author | desharna |
Fri, 12 Sep 2014 13:50:51 +0200 | |
changeset 58327 | a147bd03cad0 |
parent 58326 | 7e142efcee1a |
child 58352 | 37745650a3f4 |
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_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_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 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 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 @{thm 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 THEN' rotate_tac ~1) k) THEN |
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ALLGOALS (REPEAT_ALL_NEW (atac ORELSE' rtac refl ORELSE' dtac @{thm rel_funD})) |
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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 (@{thm 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 @{thm 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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unfold_thms_tac ctxt (ctr_def :: 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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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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let |
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val ss = ss_only (pre_map_def :: abs_inverse :: map_ident0s @ corec_unfold_thms @ |
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@{thms o_apply vimage2p_def if_True if_False}) ctxt; |
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in |
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unfold_thms_tac ctxt (ctr_def :: corec_defs) THEN |
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HEADGOAL (rtac (ctor_dtor_corec RS trans) THEN' asm_simp_tac ss) THEN_MAYBE |
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HEADGOAL (rtac refl ORELSE' rtac (@{thm unit_eq} RS arg_cong)) |
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end; |
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fun mk_corec_disc_iff_tac case_splits' corecs discs ctxt = |
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EVERY (map3 (fn case_split_tac => fn corec_thm => fn disc => |
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HEADGOAL case_split_tac THEN unfold_thms_tac ctxt [corec_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]) corecs 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 fp_abs_inverses abs_inverses set_maps |
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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 @ fp_abs_inverses @ abs_inverses @ set_maps @ |
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sumprod_thms_set)), |
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solve_prem_prem_tac ctxt]) (rev kks))); |
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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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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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proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
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189 |
if r > 0 then ALLGOALS (Goal.norm_hhf_tac ctxt) else all_tac, HEADGOAL atac, |
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|
190 |
mk_induct_leverage_prem_prems_tac ctxt nn kks fp_abs_inverses abs_inverses set_maps |
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|
191 |
pre_set_defs] |
49391 | 192 |
end; |
49368 | 193 |
|
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194 |
fun mk_induct_tac ctxt nn ns mss kkss ctr_defs ctor_induct' fp_abs_inverses abs_inverses set_maps |
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|
195 |
pre_set_defss = |
49590 | 196 |
let val n = Integer.sum ns in |
54922 | 197 |
unfold_thms_tac ctxt ctr_defs THEN HEADGOAL (rtac ctor_induct') THEN |
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|
198 |
co_induct_inst_as_projs_tac ctxt 0 THEN |
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|
199 |
EVERY (map4 (EVERY oooo map3 o |
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|
200 |
mk_induct_discharge_prem_tac ctxt nn n fp_abs_inverses abs_inverses set_maps) |
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|
201 |
pre_set_defss mss (unflat mss (1 upto n)) kkss) |
49368 | 202 |
end; |
203 |
||
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204 |
fun mk_coinduct_same_ctr_tac ctxt rel_eqs pre_rel_def fp_abs_inverse abs_inverse dtor_ctor ctr_def |
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205 |
discs sels = |
51798 | 206 |
hyp_subst_tac ctxt THEN' |
49665 | 207 |
CONVERSION (hhf_concl_conv |
208 |
(Conv.top_conv (K (Conv.try_conv (Conv.rewr_conv ctr_def))) ctxt) ctxt) THEN' |
|
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fixed simplification of prod and sum relators to avoid issues with e.g. codata ('a, 'b) k = K "'a + 'b"
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|
209 |
SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: dtor_ctor :: sels)) THEN' |
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|
210 |
SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: fp_abs_inverse :: abs_inverse :: dtor_ctor :: |
55966 | 211 |
sels @ sumprod_thms_rel @ @{thms o_apply vimage2p_def})) THEN' |
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212 |
(atac ORELSE' REPEAT o etac conjE THEN' |
56765 | 213 |
full_simp_tac (ss_only (no_refl discs @ rel_eqs @ more_simp_thms) ctxt) THEN' |
54241 | 214 |
REPEAT o etac conjE THEN_MAYBE' REPEAT o hyp_subst_tac ctxt THEN' |
215 |
REPEAT o (resolve_tac [refl, conjI] ORELSE' atac)); |
|
49590 | 216 |
|
52966 | 217 |
fun mk_coinduct_distinct_ctrs_tac ctxt discs discs' = |
54198
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218 |
let |
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219 |
val discs'' = map (perhaps (try (fn th => th RS @{thm notnotD}))) (discs @ discs') |
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220 |
|> distinct Thm.eq_thm_prop; |
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|
221 |
in |
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|
222 |
hyp_subst_tac ctxt THEN' REPEAT o etac conjE THEN' |
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|
223 |
full_simp_tac (ss_only (refl :: no_refl discs'' @ basic_simp_thms) ctxt) |
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224 |
end; |
49590 | 225 |
|
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|
226 |
fun mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn kk n pre_rel_def fp_abs_inverse abs_inverse |
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|
227 |
dtor_ctor exhaust ctr_defs discss selss = |
49590 | 228 |
let val ks = 1 upto n in |
54837 | 229 |
EVERY' ([rtac allI, rtac allI, rtac impI, select_prem_tac nn (dtac meta_spec) kk, |
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|
230 |
dtac meta_spec, dtac meta_mp, atac, rtac exhaust, K (co_induct_inst_as_projs_tac ctxt 0), |
51798 | 231 |
hyp_subst_tac ctxt] @ |
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|
232 |
map4 (fn k => fn ctr_def => fn discs => fn sels => |
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|
233 |
EVERY' ([rtac exhaust, K (co_induct_inst_as_projs_tac ctxt 1)] @ |
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|
234 |
map2 (fn k' => fn discs' => |
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|
235 |
if k' = k then |
55803
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changeset
|
236 |
mk_coinduct_same_ctr_tac ctxt rel_eqs' pre_rel_def fp_abs_inverse abs_inverse |
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|
237 |
dtor_ctor ctr_def discs sels |
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|
238 |
else |
52966 | 239 |
mk_coinduct_distinct_ctrs_tac ctxt discs discs') ks discss)) ks ctr_defs discss selss) |
49590 | 240 |
end; |
241 |
||
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changeset
|
242 |
fun mk_coinduct_tac ctxt rel_eqs' nn ns dtor_coinduct' pre_rel_defs fp_abs_inverses abs_inverses |
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changeset
|
243 |
dtor_ctors exhausts ctr_defss discsss selsss = |
52324 | 244 |
HEADGOAL (rtac dtor_coinduct' THEN' |
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changeset
|
245 |
EVERY' (map10 (mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn) |
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changeset
|
246 |
(1 upto nn) ns pre_rel_defs fp_abs_inverses abs_inverses dtor_ctors exhausts ctr_defss discsss |
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changeset
|
247 |
selsss)); |
49590 | 248 |
|
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changeset
|
249 |
fun mk_map_disc_iff_tac ctxt ct exhaust discs maps = |
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changeset
|
250 |
TRYALL Goal.conjunction_tac THEN |
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changeset
|
251 |
ALLGOALS (rtac (cterm_instantiate_pos [SOME ct] exhaust) THEN_ALL_NEW |
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changeset
|
252 |
REPEAT_DETERM o hyp_subst_tac ctxt) THEN |
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changeset
|
253 |
unfold_thms_tac ctxt maps THEN |
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parents:
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diff
changeset
|
254 |
unfold_thms_tac ctxt (map (fn thm => thm RS eqFalseI |
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parents:
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diff
changeset
|
255 |
handle THM _ => thm RS eqTrueI) discs) THEN |
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changeset
|
256 |
ALLGOALS (rtac refl ORELSE' rtac TrueI); |
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reordered some (co)datatype property names for more consistency
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parents:
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diff
changeset
|
257 |
|
58326
7e142efcee1a
make 'rel_sel' and 'map_sel' tactics more robust
desharna
parents:
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diff
changeset
|
258 |
fun mk_map_sel_tac ctxt ct exhaust discs maps sels map_id0s = |
57983
6edc3529bb4e
reordered some (co)datatype property names for more consistency
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parents:
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diff
changeset
|
259 |
TRYALL Goal.conjunction_tac THEN |
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diff
changeset
|
260 |
ALLGOALS (rtac (cterm_instantiate_pos [SOME ct] exhaust) THEN_ALL_NEW |
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reordered some (co)datatype property names for more consistency
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diff
changeset
|
261 |
REPEAT_DETERM o hyp_subst_tac ctxt) THEN |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
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parents:
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diff
changeset
|
262 |
unfold_thms_tac ctxt ((discs RL [eqTrueI, eqFalseI]) @ |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
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parents:
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diff
changeset
|
263 |
@{thms not_True_eq_False not_False_eq_True}) THEN |
6edc3529bb4e
reordered some (co)datatype property names for more consistency
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parents:
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diff
changeset
|
264 |
TRYALL (etac FalseE ORELSE' etac @{thm TrueE}) THEN |
58326
7e142efcee1a
make 'rel_sel' and 'map_sel' tactics more robust
desharna
parents:
58181
diff
changeset
|
265 |
unfold_thms_tac ctxt (@{thm id_apply} :: maps @ sels @ map_id0s) THEN |
57983
6edc3529bb4e
reordered some (co)datatype property names for more consistency
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parents:
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diff
changeset
|
266 |
ALLGOALS (rtac refl); |
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reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
267 |
|
57824
615223745d4e
made tactic more robust w.r.t. dead variables; tuned;
desharna
parents:
57670
diff
changeset
|
268 |
fun mk_rel_cases_tac ctxt ct1 ct2 exhaust injects rel_injects distincts rel_distincts rel_eqs= |
57525 | 269 |
HEADGOAL (rtac (cterm_instantiate_pos [SOME ct1] exhaust) THEN_ALL_NEW |
270 |
rtac (cterm_instantiate_pos [SOME ct2] exhaust) THEN_ALL_NEW |
|
271 |
hyp_subst_tac ctxt) THEN |
|
57824
615223745d4e
made tactic more robust w.r.t. dead variables; tuned;
desharna
parents:
57670
diff
changeset
|
272 |
unfold_thms_tac ctxt (rel_eqs @ injects @ rel_injects @ @{thms conj_imp_eq_imp_imp simp_thms(6) |
57525 | 273 |
True_implies_equals conj_imp_eq_imp_imp} @ |
57529 | 274 |
map (fn thm => thm RS eqFalseI) (distincts @ rel_distincts) @ |
275 |
map (fn thm => thm RS eqTrueI) rel_injects) THEN |
|
57562 | 276 |
TRYALL (atac ORELSE' etac FalseE ORELSE' |
277 |
(REPEAT_DETERM o dtac @{thm meta_spec} THEN' |
|
278 |
TRY o filter_prems_tac |
|
279 |
(forall (curry (op <>) (HOLogic.mk_Trueprop @{term False})) o Logic.strip_imp_prems) THEN' |
|
280 |
REPEAT_DETERM o (dtac @{thm meta_mp} THEN' rtac refl) THEN' Goal.assume_rule_tac ctxt)); |
|
57525 | 281 |
|
57301
7b997028aaac
generate 'rel_coinduct0' theorem for codatatypes
desharna
parents:
57152
diff
changeset
|
282 |
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
|
283 |
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
|
284 |
rtac dtor_rel_coinduct 1 THEN |
57670 | 285 |
EVERY (map11 (fn ct => fn assm => fn exhaust => fn discs => fn sels => fn ctor_defs => |
286 |
fn dtor_ctor => fn ctor_inject => fn abs_inject => fn rel_pre_def => fn abs_inverse => |
|
287 |
(rtac exhaust THEN_ALL_NEW (rtac exhaust THEN_ALL_NEW |
|
58093 | 288 |
(dtac (rotate_prems ~1 (cterm_instantiate_pos [NONE, NONE, NONE, NONE, SOME ct] |
57670 | 289 |
@{thm arg_cong2} RS iffD1)) THEN' |
290 |
atac THEN' atac THEN' hyp_subst_tac ctxt THEN' dtac assm THEN' |
|
291 |
REPEAT_DETERM o etac conjE))) 1 THEN |
|
57668 | 292 |
unfold_thms_tac ctxt ((discs RL [eqTrueI, eqFalseI]) @ sels @ simp_thms') THEN |
57528 | 293 |
unfold_thms_tac ctxt (dtor_ctor :: rel_pre_def :: abs_inverse :: ctor_inject :: |
58128 | 294 |
abs_inject :: ctor_defs @ nesting_rel_eqs @ simp_thms' @ |
58181 | 295 |
@{thms BNF_Composition.id_bnf_def rel_sum_simps rel_prod_apply vimage2p_def |
58128 | 296 |
Inl_Inr_False 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
|
297 |
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
|
298 |
(rtac refl ORELSE' atac)))) |
7b997028aaac
generate 'rel_coinduct0' theorem for codatatypes
desharna
parents:
57152
diff
changeset
|
299 |
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
|
300 |
abs_inverses); |
7b997028aaac
generate 'rel_coinduct0' theorem for codatatypes
desharna
parents:
57152
diff
changeset
|
301 |
|
57471 | 302 |
fun mk_rel_induct0_tac ctxt ctor_rel_induct assms cterms exhausts ctor_defss ctor_injects |
303 |
rel_pre_list_defs Abs_inverses nesting_rel_eqs = |
|
304 |
rtac ctor_rel_induct 1 THEN EVERY (map6 (fn cterm => fn exhaust => fn ctor_defs => |
|
305 |
fn ctor_inject => fn rel_pre_list_def => fn Abs_inverse => |
|
306 |
HEADGOAL (rtac exhaust THEN_ALL_NEW (rtac exhaust THEN_ALL_NEW |
|
307 |
(rtac (cterm_instantiate_pos (replicate 4 NONE @ [SOME cterm]) @{thm arg_cong2} RS iffD2) |
|
308 |
THEN' atac THEN' atac THEN' TRY o resolve_tac assms))) THEN |
|
57700 | 309 |
unfold_thms_tac ctxt (ctor_inject :: rel_pre_list_def :: ctor_defs @ nesting_rel_eqs @ |
58181 | 310 |
@{thms BNF_Composition.id_bnf_def vimage2p_def}) THEN |
57471 | 311 |
TRYALL (hyp_subst_tac ctxt) THEN |
57824
615223745d4e
made tactic more robust w.r.t. dead variables; tuned;
desharna
parents:
57670
diff
changeset
|
312 |
unfold_thms_tac ctxt (Abs_inverse :: @{thms rel_sum_simps rel_prod_apply Inl_Inr_False |
57471 | 313 |
Inr_Inl_False sum.inject prod.inject}) THEN |
58020 | 314 |
TRYALL (rtac refl ORELSE' etac FalseE ORELSE' (REPEAT_DETERM o etac conjE) THEN' atac)) |
57471 | 315 |
cterms exhausts ctor_defss ctor_injects rel_pre_list_defs Abs_inverses); |
316 |
||
58326
7e142efcee1a
make 'rel_sel' and 'map_sel' tactics more robust
desharna
parents:
58181
diff
changeset
|
317 |
fun mk_rel_sel_tac ctxt ct1 ct2 exhaust discs sels rel_injects distincts rel_distincts rel_eqs = |
57563 | 318 |
HEADGOAL (rtac (cterm_instantiate_pos [SOME ct1] exhaust) THEN_ALL_NEW |
319 |
rtac (cterm_instantiate_pos [SOME ct2] exhaust) THEN_ALL_NEW |
|
320 |
hyp_subst_tac ctxt) THEN |
|
58326
7e142efcee1a
make 'rel_sel' and 'map_sel' tactics more robust
desharna
parents:
58181
diff
changeset
|
321 |
unfold_thms_tac ctxt (sels @ rel_injects @ rel_eqs @ @{thms simp_thms(6,7,8,11,12,15,16,21,22,24)} @ |
57563 | 322 |
((discs @ distincts) RL @{thms iffD2[OF eq_True] iffD2[OF eq_False]}) @ |
323 |
(rel_injects RL @{thms iffD2[OF eq_True]}) @ |
|
324 |
(rel_distincts RL @{thms iffD2[OF eq_False]})) THEN |
|
325 |
TRYALL (resolve_tac [TrueI, refl]); |
|
326 |
||
57983
6edc3529bb4e
reordered some (co)datatype property names for more consistency
blanchet
parents:
57893
diff
changeset
|
327 |
fun mk_set_sel_tac ctxt ct exhaust discs sels sets = |
57152 | 328 |
TRYALL Goal.conjunction_tac THEN |
329 |
ALLGOALS (rtac (cterm_instantiate_pos [SOME ct] exhaust) THEN_ALL_NEW |
|
330 |
REPEAT_DETERM o hyp_subst_tac ctxt) THEN |
|
57529 | 331 |
unfold_thms_tac ctxt ((discs RL [eqTrueI, eqFalseI]) @ |
57152 | 332 |
@{thms not_True_eq_False not_False_eq_True}) THEN |
333 |
TRYALL (etac FalseE ORELSE' etac @{thm TrueE}) THEN |
|
57528 | 334 |
unfold_thms_tac ctxt (sels @ sets) THEN |
57558
6bb3dd7f8097
took out 'rel_cases' for now because of failing tactic
blanchet
parents:
57529
diff
changeset
|
335 |
ALLGOALS (REPEAT o (resolve_tac @{thms UnI1 UnI2 imageI} ORELSE' |
57152 | 336 |
eresolve_tac @{thms UN_I UN_I[rotated] imageE} ORELSE' |
337 |
hyp_subst_tac ctxt) THEN' |
|
338 |
(rtac @{thm singletonI} ORELSE' atac)); |
|
339 |
||
57893 | 340 |
fun mk_set_cases_tac ctxt ct assms exhaust sets = |
341 |
HEADGOAL (rtac (cterm_instantiate_pos [SOME ct] exhaust) THEN_ALL_NEW hyp_subst_tac ctxt) THEN |
|
342 |
unfold_thms_tac ctxt sets THEN |
|
343 |
REPEAT_DETERM (HEADGOAL |
|
344 |
(eresolve_tac @{thms FalseE emptyE singletonE UnE UN_E insertE} ORELSE' |
|
345 |
hyp_subst_tac ctxt ORELSE' |
|
346 |
SELECT_GOAL (SOLVE (HEADGOAL (eresolve_tac assms THEN' REPEAT_DETERM o atac))))); |
|
347 |
||
57891 | 348 |
fun mk_set_intros_tac ctxt sets = |
349 |
TRYALL Goal.conjunction_tac THEN |
|
350 |
unfold_thms_tac ctxt sets THEN |
|
351 |
TRYALL (REPEAT o |
|
57893 | 352 |
(resolve_tac @{thms UnI1 UnI2} ORELSE' |
353 |
eresolve_tac @{thms UN_I UN_I[rotated]}) THEN' (rtac @{thm singletonI} ORELSE' atac)); |
|
57891 | 354 |
|
57700 | 355 |
fun mk_set_induct0_tac ctxt cts assms dtor_set_inducts exhausts set_pre_defs ctor_defs dtor_ctors |
356 |
Abs_pre_inverses = |
|
357 |
let |
|
358 |
val assms_ctor_defs = |
|
58181 | 359 |
map (unfold_thms ctxt (@{thm BNF_Composition.id_bnf_def} :: ctor_defs)) assms; |
57700 | 360 |
val exhausts' = map (fn thm => thm RS @{thm asm_rl[of "P x y" for P x y]}) exhausts |
361 |
|> map2 (fn ct => cterm_instantiate_pos [NONE, SOME ct]) cts; |
|
362 |
in |
|
363 |
ALLGOALS (resolve_tac dtor_set_inducts) THEN |
|
364 |
TRYALL (resolve_tac exhausts' THEN_ALL_NEW |
|
365 |
(resolve_tac (map (fn ct => refl RS |
|
366 |
cterm_instantiate_pos (replicate 4 NONE @ [SOME ct]) @{thm arg_cong2} RS iffD2) cts) |
|
367 |
THEN' atac THEN' hyp_subst_tac ctxt)) THEN |
|
368 |
unfold_thms_tac ctxt (Abs_pre_inverses @ dtor_ctors @ set_pre_defs @ ctor_defs @ |
|
58181 | 369 |
@{thms BNF_Composition.id_bnf_def o_apply sum_set_simps prod_set_simps UN_empty UN_insert |
57700 | 370 |
Un_empty_left Un_empty_right empty_iff singleton_iff}) THEN |
371 |
REPEAT_DETERM (HEADGOAL |
|
372 |
(TRY o etac UnE THEN' TRY o etac @{thm singletonE} THEN' TRY o hyp_subst_tac ctxt THEN' |
|
373 |
REPEAT_DETERM o eresolve_tac @{thms UN_E UnE singletonE} THEN' |
|
374 |
fold (curry (op ORELSE')) (map (fn thm => |
|
375 |
funpow (length (prems_of thm)) (fn tac => tac THEN' atac) (rtac thm)) assms_ctor_defs) |
|
376 |
(etac FalseE))) |
|
377 |
end; |
|
378 |
||
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
diff
changeset
|
379 |
end; |