold_thms_tac ctxt ctr_defs) THEN |
58352
37745650a3f4
register 'prod' and 'sum' as datatypes, to allow N2M through them
blanchet
parents:
58327
diff
changeset
|
317 |
HEADGOAL (rtac ctor_induct') THEN co_induct_inst_as_projs_tac ctxt 0 THEN |
55803
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
traytel
parents:
55642
diff
changeset
|
318 |
EVERY (map4 (EVERY oooo map3 o |
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
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parents:
55642
diff
changeset
|
319 |
mk_induct_discharge_prem_tac ctxt nn n fp_abs_inverses abs_inverses set_maps) |
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
traytel
parents:
55642
diff
changeset
|
320 |
pre_set_defss mss (unflat mss (1 upto n)) kkss) |
49368 | 321 |
end; |
322 |
||
55803
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
traytel
parents:
55642
diff
changeset
|
323 |
fun mk_coinduct_same_ctr_tac ctxt rel_eqs pre_rel_def fp_abs_inverse abs_inverse dtor_ctor ctr_def |
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
traytel
parents:
55642
diff
changeset
|
324 |
discs sels = |
51798 | 325 |
hyp_subst_tac ctxt THEN' |
49665 | 326 |
CONVERSION (hhf_concl_conv |
327 |
(Conv.top_conv (K (Conv.try_conv (Conv.rewr_conv ctr_def))) ctxt) ctxt) THEN' |
|
49642
9f884142334c
fixed simplification of prod and sum relators to avoid issues with e.g. codata ('a, 'b) k = K "'a + 'b"
blanchet
parents:
49639
diff
changeset
|
328 |
SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: dtor_ctor :: sels)) THEN' |
55803
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
traytel
parents:
55642
diff
changeset
|
329 |
SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: fp_abs_inverse :: abs_inverse :: dtor_ctor :: |
55966 | 330 |
sels @ sumprod_thms_rel @ @{thms o_apply vimage2p_def})) THEN' |
49591
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
331 |
(atac ORELSE' REPEAT o etac conjE THEN' |
56765 | 332 |
full_simp_tac (ss_only (no_refl discs @ rel_eqs @ more_simp_thms) ctxt) THEN' |
54241 | 333 |
REPEAT o etac conjE THEN_MAYBE' REPEAT o hyp_subst_tac ctxt THEN' |
334 |
REPEAT o (resolve_tac [refl, conjI] ORELSE' atac)); |
|
49590 | 335 |
|
52966 | 336 |
fun mk_coinduct_distinct_ctrs_tac ctxt discs discs' = |
54198
4fadf746f2d5
got rid of annoying duplicate rewrite rule warnings
blanchet
parents:
53690
diff
changeset
|
337 |
let |
4fadf746f2d5
got rid of annoying duplicate rewrite rule warnings
blanchet
parents:
53690
diff
changeset
|
338 |
val discs'' = map (perhaps (try (fn th => th RS @{thm notnotD}))) (discs @ discs') |
4fadf746f2d5
got rid of annoying duplicate rewrite rule warnings
blanchet
parents:
53690
diff
changeset
|
339 |
|> distinct Thm.eq_thm_prop; |
4fadf746f2d5
got rid of annoying duplicate rewrite rule warnings
blanchet
parents:
53690
diff
changeset
|
340 |
in |
4fadf746f2d5
got rid of annoying duplicate rewrite rule warnings
blanchet
parents:
53690
diff
changeset
|
341 |
hyp_subst_tac ctxt THEN' REPEAT o etac conjE THEN' |
4fadf746f2d5
got rid of annoying duplicate rewrite rule warnings
blanchet
parents:
53690
diff
changeset
|
342 |
full_simp_tac (ss_only (refl :: no_refl discs'' @ basic_simp_thms) ctxt) |
4fadf746f2d5
got rid of annoying duplicate rewrite rule warnings
blanchet
parents:
53690
diff
changeset
|
343 |
end; |
49590 | 344 |
|
55803
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
traytel
parents:
55642
diff
changeset
|
345 |
fun mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn kk n pre_rel_def fp_abs_inverse abs_inverse |
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
traytel
parents:
55642
diff
changeset
|
346 |
dtor_ctor exhaust ctr_defs discss selss = |
49590 | 347 |
let val ks = 1 upto n in |
54837 | 348 |
EVERY' ([rtac allI, rtac allI, rtac impI, select_prem_tac nn (dtac meta_spec) kk, |
54923
ffed2452f5f6
instantiate schematics as projections to avoid HOU trouble
blanchet
parents:
54922
diff
changeset
|
349 |
dtac meta_spec, dtac meta_mp, atac, rtac exhaust, K (co_induct_inst_as_projs_tac ctxt 0), |
51798 | 350 |
hyp_subst_tac ctxt] @ |
49591
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
351 |
map4 (fn k => fn ctr_def => fn discs => fn sels => |
54923
ffed2452f5f6
instantiate schematics as projections to avoid HOU trouble
blanchet
parents:
54922
diff
changeset
|
352 |
EVERY' ([rtac exhaust, K (co_induct_inst_as_projs_tac ctxt 1)] @ |
49591
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
353 |
map2 (fn k' => fn discs' => |
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
354 |
if k' = k then |
55803
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
traytel
parents:
55642
diff
changeset
|
355 |
mk_coinduct_same_ctr_tac ctxt rel_eqs' pre_rel_def fp_abs_inverse abs_inverse |
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
traytel
parents:
55642
diff
changeset
|
356 |
dtor_ctor ctr_def discs sels |
49591
91b228e26348
generate high-level "coinduct" and "strong_coinduct" properties
blanchet
parents:
49590
diff
changeset
|
357 |
else |
52966 | 358 |
mk_coinduct_distinct_ctrs_tac ctxt discs discs') ks discss)) ks ctr_defs discss selss) |
49590 | 359 |
end; |
360 |
||
55803
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
traytel
parents:
55642
diff
changeset
|
361 |
fun mk_coinduct_tac ctxt rel_eqs' nn ns dtor_coinduct' pre_rel_defs fp_abs_inverses abs_inverses |
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
traytel
parents:
55642
diff
changeset
|
362 |
dtor_ctors exhausts ctr_defss discsss selsss = |
52324 | 363 |
HEADGOAL (rtac dtor_coinduct' THEN' |
55803
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
traytel
parents:
55642
diff
changeset
|
364 |
EVERY' (map10 (mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn) |
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
traytel
parents:
55642
diff
changeset
|
365 |
(1 upto nn) ns pre_rel_defs fp_abs_inverses abs_inverses dtor_ctors exhausts ctr_defss discsss |
74d3fe9031d8
joint work with blanchet: intermediate typedef for the input to fp-operations
traytel
parents:
55642
diff
changeset
|
366 |
selsss)); |
49590 | 367 |
|
57983
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
368 |
fun mk_map_disc_iff_tac ctxt ct exhaust discs maps = |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
369 |
TRYALL Goal.conjunction_tac THEN |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
370 |
ALLGOALS (rtac (cterm_instantiate_pos [SOME ct] exhaust) THEN_ALL_NEW |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
371 |
REPEAT_DETERM o hyp_subst_tac ctxt) THEN |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
372 |
unfold_thms_tac ctxt maps THEN |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
373 |
unfold_thms_tac ctxt (map (fn thm => thm RS eqFalseI |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
374 |
handle THM _ => thm RS eqTrueI) discs) THEN |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
375 |
ALLGOALS (rtac refl ORELSE' rtac TrueI); |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
376 |
|
58326
7e142efcee1a
make 'rel_sel' and 'map_sel' tactics more robust
desharna
parents:
58181
diff
changeset
|
377 |
fun mk_map_sel_tac ctxt ct exhaust discs maps sels map_id0s = |
57983
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
378 |
TRYALL Goal.conjunction_tac THEN |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
379 |
ALLGOALS (rtac (cterm_instantiate_pos [SOME ct] exhaust) THEN_ALL_NEW |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
380 |
REPEAT_DETERM o hyp_subst_tac ctxt) THEN |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
381 |
unfold_thms_tac ctxt ((discs RL [eqTrueI, eqFalseI]) @ |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
382 |
@{thms not_True_eq_False not_False_eq_True}) THEN |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
383 |
TRYALL (etac FalseE ORELSE' etac @{thm TrueE}) THEN |
58326
7e142efcee1a
make 'rel_sel' and 'map_sel' tactics more robust
desharna
parents:
58181
diff
changeset
|
384 |
unfold_thms_tac ctxt (@{thm id_apply} :: maps @ sels @ map_id0s) THEN |
57983
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
385 |
ALLGOALS (rtac refl); |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
386 |
|
57824
615223745d4e
made tactic more robust w.r.t. dead variables; tuned;
desharna
parents:
57670
diff
changeset
|
387 |
fun mk_rel_cases_tac ctxt ct1 ct2 exhaust injects rel_injects distincts rel_distincts rel_eqs= |
57525 | 388 |
HEADGOAL (rtac (cterm_instantiate_pos [SOME ct1] exhaust) THEN_ALL_NEW |
389 |
rtac (cterm_instantiate_pos [SOME ct2] exhaust) THEN_ALL_NEW |
|
390 |
hyp_subst_tac ctxt) THEN |
|
57824
615223745d4e
made tactic more robust w.r.t. dead variables; tuned;
desharna
parents:
57670
diff
changeset
|
391 |
unfold_thms_tac ctxt (rel_eqs @ injects @ rel_injects @ @{thms conj_imp_eq_imp_imp simp_thms(6) |
57525 | 392 |
True_implies_equals conj_imp_eq_imp_imp} @ |
57529 | 393 |
map (fn thm => thm RS eqFalseI) (distincts @ rel_distincts) @ |
394 |
map (fn thm => thm RS eqTrueI) rel_injects) THEN |
|
57562 | 395 |
TRYALL (atac ORELSE' etac FalseE ORELSE' |
396 |
(REPEAT_DETERM o dtac @{thm meta_spec} THEN' |
|
397 |
TRY o filter_prems_tac |
|
398 |
(forall (curry (op <>) (HOLogic.mk_Trueprop @{term False})) o Logic.strip_imp_prems) THEN' |
|
399 |
REPEAT_DETERM o (dtac @{thm meta_mp} THEN' rtac refl) THEN' Goal.assume_rule_tac ctxt)); |
|
57525 | 400 |
|
57301
7b997028aaac
generate 'rel_coinduct0' theorem for codatatypes
desharna
parents:
57152
diff
changeset
|
401 |
fun mk_rel_coinduct0_tac ctxt dtor_rel_coinduct cts assms exhausts discss selss ctor_defss |
57558
6bb3dd7f8097
took out 'rel_cases' for now because of failing tactic
blanchet
parents:
57529
diff
changeset
|
402 |
dtor_ctors ctor_injects abs_injects rel_pre_defs abs_inverses nesting_rel_eqs = |
57301
7b997028aaac
generate 'rel_coinduct0' theorem for codatatypes
desharna
parents:
57152
diff
changeset
|
403 |
rtac dtor_rel_coinduct 1 THEN |
57670 | 404 |
EVERY (map11 (fn ct => fn assm => fn exhaust => fn discs => fn sels => fn ctor_defs => |
405 |
fn dtor_ctor => fn ctor_inject => fn abs_inject => fn rel_pre_def => fn abs_inverse => |
|
406 |
(rtac exhaust THEN_ALL_NEW (rtac exhaust THEN_ALL_NEW |
|
58093 | 407 |
(dtac (rotate_prems ~1 (cterm_instantiate_pos [NONE, NONE, NONE, NONE, SOME ct] |
57670 | 408 |
@{thm arg_cong2} RS iffD1)) THEN' |
409 |
atac THEN' atac THEN' hyp_subst_tac ctxt THEN' dtac assm THEN' |
|
410 |
REPEAT_DETERM o etac conjE))) 1 THEN |
|
57668 | 411 |
unfold_thms_tac ctxt ((discs RL [eqTrueI, eqFalseI]) @ sels @ simp_thms') THEN |
57528 | 412 |
unfold_thms_tac ctxt (dtor_ctor :: rel_pre_def :: abs_inverse :: ctor_inject :: |
58128 | 413 |
abs_inject :: ctor_defs @ nesting_rel_eqs @ simp_thms' @ |
58353 | 414 |
@{thms id_bnf_def rel_sum_simps rel_prod_apply vimage2p_def Inl_Inr_False |
415 |
iffD2[OF eq_False Inr_not_Inl] sum.inject prod.inject}) THEN |
|
57301
7b997028aaac
generate 'rel_coinduct0' theorem for codatatypes
desharna
parents:
57152
diff
changeset
|
416 |
REPEAT_DETERM (HEADGOAL ((REPEAT_DETERM o etac conjE) THEN' (REPEAT_DETERM o rtac conjI) THEN' |
7b997028aaac
generate 'rel_coinduct0' theorem for codatatypes
desharna
parents:
57152
diff
changeset
|
417 |
(rtac refl ORELSE' atac)))) |
7b997028aaac
generate 'rel_coinduct0' theorem for codatatypes
desharna
parents:
57152
diff
changeset
|
418 |
cts assms exhausts discss selss ctor_defss dtor_ctors ctor_injects abs_injects rel_pre_defs |
7b997028aaac
generate 'rel_coinduct0' theorem for codatatypes
desharna
parents:
57152
diff
changeset
|
419 |
abs_inverses); |
7b997028aaac
generate 'rel_coinduct0' theorem for codatatypes
desharna
parents:
57152
diff
changeset
|
420 |
|
57471 | 421 |
fun mk_rel_induct0_tac ctxt ctor_rel_induct assms cterms exhausts ctor_defss ctor_injects |
422 |
rel_pre_list_defs Abs_inverses nesting_rel_eqs = |
|
423 |
rtac ctor_rel_induct 1 THEN EVERY (map6 (fn cterm => fn exhaust => fn ctor_defs => |
|
424 |
fn ctor_inject => fn rel_pre_list_def => fn Abs_inverse => |
|
425 |
HEADGOAL (rtac exhaust THEN_ALL_NEW (rtac exhaust THEN_ALL_NEW |
|
426 |
(rtac (cterm_instantiate_pos (replicate 4 NONE @ [SOME cterm]) @{thm arg_cong2} RS iffD2) |
|
427 |
THEN' atac THEN' atac THEN' TRY o resolve_tac assms))) THEN |
|
57700 | 428 |
unfold_thms_tac ctxt (ctor_inject :: rel_pre_list_def :: ctor_defs @ nesting_rel_eqs @ |
58353 | 429 |
@{thms id_bnf_def vimage2p_def}) THEN |
57471 | 430 |
TRYALL (hyp_subst_tac ctxt) THEN |
57824
615223745d4e
made tactic more robust w.r.t. dead variables; tuned;
desharna
parents:
57670
diff
changeset
|
431 |
unfold_thms_tac ctxt (Abs_inverse :: @{thms rel_sum_simps rel_prod_apply Inl_Inr_False |
57471 | 432 |
Inr_Inl_False sum.inject prod.inject}) THEN |
58020 | 433 |
TRYALL (rtac refl ORELSE' etac FalseE ORELSE' (REPEAT_DETERM o etac conjE) THEN' atac)) |
57471 | 434 |
cterms exhausts ctor_defss ctor_injects rel_pre_list_defs Abs_inverses); |
435 |
||
58326
7e142efcee1a
make 'rel_sel' and 'map_sel' tactics more robust
desharna
parents:
58181
diff
changeset
|
436 |
fun mk_rel_sel_tac ctxt ct1 ct2 exhaust discs sels rel_injects distincts rel_distincts rel_eqs = |
57563 | 437 |
HEADGOAL (rtac (cterm_instantiate_pos [SOME ct1] exhaust) THEN_ALL_NEW |
438 |
rtac (cterm_instantiate_pos [SOME ct2] exhaust) THEN_ALL_NEW |
|
439 |
hyp_subst_tac ctxt) THEN |
|
58326
7e142efcee1a
make 'rel_sel' and 'map_sel' tactics more robust
desharna
parents:
58181
diff
changeset
|
440 |
unfold_thms_tac ctxt (sels @ rel_injects @ rel_eqs @ @{thms simp_thms(6,7,8,11,12,15,16,21,22,24)} @ |
57563 | 441 |
((discs @ distincts) RL @{thms iffD2[OF eq_True] iffD2[OF eq_False]}) @ |
442 |
(rel_injects RL @{thms iffD2[OF eq_True]}) @ |
|
443 |
(rel_distincts RL @{thms iffD2[OF eq_False]})) THEN |
|
444 |
TRYALL (resolve_tac [TrueI, refl]); |
|
445 |
||
57983
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
446 |
fun mk_set_sel_tac ctxt ct exhaust discs sels sets = |
57152 | 447 |
TRYALL Goal.conjunction_tac THEN |
448 |
ALLGOALS (rtac (cterm_instantiate_pos [SOME ct] exhaust) THEN_ALL_NEW |
|
449 |
REPEAT_DETERM o hyp_subst_tac ctxt) THEN |
|
57529 | 450 |
unfold_thms_tac ctxt ((discs RL [eqTrueI, eqFalseI]) @ |
57152 | 451 |
@{thms not_True_eq_False not_False_eq_True}) THEN |
452 |
TRYALL (etac FalseE ORELSE' etac @{thm TrueE}) THEN |
|
57528 | 453 |
unfold_thms_tac ctxt (sels @ sets) THEN |
57558
6bb3dd7f8097
took out 'rel_cases' for now because of failing tactic
blanchet
parents:
57529
diff
changeset
|
454 |
ALLGOALS (REPEAT o (resolve_tac @{thms UnI1 UnI2 imageI} ORELSE' |
57152 | 455 |
eresolve_tac @{thms UN_I UN_I[rotated] imageE} ORELSE' |
456 |
hyp_subst_tac ctxt) THEN' |
|
457 |
(rtac @{thm singletonI} ORELSE' atac)); |
|
458 |
||
57893 | 459 |
fun mk_set_cases_tac ctxt ct assms exhaust sets = |
460 |
HEADGOAL (rtac (cterm_instantiate_pos [SOME ct] exhaust) THEN_ALL_NEW hyp_subst_tac ctxt) THEN |
|
461 |
unfold_thms_tac ctxt sets THEN |
|
462 |
REPEAT_DETERM (HEADGOAL |
|
463 |
(eresolve_tac @{thms FalseE emptyE singletonE UnE UN_E insertE} ORELSE' |
|
464 |
hyp_subst_tac ctxt ORELSE' |
|
465 |
SELECT_GOAL (SOLVE (HEADGOAL (eresolve_tac assms THEN' REPEAT_DETERM o atac))))); |
|
466 |
||
57891 | 467 |
fun mk_set_intros_tac ctxt sets = |
468 |
TRYALL Goal.conjunction_tac THEN |
|
469 |
unfold_thms_tac ctxt sets THEN |
|
470 |
TRYALL (REPEAT o |
|
57893 | 471 |
(resolve_tac @{thms UnI1 UnI2} ORELSE' |
472 |
eresolve_tac @{thms UN_I UN_I[rotated]}) THEN' (rtac @{thm singletonI} ORELSE' atac)); |
|
57891 | 473 |
|
57700 | 474 |
fun mk_set_induct0_tac ctxt cts assms dtor_set_inducts exhausts set_pre_defs ctor_defs dtor_ctors |
475 |
Abs_pre_inverses = |
|
476 |
let |
|
58417
fa50722ad6cb
make 'set_induct0' tactic more robust w.r.t multiple arguments constructors
desharna
parents:
58359
diff
changeset
|
477 |
val assms_tac = |
fa50722ad6cb
make 'set_induct0' tactic more robust w.r.t multiple arguments constructors
desharna
parents:
58359
diff
changeset
|
478 |
let val assms' = map (unfold_thms ctxt (@{thm id_bnf_def} :: ctor_defs)) assms in |
fa50722ad6cb
make 'set_induct0' tactic more robust w.r.t multiple arguments constructors
desharna
parents:
58359
diff
changeset
|
479 |
fold (curry (op ORELSE')) (map (fn thm => |
fa50722ad6cb
make 'set_induct0' tactic more robust w.r.t multiple arguments constructors
desharna
parents:
58359
diff
changeset
|
480 |
funpow (length (prems_of thm)) (fn tac => tac THEN' atac) (rtac thm)) assms') |
fa50722ad6cb
make 'set_induct0' tactic more robust w.r.t multiple arguments constructors
desharna
parents:
58359
diff
changeset
|
481 |
(etac FalseE) |
fa50722ad6cb
make 'set_induct0' tactic more robust w.r.t multiple arguments constructors
desharna
parents:
58359
diff
changeset
|
482 |
end; |
57700 | 483 |
val exhausts' = map (fn thm => thm RS @{thm asm_rl[of "P x y" for P x y]}) exhausts |
484 |
|> map2 (fn ct => cterm_instantiate_pos [NONE, SOME ct]) cts; |
|
485 |
in |
|
486 |
ALLGOALS (resolve_tac dtor_set_inducts) THEN |
|
487 |
TRYALL (resolve_tac exhausts' THEN_ALL_NEW |
|
488 |
(resolve_tac (map (fn ct => refl RS |
|
489 |
cterm_instantiate_pos (replicate 4 NONE @ [SOME ct]) @{thm arg_cong2} RS iffD2) cts) |
|
490 |
THEN' atac THEN' hyp_subst_tac ctxt)) THEN |
|
491 |
unfold_thms_tac ctxt (Abs_pre_inverses @ dtor_ctors @ set_pre_defs @ ctor_defs @ |
|
58353 | 492 |
@{thms id_bnf_def o_apply sum_set_simps prod_set_simps UN_empty UN_insert Un_empty_left |
493 |
Un_empty_right empty_iff singleton_iff}) THEN |
|
58417
fa50722ad6cb
make 'set_induct0' tactic more robust w.r.t multiple arguments constructors
desharna
parents:
58359
diff
changeset
|
494 |
REPEAT (HEADGOAL (hyp_subst_tac ctxt ORELSE' eresolve_tac @{thms UN_E UnE singletonE} ORELSE' |
fa50722ad6cb
make 'set_induct0' tactic more robust w.r.t multiple arguments constructors
desharna
parents:
58359
diff
changeset
|
495 |
assms_tac)) |
57700 | 496 |
end; |
497 |
||
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
498 |
end; |