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(* Title: HOL/Tools/BNF/bnf_fp_util_tactics.ML
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Author: Dmitriy Traytel, ETH Zürich
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Copyright 2016
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Common tactics for datatype and codatatype constructions.
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*)
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signature BNF_FP_UTIL_TACTICS =
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sig
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val mk_xtor_un_fold_xtor_tac: Proof.context -> thm -> thm list -> thm list -> tactic
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val mk_xtor_co_rec_id_tac: Proof.context -> thm list -> thm -> thm list -> thm list -> tactic
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val mk_xtor_co_rec_tac: Proof.context -> thm -> thm list -> thm list -> tactic
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val mk_xtor_co_rec_unique_tac: Proof.context -> BNF_Util.fp_kind -> thm list -> thm list -> thm ->
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thm list -> thm list -> tactic
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val mk_xtor_co_rec_transfer_tac: Proof.context -> BNF_Util.fp_kind -> int -> int -> thm list ->
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thm list -> thm list -> thm list -> tactic
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end
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structure BNF_FP_Util_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_xtor_un_fold_xtor_tac ctxt xtor_un_fold_unique map_id0s inverses =
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HEADGOAL (rtac ctxt xtor_un_fold_unique THEN_ALL_NEW rtac ctxt ext) THEN
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unfold_thms_tac ctxt (@{thms o_apply id_o o_id} @ map_id0s @ inverses) THEN
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ALLGOALS (rtac ctxt refl);
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fun mk_conj_arg_congN 1 = @{thm DEADID.rel_mono_strong}
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| mk_conj_arg_congN n = mk_conj_arg_congN (n - 1) RSN (2, @{thm arg_cong2[of _ _ _ _ "(\<and>)"]});
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fun mk_xtor_co_rec_id_tac ctxt xtor_un_fold_xtors xtor_un_fold_unique xtor_un_folds map_comps =
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HEADGOAL (rtac ctxt (mk_conj_arg_congN (length xtor_un_fold_xtors) RS iffD1 OF
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(map (fn thm => @{thm DEADID.rel_cong} OF [refl, thm]) xtor_un_fold_xtors)) THEN'
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rtac ctxt xtor_un_fold_unique THEN_ALL_NEW EVERY' [rtac ctxt ext,
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SELECT_GOAL (unfold_thms_tac ctxt
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(o_apply :: @{thms fst_convol' id_o sum.case} @ map_comps @ xtor_un_folds)),
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rtac ctxt refl]);
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fun mk_xtor_co_rec_tac ctxt un_fold co_rec_defs co_rec_expand_thms =
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unfold_thms_tac ctxt (un_fold ::
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@{thms o_apply sum.case snd_convol' case_sum_o_inj(2)} @ co_rec_defs @ co_rec_expand_thms) THEN
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HEADGOAL (rtac ctxt refl);
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fun mk_xtor_co_rec_unique_tac ctxt fp co_rec_defs co_rec_expand's un_fold_unique map_ids map_comps
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inverses =
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unfold_thms_tac ctxt (co_rec_defs @ co_rec_expand's) THEN
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HEADGOAL (EVERY' [rtac ctxt un_fold_unique]) THEN
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unfold_thms_tac ctxt (map_ids @ map_comps @ inverses @ case_fp fp
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@{thms id_o o_id convol_o fst_convol o_assoc[symmetric]}
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@{thms id_o o_id o_case_sum case_sum_o_inj(1) o_assoc}) THEN
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ALLGOALS (etac ctxt (case_fp fp
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@{thm arg_cong2[of _ _ _ _ BNF_Def.convol, OF refl]}
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@{thm arg_cong2[of _ _ _ _ case_sum, OF refl]}));
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fun mk_xtor_co_rec_transfer_tac ctxt fp n m defs un_fold_transfers pre_T_map_transfers xtor_rels =
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case_fp fp
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(CONJ_WRAP (fn (def, un_fold_transfer) =>
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REPEAT_DETERM (HEADGOAL (rtac ctxt rel_funI)) THEN
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unfold_thms_tac ctxt [def, o_apply] THEN
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HEADGOAL (rtac ctxt @{thm rel_funD[OF snd_transfer]} THEN'
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etac ctxt (mk_rel_funDN_rotated (n + 1) un_fold_transfer) THEN'
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EVERY' (map2 (fn pre_T_map_transfer => fn xtor_rel =>
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etac ctxt (mk_rel_funDN_rotated 2 @{thm convol_transfer}) THEN'
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rtac ctxt (mk_rel_funDN_rotated 2 @{thm comp_transfer}) THEN'
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rtac ctxt (mk_rel_funDN (m + n) pre_T_map_transfer) THEN'
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REPEAT_DETERM_N m o rtac ctxt @{thm id_transfer} THEN'
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REPEAT_DETERM o rtac ctxt @{thm fst_transfer} THEN'
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rtac ctxt rel_funI THEN'
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etac ctxt (xtor_rel RS iffD2)) pre_T_map_transfers xtor_rels)))
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(defs ~~ un_fold_transfers))
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(CONJ_WRAP (fn (def, un_fold_transfer) =>
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REPEAT_DETERM (HEADGOAL (rtac ctxt rel_funI)) THEN
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unfold_thms_tac ctxt [def, o_apply] THEN
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HEADGOAL (rtac ctxt (mk_rel_funDN (n + 1) un_fold_transfer) THEN'
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EVERY' (map2 (fn pre_T_map_transfer => fn xtor_rel =>
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etac ctxt (mk_rel_funDN_rotated 2 @{thm case_sum_transfer}) THEN'
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rtac ctxt (mk_rel_funDN 2 @{thm comp_transfer}) THEN'
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rtac ctxt (mk_rel_funDN (m + n) pre_T_map_transfer) THEN'
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REPEAT_DETERM_N m o rtac ctxt @{thm id_transfer} THEN'
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REPEAT_DETERM_N n o rtac ctxt @{thm Inl_transfer} THEN'
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rtac ctxt rel_funI THEN'
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etac ctxt (xtor_rel RS iffD1)) pre_T_map_transfers xtor_rels) THEN'
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etac ctxt (mk_rel_funDN 1 @{thm Inr_transfer})))
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(defs ~~ un_fold_transfers));
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end
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