diff --git a/src/HOL/Tools/BNF/bnf_fp_util.ML b/src/HOL/Tools/BNF/bnf_fp_util.ML --- a/src/HOL/Tools/BNF/bnf_fp_util.ML +++ b/src/HOL/Tools/BNF/bnf_fp_util.ML @@ -1,1021 +1,1027 @@ (* Title: HOL/Tools/BNF/bnf_fp_util.ML Author: Dmitriy Traytel, TU Muenchen Author: Jasmin Blanchette, TU Muenchen Author: Martin Desharnais, TU Muenchen Author: Stefan Berghofer, TU Muenchen Copyright 2012, 2013, 2014 Shared library for the datatype and codatatype constructions. *) signature BNF_FP_UTIL = sig exception EMPTY_DATATYPE of string type fp_result = {Ts: typ list, bnfs: BNF_Def.bnf list, pre_bnfs: BNF_Def.bnf list, absT_infos: BNF_Comp.absT_info list, ctors: term list, dtors: term list, xtor_un_folds: term list, xtor_co_recs: term list, xtor_co_induct: thm, dtor_ctors: thm list, ctor_dtors: thm list, ctor_injects: thm list, dtor_injects: thm list, xtor_maps: thm list, xtor_map_unique: thm, xtor_setss: thm list list, xtor_rels: thm list, xtor_un_fold_thms: thm list, xtor_co_rec_thms: thm list, xtor_un_fold_unique: thm, xtor_co_rec_unique: thm, xtor_un_fold_o_maps: thm list, xtor_co_rec_o_maps: thm list, xtor_un_fold_transfers: thm list, xtor_co_rec_transfers: thm list, xtor_rel_co_induct: thm, dtor_set_inducts: thm list} val morph_fp_result: morphism -> fp_result -> fp_result val time: Proof.context -> Timer.real_timer -> string -> Timer.real_timer val fixpoint: ('a * 'a -> bool) -> ('a list -> 'a list) -> 'a list -> 'a list val IITN: string val LevN: string val algN: string val behN: string val bisN: string val carTN: string val caseN: string val coN: string val coinductN: string val coinduct_strongN: string val corecN: string val corec_discN: string val corec_disc_iffN: string val ctorN: string val ctor_dtorN: string val ctor_exhaustN: string val ctor_induct2N: string val ctor_inductN: string val ctor_injectN: string val ctor_foldN: string val ctor_fold_o_mapN: string val ctor_fold_transferN: string val ctor_fold_uniqueN: string val ctor_mapN: string val ctor_map_uniqueN: string val ctor_recN: string val ctor_rec_o_mapN: string val ctor_rec_transferN: string val ctor_rec_uniqueN: string val ctor_relN: string val ctor_rel_inductN: string val ctor_set_inclN: string val ctor_set_set_inclN: string val dtorN: string val dtor_coinductN: string val dtor_corecN: string val dtor_corec_o_mapN: string val dtor_corec_transferN: string val dtor_corec_uniqueN: string val dtor_ctorN: string val dtor_exhaustN: string val dtor_injectN: string val dtor_mapN: string val dtor_map_coinductN: string val dtor_map_coinduct_strongN: string val dtor_map_uniqueN: string val dtor_relN: string val dtor_rel_coinductN: string val dtor_set_inclN: string val dtor_set_set_inclN: string val dtor_coinduct_strongN: string val dtor_unfoldN: string val dtor_unfold_o_mapN: string val dtor_unfold_transferN: string val dtor_unfold_uniqueN: string val exhaustN: string val colN: string val inductN: string val injectN: string val isNodeN: string val lsbisN: string val mapN: string val map_uniqueN: string val min_algN: string val morN: string val nchotomyN: string val recN: string val rel_casesN: string val rel_coinductN: string val rel_inductN: string val rel_injectN: string val rel_introsN: string val rel_distinctN: string val rel_selN: string val rvN: string val corec_selN: string val set_inclN: string val set_set_inclN: string val setN: string val simpsN: string val strTN: string val str_initN: string val sum_bdN: string val sum_bdTN: string val uniqueN: string (* TODO: Don't index set facts. Isabelle packages traditionally generate uniform names. *) val mk_ctor_setN: int -> string val mk_dtor_setN: int -> string val mk_dtor_set_inductN: int -> string val mk_set_inductN: int -> string val co_prefix: BNF_Util.fp_kind -> string val split_conj_thm: thm -> thm list val split_conj_prems: int -> thm -> thm val mk_sumTN: typ list -> typ val mk_sumTN_balanced: typ list -> typ val mk_tupleT_balanced: typ list -> typ val mk_sumprodT_balanced: typ list list -> typ val mk_proj: typ -> int -> int -> term val mk_convol: term * term -> term val mk_rel_prod: term -> term -> term val mk_rel_sum: term -> term -> term val Inl_const: typ -> typ -> term val Inr_const: typ -> typ -> term val mk_tuple_balanced: term list -> term val mk_tuple1_balanced: typ list -> term list -> term val abs_curried_balanced: typ list -> term -> term val mk_tupled_fun: term -> term -> term list -> term val mk_case_sum: term * term -> term val mk_case_sumN: term list -> term val mk_case_absumprod: typ -> term -> term list -> term list list -> term list list -> term val mk_Inl: typ -> term -> term val mk_Inr: typ -> term -> term val mk_sumprod_balanced: typ -> int -> int -> term list -> term val mk_absumprod: typ -> term -> int -> int -> term list -> term val dest_sumT: typ -> typ * typ val dest_sumTN_balanced: int -> typ -> typ list val dest_tupleT_balanced: int -> typ -> typ list val dest_absumprodT: typ -> typ -> int -> int list -> typ -> typ list list val If_const: typ -> term val mk_Field: term -> term val mk_If: term -> term -> term -> term val mk_absumprodE: thm -> int list -> thm val mk_sum_caseN: int -> int -> thm val mk_sum_caseN_balanced: int -> int -> thm val mk_sum_Cinfinite: thm list -> thm val mk_sum_card_order: thm list -> thm val force_typ: Proof.context -> typ -> term -> term val mk_xtor_rel_co_induct_thm: BNF_Util.fp_kind -> term list -> term list -> term list -> term list -> term list -> term list -> term list -> term list -> ({prems: thm list, context: Proof.context} -> tactic) -> Proof.context -> thm val mk_xtor_co_iter_transfer_thms: BNF_Util.fp_kind -> term list -> term list -> term list -> term list -> term list -> term list -> term list -> ({prems: thm list, context: Proof.context} -> tactic) -> Proof.context -> thm list val mk_xtor_co_iter_o_map_thms: BNF_Util.fp_kind -> bool -> int -> thm -> thm list -> thm list -> thm list -> thm list -> thm list val derive_xtor_co_recs: BNF_Util.fp_kind -> binding list -> (typ list -> typ list) -> (typ list list * typ list) -> BNF_Def.bnf list -> term list -> term list -> thm -> thm list -> thm list -> thm list -> thm list -> (BNF_Comp.absT_info * BNF_Comp.absT_info) option list -> local_theory -> (term list * (thm list * thm * thm list * thm list)) * local_theory val raw_qualify: (binding -> binding) -> binding -> binding -> binding val fixpoint_bnf: bool -> (binding -> binding) -> (binding list -> (string * sort) list -> typ list * typ list list -> BNF_Def.bnf list -> BNF_Comp.absT_info list -> local_theory -> 'a) -> binding list -> (string * sort) list -> (string * sort) list -> (string * sort) list -> typ list -> BNF_Comp.comp_cache -> local_theory -> ((BNF_Def.bnf list * BNF_Comp.absT_info list) * BNF_Comp.comp_cache) * 'a end; structure BNF_FP_Util : BNF_FP_UTIL = struct open Ctr_Sugar open BNF_Comp open BNF_Def open BNF_Util open BNF_FP_Util_Tactics exception EMPTY_DATATYPE of string; type fp_result = {Ts: typ list, bnfs: bnf list, pre_bnfs: BNF_Def.bnf list, absT_infos: BNF_Comp.absT_info list, ctors: term list, dtors: term list, xtor_un_folds: term list, xtor_co_recs: term list, xtor_co_induct: thm, dtor_ctors: thm list, ctor_dtors: thm list, ctor_injects: thm list, dtor_injects: thm list, xtor_maps: thm list, xtor_map_unique: thm, xtor_setss: thm list list, xtor_rels: thm list, xtor_un_fold_thms: thm list, xtor_co_rec_thms: thm list, xtor_un_fold_unique: thm, xtor_co_rec_unique: thm, xtor_un_fold_o_maps: thm list, xtor_co_rec_o_maps: thm list, xtor_un_fold_transfers: thm list, xtor_co_rec_transfers: thm list, xtor_rel_co_induct: thm, dtor_set_inducts: thm list}; fun morph_fp_result phi {Ts, bnfs, pre_bnfs, absT_infos, ctors, dtors, xtor_un_folds, xtor_co_recs, xtor_co_induct, dtor_ctors, ctor_dtors, ctor_injects, dtor_injects, xtor_maps, xtor_map_unique, xtor_setss, xtor_rels, xtor_un_fold_thms, xtor_co_rec_thms, xtor_un_fold_unique, xtor_co_rec_unique, xtor_un_fold_o_maps, xtor_co_rec_o_maps, xtor_un_fold_transfers, xtor_co_rec_transfers, xtor_rel_co_induct, dtor_set_inducts} = {Ts = map (Morphism.typ phi) Ts, bnfs = map (morph_bnf phi) bnfs, pre_bnfs = map (morph_bnf phi) pre_bnfs, absT_infos = map (morph_absT_info phi) absT_infos, ctors = map (Morphism.term phi) ctors, dtors = map (Morphism.term phi) dtors, xtor_un_folds = map (Morphism.term phi) xtor_un_folds, xtor_co_recs = map (Morphism.term phi) xtor_co_recs, xtor_co_induct = Morphism.thm phi xtor_co_induct, dtor_ctors = map (Morphism.thm phi) dtor_ctors, ctor_dtors = map (Morphism.thm phi) ctor_dtors, ctor_injects = map (Morphism.thm phi) ctor_injects, dtor_injects = map (Morphism.thm phi) dtor_injects, xtor_maps = map (Morphism.thm phi) xtor_maps, xtor_map_unique = Morphism.thm phi xtor_map_unique, xtor_setss = map (map (Morphism.thm phi)) xtor_setss, xtor_rels = map (Morphism.thm phi) xtor_rels, xtor_un_fold_thms = map (Morphism.thm phi) xtor_un_fold_thms, xtor_co_rec_thms = map (Morphism.thm phi) xtor_co_rec_thms, xtor_un_fold_unique = Morphism.thm phi xtor_un_fold_unique, xtor_co_rec_unique = Morphism.thm phi xtor_co_rec_unique, xtor_un_fold_o_maps = map (Morphism.thm phi) xtor_un_fold_o_maps, xtor_co_rec_o_maps = map (Morphism.thm phi) xtor_co_rec_o_maps, xtor_un_fold_transfers = map (Morphism.thm phi) xtor_un_fold_transfers, xtor_co_rec_transfers = map (Morphism.thm phi) xtor_co_rec_transfers, xtor_rel_co_induct = Morphism.thm phi xtor_rel_co_induct, dtor_set_inducts = map (Morphism.thm phi) dtor_set_inducts}; fun time ctxt timer msg = (if Config.get ctxt bnf_timing then warning (msg ^ ": " ^ string_of_int (Time.toMilliseconds (Timer.checkRealTimer timer)) ^ " ms") else (); Timer.startRealTimer ()); val preN = "pre_" val rawN = "raw_" val coN = "co" val unN = "un" val algN = "alg" val IITN = "IITN" val foldN = "fold" val unfoldN = unN ^ foldN val uniqueN = "unique" val transferN = "transfer" val simpsN = "simps" val ctorN = "ctor" val dtorN = "dtor" val ctor_foldN = ctorN ^ "_" ^ foldN val dtor_unfoldN = dtorN ^ "_" ^ unfoldN val ctor_fold_uniqueN = ctor_foldN ^ "_" ^ uniqueN val ctor_fold_o_mapN = ctor_foldN ^ "_o_" ^ mapN val dtor_unfold_uniqueN = dtor_unfoldN ^ "_" ^ uniqueN val dtor_unfold_o_mapN = dtor_unfoldN ^ "_o_" ^ mapN val ctor_fold_transferN = ctor_foldN ^ "_" ^ transferN val dtor_unfold_transferN = dtor_unfoldN ^ "_" ^ transferN val ctor_mapN = ctorN ^ "_" ^ mapN val dtor_mapN = dtorN ^ "_" ^ mapN val map_uniqueN = mapN ^ "_" ^ uniqueN val ctor_map_uniqueN = ctorN ^ "_" ^ map_uniqueN val dtor_map_uniqueN = dtorN ^ "_" ^ map_uniqueN val min_algN = "min_alg" val morN = "mor" val bisN = "bis" val lsbisN = "lsbis" val sum_bdTN = "sbdT" val sum_bdN = "sbd" val carTN = "carT" val strTN = "strT" val isNodeN = "isNode" val LevN = "Lev" val rvN = "recover" val behN = "beh" val setN = "set" val mk_ctor_setN = prefix (ctorN ^ "_") o mk_setN val mk_dtor_setN = prefix (dtorN ^ "_") o mk_setN fun mk_set_inductN i = mk_setN i ^ "_induct" val mk_dtor_set_inductN = prefix (dtorN ^ "_") o mk_set_inductN val str_initN = "str_init" val recN = "rec" val corecN = coN ^ recN val ctor_recN = ctorN ^ "_" ^ recN val ctor_rec_o_mapN = ctor_recN ^ "_o_" ^ mapN val ctor_rec_transferN = ctor_recN ^ "_" ^ transferN val ctor_rec_uniqueN = ctor_recN ^ "_" ^ uniqueN val dtor_corecN = dtorN ^ "_" ^ corecN val dtor_corec_o_mapN = dtor_corecN ^ "_o_" ^ mapN val dtor_corec_transferN = dtor_corecN ^ "_" ^ transferN val dtor_corec_uniqueN = dtor_corecN ^ "_" ^ uniqueN val ctor_dtorN = ctorN ^ "_" ^ dtorN val dtor_ctorN = dtorN ^ "_" ^ ctorN val nchotomyN = "nchotomy" val injectN = "inject" val exhaustN = "exhaust" val ctor_injectN = ctorN ^ "_" ^ injectN val ctor_exhaustN = ctorN ^ "_" ^ exhaustN val dtor_injectN = dtorN ^ "_" ^ injectN val dtor_exhaustN = dtorN ^ "_" ^ exhaustN val ctor_relN = ctorN ^ "_" ^ relN val dtor_relN = dtorN ^ "_" ^ relN val inductN = "induct" val coinductN = coN ^ inductN val ctor_inductN = ctorN ^ "_" ^ inductN val ctor_induct2N = ctor_inductN ^ "2" val dtor_map_coinductN = dtor_mapN ^ "_" ^ coinductN val dtor_coinductN = dtorN ^ "_" ^ coinductN val coinduct_strongN = coinductN ^ "_strong" val dtor_map_coinduct_strongN = dtor_mapN ^ "_" ^ coinduct_strongN val dtor_coinduct_strongN = dtorN ^ "_" ^ coinduct_strongN val colN = "col" val set_inclN = "set_incl" val ctor_set_inclN = ctorN ^ "_" ^ set_inclN val dtor_set_inclN = dtorN ^ "_" ^ set_inclN val set_set_inclN = "set_set_incl" val ctor_set_set_inclN = ctorN ^ "_" ^ set_set_inclN val dtor_set_set_inclN = dtorN ^ "_" ^ set_set_inclN val caseN = "case" val discN = "disc" val corec_discN = corecN ^ "_" ^ discN val iffN = "_iff" val corec_disc_iffN = corec_discN ^ iffN val distinctN = "distinct" val rel_distinctN = relN ^ "_" ^ distinctN val injectN = "inject" val rel_casesN = relN ^ "_cases" val rel_injectN = relN ^ "_" ^ injectN val rel_introsN = relN ^ "_intros" val rel_coinductN = relN ^ "_" ^ coinductN val rel_selN = relN ^ "_sel" val dtor_rel_coinductN = dtorN ^ "_" ^ rel_coinductN val rel_inductN = relN ^ "_" ^ inductN val ctor_rel_inductN = ctorN ^ "_" ^ rel_inductN val selN = "sel" val corec_selN = corecN ^ "_" ^ selN fun co_prefix fp = case_fp fp "" "co"; fun dest_sumT (Type (\<^type_name>\sum\, [T, T'])) = (T, T'); val dest_sumTN_balanced = Balanced_Tree.dest dest_sumT; fun dest_tupleT_balanced 0 \<^typ>\unit\ = [] | dest_tupleT_balanced n T = Balanced_Tree.dest HOLogic.dest_prodT n T; fun dest_absumprodT absT repT n ms = map2 dest_tupleT_balanced ms o dest_sumTN_balanced n o mk_repT absT repT; val mk_sumTN = Library.foldr1 mk_sumT; val mk_sumTN_balanced = Balanced_Tree.make mk_sumT; fun mk_tupleT_balanced [] = HOLogic.unitT | mk_tupleT_balanced Ts = Balanced_Tree.make HOLogic.mk_prodT Ts; val mk_sumprodT_balanced = mk_sumTN_balanced o map mk_tupleT_balanced; fun mk_proj T n k = let val (binders, _) = strip_typeN n T in fold_rev (fn T => fn t => Abs (Name.uu, T, t)) binders (Bound (n - k - 1)) end; fun mk_convol (f, g) = let val (fU, fTU) = `range_type (fastype_of f); val ((gT, gU), gTU) = `dest_funT (fastype_of g); val convolT = fTU --> gTU --> gT --> HOLogic.mk_prodT (fU, gU); in Const (\<^const_name>\convol\, convolT) $ f $ g end; fun mk_rel_prod R S = let val ((A1, A2), RT) = `dest_pred2T (fastype_of R); val ((B1, B2), ST) = `dest_pred2T (fastype_of S); val rel_prodT = RT --> ST --> mk_pred2T (HOLogic.mk_prodT (A1, B1)) (HOLogic.mk_prodT (A2, B2)); in Const (\<^const_name>\rel_prod\, rel_prodT) $ R $ S end; fun mk_rel_sum R S = let val ((A1, A2), RT) = `dest_pred2T (fastype_of R); val ((B1, B2), ST) = `dest_pred2T (fastype_of S); val rel_sumT = RT --> ST --> mk_pred2T (mk_sumT (A1, B1)) (mk_sumT (A2, B2)); in Const (\<^const_name>\rel_sum\, rel_sumT) $ R $ S end; fun Inl_const LT RT = Const (\<^const_name>\Inl\, LT --> mk_sumT (LT, RT)); fun mk_Inl RT t = Inl_const (fastype_of t) RT $ t; fun Inr_const LT RT = Const (\<^const_name>\Inr\, RT --> mk_sumT (LT, RT)); fun mk_Inr LT t = Inr_const LT (fastype_of t) $ t; fun mk_prod1 bound_Ts (t, u) = HOLogic.pair_const (fastype_of1 (bound_Ts, t)) (fastype_of1 (bound_Ts, u)) $ t $ u; fun mk_tuple1_balanced _ [] = HOLogic.unit | mk_tuple1_balanced bound_Ts ts = Balanced_Tree.make (mk_prod1 bound_Ts) ts; val mk_tuple_balanced = mk_tuple1_balanced []; fun abs_curried_balanced Ts t = t $ mk_tuple1_balanced (List.rev Ts) (map Bound (length Ts - 1 downto 0)) |> fold_rev (Term.abs o pair Name.uu) Ts; fun mk_sumprod_balanced T n k ts = Sum_Tree.mk_inj T n k (mk_tuple_balanced ts); fun mk_absumprod absT abs0 n k ts = let val abs = mk_abs absT abs0; in abs $ mk_sumprod_balanced (domain_type (fastype_of abs)) n k ts end; fun mk_case_sum (f, g) = let val (fT, T') = dest_funT (fastype_of f); val (gT, _) = dest_funT (fastype_of g); in Sum_Tree.mk_sumcase fT gT T' f g end; val mk_case_sumN = Library.foldr1 mk_case_sum; val mk_case_sumN_balanced = Balanced_Tree.make mk_case_sum; fun mk_tupled_fun f x xs = if xs = [x] then f else HOLogic.tupled_lambda x (Term.list_comb (f, xs)); fun mk_case_absumprod absT rep fs xss xss' = HOLogic.mk_comp (mk_case_sumN_balanced (@{map 3} mk_tupled_fun fs (map mk_tuple_balanced xss) xss'), mk_rep absT rep); fun If_const T = Const (\<^const_name>\If\, HOLogic.boolT --> T --> T --> T); fun mk_If p t f = let val T = fastype_of t in If_const T $ p $ t $ f end; fun mk_Field r = let val T = fst (dest_relT (fastype_of r)); in Const (\<^const_name>\Field\, mk_relT (T, T) --> HOLogic.mk_setT T) $ r end; (*dangerous; use with monotonic, converging functions only!*) fun fixpoint eq f X = if subset eq (f X, X) then X else fixpoint eq f (f X); (* stolen from "~~/src/HOL/Tools/Datatype/datatype_aux.ML" *) fun split_conj_thm th = ((th RS conjunct1) :: split_conj_thm (th RS conjunct2)) handle THM _ => [th]; fun split_conj_prems limit th = let fun split n i th = if i = n then th else split n (i + 1) (conjI RSN (i, th)) handle THM _ => th; in split limit 1 th end; fun mk_obj_sumEN_balanced n = Balanced_Tree.make (fn (thm1, thm2) => thm1 RSN (1, thm2 RSN (2, @{thm obj_sumE_f}))) (replicate n asm_rl); fun mk_tupled_allIN_balanced 0 = @{thm unit_all_impI} | mk_tupled_allIN_balanced n = let val (tfrees, _) = BNF_Util.mk_TFrees n \<^context>; val T = mk_tupleT_balanced tfrees; in @{thm asm_rl[of "\x. P x \ Q x" for P Q]} |> Thm.instantiate' [SOME (Thm.ctyp_of \<^context> T)] [] |> Raw_Simplifier.rewrite_goals_rule \<^context> @{thms split_paired_All[THEN eq_reflection]} |> (fn thm => impI RS funpow n (fn th => allI RS th) thm) |> Thm.varifyT_global end; fun mk_absumprodE type_definition ms = let val n = length ms in mk_obj_sumEN_balanced n OF map mk_tupled_allIN_balanced ms RS (type_definition RS @{thm type_copy_obj_one_point_absE}) end; fun mk_sum_caseN 1 1 = refl | mk_sum_caseN _ 1 = @{thm sum.case(1)} | mk_sum_caseN 2 2 = @{thm sum.case(2)} | mk_sum_caseN n k = trans OF [@{thm case_sum_step(2)}, mk_sum_caseN (n - 1) (k - 1)]; fun mk_sum_step base step thm = if Thm.eq_thm_prop (thm, refl) then base else trans OF [step, thm]; fun mk_sum_caseN_balanced 1 1 = refl | mk_sum_caseN_balanced n k = Balanced_Tree.access {left = mk_sum_step @{thm sum.case(1)} @{thm case_sum_step(1)}, right = mk_sum_step @{thm sum.case(2)} @{thm case_sum_step(2)}, init = refl} n k; fun mk_sum_Cinfinite [thm] = thm | mk_sum_Cinfinite (thm :: thms) = @{thm Cinfinite_csum_weak} OF [thm, mk_sum_Cinfinite thms]; fun mk_sum_card_order [thm] = thm | mk_sum_card_order (thm :: thms) = @{thm card_order_csum} OF [thm, mk_sum_card_order thms]; fun mk_xtor_rel_co_induct_thm fp pre_rels pre_phis rels phis xs ys xtors xtor's tac lthy = let val pre_relphis = map (fn rel => Term.list_comb (rel, phis @ pre_phis)) pre_rels; val relphis = map (fn rel => Term.list_comb (rel, phis)) rels; fun mk_xtor fp' xtor x = if fp = fp' then xtor $ x else x; val dtor = mk_xtor Greatest_FP; val ctor = mk_xtor Least_FP; fun flip f x y = if fp = Greatest_FP then f y x else f x y; fun mk_prem pre_relphi phi x y xtor xtor' = HOLogic.mk_Trueprop (list_all_free [x, y] (flip (curry HOLogic.mk_imp) (pre_relphi $ (dtor xtor x) $ (dtor xtor' y)) (phi $ (ctor xtor x) $ (ctor xtor' y)))); val prems = @{map 6} mk_prem pre_relphis pre_phis xs ys xtors xtor's; val concl = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (flip mk_leq) relphis pre_phis)); in Goal.prove_sorry lthy (map (fst o dest_Free) (phis @ pre_phis)) prems concl tac |> Thm.close_derivation \<^here> |> (fn thm => thm OF (replicate (length pre_rels) @{thm allI[OF allI[OF impI]]})) end; fun mk_xtor_co_iter_transfer_thms fp pre_rels pre_iphis pre_ophis rels phis un_folds un_folds' tac lthy = let val pre_relphis = map (fn rel => Term.list_comb (rel, phis @ pre_iphis)) pre_rels; val relphis = map (fn rel => Term.list_comb (rel, phis)) rels; fun flip f x y = if fp = Greatest_FP then f y x else f x y; val arg_rels = map2 (flip mk_rel_fun) pre_relphis pre_ophis; fun mk_transfer relphi pre_phi un_fold un_fold' = fold_rev mk_rel_fun arg_rels (flip mk_rel_fun relphi pre_phi) $ un_fold $ un_fold'; val transfers = @{map 4} mk_transfer relphis pre_ophis un_folds un_folds'; val goal = fold_rev Logic.all (phis @ pre_ophis) (HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj transfers)); in Goal.prove_sorry lthy [] [] goal tac |> Thm.close_derivation \<^here> |> split_conj_thm end; fun mk_xtor_co_iter_o_map_thms fp is_rec m un_fold_unique xtor_maps xtor_un_folds sym_map_comps map_cong0s = let val n = length sym_map_comps; val rewrite_comp_comp2 = case_fp fp @{thm rewriteR_comp_comp2} @{thm rewriteL_comp_comp2}; val rewrite_comp_comp = case_fp fp @{thm rewriteR_comp_comp} @{thm rewriteL_comp_comp}; val map_cong_passive_args1 = replicate m (case_fp fp @{thm id_comp} @{thm comp_id} RS fun_cong); val map_cong_active_args1 = replicate n (if is_rec then case_fp fp @{thm convol_o} @{thm o_case_sum} RS fun_cong else refl); val map_cong_passive_args2 = replicate m (case_fp fp @{thm comp_id} @{thm id_comp} RS fun_cong); val map_cong_active_args2 = replicate n (if is_rec then case_fp fp @{thm map_prod_o_convol_id} @{thm case_sum_o_map_sum_id} else case_fp fp @{thm id_comp} @{thm comp_id} RS fun_cong); fun mk_map_congs passive active = map (fn thm => thm OF (passive @ active) RS @{thm ext}) map_cong0s; val map_cong1s = mk_map_congs map_cong_passive_args1 map_cong_active_args1; val map_cong2s = mk_map_congs map_cong_passive_args2 map_cong_active_args2; fun mk_rewrites map_congs = map2 (fn sym_map_comp => fn map_cong => mk_trans sym_map_comp map_cong RS rewrite_comp_comp) sym_map_comps map_congs; val rewrite1s = mk_rewrites map_cong1s; val rewrite2s = mk_rewrites map_cong2s; val unique_prems = @{map 4} (fn xtor_map => fn un_fold => fn rewrite1 => fn rewrite2 => mk_trans (rewrite_comp_comp2 OF [xtor_map, un_fold]) (mk_trans rewrite1 (mk_sym rewrite2))) xtor_maps xtor_un_folds rewrite1s rewrite2s; in split_conj_thm (un_fold_unique OF map (case_fp fp I mk_sym) unique_prems) end; fun force_typ ctxt T = Term.map_types Type_Infer.paramify_vars #> Type.constraint T #> Syntax.check_term ctxt #> singleton (Variable.polymorphic ctxt); fun absT_info_encodeT thy (SOME (src : absT_info, dst : absT_info)) src_absT = let val src_repT = mk_repT (#absT src) (#repT src) src_absT; val dst_absT = mk_absT thy (#repT dst) (#absT dst) src_repT; in dst_absT end | absT_info_encodeT _ NONE T = T; fun absT_info_decodeT thy = absT_info_encodeT thy o Option.map swap; fun absT_info_encode thy fp (opt as SOME (src : absT_info, dst : absT_info)) t = let val co_alg_funT = case_fp fp domain_type range_type; fun co_swap pair = case_fp fp I swap pair; val mk_co_comp = curry (HOLogic.mk_comp o co_swap); val mk_co_abs = case_fp fp mk_abs mk_rep; val mk_co_rep = case_fp fp mk_rep mk_abs; val co_abs = case_fp fp #abs #rep; val co_rep = case_fp fp #rep #abs; val src_absT = co_alg_funT (fastype_of t); val dst_absT = absT_info_encodeT thy opt src_absT; val co_src_abs = mk_co_abs src_absT (co_abs src); val co_dst_rep = mk_co_rep dst_absT (co_rep dst); in mk_co_comp (mk_co_comp t co_src_abs) co_dst_rep end | absT_info_encode _ _ NONE t = t; fun absT_info_decode thy fp = absT_info_encode thy fp o Option.map swap; fun mk_xtor_un_fold_xtor_thms ctxt fp un_folds xtors xtor_un_fold_unique map_id0s absT_info_opts = let val thy = Proof_Context.theory_of ctxt; fun mk_goal un_fold = let val rhs = list_comb (un_fold, @{map 2} (absT_info_encode thy fp) absT_info_opts xtors); val T = range_type (fastype_of rhs); in HOLogic.mk_eq (HOLogic.id_const T, rhs) end; val goal = HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map mk_goal un_folds)); fun mk_inverses NONE = [] | mk_inverses (SOME (src, dst)) = [#type_definition dst RS @{thm type_definition.Abs_inverse[OF _ UNIV_I]}, #type_definition src RS @{thm type_definition.Rep_inverse}]; val inverses = maps mk_inverses absT_info_opts; in Goal.prove_sorry ctxt [] [] goal (fn {context = ctxt, prems = _} => mk_xtor_un_fold_xtor_tac ctxt xtor_un_fold_unique map_id0s inverses) |> split_conj_thm |> map mk_sym end; fun derive_xtor_co_recs fp bs mk_Ts (Dss, resDs) pre_bnfs xtors0 un_folds0 xtor_un_fold_unique xtor_un_folds xtor_un_fold_transfers xtor_maps xtor_rels absT_info_opts lthy = let val thy = Proof_Context.theory_of lthy; fun co_swap pair = case_fp fp I swap pair; val mk_co_comp = curry (HOLogic.mk_comp o co_swap); fun mk_co_algT T U = case_fp fp (T --> U) (U --> T); val co_alg_funT = case_fp fp domain_type range_type; val mk_co_product = curry (case_fp fp mk_convol mk_case_sum); val co_proj1_const = case_fp fp fst_const (uncurry Inl_const o dest_sumT) o co_alg_funT; val co_proj2_const = case_fp fp snd_const (uncurry Inr_const o dest_sumT) o co_alg_funT; val mk_co_productT = curry (case_fp fp HOLogic.mk_prodT mk_sumT); val rewrite_comp_comp = case_fp fp @{thm rewriteL_comp_comp} @{thm rewriteR_comp_comp}; val n = length pre_bnfs; val live = live_of_bnf (hd pre_bnfs); val m = live - n; val ks = 1 upto n; val map_id0s = map map_id0_of_bnf pre_bnfs; val map_comps = map map_comp_of_bnf pre_bnfs; val map_cong0s = map map_cong0_of_bnf pre_bnfs; val map_transfers = map map_transfer_of_bnf pre_bnfs; val sym_map_comp0s = map (mk_sym o map_comp0_of_bnf) pre_bnfs; val deads = fold (union (op =)) Dss resDs; val ((((As, Bs), Xs), Ys), names_lthy) = lthy |> fold Variable.declare_typ deads |> mk_TFrees m ||>> mk_TFrees m ||>> mk_TFrees n ||>> mk_TFrees n; val XFTs = @{map 2} (fn Ds => mk_T_of_bnf Ds (As @ Xs)) Dss pre_bnfs; val co_algXFTs = @{map 2} mk_co_algT XFTs Xs; val Ts = mk_Ts As; val un_foldTs = @{map 2} (fn T => fn X => co_algXFTs ---> mk_co_algT T X) Ts Xs; val un_folds = @{map 2} (force_typ names_lthy) un_foldTs un_folds0; val ABs = As ~~ Bs; val XYs = Xs ~~ Ys; val Us = map (typ_subst_atomic ABs) Ts; val TFTs = @{map 2} (fn Ds => mk_T_of_bnf Ds (As @ Ts)) Dss pre_bnfs; val TFTs' = @{map 2} (absT_info_decodeT thy) absT_info_opts TFTs; val xtors = @{map 3} (force_typ names_lthy oo mk_co_algT) TFTs' Ts xtors0; val ids = map HOLogic.id_const As; val co_rec_Xs = @{map 2} mk_co_productT Ts Xs; val co_rec_Ys = @{map 2} mk_co_productT Us Ys; val co_rec_algXs = @{map 2} mk_co_algT co_rec_Xs Xs; val co_proj1s = map co_proj1_const co_rec_algXs; val co_rec_maps = @{map 2} (fn Ds => mk_map_of_bnf Ds (As @ case_fp fp co_rec_Xs Ts) (As @ case_fp fp Ts co_rec_Xs)) Dss pre_bnfs; val co_rec_Ts = @{map 2} (fn Ds => mk_T_of_bnf Ds (As @ co_rec_Xs)) Dss pre_bnfs val co_rec_argTs = @{map 2} mk_co_algT co_rec_Ts Xs; val co_rec_resTs = @{map 2} mk_co_algT Ts Xs; val (((co_rec_ss, fs), xs), names_lthy) = names_lthy |> mk_Frees "s" co_rec_argTs ||>> mk_Frees "f" co_rec_resTs ||>> mk_Frees "x" (case_fp fp TFTs' Xs); val co_rec_strs = @{map 4} (fn xtor => fn s => fn mapx => fn absT_info_opt => mk_co_product (mk_co_comp (absT_info_encode thy fp absT_info_opt xtor) (list_comb (mapx, ids @ co_proj1s))) s) xtors co_rec_ss co_rec_maps absT_info_opts; val theta = Xs ~~ co_rec_Xs; val co_rec_un_folds = map (subst_atomic_types theta) un_folds; val co_rec_spec0s = map (fn un_fold => list_comb (un_fold, co_rec_strs)) co_rec_un_folds; val co_rec_ids = @{map 2} (mk_co_comp o co_proj1_const) co_rec_algXs co_rec_spec0s; val co_rec_specs = @{map 2} (mk_co_comp o co_proj2_const) co_rec_algXs co_rec_spec0s; val co_recN = case_fp fp ctor_recN dtor_corecN; fun co_rec_bind i = nth bs (i - 1) |> Binding.prefix_name (co_recN ^ "_"); val co_rec_def_bind = rpair [] o Binding.concealed o Thm.def_binding o co_rec_bind; fun co_rec_spec i = fold_rev (Term.absfree o Term.dest_Free) co_rec_ss (nth co_rec_specs (i - 1)); val ((co_rec_frees, (_, co_rec_def_frees)), (lthy, lthy_old)) = lthy |> Local_Theory.open_target |> snd |> fold_map (fn i => Local_Theory.define ((co_rec_bind i, NoSyn), (co_rec_def_bind i, co_rec_spec i))) ks |>> apsnd split_list o split_list ||> `Local_Theory.close_target; val phi = Proof_Context.export_morphism lthy_old lthy; val co_rec_names = map (fst o dest_Const o Morphism.term phi) co_rec_frees; val co_recs = @{map 2} (fn name => fn resT => Const (name, co_rec_argTs ---> resT)) co_rec_names co_rec_resTs; val co_rec_defs = map (fn def => mk_unabs_def n (HOLogic.mk_obj_eq (Morphism.thm phi def))) co_rec_def_frees; val xtor_un_fold_xtor_thms = mk_xtor_un_fold_xtor_thms lthy fp (map (Term.subst_atomic_types (Xs ~~ Ts)) un_folds) xtors xtor_un_fold_unique map_id0s absT_info_opts; val co_rec_id_thms = let val goal = @{map 2} (fn T => fn t => HOLogic.mk_eq (t, HOLogic.id_const T)) Ts co_rec_ids |> Library.foldr1 HOLogic.mk_conj |> HOLogic.mk_Trueprop; val vars = Variable.add_free_names lthy goal []; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_xtor_co_rec_id_tac ctxt xtor_un_fold_xtor_thms xtor_un_fold_unique xtor_un_folds map_comps) |> Thm.close_derivation \<^here> |> split_conj_thm end; val co_rec_app_ss = map (fn co_rec => list_comb (co_rec, co_rec_ss)) co_recs; val co_products = @{map 2} (fn T => mk_co_product (HOLogic.id_const T)) Ts co_rec_app_ss; val co_rec_maps_rev = @{map 2} (fn Ds => mk_map_of_bnf Ds (As @ case_fp fp Ts co_rec_Xs) (As @ case_fp fp co_rec_Xs Ts)) Dss pre_bnfs; fun mk_co_app f g x = case_fp fp (f $ (g $ x)) (g $ (f $ x)); val co_rec_expand_thms = map (fn thm => thm RS case_fp fp @{thm convol_expand_snd} @{thm case_sum_expand_Inr_pointfree}) co_rec_id_thms; val xtor_co_rec_thms = let fun mk_goal co_rec s mapx xtor x absT_info_opt = let val lhs = mk_co_app co_rec xtor x; val rhs = mk_co_app s (list_comb (mapx, ids @ co_products) |> absT_info_decode thy fp absT_info_opt) x; in mk_Trueprop_eq (lhs, rhs) end; val goals = @{map 6} mk_goal co_rec_app_ss co_rec_ss co_rec_maps_rev xtors xs absT_info_opts; in map2 (fn goal => fn un_fold => Variable.add_free_names lthy goal [] |> (fn vars => Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_xtor_co_rec_tac ctxt un_fold co_rec_defs co_rec_expand_thms)) |> Thm.close_derivation \<^here>) goals xtor_un_folds end; val co_product_fs = @{map 2} (fn T => mk_co_product (HOLogic.id_const T)) Ts fs; val co_rec_expand'_thms = map (fn thm => thm RS case_fp fp @{thm convol_expand_snd'} @{thm case_sum_expand_Inr'}) co_rec_id_thms; val xtor_co_rec_unique_thm = let fun mk_prem f s mapx xtor absT_info_opt = let val lhs = mk_co_comp f xtor; val rhs = mk_co_comp s (list_comb (mapx, ids @ co_product_fs)) |> absT_info_decode thy fp absT_info_opt; in mk_Trueprop_eq (co_swap (lhs, rhs)) end; val prems = @{map 5} mk_prem fs co_rec_ss co_rec_maps_rev xtors absT_info_opts; val concl = @{map 2} (curry HOLogic.mk_eq) fs co_rec_app_ss |> Library.foldr1 HOLogic.mk_conj |> HOLogic.mk_Trueprop; val goal = Logic.list_implies (prems, concl); val vars = Variable.add_free_names lthy goal []; fun mk_inverses NONE = [] | mk_inverses (SOME (src, dst)) = [#type_definition dst RS @{thm type_copy_Rep_o_Abs} RS rewrite_comp_comp, #type_definition src RS @{thm type_copy_Abs_o_Rep}]; val inverses = maps mk_inverses absT_info_opts; in Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} => mk_xtor_co_rec_unique_tac ctxt fp co_rec_defs co_rec_expand'_thms xtor_un_fold_unique map_id0s sym_map_comp0s inverses) |> Thm.close_derivation \<^here> end; val xtor_co_rec_o_map_thms = if forall is_none absT_info_opts then mk_xtor_co_iter_o_map_thms fp true m xtor_co_rec_unique_thm (map (mk_pointfree2 lthy) xtor_maps) (map (mk_pointfree2 lthy) xtor_co_rec_thms) sym_map_comp0s map_cong0s else replicate n refl (* FIXME *); val ABphiTs = @{map 2} mk_pred2T As Bs; val XYphiTs = @{map 2} mk_pred2T Xs Ys; val ((ABphis, XYphis), names_lthy) = names_lthy |> mk_Frees "R" ABphiTs ||>> mk_Frees "S" XYphiTs; val xtor_co_rec_transfer_thms = if forall is_none absT_info_opts then let val pre_rels = @{map 2} (fn Ds => mk_rel_of_bnf Ds (As @ co_rec_Xs) (Bs @ co_rec_Ys)) Dss pre_bnfs; val rels = @{map 3} (fn T => fn T' => Thm.prop_of #> HOLogic.dest_Trueprop #> fst o dest_comb #> fst o dest_comb #> funpow n (snd o dest_comb) #> case_fp fp (fst o dest_comb #> snd o dest_comb) (snd o dest_comb) #> head_of #> force_typ names_lthy (ABphiTs ---> mk_pred2T T T')) Ts Us xtor_un_fold_transfers; fun tac {context = ctxt, prems = _} = mk_xtor_co_rec_transfer_tac ctxt fp n m co_rec_defs xtor_un_fold_transfers map_transfers xtor_rels; val mk_rel_co_product = case_fp fp mk_rel_prod mk_rel_sum; val rec_phis = map2 (fn rel => mk_rel_co_product (Term.list_comb (rel, ABphis))) rels XYphis; in mk_xtor_co_iter_transfer_thms fp pre_rels rec_phis XYphis rels ABphis co_recs (map (subst_atomic_types (ABs @ XYs)) co_recs) tac lthy end else replicate n TrueI (* FIXME *); val notes = [(case_fp fp ctor_recN dtor_corecN, xtor_co_rec_thms), (case_fp fp ctor_rec_uniqueN dtor_corec_uniqueN, split_conj_thm xtor_co_rec_unique_thm), (case_fp fp ctor_rec_o_mapN dtor_corec_o_mapN, xtor_co_rec_o_map_thms), (case_fp fp ctor_rec_transferN dtor_corec_transferN, xtor_co_rec_transfer_thms)] |> map (apsnd (map single)) |> maps (fn (thmN, thmss) => map2 (fn b => fn thms => ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])) bs thmss); val lthy = lthy |> Config.get lthy bnf_internals ? snd o Local_Theory.notes notes; in ((co_recs, (xtor_co_rec_thms, xtor_co_rec_unique_thm, xtor_co_rec_o_map_thms, xtor_co_rec_transfer_thms)), lthy) end; fun raw_qualify extra_qualify base_b = let val qs = Binding.path_of base_b; val n = Binding.name_of base_b; in Binding.prefix_name rawN #> fold_rev (fn (s, mand) => Binding.qualify mand s) (qs @ [(n, true)]) #> extra_qualify #> Binding.concealed end; fun fixpoint_bnf force_out_of_line extra_qualify construct_fp bs resBs Ds0 Xs rhsXs comp_cache0 lthy = let val time = time lthy; val timer = time (Timer.startRealTimer ()); fun flatten_tyargs Ass = subtract (op =) Xs (filter (fn T => exists (fn Ts => member (op =) Ts T) Ass) resBs) @ Xs; val ((bnfs, (deadss, livess)), (comp_cache_unfold_set, lthy')) = apfst (apsnd split_list o split_list) (@{fold_map 2} (fn b => bnf_of_typ true Smart_Inline (raw_qualify extra_qualify b) flatten_tyargs Xs Ds0) bs rhsXs ((comp_cache0, empty_unfolds), lthy)); fun norm_qualify i = Binding.qualify true (Binding.name_of (nth bs (Int.max (0, i - 1)))) #> extra_qualify #> Binding.concealed; val Ass = map (map dest_TFree) livess; val Ds' = fold (fold Term.add_tfreesT) deadss []; val Ds = union (op =) Ds' Ds0; val missing = resBs |> fold (subtract (op =)) (Ds' :: Ass); val (dead_phantoms, live_phantoms) = List.partition (member (op =) Ds0) missing; val resBs' = resBs |> fold (subtract (op =)) [dead_phantoms, Ds]; val timer = time (timer "Construction of BNFs"); val ((kill_posss, _), (bnfs', ((comp_cache', unfold_set'), lthy''))) = normalize_bnfs norm_qualify Ass Ds (K (resBs' @ Xs)) bnfs (comp_cache_unfold_set, lthy'); val Dss = @{map 3} (fn lives => fn kill_posss => fn deads => deads @ map (nth lives) kill_posss) livess kill_posss deadss; val all_Dss = Dss |> force_out_of_line ? map (fn Ds' => union (op =) Ds' (map TFree Ds0)); fun pre_qualify b = Binding.qualify false (Binding.name_of b) #> extra_qualify #> not (Config.get lthy'' bnf_internals) ? Binding.concealed; val ((pre_bnfs, (deadss, absT_infos)), lthy''') = lthy'' |> @{fold_map 5} (fn b => seal_bnf (pre_qualify b) unfold_set' (Binding.prefix_name preN b)) bs (replicate (length rhsXs) (force_out_of_line orelse not (null live_phantoms))) Dss all_Dss bnfs' |>> split_list |>> apsnd split_list; val timer = time (timer "Normalization & sealing of BNFs"); val res = construct_fp bs resBs (map TFree dead_phantoms, deadss) pre_bnfs absT_infos lthy'''; val timer = time (timer "FP construction in total"); in (((pre_bnfs, absT_infos), comp_cache'), res) end; (** document antiquotations **) local -fun antiquote_setup binding = +fun antiquote_setup binding co = Thy_Output.antiquotation_pretty_source_embedded binding - (Args.type_name {proper = true, strict = true}) - (fn ctxt => fn fcT_name => - (case Ctr_Sugar.ctr_sugar_of ctxt fcT_name of - NONE => error ("Not a known freely generated type name: " ^ quote fcT_name) - | SOME {T = T0, ctrs = ctrs0, ...} => - let - val freezeT = Term.map_atyps (fn TVar ((s, _), S) => TFree (s, S) | T => T); + ((Scan.ahead (Scan.lift Parse.not_eof) >> Token.pos_of) -- + Args.type_name {proper = true, strict = true}) + (fn ctxt => fn (pos, type_name) => + let + fun err () = + error ("Bad " ^ Binding.name_of binding ^ ": " ^ quote type_name ^ Position.here pos); + in + (case Ctr_Sugar.ctr_sugar_of ctxt type_name of + NONE => err () + | SOME {kind, T = T0, ctrs = ctrs0, ...} => + let + val _ = if co = (kind = Codatatype) then () else err (); - val T = freezeT T0; - val ctrs = map (Term.map_types freezeT) ctrs0; + val T = Logic.unvarifyT_global T0; + val ctrs = map Logic.unvarify_global ctrs0; - val pretty_typ_bracket = Syntax.pretty_typ (Config.put pretty_priority 1001 ctxt); - fun pretty_ctr ctr = - Pretty.block (Pretty.breaks (Syntax.pretty_term ctxt ctr :: - map pretty_typ_bracket (binder_types (fastype_of ctr)))); - in - Pretty.block (Pretty.keyword1 (Binding.name_of binding) :: Pretty.brk 1 :: - Syntax.pretty_typ ctxt T :: Pretty.str " =" :: Pretty.brk 1 :: - flat (separate [Pretty.brk 1, Pretty.str "| "] (map (single o pretty_ctr) ctrs))) - end)); + val pretty_typ_bracket = Syntax.pretty_typ (Config.put pretty_priority 1001 ctxt); + fun pretty_ctr ctr = + Pretty.block (Pretty.breaks (Syntax.pretty_term ctxt ctr :: + map pretty_typ_bracket (binder_types (fastype_of ctr)))); + in + Pretty.block (Pretty.keyword1 (Binding.name_of binding) :: Pretty.brk 1 :: + Syntax.pretty_typ ctxt T :: Pretty.str " =" :: Pretty.brk 1 :: + flat (separate [Pretty.brk 1, Pretty.str "| "] (map (single o pretty_ctr) ctrs))) + end) + end); in val _ = Theory.setup - (antiquote_setup \<^binding>\datatype\ #> - antiquote_setup \<^binding>\codatatype\); + (antiquote_setup \<^binding>\datatype\ false #> + antiquote_setup \<^binding>\codatatype\ true); end; end;