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(* Title: HOL/Codatatype/Tools/bnf_fp_sugar_tactics.ML
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Author: Jasmin Blanchette, TU Muenchen
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Copyright 2012
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Tactics for the LFP/GFP sugar.
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*)
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signature BNF_FP_SUGAR_TACTICS =
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sig
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val mk_case_tac: Proof.context -> int -> int -> int -> thm -> thm -> thm -> tactic
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val mk_coiter_like_tac: thm list -> thm list -> thm -> thm -> thm -> Proof.context -> tactic
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val mk_exhaust_tac: Proof.context -> int -> thm list -> thm -> thm -> tactic
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val mk_fld_iff_unf_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm
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-> tactic
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val mk_half_distinct_tac: Proof.context -> thm -> thm list -> tactic
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val mk_inject_tac: Proof.context -> thm -> thm -> tactic
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val mk_iter_like_tac: thm list -> thm list -> thm list -> thm -> thm -> Proof.context -> tactic
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end;
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structure BNF_FP_Sugar_Tactics : BNF_FP_SUGAR_TACTICS =
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struct
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open BNF_Tactics
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open BNF_Util
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fun mk_case_tac ctxt n k m case_def ctr_def unf_fld =
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Local_Defs.unfold_tac ctxt [case_def, ctr_def, unf_fld] THEN
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(rtac (BNF_FP_Util.mk_sum_casesN n k RS ssubst) THEN'
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REPEAT_DETERM_N (Int.max (0, m - 1)) o rtac (@{thm split} RS ssubst) THEN'
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rtac refl) 1;
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fun mk_exhaust_tac ctxt n ctr_defs fld_iff_unf sumEN' =
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Local_Defs.unfold_tac ctxt (fld_iff_unf :: ctr_defs) THEN rtac sumEN' 1 THEN
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Local_Defs.unfold_tac ctxt @{thms all_prod_eq} THEN
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EVERY' (maps (fn k => [select_prem_tac n (rotate_tac 1) k, REPEAT_DETERM o dtac @{thm meta_spec},
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etac @{thm meta_mp}, atac]) (1 upto n)) 1;
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fun mk_fld_iff_unf_tac ctxt cTs cfld cunf fld_unf unf_fld =
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(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 (Local_Defs.unfold_tac ctxt [th]) THEN'
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atac) [rev cTs, cTs] [cunf, cfld] [unf_fld, fld_unf])) 1;
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fun mk_half_distinct_tac ctxt fld_inject ctr_defs =
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Local_Defs.unfold_tac ctxt (fld_inject :: @{thms sum.inject} @ ctr_defs) THEN
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rtac @{thm sum.distinct(1)} 1;
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fun mk_inject_tac ctxt ctr_def fld_inject =
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Local_Defs.unfold_tac ctxt [ctr_def] THEN rtac (fld_inject RS ssubst) 1 THEN
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Local_Defs.unfold_tac ctxt @{thms sum.inject Pair_eq conj_assoc} THEN rtac refl 1;
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val iter_like_thms =
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@{thms case_unit comp_def convol_def map_pair_def sum.simps(5,6) sum_map.simps split_conv};
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fun mk_iter_like_tac pre_map_defs map_ids iter_like_defs fld_iter_like ctr_def ctxt =
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Local_Defs.unfold_tac ctxt (ctr_def :: fld_iter_like :: iter_like_defs @ pre_map_defs @ map_ids @
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iter_like_thms) THEN Local_Defs.unfold_tac ctxt @{thms id_def} THEN rtac refl 1;
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val coiter_like_ss = ss_only @{thms if_True if_False};
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val coiter_like_thms = @{thms map_pair_def sum_map.simps prod.cases};
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fun mk_coiter_like_tac coiter_like_defs map_ids fld_unf_coiter_like pre_map_def ctr_def ctxt =
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Local_Defs.unfold_tac ctxt (ctr_def :: coiter_like_defs) THEN
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subst_tac ctxt [fld_unf_coiter_like] 1 THEN asm_simp_tac coiter_like_ss 1 THEN
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Local_Defs.unfold_tac ctxt (pre_map_def :: coiter_like_thms @ map_ids) THEN
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Local_Defs.unfold_tac ctxt @{thms id_def} THEN rtac refl 1;
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end;
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