author | desharna |
Tue, 24 Jun 2014 13:48:14 +0200 | |
changeset 57303 | 498a62e65f5f |
parent 57301 | 7b997028aaac |
child 57399 | cfc19f0a6261 |
permissions | -rw-r--r-- |
55061 | 1 |
(* Title: HOL/Tools/BNF/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 sumprod_thms_map: thm list |
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val sumprod_thms_set: thm list |
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val sumprod_thms_rel: thm list |
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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_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_corec_iff_tac: thm list -> thm list -> thm list -> Proof.context -> tactic |
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val mk_disc_map_iff_tac: Proof.context -> cterm -> thm -> thm list -> 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_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_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 -> tactic |
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val mk_sel_map_tac: Proof.context -> cterm -> thm -> thm list -> thm list -> thm list -> tactic |
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val mk_sel_set_tac: Proof.context -> cterm -> thm -> thm list -> thm list -> thm list -> tactic |
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val mk_set_empty_tac: Proof.context -> cterm -> thm -> 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 sumprod_thms_set = |
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@{thms UN_empty UN_insert Un_empty_left Un_empty_right Un_iff UN_simps(10) UN_iff |
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Union_Un_distrib image_iff o_apply map_prod_simp |
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mem_Collect_eq prod_set_simps map_sum.simps sum_set_simps}; |
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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_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_idents 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_idents @ 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_idents 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_idents @ 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_disc_corec_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 mk_disc_map_iff_tac ctxt ct exhaust discs maps = |
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TRYALL Goal.conjunction_tac THEN |
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ALLGOALS (rtac (cterm_instantiate_pos [SOME ct] exhaust) THEN_ALL_NEW |
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REPEAT_DETERM o hyp_subst_tac ctxt) THEN |
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unfold_thms_tac ctxt maps THEN |
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unfold_thms_tac ctxt (map (fn thm => thm RS @{thm iffD2[OF eq_False]} |
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handle THM _ => thm RS @{thm iffD2[OF eq_True]}) discs) THEN |
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ALLGOALS (rtac refl ORELSE' rtac TrueI); |
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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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if r > 0 then ALLGOALS (Goal.norm_hhf_tac ctxt) else all_tac, HEADGOAL atac, |
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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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end; |
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fun mk_induct_tac ctxt nn ns mss kkss ctr_defs ctor_induct' fp_abs_inverses abs_inverses set_maps |
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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 HEADGOAL (rtac ctor_induct') THEN |
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co_induct_inst_as_projs_tac ctxt 0 THEN |
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EVERY (map4 (EVERY oooo map3 o |
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mk_induct_discharge_prem_tac ctxt nn n fp_abs_inverses abs_inverses set_maps) |
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164 |
pre_set_defss mss (unflat mss (1 upto n)) kkss) |
49368 | 165 |
end; |
166 |
||
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167 |
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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168 |
discs sels = |
51798 | 169 |
hyp_subst_tac ctxt THEN' |
49665 | 170 |
CONVERSION (hhf_concl_conv |
171 |
(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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173 |
SELECT_GOAL (unfold_thms_tac ctxt (pre_rel_def :: fp_abs_inverse :: abs_inverse :: dtor_ctor :: |
55966 | 174 |
sels @ sumprod_thms_rel @ @{thms o_apply vimage2p_def})) THEN' |
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(atac ORELSE' REPEAT o etac conjE THEN' |
56765 | 176 |
full_simp_tac (ss_only (no_refl discs @ rel_eqs @ more_simp_thms) ctxt) THEN' |
54241 | 177 |
REPEAT o etac conjE THEN_MAYBE' REPEAT o hyp_subst_tac ctxt THEN' |
178 |
REPEAT o (resolve_tac [refl, conjI] ORELSE' atac)); |
|
49590 | 179 |
|
52966 | 180 |
fun mk_coinduct_distinct_ctrs_tac ctxt discs discs' = |
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181 |
let |
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val discs'' = map (perhaps (try (fn th => th RS @{thm notnotD}))) (discs @ discs') |
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|> distinct Thm.eq_thm_prop; |
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184 |
in |
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185 |
hyp_subst_tac ctxt THEN' REPEAT o etac conjE THEN' |
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186 |
full_simp_tac (ss_only (refl :: no_refl discs'' @ basic_simp_thms) ctxt) |
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187 |
end; |
49590 | 188 |
|
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189 |
fun mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn kk n pre_rel_def fp_abs_inverse abs_inverse |
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190 |
dtor_ctor exhaust ctr_defs discss selss = |
49590 | 191 |
let val ks = 1 upto n in |
54837 | 192 |
EVERY' ([rtac allI, rtac allI, rtac impI, select_prem_tac nn (dtac meta_spec) kk, |
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193 |
dtac meta_spec, dtac meta_mp, atac, rtac exhaust, K (co_induct_inst_as_projs_tac ctxt 0), |
51798 | 194 |
hyp_subst_tac ctxt] @ |
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195 |
map4 (fn k => fn ctr_def => fn discs => fn sels => |
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EVERY' ([rtac exhaust, K (co_induct_inst_as_projs_tac ctxt 1)] @ |
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197 |
map2 (fn k' => fn discs' => |
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if k' = k then |
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|
199 |
mk_coinduct_same_ctr_tac ctxt rel_eqs' pre_rel_def fp_abs_inverse abs_inverse |
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200 |
dtor_ctor ctr_def discs sels |
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201 |
else |
52966 | 202 |
mk_coinduct_distinct_ctrs_tac ctxt discs discs') ks discss)) ks ctr_defs discss selss) |
49590 | 203 |
end; |
204 |
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205 |
fun mk_coinduct_tac ctxt rel_eqs' nn ns dtor_coinduct' pre_rel_defs fp_abs_inverses abs_inverses |
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|
206 |
dtor_ctors exhausts ctr_defss discsss selsss = |
52324 | 207 |
HEADGOAL (rtac dtor_coinduct' THEN' |
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208 |
EVERY' (map10 (mk_coinduct_discharge_prem_tac ctxt rel_eqs' nn) |
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|
209 |
(1 upto nn) ns pre_rel_defs fp_abs_inverses abs_inverses dtor_ctors exhausts ctr_defss discsss |
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|
210 |
selsss)); |
49590 | 211 |
|
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|
212 |
fun mk_rel_coinduct0_tac ctxt dtor_rel_coinduct cts assms exhausts discss selss ctor_defss |
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|
213 |
dtor_ctors ctor_injects abs_injects rel_pre_defs abs_inverses = |
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|
214 |
rtac dtor_rel_coinduct 1 THEN |
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|
215 |
EVERY (map11 (fn ct => fn assm => fn exhaust => fn discs => fn sels => fn ctor_defs => |
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|
216 |
fn dtor_ctor => fn ctor_inject => fn abs_inject => fn rel_pre_def => fn abs_inverse => |
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|
217 |
(rtac exhaust THEN_ALL_NEW (rtac exhaust THEN_ALL_NEW |
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|
218 |
(dtac (rotate_prems (~1) ((cterm_instantiate_pos [NONE, NONE, NONE, NONE, SOME ct] @{thm |
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|
219 |
arg_cong2}) RS iffD1)) THEN' |
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|
220 |
atac THEN' atac THEN' hyp_subst_tac ctxt THEN' dtac assm THEN' |
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|
221 |
REPEAT_DETERM o etac conjE))) 1 THEN |
57303 | 222 |
Local_Defs.unfold_tac ctxt ((discs RL @{thms iffD2[OF eq_True] iffD2[OF eq_False]}) @ sels |
223 |
@ simp_thms') THEN |
|
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|
224 |
Local_Defs.unfold_tac ctxt (dtor_ctor :: rel_pre_def :: abs_inverse :: ctor_inject :: |
57303 | 225 |
abs_inject :: ctor_defs @ simp_thms' @ @{thms BNF_Comp.id_bnf_comp_def rel_sum_simps |
226 |
rel_prod_apply vimage2p_def Inl_Inr_False iffD2[OF eq_False Inr_not_Inl] sum.inject |
|
227 |
prod.inject}) THEN |
|
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|
228 |
REPEAT_DETERM (HEADGOAL ((REPEAT_DETERM o etac conjE) THEN' (REPEAT_DETERM o rtac conjI) THEN' |
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|
229 |
(rtac refl ORELSE' atac)))) |
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|
230 |
cts assms exhausts discss selss ctor_defss dtor_ctors ctor_injects abs_injects rel_pre_defs |
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|
231 |
abs_inverses); |
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|
232 |
|
57046
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|
233 |
fun mk_sel_map_tac ctxt ct exhaust discs maps sels = |
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|
234 |
TRYALL Goal.conjunction_tac THEN |
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|
235 |
ALLGOALS (rtac (cterm_instantiate_pos [SOME ct] exhaust) THEN_ALL_NEW |
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|
236 |
REPEAT_DETERM o hyp_subst_tac ctxt) THEN |
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|
237 |
Local_Defs.unfold_tac ctxt ((discs RL @{thms iffD2[OF eq_True] iffD2[OF eq_False]}) @ |
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generate 'sel_map[simp]' theorem for (co)datatypes and tuning 'disc_map_iff'
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|
238 |
@{thms not_True_eq_False not_False_eq_True}) THEN |
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generate 'sel_map[simp]' theorem for (co)datatypes and tuning 'disc_map_iff'
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changeset
|
239 |
TRYALL (etac FalseE ORELSE' etac @{thm TrueE}) THEN |
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|
240 |
Local_Defs.unfold_tac ctxt (maps @ sels) THEN |
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|
241 |
ALLGOALS (rtac refl); |
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|
242 |
|
57152 | 243 |
fun mk_sel_set_tac ctxt ct exhaust discs sels sets = |
244 |
TRYALL Goal.conjunction_tac THEN |
|
245 |
ALLGOALS (rtac (cterm_instantiate_pos [SOME ct] exhaust) THEN_ALL_NEW |
|
246 |
REPEAT_DETERM o hyp_subst_tac ctxt) THEN |
|
247 |
Local_Defs.unfold_tac ctxt ((discs RL @{thms iffD2[OF eq_True] iffD2[OF eq_False]}) @ |
|
248 |
@{thms not_True_eq_False not_False_eq_True}) THEN |
|
249 |
TRYALL (etac FalseE ORELSE' etac @{thm TrueE}) THEN |
|
250 |
Local_Defs.unfold_tac ctxt (sels @ sets) THEN |
|
251 |
ALLGOALS ( |
|
252 |
REPEAT o (resolve_tac @{thms UnI1 UnI2 imageI} ORELSE' |
|
253 |
eresolve_tac @{thms UN_I UN_I[rotated] imageE} ORELSE' |
|
254 |
hyp_subst_tac ctxt) THEN' |
|
255 |
(rtac @{thm singletonI} ORELSE' atac)); |
|
256 |
||
56956 | 257 |
fun mk_set_empty_tac ctxt ct exhaust sets discs = |
258 |
TRYALL Goal.conjunction_tac THEN |
|
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changeset
|
259 |
ALLGOALS (rtac (cterm_instantiate_pos [SOME ct] exhaust) THEN_ALL_NEW |
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|
260 |
REPEAT_DETERM o hyp_subst_tac ctxt) THEN |
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|
261 |
unfold_thms_tac ctxt (sets @ map_filter (fn thm => |
56956 | 262 |
SOME (thm RS @{thm iffD2[OF eq_False]}) handle THM _ => NONE) discs) THEN |
56991
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changeset
|
263 |
ALLGOALS (rtac refl ORELSE' etac FalseE); |
56956 | 264 |
|
49123
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|
265 |
end; |