diff -r 8c3eec5812d8 -r ae44f16dcea5 src/HOL/Tools/BNF/bnf_def.ML --- a/src/HOL/Tools/BNF/bnf_def.ML Tue Feb 16 17:01:40 2016 +0100 +++ b/src/HOL/Tools/BNF/bnf_def.ML Tue Feb 16 22:28:19 2016 +0100 @@ -32,18 +32,21 @@ val nwits_of_bnf: bnf -> int val mapN: string + val predN: string val relN: string val setN: string val mk_setN: int -> string val mk_witN: int -> string val map_of_bnf: bnf -> term + val pred_of_bnf: bnf -> term + val rel_of_bnf: bnf -> term val sets_of_bnf: bnf -> term list - val rel_of_bnf: bnf -> term val mk_T_of_bnf: typ list -> typ list -> bnf -> typ val mk_bd_of_bnf: typ list -> typ list -> bnf -> term val mk_map_of_bnf: typ list -> typ list -> typ list -> bnf -> term + val mk_pred_of_bnf: typ list -> typ list -> bnf -> term val mk_rel_of_bnf: typ list -> typ list -> typ list -> bnf -> term val mk_sets_of_bnf: typ list list -> typ list list -> bnf -> term list val mk_wits_of_bnf: typ list list -> typ list list -> bnf -> (int list * term) list @@ -60,10 +63,12 @@ val in_rel_of_bnf: bnf -> thm val inj_map_of_bnf: bnf -> thm val inj_map_strong_of_bnf: bnf -> thm + val le_rel_OO_of_bnf: bnf -> thm val map_comp0_of_bnf: bnf -> thm val map_comp_of_bnf: bnf -> thm val map_cong0_of_bnf: bnf -> thm val map_cong_of_bnf: bnf -> thm + val map_cong_pred_of_bnf: bnf -> thm val map_cong_simp_of_bnf: bnf -> thm val map_def_of_bnf: bnf -> thm val map_id0_of_bnf: bnf -> thm @@ -71,27 +76,36 @@ val map_ident0_of_bnf: bnf -> thm val map_ident_of_bnf: bnf -> thm val map_transfer_of_bnf: bnf -> thm - val le_rel_OO_of_bnf: bnf -> thm - val rel_def_of_bnf: bnf -> thm + val pred_cong0_of_bnf: bnf -> thm + val pred_cong_of_bnf: bnf -> thm + val pred_cong_simp_of_bnf: bnf -> thm + val pred_def_of_bnf: bnf -> thm + val pred_map_of_bnf: bnf -> thm + val pred_mono_strong0_of_bnf: bnf -> thm + val pred_mono_strong_of_bnf: bnf -> thm + val pred_set_of_bnf: bnf -> thm + val pred_rel_of_bnf: bnf -> thm val rel_Grp_of_bnf: bnf -> thm + val rel_OO_Grp_of_bnf: bnf -> thm val rel_OO_of_bnf: bnf -> thm - val rel_OO_Grp_of_bnf: bnf -> thm val rel_cong0_of_bnf: bnf -> thm val rel_cong_of_bnf: bnf -> thm val rel_cong_simp_of_bnf: bnf -> thm val rel_conversep_of_bnf: bnf -> thm + val rel_def_of_bnf: bnf -> thm + val rel_eq_of_bnf: bnf -> thm + val rel_flip_of_bnf: bnf -> thm + val rel_map_of_bnf: bnf -> thm list val rel_mono_of_bnf: bnf -> thm val rel_mono_strong0_of_bnf: bnf -> thm val rel_mono_strong_of_bnf: bnf -> thm + val rel_eq_onp_of_bnf: bnf -> thm val rel_refl_of_bnf: bnf -> thm val rel_refl_strong_of_bnf: bnf -> thm val rel_reflp_of_bnf: bnf -> thm val rel_symp_of_bnf: bnf -> thm + val rel_transfer_of_bnf: bnf -> thm val rel_transp_of_bnf: bnf -> thm - val rel_map_of_bnf: bnf -> thm list - val rel_transfer_of_bnf: bnf -> thm - val rel_eq_of_bnf: bnf -> thm - val rel_flip_of_bnf: bnf -> thm val set_bd_of_bnf: bnf -> thm list val set_defs_of_bnf: bnf -> thm list val set_map0_of_bnf: bnf -> thm list @@ -114,7 +128,7 @@ val minimize_wits: (''a list * 'b) list -> (''a list * 'b) list val wits_of_bnf: bnf -> nonemptiness_witness list - val zip_axioms: 'a -> 'a -> 'a -> 'a list -> 'a -> 'a -> 'a list -> 'a -> 'a -> 'a list + val zip_axioms: 'a -> 'a -> 'a -> 'a list -> 'a -> 'a -> 'a list -> 'a -> 'a -> 'a -> 'a list datatype inline_policy = Dont_Inline | Hardly_Inline | Smart_Inline | Do_Inline datatype fact_policy = Dont_Note | Note_Some | Note_All @@ -128,30 +142,34 @@ val print_bnfs: Proof.context -> unit val prepare_def: inline_policy -> (Proof.context -> fact_policy) -> bool -> (binding -> binding) -> (Proof.context -> 'a -> typ) -> (Proof.context -> 'b -> term) -> - typ list option -> binding -> binding -> binding list -> - (((((binding * 'a) * 'b) * 'b list) * 'b) * 'b list) * 'b option -> Proof.context -> + typ list option -> binding -> binding -> binding -> binding list -> + ((((((binding * 'a) * 'b) * 'b list) * 'b) * 'b list) * 'b option) * 'b option -> + Proof.context -> string * term list * ((Proof.context -> thm list -> tactic) option * term list list) * ((thm list -> thm list list) -> thm list list -> Proof.context -> bnf * local_theory) * local_theory * thm list val define_bnf_consts: inline_policy -> fact_policy -> bool -> typ list option -> - binding -> binding -> binding list -> - (((((binding * typ) * term) * term list) * term) * term list) * term option -> local_theory -> + binding -> binding -> binding -> binding list -> + ((((((binding * typ) * term) * term list) * term) * term list) * term option) * term option -> + local_theory -> ((typ list * typ list * typ list * typ) * - (term * term list * term * (int list * term) list * term) * - (thm * thm list * thm * thm list * thm) * + (term * term list * term * (int list * term) list * term * term) * + (thm * thm list * thm * thm list * thm * thm) * ((typ list -> typ list -> typ list -> term) * (typ list -> typ list -> term -> term) * (typ list -> typ list -> typ -> typ) * (typ list -> typ list -> typ list -> term) * - (typ list -> typ list -> typ list -> term))) * local_theory + (typ list -> typ list -> term) * + (typ list -> typ list -> typ list -> term) * + (typ list -> typ list -> term))) * local_theory val bnf_def: inline_policy -> (Proof.context -> fact_policy) -> bool -> (binding -> binding) -> (Proof.context -> tactic) list -> (Proof.context -> tactic) -> typ list option -> binding -> - binding -> binding list -> - (((((binding * typ) * term) * term list) * term) * term list) * term option -> local_theory -> - bnf * local_theory - val bnf_cmd: ((((((binding * string) * string) * string list) * string) * string list) - * string option) * (Proof.context -> Plugin_Name.filter) -> + binding -> binding -> binding list -> + ((((((binding * typ) * term) * term list) * term) * term list) * term option) * term option -> + local_theory -> bnf * local_theory + val bnf_cmd: (((((((binding * string) * string) * string list) * string) * string list) + * string option) * string option) * (Proof.context -> Plugin_Name.filter) -> Proof.context -> Proof.state end; @@ -174,12 +192,13 @@ bd_cinfinite: thm, set_bd: thm list, le_rel_OO: thm, - rel_OO_Grp: thm + rel_OO_Grp: thm, + pred_set: thm }; -fun mk_axioms' ((((((((id, comp), cong), map), c_o), cinf), set_bd), le_rel_OO), rel) = +fun mk_axioms' (((((((((id, comp), cong), map), c_o), cinf), set_bd), le_rel_OO), rel), pred) = {map_id0 = id, map_comp0 = comp, map_cong0 = cong, set_map0 = map, bd_card_order = c_o, - bd_cinfinite = cinf, set_bd = set_bd, le_rel_OO = le_rel_OO, rel_OO_Grp = rel}; + bd_cinfinite = cinf, set_bd = set_bd, le_rel_OO = le_rel_OO, rel_OO_Grp = rel, pred_set = pred}; fun dest_cons [] = raise List.Empty | dest_cons (x :: xs) = (x, xs); @@ -194,19 +213,15 @@ ||>> dest_cons ||>> chop n ||>> dest_cons + ||>> dest_cons ||> the_single |> mk_axioms'; -fun zip_axioms mid mcomp mcong smap bdco bdinf sbd le_rel_OO rel = - [mid, mcomp, mcong] @ smap @ [bdco, bdinf] @ sbd @ [le_rel_OO, rel]; - -fun dest_axioms {map_id0, map_comp0, map_cong0, set_map0, bd_card_order, bd_cinfinite, set_bd, - le_rel_OO, rel_OO_Grp} = - zip_axioms map_id0 map_comp0 map_cong0 set_map0 bd_card_order bd_cinfinite set_bd le_rel_OO - rel_OO_Grp; +fun zip_axioms mid mcomp mcong smap bdco bdinf sbd le_rel_OO rel pred = + [mid, mcomp, mcong] @ smap @ [bdco, bdinf] @ sbd @ [le_rel_OO, rel, pred]; fun map_axioms f {map_id0, map_comp0, map_cong0, set_map0, bd_card_order, bd_cinfinite, set_bd, - le_rel_OO, rel_OO_Grp} = + le_rel_OO, rel_OO_Grp,pred_set} = {map_id0 = f map_id0, map_comp0 = f map_comp0, map_cong0 = f map_cong0, @@ -215,20 +230,22 @@ bd_cinfinite = f bd_cinfinite, set_bd = map f set_bd, le_rel_OO = f le_rel_OO, - rel_OO_Grp = f rel_OO_Grp}; + rel_OO_Grp = f rel_OO_Grp, + pred_set = f pred_set}; val morph_axioms = map_axioms o Morphism.thm; type defs = { map_def: thm, set_defs: thm list, - rel_def: thm + rel_def: thm, + pred_def: thm } -fun mk_defs map sets rel = {map_def = map, set_defs = sets, rel_def = rel}; +fun mk_defs map sets rel pred = {map_def = map, set_defs = sets, rel_def = rel, pred_def = pred}; -fun map_defs f {map_def, set_defs, rel_def} = - {map_def = f map_def, set_defs = map f set_defs, rel_def = f rel_def}; +fun map_defs f {map_def, set_defs, rel_def, pred_def} = + {map_def = f map_def, set_defs = map f set_defs, rel_def = f rel_def, pred_def = f pred_def}; val morph_defs = map_defs o Morphism.thm; @@ -246,6 +263,7 @@ map_comp: thm lazy, map_cong: thm lazy, map_cong_simp: thm lazy, + map_cong_pred: thm lazy, map_id: thm lazy, map_ident0: thm lazy, map_ident: thm lazy, @@ -269,14 +287,24 @@ rel_reflp: thm lazy, rel_symp: thm lazy, rel_transp: thm lazy, - rel_transfer: thm lazy + rel_transfer: thm lazy, + rel_eq_onp: thm lazy, + pred_True: thm lazy, + pred_map: thm lazy, + pred_rel: thm lazy, + pred_mono_strong0: thm lazy, + pred_mono_strong: thm lazy, + pred_cong0: thm lazy, + pred_cong: thm lazy, + pred_cong_simp: thm lazy }; fun mk_facts bd_Card_order bd_Cinfinite bd_Cnotzero collect_set_map in_bd in_cong in_mono in_rel - inj_map inj_map_strong map_comp map_cong map_cong_simp map_id map_ident0 map_ident map_transfer - rel_eq rel_flip set_map rel_cong0 rel_cong rel_cong_simp rel_map rel_mono rel_mono_strong0 - rel_mono_strong set_transfer rel_Grp rel_conversep rel_OO rel_refl rel_refl_strong rel_reflp - rel_symp rel_transp rel_transfer = { + inj_map inj_map_strong map_comp map_cong map_cong_simp map_cong_pred map_id map_ident0 map_ident + map_transfer rel_eq rel_flip set_map rel_cong0 rel_cong rel_cong_simp rel_map rel_mono + rel_mono_strong0 rel_mono_strong set_transfer rel_Grp rel_conversep rel_OO rel_refl + rel_refl_strong rel_reflp rel_symp rel_transp rel_transfer rel_eq_onp pred_True pred_map pred_rel + pred_mono_strong0 pred_mono_strong pred_cong0 pred_cong pred_cong_simp = { bd_Card_order = bd_Card_order, bd_Cinfinite = bd_Cinfinite, bd_Cnotzero = bd_Cnotzero, @@ -290,6 +318,7 @@ map_comp = map_comp, map_cong = map_cong, map_cong_simp = map_cong_simp, + map_cong_pred = map_cong_pred, map_id = map_id, map_ident0 = map_ident0, map_ident = map_ident, @@ -313,7 +342,16 @@ rel_reflp = rel_reflp, rel_symp = rel_symp, rel_transp = rel_transp, - set_transfer = set_transfer}; + set_transfer = set_transfer, + rel_eq_onp = rel_eq_onp, + pred_True = pred_True, + pred_map = pred_map, + pred_rel = pred_rel, + pred_mono_strong0 = pred_mono_strong0, + pred_mono_strong = pred_mono_strong, + pred_cong0 = pred_cong0, + pred_cong = pred_cong, + pred_cong_simp = pred_cong_simp}; fun map_facts f { bd_Card_order, @@ -329,6 +367,7 @@ map_comp, map_cong, map_cong_simp, + map_cong_pred, map_id, map_ident0, map_ident, @@ -352,7 +391,16 @@ rel_reflp, rel_symp, rel_transp, - set_transfer} = + set_transfer, + rel_eq_onp, + pred_True, + pred_map, + pred_rel, + pred_mono_strong0, + pred_mono_strong, + pred_cong0, + pred_cong, + pred_cong_simp} = {bd_Card_order = f bd_Card_order, bd_Cinfinite = f bd_Cinfinite, bd_Cnotzero = f bd_Cnotzero, @@ -366,6 +414,7 @@ map_comp = Lazy.map f map_comp, map_cong = Lazy.map f map_cong, map_cong_simp = Lazy.map f map_cong_simp, + map_cong_pred = Lazy.map f map_cong_pred, map_id = Lazy.map f map_id, map_ident0 = Lazy.map f map_ident0, map_ident = Lazy.map f map_ident, @@ -389,7 +438,16 @@ rel_reflp = Lazy.map f rel_reflp, rel_symp = Lazy.map f rel_symp, rel_transp = Lazy.map f rel_transp, - set_transfer = Lazy.map (map f) set_transfer}; + set_transfer = Lazy.map (map f) set_transfer, + rel_eq_onp = Lazy.map f rel_eq_onp, + pred_True = Lazy.map f pred_True, + pred_map = Lazy.map f pred_map, + pred_rel = Lazy.map f pred_rel, + pred_mono_strong0 = Lazy.map f pred_mono_strong0, + pred_mono_strong = Lazy.map f pred_mono_strong, + pred_cong0 = Lazy.map f pred_cong0, + pred_cong = Lazy.map f pred_cong, + pred_cong_simp = Lazy.map f pred_cong_simp}; val morph_facts = map_facts o Morphism.thm; @@ -419,7 +477,8 @@ facts: facts, nwits: int, wits: nonemptiness_witness list, - rel: term + rel: term, + pred: term }; (* getters *) @@ -482,13 +541,20 @@ Term.subst_atomic_types ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts) @ (#lives' bnf_rep ~~ Us)) (#rel bnf_rep) end; +val pred_of_bnf = #pred o rep_bnf; +fun mk_pred_of_bnf Ds Ts bnf = + let val bnf_rep = rep_bnf bnf; + in + Term.subst_atomic_types + ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts)) (#pred bnf_rep) + end; (*thms*) -val bd_card_order_of_bnf = #bd_card_order o #axioms o rep_bnf; -val bd_cinfinite_of_bnf = #bd_cinfinite o #axioms o rep_bnf; val bd_Card_order_of_bnf = #bd_Card_order o #facts o rep_bnf; val bd_Cinfinite_of_bnf = #bd_Cinfinite o #facts o rep_bnf; val bd_Cnotzero_of_bnf = #bd_Cnotzero o #facts o rep_bnf; +val bd_card_order_of_bnf = #bd_card_order o #axioms o rep_bnf; +val bd_cinfinite_of_bnf = #bd_cinfinite o #axioms o rep_bnf; val collect_set_map_of_bnf = Lazy.force o #collect_set_map o #facts o rep_bnf; val in_bd_of_bnf = Lazy.force o #in_bd o #facts o rep_bnf; val in_cong_of_bnf = Lazy.force o #in_cong o #facts o rep_bnf; @@ -496,29 +562,40 @@ val in_rel_of_bnf = Lazy.force o #in_rel o #facts o rep_bnf; val inj_map_of_bnf = Lazy.force o #inj_map o #facts o rep_bnf; val inj_map_strong_of_bnf = Lazy.force o #inj_map_strong o #facts o rep_bnf; +val le_rel_OO_of_bnf = #le_rel_OO o #axioms o rep_bnf; +val map_comp0_of_bnf = #map_comp0 o #axioms o rep_bnf; +val map_comp_of_bnf = Lazy.force o #map_comp o #facts o rep_bnf; +val map_cong0_of_bnf = #map_cong0 o #axioms o rep_bnf; +val map_cong_of_bnf = Lazy.force o #map_cong o #facts o rep_bnf; +val map_cong_pred_of_bnf = Lazy.force o #map_cong_pred o #facts o rep_bnf; +val map_cong_simp_of_bnf = Lazy.force o #map_cong_simp o #facts o rep_bnf; val map_def_of_bnf = #map_def o #defs o rep_bnf; val map_id0_of_bnf = #map_id0 o #axioms o rep_bnf; val map_id_of_bnf = Lazy.force o #map_id o #facts o rep_bnf; val map_ident0_of_bnf = Lazy.force o #map_ident0 o #facts o rep_bnf; val map_ident_of_bnf = Lazy.force o #map_ident o #facts o rep_bnf; -val map_comp0_of_bnf = #map_comp0 o #axioms o rep_bnf; -val map_comp_of_bnf = Lazy.force o #map_comp o #facts o rep_bnf; -val map_cong0_of_bnf = #map_cong0 o #axioms o rep_bnf; -val map_cong_of_bnf = Lazy.force o #map_cong o #facts o rep_bnf; -val map_cong_simp_of_bnf = Lazy.force o #map_cong_simp o #facts o rep_bnf; val map_transfer_of_bnf = Lazy.force o #map_transfer o #facts o rep_bnf; -val le_rel_OO_of_bnf = #le_rel_OO o #axioms o rep_bnf; +val rel_eq_onp_of_bnf = Lazy.force o #rel_eq_onp o #facts o rep_bnf; +val pred_rel_of_bnf = Lazy.force o #pred_rel o #facts o rep_bnf; +val pred_map_of_bnf = Lazy.force o #pred_map o #facts o rep_bnf; +val pred_mono_strong0_of_bnf = Lazy.force o #pred_mono_strong0 o #facts o rep_bnf; +val pred_mono_strong_of_bnf = Lazy.force o #pred_mono_strong o #facts o rep_bnf; +val pred_cong0_of_bnf = Lazy.force o #pred_cong0 o #facts o rep_bnf; +val pred_cong_of_bnf = Lazy.force o #pred_cong o #facts o rep_bnf; +val pred_cong_simp_of_bnf = Lazy.force o #pred_cong_simp o #facts o rep_bnf; +val pred_def_of_bnf = #pred_def o #defs o rep_bnf; +val pred_set_of_bnf = #pred_set o #axioms o rep_bnf; +val rel_Grp_of_bnf = Lazy.force o #rel_Grp o #facts o rep_bnf; +val rel_OO_Grp_of_bnf = #rel_OO_Grp o #axioms o rep_bnf; +val rel_OO_of_bnf = Lazy.force o #rel_OO o #facts o rep_bnf; +val rel_cong0_of_bnf = Lazy.force o #rel_cong0 o #facts o rep_bnf; +val rel_cong_of_bnf = Lazy.force o #rel_cong o #facts o rep_bnf; +val rel_cong_simp_of_bnf = Lazy.force o #rel_cong_simp o #facts o rep_bnf; +val rel_conversep_of_bnf = Lazy.force o #rel_conversep o #facts o rep_bnf; val rel_def_of_bnf = #rel_def o #defs o rep_bnf; val rel_eq_of_bnf = Lazy.force o #rel_eq o #facts o rep_bnf; val rel_flip_of_bnf = Lazy.force o #rel_flip o #facts o rep_bnf; -val set_bd_of_bnf = #set_bd o #axioms o rep_bnf; -val set_defs_of_bnf = #set_defs o #defs o rep_bnf; -val set_map0_of_bnf = #set_map0 o #axioms o rep_bnf; -val set_map_of_bnf = map Lazy.force o #set_map o #facts o rep_bnf; -val set_transfer_of_bnf = Lazy.force o #set_transfer o #facts o rep_bnf; -val rel_cong0_of_bnf = Lazy.force o #rel_cong0 o #facts o rep_bnf; -val rel_cong_of_bnf = Lazy.force o #rel_cong o #facts o rep_bnf; -val rel_cong_simp_of_bnf = Lazy.force o #rel_cong_simp o #facts o rep_bnf; +val rel_map_of_bnf = Lazy.force o #rel_map o #facts o rep_bnf; val rel_mono_of_bnf = Lazy.force o #rel_mono o #facts o rep_bnf; val rel_mono_strong0_of_bnf = Lazy.force o #rel_mono_strong0 o #facts o rep_bnf; val rel_mono_strong_of_bnf = Lazy.force o #rel_mono_strong o #facts o rep_bnf; @@ -526,33 +603,33 @@ val rel_refl_strong_of_bnf = Lazy.force o #rel_refl_strong o #facts o rep_bnf; val rel_reflp_of_bnf = Lazy.force o #rel_reflp o #facts o rep_bnf; val rel_symp_of_bnf = Lazy.force o #rel_symp o #facts o rep_bnf; +val rel_transfer_of_bnf = Lazy.force o #rel_transfer o #facts o rep_bnf; val rel_transp_of_bnf = Lazy.force o #rel_transp o #facts o rep_bnf; -val rel_map_of_bnf = Lazy.force o #rel_map o #facts o rep_bnf; -val rel_transfer_of_bnf = Lazy.force o #rel_transfer o #facts o rep_bnf; -val rel_Grp_of_bnf = Lazy.force o #rel_Grp o #facts o rep_bnf; -val rel_conversep_of_bnf = Lazy.force o #rel_conversep o #facts o rep_bnf; -val rel_OO_of_bnf = Lazy.force o #rel_OO o #facts o rep_bnf; -val rel_OO_Grp_of_bnf = #rel_OO_Grp o #axioms o rep_bnf; +val set_bd_of_bnf = #set_bd o #axioms o rep_bnf; +val set_defs_of_bnf = #set_defs o #defs o rep_bnf; +val set_map0_of_bnf = #set_map0 o #axioms o rep_bnf; +val set_map_of_bnf = map Lazy.force o #set_map o #facts o rep_bnf; +val set_transfer_of_bnf = Lazy.force o #set_transfer o #facts o rep_bnf; val wit_thms_of_bnf = maps #prop o wits_of_bnf; val wit_thmss_of_bnf = map #prop o wits_of_bnf; -fun mk_bnf name T live lives lives' dead deads map sets bd axioms defs facts wits rel = +fun mk_bnf name T live lives lives' dead deads map sets bd axioms defs facts wits rel pred = BNF {name = name, T = T, live = live, lives = lives, lives' = lives', dead = dead, deads = deads, map = map, sets = sets, bd = bd, axioms = axioms, defs = defs, facts = facts, - nwits = length wits, wits = wits, rel = rel}; + nwits = length wits, wits = wits, rel = rel, pred = pred}; -fun map_bnf f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 +fun map_bnf f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 (BNF {name = name, T = T, live = live, lives = lives, lives' = lives', dead = dead, deads = deads, map = map, sets = sets, bd = bd, axioms = axioms, defs = defs, facts = facts, - nwits = nwits, wits = wits, rel = rel}) = + nwits = nwits, wits = wits, rel = rel, pred = pred}) = BNF {name = f1 name, T = f2 T, live = f3 live, lives = f4 lives, lives' = f5 lives', dead = f6 dead, deads = f7 deads, map = f8 map, sets = f9 sets, bd = f10 bd, axioms = f11 axioms, defs = f12 defs, facts = f13 facts, - nwits = f14 nwits, wits = f15 wits, rel = f16 rel}; + nwits = f14 nwits, wits = f15 wits, rel = f16 rel, pred = f17 pred}; fun morph_bnf phi = let @@ -560,10 +637,10 @@ val tphi = Morphism.term phi; in map_bnf (Morphism.binding phi) Tphi I (map Tphi) (map Tphi) I (map Tphi) tphi (map tphi) tphi - (morph_axioms phi) (morph_defs phi) (morph_facts phi) I (map (morph_witness phi)) tphi + (morph_axioms phi) (morph_defs phi) (morph_facts phi) I (map (morph_witness phi)) tphi tphi end; -fun morph_bnf_defs phi = map_bnf I I I I I I I I I I I (morph_defs phi) I I I I; +fun morph_bnf_defs phi = map_bnf I I I I I I I I I I I (morph_defs phi) I I I I I; val transfer_bnf = morph_bnf o Morphism.transfer_morphism; @@ -600,6 +677,15 @@ in Envir.subst_term (tyenv, Vartab.empty) rel end handle Type.TYPE_MATCH => error "Bad relator"; +fun normalize_pred ctxt instTs instA pred = + let + val thy = Proof_Context.theory_of ctxt; + val tyenv = + Sign.typ_match thy (fastype_of pred, Library.foldr (op -->) (instTs, mk_pred1T instA)) + Vartab.empty; + in Envir.subst_term (tyenv, Vartab.empty) pred end + handle Type.TYPE_MATCH => error "Bad predicator"; + fun normalize_wit insts CA As wit = let fun strip_param (Ts, T as Type (@{type_name fun}, [T1, T2])) = @@ -677,49 +763,60 @@ val witN = "wit"; fun mk_witN i = witN ^ nonzero_string_of_int i; val relN = "rel"; +val predN = "pred"; -val bd_card_orderN = "bd_card_order"; -val bd_cinfiniteN = "bd_cinfinite"; val bd_Card_orderN = "bd_Card_order"; val bd_CinfiniteN = "bd_Cinfinite"; val bd_CnotzeroN = "bd_Cnotzero"; +val bd_card_orderN = "bd_card_order"; +val bd_cinfiniteN = "bd_cinfinite"; val collect_set_mapN = "collect_set_map"; val in_bdN = "in_bd"; val in_monoN = "in_mono"; val in_relN = "in_rel"; val inj_mapN = "inj_map"; val inj_map_strongN = "inj_map_strong"; -val map_id0N = "map_id0"; -val map_idN = "map_id"; -val map_identN = "map_ident"; val map_comp0N = "map_comp0"; val map_compN = "map_comp"; val map_cong0N = "map_cong0"; val map_congN = "map_cong"; val map_cong_simpN = "map_cong_simp"; +val map_cong_predN = "map_cong_pred"; +val map_id0N = "map_id0"; +val map_idN = "map_id"; +val map_identN = "map_ident"; val map_transferN = "map_transfer"; +val pred_mono_strong0N = "pred_mono_strong0"; +val pred_mono_strongN = "pred_mono_strong"; +val pred_TrueN = "pred_True"; +val pred_mapN = "pred_map"; +val pred_relN = "pred_rel"; +val pred_setN = "pred_set"; +val pred_congN = "pred_cong"; +val pred_cong_simpN = "pred_cong_simp"; +val rel_GrpN = "rel_Grp"; +val rel_comppN = "rel_compp"; +val rel_compp_GrpN = "rel_compp_Grp"; +val rel_congN = "rel_cong"; +val rel_cong_simpN = "rel_cong_simp"; +val rel_conversepN = "rel_conversep"; val rel_eqN = "rel_eq"; +val rel_eq_onpN = "rel_eq_onp"; val rel_flipN = "rel_flip"; -val set_map0N = "set_map0"; -val set_mapN = "set_map"; -val set_bdN = "set_bd"; -val set_transferN = "set_transfer"; -val rel_GrpN = "rel_Grp"; -val rel_conversepN = "rel_conversep"; val rel_mapN = "rel_map"; val rel_monoN = "rel_mono"; val rel_mono_strong0N = "rel_mono_strong0"; val rel_mono_strongN = "rel_mono_strong"; -val rel_congN = "rel_cong"; -val rel_cong_simpN = "rel_cong_simp"; val rel_reflN = "rel_refl"; val rel_refl_strongN = "rel_refl_strong"; val rel_reflpN = "rel_reflp"; val rel_sympN = "rel_symp"; +val rel_transferN = "rel_transfer"; val rel_transpN = "rel_transp"; -val rel_transferN = "rel_transfer"; -val rel_comppN = "rel_compp"; -val rel_compp_GrpN = "rel_compp_Grp"; +val set_bdN = "set_bd"; +val set_map0N = "set_map0"; +val set_mapN = "set_map"; +val set_transferN = "set_transfer"; datatype inline_policy = Dont_Inline | Hardly_Inline | Smart_Inline | Do_Inline; @@ -755,6 +852,7 @@ (in_monoN, [Lazy.force (#in_mono facts)]), (map_comp0N, [#map_comp0 axioms]), (rel_mono_strong0N, [Lazy.force (#rel_mono_strong0 facts)]), + (pred_mono_strong0N, [Lazy.force (#pred_mono_strong0 facts)]), (set_map0N, #set_map0 axioms), (set_bdN, #set_bd axioms)] @ (witNs ~~ wit_thmss_of_bnf bnf) @@ -775,14 +873,23 @@ (map_cong0N, [#map_cong0 axioms], []), (map_congN, [Lazy.force (#map_cong facts)], fundefcong_attrs), (map_cong_simpN, [Lazy.force (#map_cong_simp facts)], []), + (map_cong_predN, [Lazy.force (#map_cong_pred facts)], []), (map_idN, [Lazy.force (#map_id facts)], []), (map_id0N, [#map_id0 axioms], []), (map_transferN, [Lazy.force (#map_transfer facts)], []), (map_identN, [Lazy.force (#map_ident facts)], []), + (pred_mono_strongN, [Lazy.force (#pred_mono_strong facts)], []), + (pred_congN, [Lazy.force (#pred_cong facts)], fundefcong_attrs), + (pred_cong_simpN, [Lazy.force (#pred_cong_simp facts)], []), + (pred_mapN, [Lazy.force (#pred_map facts)], []), + (pred_relN, [Lazy.force (#pred_rel facts)], []), + (pred_TrueN, [Lazy.force (#pred_True facts)], []), + (pred_setN, [#pred_set axioms], []), (rel_comppN, [Lazy.force (#rel_OO facts)], []), (rel_compp_GrpN, no_refl [#rel_OO_Grp axioms], []), (rel_conversepN, [Lazy.force (#rel_conversep facts)], []), (rel_eqN, [Lazy.force (#rel_eq facts)], []), + (rel_eq_onpN, [Lazy.force (#rel_eq_onp facts)], []), (rel_flipN, [Lazy.force (#rel_flip facts)], []), (rel_GrpN, [Lazy.force (#rel_Grp facts)], []), (rel_mapN, Lazy.force (#rel_map facts), []), @@ -831,8 +938,9 @@ (* Define new BNFs *) -fun define_bnf_consts const_policy fact_policy internal Ds_opt map_b rel_b set_bs - ((((((bnf_b, T_rhs), map_rhs), set_rhss), bd_rhs), wit_rhss), rel_rhs_opt) no_defs_lthy = +fun define_bnf_consts const_policy fact_policy internal Ds_opt map_b rel_b pred_b set_bs + (((((((bnf_b, T_rhs), map_rhs), set_rhss), bd_rhs), wit_rhss), rel_rhs_opt), pred_rhs_opt) + no_defs_lthy = let val live = length set_rhss; @@ -947,7 +1055,7 @@ (*Grp (in (Collect (split R1) .. Collect (split Rn))) (map fst .. fst)^--1 OO Grp (in (Collect (split R1) .. Collect (split Rn))) (map snd .. snd)*) - val OO_Grp = + val rel_spec = let val map1 = Term.list_comb (mk_bnf_map Ds RTs As, map fst_const RTs); val map2 = Term.list_comb (mk_bnf_map Ds RTs Bs, map snd_const RTs); @@ -957,12 +1065,34 @@ |> fold_rev Term.absfree Rs' end; - val rel_rhs = the_default OO_Grp rel_rhs_opt; + val rel_rhs = the_default rel_spec rel_rhs_opt; val rel_bind_def = (fn () => def_qualify (if Binding.is_empty rel_b then mk_prefix_binding relN else rel_b), rel_rhs); + val pred_spec = + if live = 0 then Term.absdummy (mk_bnf_T Ds As Calpha) @{term True} else + let + val sets = map (mk_bnf_t Ds As) bnf_sets; + val argTs = map mk_pred1T As; + val T = mk_bnf_T Ds As Calpha; + val ((Ps, Ps'), x) = lthy + |> mk_Frees' "P" argTs + ||>> yield_singleton (mk_Frees "x") T + |> fst; + val conjs = map2 (fn set => fn P => mk_Ball (set $ x) P) sets Ps; + in + fold_rev Term.absfree Ps' + (Term.absfree (dest_Free x) (Library.foldr1 HOLogic.mk_conj conjs)) + end; + + val pred_rhs = the_default pred_spec pred_rhs_opt; + + val pred_bind_def = + (fn () => def_qualify (if Binding.is_empty pred_b then mk_prefix_binding predN else pred_b), + pred_rhs); + val wit_rhss = if null wit_rhss then [fold_rev Term.absdummy As (Term.list_comb (mk_bnf_map Ds As As, @@ -976,10 +1106,12 @@ else map (fn i => fn () => def_qualify (mk_prefix_binding (mk_witN i))) (1 upto nwits); in bs ~~ wit_rhss end; - val (((bnf_rel_term, raw_rel_def), (bnf_wit_terms, raw_wit_defs)), (lthy, lthy_old)) = + val ((((bnf_rel_term, raw_rel_def), (bnf_pred_term, raw_pred_def)), + (bnf_wit_terms, raw_wit_defs)), (lthy, lthy_old)) = lthy |> Local_Theory.open_target |> snd |> maybe_define (is_some rel_rhs_opt) rel_bind_def + ||>> maybe_define (is_some pred_rhs_opt) pred_bind_def ||>> apfst split_list o fold_map (maybe_define (not (null wit_rhss))) wit_binds_defs ||> `Local_Theory.close_target; @@ -990,22 +1122,30 @@ normalize_rel lthy (map2 mk_pred2T As' Bs') (mk_bnf_T Ds As' Calpha) (mk_bnf_T Ds Bs' Calpha) bnf_rel; + val bnf_pred_def = Morphism.thm phi raw_pred_def; + val bnf_pred = Morphism.term phi bnf_pred_term; + fun mk_bnf_pred Ds As' = + normalize_pred lthy (map mk_pred1T As') (mk_bnf_T Ds As' Calpha) bnf_pred; + val bnf_wit_defs = map (Morphism.thm phi) raw_wit_defs; val bnf_wits = map (normalize_wit Calpha_params Calpha alphas o Morphism.term phi) bnf_wit_terms; - fun mk_OO_Grp Ds' As' Bs' = - Term.subst_atomic_types ((Ds ~~ Ds') @ (As ~~ As') @ (Bs ~~ Bs')) OO_Grp; + fun mk_rel_spec Ds' As' Bs' = + Term.subst_atomic_types ((Ds ~~ Ds') @ (As ~~ As') @ (Bs ~~ Bs')) rel_spec; + + fun mk_pred_spec Ds' As' = + Term.subst_atomic_types ((Ds ~~ Ds') @ (As ~~ As')) pred_spec; in (((alphas, betas, deads, Calpha), - (bnf_map, bnf_sets, bnf_bd, bnf_wits, bnf_rel), - (bnf_map_def, bnf_set_defs, bnf_bd_def, bnf_wit_defs, bnf_rel_def), - (mk_bnf_map, mk_bnf_t, mk_bnf_T, mk_bnf_rel, mk_OO_Grp)), lthy) + (bnf_map, bnf_sets, bnf_bd, bnf_wits, bnf_rel, bnf_pred), + (bnf_map_def, bnf_set_defs, bnf_bd_def, bnf_wit_defs, bnf_rel_def, bnf_pred_def), + (mk_bnf_map, mk_bnf_t, mk_bnf_T, mk_bnf_rel, mk_bnf_pred, mk_rel_spec, mk_pred_spec)), lthy) end; fun prepare_def const_policy mk_fact_policy internal qualify prep_typ prep_term Ds_opt map_b rel_b - set_bs ((((((raw_bnf_b, raw_bnf_T), raw_map), raw_sets), raw_bd), raw_wits), raw_rel_opt) - no_defs_lthy = + pred_b set_bs (((((((raw_bnf_b, raw_bnf_T), raw_map), raw_sets), raw_bd), raw_wits), raw_rel_opt), + raw_pred_opt) no_defs_lthy = let val fact_policy = mk_fact_policy no_defs_lthy; val bnf_b = qualify raw_bnf_b; @@ -1017,6 +1157,7 @@ val bd_rhs = prep_term no_defs_lthy raw_bd; val wit_rhss = map (prep_term no_defs_lthy) raw_wits; val rel_rhs_opt = Option.map (prep_term no_defs_lthy) raw_rel_opt; + val pred_rhs_opt = Option.map (prep_term no_defs_lthy) raw_pred_opt; fun err T = error ("Trying to register the type " ^ quote (Syntax.string_of_typ no_defs_lthy T) ^ @@ -1031,11 +1172,12 @@ else (bnf_b, Local_Theory.full_name no_defs_lthy bnf_b); val (((alphas, betas, deads, Calpha), - (bnf_map, bnf_sets, bnf_bd, bnf_wits, bnf_rel), - (bnf_map_def, bnf_set_defs, bnf_bd_def, bnf_wit_defs, bnf_rel_def), - (mk_bnf_map_Ds, mk_bnf_t_Ds, mk_bnf_T_Ds, _, mk_OO_Grp)), lthy) = - define_bnf_consts const_policy fact_policy internal Ds_opt map_b rel_b set_bs - ((((((bnf_b, T_rhs), map_rhs), set_rhss), bd_rhs), wit_rhss), rel_rhs_opt) no_defs_lthy; + (bnf_map, bnf_sets, bnf_bd, bnf_wits, bnf_rel, bnf_pred), + (bnf_map_def, bnf_set_defs, bnf_bd_def, bnf_wit_defs, bnf_rel_def, bnf_pred_def), + (mk_bnf_map_Ds, mk_bnf_t_Ds, mk_bnf_T_Ds, _, _, mk_rel_spec, mk_pred_spec)), lthy) = + define_bnf_consts const_policy fact_policy internal Ds_opt map_b rel_b pred_b set_bs + (((((((bnf_b, T_rhs), map_rhs), set_rhss), bd_rhs), wit_rhss), rel_rhs_opt), pred_rhs_opt) + no_defs_lthy; val dead = length deads; @@ -1057,6 +1199,8 @@ val mk_bnf_t = mk_bnf_t_Ds Ds; val mk_bnf_T = mk_bnf_T_Ds Ds; + val pred1PTs = map mk_pred1T As'; + val pred1QTs = map mk_pred1T Bs'; val pred2RTs = map2 mk_pred2T As' Bs'; val pred2RTsAsCs = map2 mk_pred2T As' Cs; val pred2RTsBsCs = map2 mk_pred2T Bs' Cs; @@ -1083,11 +1227,11 @@ val bnf_sets_Bs = map (mk_bnf_t Bs') bnf_sets; val bnf_bd_As = mk_bnf_t As' bnf_bd; fun mk_bnf_rel RTs CA CB = normalize_rel lthy RTs CA CB bnf_rel; + fun mk_bnf_pred PTs CA = normalize_pred lthy PTs CA bnf_pred; - val pre_names_lthy = lthy; - val (((((((((((((((((((((((fs, fs'), gs), hs), is), x), x'), y), y'), zs), zs'), ys), As), - As_copy), bs), Rs), Rs_copy), Ss), S_AsCs), S_CsBs), S_BsEs), - transfer_domRs), transfer_ranRs), names_lthy) = pre_names_lthy + val ((((((((((((((((((((((((((fs, fs'), gs), hs), is), x), x'), y), y'), zs), zs'), ys), As), + As_copy), bs), (Ps, Ps')), Ps_copy), Qs), Rs), Rs_copy), Ss), S_AsCs), S_CsBs), S_BsEs), + transfer_domRs), transfer_ranRs), _) = lthy |> mk_Frees "f" (map2 (curry op -->) As' Bs') ||>> mk_Frees "f" (map2 (curry op -->) As' Bs') ||>> mk_Frees "g" (map2 (curry op -->) Bs' Cs) @@ -1103,6 +1247,9 @@ ||>> mk_Frees "A" (map HOLogic.mk_setT As') ||>> mk_Frees "A" (map HOLogic.mk_setT As') ||>> mk_Frees "b" As' + ||>> mk_Frees' "P" pred1PTs + ||>> mk_Frees "P" pred1PTs + ||>> mk_Frees "Q" pred1QTs ||>> mk_Frees "R" pred2RTs ||>> mk_Frees "R" pred2RTs ||>> mk_Frees "S" pred2RTsBsCs @@ -1117,6 +1264,8 @@ val y_copy = retype_const_or_free CB' x'; val rel = mk_bnf_rel pred2RTs CA' CB'; + val pred = mk_bnf_pred pred1PTs CA'; + val pred' = mk_bnf_pred pred1QTs CB'; val relCsEs = mk_bnf_rel pred2RTsCsEs CC' CE'; val relAsAs = mk_bnf_rel self_pred2RTs CA' CA'; val bnf_wit_As = map (apsnd (mk_bnf_t As')) bnf_wits; @@ -1181,10 +1330,13 @@ fold_rev Logic.all (Rs @ Ss) (HOLogic.mk_Trueprop (mk_leq rel_OO_rhs rel_OO_lhs)); val rel_OO_Grp_goal = fold_rev Logic.all Rs (mk_Trueprop_eq (Term.list_comb (rel, Rs), - Term.list_comb (mk_OO_Grp Ds As' Bs', Rs))); + Term.list_comb (mk_rel_spec Ds As' Bs', Rs))); + + val pred_set_goal = fold_rev Logic.all Ps (mk_Trueprop_eq (Term.list_comb (pred, Ps), + Term.list_comb (mk_pred_spec Ds As', Ps))); val goals = zip_axioms map_id0_goal map_comp0_goal map_cong0_goal set_map0s_goal - card_order_bd_goal cinfinite_bd_goal set_bds_goal le_rel_OO_goal rel_OO_Grp_goal; + card_order_bd_goal cinfinite_bd_goal set_bds_goal le_rel_OO_goal rel_OO_Grp_goal pred_set_goal; val mk_wit_goals = mk_wit_goals bs zs bnf_sets_As; fun triv_wit_tac ctxt = mk_trivial_wit_tac ctxt bnf_wit_defs; @@ -1210,7 +1362,7 @@ (*collect {set1 ... setm} o map f1 ... fm = collect {f1` o set1 ... fm` o setm}*) val goal = fold_rev Logic.all hs (mk_Trueprop_eq (collect_map, image_collect)); in - Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} => + Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} => mk_collect_set_map_tac ctxt (#set_map0 axioms)) |> Thm.close_derivation end; @@ -1447,9 +1599,7 @@ val rel_mono_strong0 = Lazy.lazy mk_rel_mono_strong0; - fun mk_rel_mono_strong () = Object_Logic.rulify lthy (Lazy.force rel_mono_strong0) - - val rel_mono_strong = Lazy.lazy mk_rel_mono_strong; + val rel_mono_strong = Lazy.map (Object_Logic.rulify lthy) rel_mono_strong0; fun mk_rel_cong_prem mk_implies x x' z z' set set' R R_copy = Logic.all z (Logic.all z' @@ -1475,6 +1625,99 @@ val rel_cong = Lazy.lazy (mk_rel_cong Logic.mk_implies); val rel_cong_simp = Lazy.lazy (mk_rel_cong (fn (a, b) => @{term simp_implies} $ a $ b)); + fun mk_pred_prems f = map2 (HOLogic.mk_Trueprop oo f) Ps Ps_copy; + fun mk_pred_concl f = HOLogic.mk_Trueprop + (f (Term.list_comb (pred, Ps), Term.list_comb (pred, Ps_copy))); + + fun mk_pred_cong0 () = + let + val cong_prems = mk_pred_prems (curry HOLogic.mk_eq); + val cong_concl = mk_pred_concl HOLogic.mk_eq; + in + Goal.prove_sorry lthy [] [] + (fold_rev Logic.all (Ps @ Ps_copy) (Logic.list_implies (cong_prems, cong_concl))) + (fn {context = ctxt, prems = _} => (TRY o hyp_subst_tac ctxt THEN' rtac ctxt refl) 1) + |> Thm.close_derivation + end; + + val pred_cong0 = Lazy.lazy mk_pred_cong0; + + fun mk_rel_eq_onp () = + let + val lhs = Term.list_comb (relAsAs, map mk_eq_onp Ps); + val rhs = mk_eq_onp (Term.list_comb (pred, Ps)); + in + Goal.prove_sorry lthy (map fst Ps') [] (mk_Trueprop_eq (lhs, rhs)) + (fn {context = ctxt, prems = _} => + mk_rel_eq_onp_tac ctxt (#pred_set axioms) (#map_id0 axioms) (Lazy.force rel_Grp)) + |> Thm.close_derivation + end; + + val rel_eq_onp = Lazy.lazy mk_rel_eq_onp; + val pred_rel = Lazy.map (fn thm => thm RS sym RS @{thm eq_onp_eqD}) rel_eq_onp; + + fun mk_pred_mono_strong0 () = + let + fun mk_prem setA P Q a = + HOLogic.mk_Trueprop + (mk_Ball (setA $ x) (Term.absfree (dest_Free a) (HOLogic.mk_imp (P $ a, Q $ a)))); + val prems = HOLogic.mk_Trueprop (Term.list_comb (pred, Ps) $ x) :: + @{map 4} mk_prem bnf_sets_As Ps Ps_copy zs; + val concl = HOLogic.mk_Trueprop (Term.list_comb (pred, Ps_copy) $ x); + in + Goal.prove_sorry lthy [] [] + (fold_rev Logic.all (x :: Ps @ Ps_copy) (Logic.list_implies (prems, concl))) + (fn {context = ctxt, prems = _} => + mk_pred_mono_strong0_tac ctxt (Lazy.force pred_rel) (Lazy.force rel_mono_strong0)) + |> Thm.close_derivation + end; + + val pred_mono_strong0 = Lazy.lazy mk_pred_mono_strong0; + + val pred_mono_strong = Lazy.map (Object_Logic.rulify lthy) pred_mono_strong0; + + fun mk_pred_cong_prem mk_implies x z set P P_copy = + Logic.all z + (mk_implies (mk_Trueprop_mem (z, set $ x), mk_Trueprop_eq (P $ z, P_copy $ z))); + + fun mk_pred_cong mk_implies () = + let + val prem0 = mk_Trueprop_eq (x, x_copy); + val prems = @{map 4} (mk_pred_cong_prem mk_implies x_copy) zs bnf_sets_As Ps Ps_copy; + val eq = mk_Trueprop_eq (Term.list_comb (pred, Ps) $ x, + Term.list_comb (pred, Ps_copy) $ x_copy); + in + fold (Variable.add_free_names lthy) (eq :: prem0 :: prems) [] + |> (fn vars => Goal.prove_sorry lthy vars (prem0 :: prems) eq + (fn {context = ctxt, prems} => + mk_rel_cong_tac ctxt (chop 1 prems) (Lazy.force pred_mono_strong))) + |> Thm.close_derivation + end; + + val pred_cong = Lazy.lazy (mk_pred_cong Logic.mk_implies); + val pred_cong_simp = Lazy.lazy (mk_pred_cong (fn (a, b) => @{term simp_implies} $ a $ b)); + + fun mk_map_cong_pred () = + let + val prem0 = mk_Trueprop_eq (x, x_copy); + fun mk_eq f g z = Term.absfree (dest_Free z) (HOLogic.mk_eq (f $ z, g $ z)); + val prem = HOLogic.mk_Trueprop + (Term.list_comb (pred, @{map 3} mk_eq fs fs_copy zs) $ x_copy); + val eq = mk_Trueprop_eq (Term.list_comb (bnf_map_AsBs, fs) $ x, + Term.list_comb (bnf_map_AsBs, fs_copy) $ x_copy); + val goal = fold_rev Logic.all (x :: x_copy :: fs @ fs_copy) + (Logic.list_implies ([prem0, prem], eq)); + in + Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} => + unfold_thms_tac ctxt [#pred_set axioms] THEN + HEADGOAL (EVERY' [REPEAT_DETERM o etac ctxt conjE, + etac ctxt (Lazy.force map_cong) THEN_ALL_NEW + (etac ctxt bspec THEN' assume_tac ctxt)])) + |> Thm.close_derivation + end; + + val map_cong_pred = Lazy.lazy mk_map_cong_pred; + fun mk_rel_map () = let fun mk_goal lhs rhs = @@ -1525,7 +1768,7 @@ Goal.prove_sorry lthy vars [] (Logic.list_implies (prems, goal)) (fn {context = ctxt, prems = _} => unfold_thms_tac ctxt [prop_conv_thm] THEN - HEADGOAL (rtac ctxt (Lazy.force thm RS sym RS @{thm ord_eq_le_trans}) + HEADGOAL (rtac ctxt (Lazy.force thm RS sym RS @{thm ord_eq_le_trans}) THEN' rtac ctxt (Lazy.force rel_mono) THEN_ALL_NEW assume_tac ctxt)) |> Thm.close_derivation end; @@ -1534,6 +1777,41 @@ val rel_symp = Lazy.lazy (mk_rel_preserves mk_symp @{thm symp_conversep} rel_conversep); val rel_transp = Lazy.lazy (mk_rel_preserves mk_transp @{thm transp_relcompp} rel_OO); + fun mk_pred_True () = + let + val lhs = Term.list_comb (pred, map (fn T => absdummy T @{term True}) As'); + val rhs = absdummy CA' @{term True}; + val goal = mk_Trueprop_eq (lhs, rhs); + in + Goal.prove_sorry lthy [] [] goal + (fn {context = ctxt, prems = _} => + HEADGOAL (EVERY' (map (rtac ctxt) [ext, Lazy.force pred_rel RS trans, + Lazy.force rel_cong0 RS fun_cong RS fun_cong RS trans OF + replicate live @{thm eq_onp_True}, + Lazy.force rel_eq RS fun_cong RS fun_cong RS trans, @{thm eqTrueI[OF refl]}]))) + |> Thm.close_derivation + end; + + val pred_True = Lazy.lazy mk_pred_True; + + fun mk_pred_map () = + let + val lhs = Term.list_comb (pred', Qs) $ (Term.list_comb (bnf_map_AsBs, fs) $ x); + val rhs = Term.list_comb (pred, @{map 2} (curry HOLogic.mk_comp) Qs fs) $ x; + val goal = mk_Trueprop_eq (lhs, rhs); + val vars = Variable.add_free_names lthy goal []; + val pred_set = #pred_set axioms RS fun_cong RS sym; + in + Goal.prove_sorry lthy vars [] goal + (fn {context = ctxt, prems = _} => + HEADGOAL (rtac ctxt (pred_set RSN (2, pred_set RSN (2, box_equals)))) THEN + unfold_thms_tac ctxt (@{thm Ball_image_comp} :: map Lazy.force set_map) THEN + HEADGOAL (rtac ctxt refl)) + |> Thm.close_derivation + end; + + val pred_map = Lazy.lazy mk_pred_map; + fun mk_map_transfer () = let val rels = map2 mk_rel_fun transfer_domRs transfer_ranRs; @@ -1621,27 +1899,32 @@ val inj_map_strong = Lazy.lazy mk_inj_map_strong; - val defs = mk_defs bnf_map_def bnf_set_defs bnf_rel_def; + val defs = mk_defs bnf_map_def bnf_set_defs bnf_rel_def bnf_pred_def; val facts = mk_facts bd_Card_order bd_Cinfinite bd_Cnotzero collect_set_map in_bd in_cong - in_mono in_rel inj_map inj_map_strong map_comp map_cong map_cong_simp map_id map_ident0 - map_ident map_transfer rel_eq rel_flip set_map rel_cong0 rel_cong rel_cong_simp rel_map - rel_mono rel_mono_strong0 rel_mono_strong set_transfer rel_Grp rel_conversep rel_OO - rel_refl rel_refl_strong rel_reflp rel_symp rel_transp rel_transfer; + in_mono in_rel inj_map inj_map_strong map_comp map_cong map_cong_simp map_cong_pred map_id + map_ident0 map_ident map_transfer rel_eq rel_flip set_map rel_cong0 rel_cong rel_cong_simp + rel_map rel_mono rel_mono_strong0 rel_mono_strong set_transfer rel_Grp rel_conversep + rel_OO rel_refl rel_refl_strong rel_reflp rel_symp rel_transp rel_transfer rel_eq_onp + pred_True pred_map pred_rel pred_mono_strong0 pred_mono_strong pred_cong0 pred_cong + pred_cong_simp; val wits = map2 mk_witness bnf_wits wit_thms; val bnf_rel = Term.subst_atomic_types ((Ds ~~ deads) @ (As' ~~ alphas) @ (Bs' ~~ betas)) rel; + val bnf_pred = Term.subst_atomic_types ((Ds ~~ deads) @ (As' ~~ alphas)) pred; + val bnf = mk_bnf bnf_b Calpha live alphas betas dead deads bnf_map bnf_sets bnf_bd axioms - defs facts wits bnf_rel; + defs facts wits bnf_rel bnf_pred; in note_bnf_thms fact_policy qualify bnf_b bnf lthy end; val one_step_defs = - no_reflexive (bnf_map_def :: bnf_bd_def :: bnf_set_defs @ bnf_wit_defs @ [bnf_rel_def]); + no_reflexive (bnf_map_def :: bnf_bd_def :: bnf_set_defs @ bnf_wit_defs @ + [bnf_rel_def, bnf_pred_def]); in (key, goals, wit_goalss, after_qed, lthy, one_step_defs) end; @@ -1661,7 +1944,8 @@ fun register_bnf plugins key bnf = register_bnf_raw key bnf #> interpret_bnf plugins bnf; -fun bnf_def const_policy fact_policy internal qualify tacs wit_tac Ds map_b rel_b set_bs raw_csts = +fun bnf_def const_policy fact_policy internal qualify tacs wit_tac Ds map_b rel_b pred_b set_bs + raw_csts = (fn (_, goals, (triv_tac_opt, wit_goalss), after_qed, lthy, one_step_defs) => let fun mk_wits_tac ctxt set_maps = @@ -1682,8 +1966,8 @@ goals (map (fn tac => fn {context = ctxt, prems = _} => unfold_thms_tac ctxt one_step_defs THEN tac ctxt) tacs) |> (fn thms => after_qed mk_wit_thms (map single thms) lthy) - end) o prepare_def const_policy fact_policy internal qualify (K I) (K I) Ds map_b rel_b set_bs - raw_csts; + end) o prepare_def const_policy fact_policy internal qualify (K I) (K I) Ds map_b rel_b pred_b + set_bs raw_csts; fun bnf_cmd (raw_csts, raw_plugins) = (fn (key, goals, (triv_tac_opt, wit_goalss), after_qed, lthy, defs) => @@ -1702,13 +1986,14 @@ NONE => (fn _ => [], map (map (rpair [])) wit_goalss) | SOME tac => (mk_triv_wit_thms tac, [])); in - Proof.unfolding ([[(defs, [])]]) - (lthy - |> Proof.theorem NONE (uncurry (register_bnf plugins key) oo after_qed mk_wit_thms) - (map (single o rpair []) goals @ nontriv_wit_goals) - |> Proof.refine_singleton (Method.primitive_text (K I))) + lthy + |> Proof.theorem NONE (uncurry (register_bnf plugins key) oo after_qed mk_wit_thms) + (map (single o rpair []) goals @ nontriv_wit_goals) + |> Proof.unfolding ([[(@{thm OO_Grp_alt} :: @{thm mem_Collect_eq} :: defs, [])]]) + |> Proof.refine_singleton (Method.Basic (fn ctxt => + Method.SIMPLE_METHOD (TRYALL (rtac ctxt refl)))) end) o prepare_def Do_Inline (user_policy Note_Some) false I Syntax.read_typ Syntax.read_term - NONE Binding.empty Binding.empty [] raw_csts; + NONE Binding.empty Binding.empty Binding.empty [] raw_csts; fun print_bnfs ctxt = let @@ -1752,6 +2037,7 @@ Scan.repeat1 (Scan.unless (Parse.reserved "rel" || Parse.reserved "plugins") Parse.term)) [] -- Scan.option ((Parse.reserved "rel" -- @{keyword ":"}) |-- Parse.term) -- + Scan.option ((Parse.reserved "pred" -- @{keyword ":"}) |-- Parse.term) -- Scan.optional Plugin_Name.parse_filter (K Plugin_Name.default_filter) >> bnf_cmd);