src/HOL/BNF/Tools/bnf_def.ML
author blanchet
Wed Apr 24 18:49:52 2013 +0200 (2013-04-24)
changeset 51767 bbcdd8519253
parent 51766 f19a4d0ab1bf
child 51787 1267c28c7bdd
permissions -rw-r--r--
honor user-specified name for relator + generalize syntax
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(*  Title:      HOL/BNF/Tools/bnf_def.ML
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    Author:     Dmitriy Traytel, TU Muenchen
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2012
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Definition of bounded natural functors.
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*)
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signature BNF_DEF =
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sig
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  type BNF
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  type nonemptiness_witness = {I: int list, wit: term, prop: thm list}
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  val bnf_of: Proof.context -> string -> BNF option
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  val register_bnf: string -> (BNF * local_theory) -> (BNF * local_theory)
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  val name_of_bnf: BNF -> binding
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  val T_of_bnf: BNF -> typ
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  val live_of_bnf: BNF -> int
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  val lives_of_bnf: BNF -> typ list
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  val dead_of_bnf: BNF -> int
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  val deads_of_bnf: BNF -> typ list
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  val nwits_of_bnf: BNF -> int
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  val mapN: string
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  val relN: string
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  val setN: string
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  val mk_setN: int -> string
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  val srelN: string
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  val map_of_bnf: BNF -> term
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  val sets_of_bnf: BNF -> term list
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  val rel_of_bnf: BNF -> term
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  val mk_T_of_bnf: typ list -> typ list -> BNF -> typ
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  val mk_bd_of_bnf: typ list -> typ list -> BNF -> term
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  val mk_map_of_bnf: typ list -> typ list -> typ list -> BNF -> term
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  val mk_rel_of_bnf: typ list -> typ list -> typ list -> BNF -> term
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  val mk_sets_of_bnf: typ list list -> typ list list -> BNF -> term list
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  val mk_srel_of_bnf: typ list -> typ list -> typ list -> BNF -> term
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  val mk_wits_of_bnf: typ list list -> typ list list -> BNF -> (int list * term) list
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  val bd_Card_order_of_bnf: BNF -> thm
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  val bd_Cinfinite_of_bnf: BNF -> thm
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  val bd_Cnotzero_of_bnf: BNF -> thm
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  val bd_card_order_of_bnf: BNF -> thm
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  val bd_cinfinite_of_bnf: BNF -> thm
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  val collect_set_map_of_bnf: BNF -> thm
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  val in_bd_of_bnf: BNF -> thm
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  val in_cong_of_bnf: BNF -> thm
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  val in_mono_of_bnf: BNF -> thm
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  val in_srel_of_bnf: BNF -> thm
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  val map_comp'_of_bnf: BNF -> thm
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  val map_comp_of_bnf: BNF -> thm
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  val map_cong0_of_bnf: BNF -> thm
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  val map_cong_of_bnf: BNF -> thm
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  val map_def_of_bnf: BNF -> thm
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  val map_id'_of_bnf: BNF -> thm
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  val map_id_of_bnf: BNF -> thm
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  val map_wppull_of_bnf: BNF -> thm
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  val map_wpull_of_bnf: BNF -> thm
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  val rel_def_of_bnf: BNF -> thm
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  val rel_eq_of_bnf: BNF -> thm
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  val rel_flip_of_bnf: BNF -> thm
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  val rel_srel_of_bnf: BNF -> thm
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  val set_bd_of_bnf: BNF -> thm list
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  val set_defs_of_bnf: BNF -> thm list
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  val set_map'_of_bnf: BNF -> thm list
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  val set_map_of_bnf: BNF -> thm list
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  val srel_def_of_bnf: BNF -> thm
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  val srel_Gr_of_bnf: BNF -> thm
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  val srel_Id_of_bnf: BNF -> thm
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  val srel_O_of_bnf: BNF -> thm
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  val srel_O_Gr_of_bnf: BNF -> thm
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  val srel_cong_of_bnf: BNF -> thm
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  val srel_converse_of_bnf: BNF -> thm
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  val srel_mono_of_bnf: BNF -> thm
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  val wit_thms_of_bnf: BNF -> thm list
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  val wit_thmss_of_bnf: BNF -> thm list list
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  val mk_witness: int list * term -> thm list -> nonemptiness_witness
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  val minimize_wits: (''a list * 'b) list -> (''a list * 'b) list
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  val wits_of_bnf: BNF -> nonemptiness_witness list
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  val zip_axioms: 'a -> 'a -> 'a -> 'a list -> 'a -> 'a -> 'a list -> 'a -> 'a -> 'a -> 'a list
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  datatype const_policy = Dont_Inline | Hardly_Inline | Smart_Inline | Do_Inline
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  datatype fact_policy = Dont_Note | Note_Some | Note_All
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  val bnf_note_all: bool Config.T
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  val user_policy: fact_policy -> Proof.context -> fact_policy
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  val print_bnfs: Proof.context -> unit
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  val bnf_def: const_policy -> (Proof.context -> fact_policy) -> (binding -> binding) ->
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    ({prems: thm list, context: Proof.context} -> tactic) list ->
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    ({prems: thm list, context: Proof.context} -> tactic) -> typ list option -> binding ->
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    binding -> binding list ->
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    ((((binding * term) * term list) * term) * term list) * term option ->
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    local_theory -> BNF * local_theory
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end;
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structure BNF_Def : BNF_DEF =
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struct
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open BNF_Util
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open BNF_Tactics
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open BNF_Def_Tactics
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val fundef_cong_attrs = @{attributes [fundef_cong]};
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type axioms = {
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  map_id: thm,
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  map_comp: thm,
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  map_cong0: thm,
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  set_map: thm list,
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  bd_card_order: thm,
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  bd_cinfinite: thm,
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  set_bd: thm list,
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  in_bd: thm,
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  map_wpull: thm,
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  srel_O_Gr: thm
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};
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fun mk_axioms' (((((((((id, comp), cong), nat), c_o), cinf), set_bd), in_bd), wpull), srel) =
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  {map_id = id, map_comp = comp, map_cong0 = cong, set_map = nat, bd_card_order = c_o,
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   bd_cinfinite = cinf, set_bd = set_bd, in_bd = in_bd, map_wpull = wpull, srel_O_Gr = srel};
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fun dest_cons [] = raise Empty
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  | dest_cons (x :: xs) = (x, xs);
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fun mk_axioms n thms = thms
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  |> map the_single
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  |> dest_cons
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  ||>> dest_cons
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  ||>> dest_cons
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  ||>> chop n
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  ||>> dest_cons
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  ||>> dest_cons
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  ||>> chop n
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  ||>> dest_cons
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  ||>> dest_cons
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  ||> the_single
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  |> mk_axioms';
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fun zip_axioms mid mcomp mcong snat bdco bdinf sbd inbd wpull srel =
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  [mid, mcomp, mcong] @ snat @ [bdco, bdinf] @ sbd @ [inbd, wpull, srel];
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fun dest_axioms {map_id, map_comp, map_cong0, set_map, bd_card_order, bd_cinfinite, set_bd, in_bd,
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  map_wpull, srel_O_Gr} =
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  zip_axioms map_id map_comp map_cong0 set_map bd_card_order bd_cinfinite set_bd in_bd map_wpull
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    srel_O_Gr;
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fun map_axioms f {map_id, map_comp, map_cong0, set_map, bd_card_order, bd_cinfinite, set_bd,
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  in_bd, map_wpull, srel_O_Gr} =
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  {map_id = f map_id,
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    map_comp = f map_comp,
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    map_cong0 = f map_cong0,
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    set_map = map f set_map,
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    bd_card_order = f bd_card_order,
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    bd_cinfinite = f bd_cinfinite,
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    set_bd = map f set_bd,
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    in_bd = f in_bd,
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    map_wpull = f map_wpull,
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    srel_O_Gr = f srel_O_Gr};
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val morph_axioms = map_axioms o Morphism.thm;
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type defs = {
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  map_def: thm,
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  set_defs: thm list,
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  rel_def: thm,
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  srel_def: thm
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}
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fun mk_defs map sets rel srel = {map_def = map, set_defs = sets, rel_def = rel, srel_def = srel};
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fun map_defs f {map_def, set_defs, rel_def, srel_def} =
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  {map_def = f map_def, set_defs = map f set_defs, rel_def = f rel_def, srel_def = f srel_def};
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val morph_defs = map_defs o Morphism.thm;
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type facts = {
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  bd_Card_order: thm,
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  bd_Cinfinite: thm,
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  bd_Cnotzero: thm,
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  collect_set_map: thm lazy,
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  in_cong: thm lazy,
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  in_mono: thm lazy,
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  in_srel: thm lazy,
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  map_comp': thm lazy,
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  map_cong: thm lazy,
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  map_id': thm lazy,
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  map_wppull: thm lazy,
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  rel_eq: thm lazy,
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  rel_flip: thm lazy,
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  rel_srel: thm lazy,
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  set_map': thm lazy list,
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  srel_cong: thm lazy,
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  srel_mono: thm lazy,
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  srel_Id: thm lazy,
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  srel_Gr: thm lazy,
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  srel_converse: thm lazy,
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  srel_O: thm lazy
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};
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fun mk_facts bd_Card_order bd_Cinfinite bd_Cnotzero collect_set_map in_cong in_mono in_srel
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    map_comp' map_cong map_id' map_wppull rel_eq rel_flip rel_srel set_map' srel_cong srel_mono
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    srel_Id srel_Gr srel_converse srel_O = {
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  bd_Card_order = bd_Card_order,
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  bd_Cinfinite = bd_Cinfinite,
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  bd_Cnotzero = bd_Cnotzero,
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  collect_set_map = collect_set_map,
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  in_cong = in_cong,
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  in_mono = in_mono,
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  in_srel = in_srel,
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  map_comp' = map_comp',
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  map_cong = map_cong,
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  map_id' = map_id',
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  map_wppull = map_wppull,
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  rel_eq = rel_eq,
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  rel_flip = rel_flip,
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  rel_srel = rel_srel,
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  set_map' = set_map',
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  srel_cong = srel_cong,
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  srel_mono = srel_mono,
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  srel_Id = srel_Id,
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  srel_Gr = srel_Gr,
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  srel_converse = srel_converse,
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  srel_O = srel_O};
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fun map_facts f {
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  bd_Card_order,
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  bd_Cinfinite,
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  bd_Cnotzero,
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  collect_set_map,
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  in_cong,
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  in_mono,
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  in_srel,
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  map_comp',
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  map_cong,
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  map_id',
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  map_wppull,
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  rel_eq,
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  rel_flip,
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  rel_srel,
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  set_map',
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  srel_cong,
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  srel_mono,
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  srel_Id,
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  srel_Gr,
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  srel_converse,
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  srel_O} =
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  {bd_Card_order = f bd_Card_order,
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    bd_Cinfinite = f bd_Cinfinite,
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    bd_Cnotzero = f bd_Cnotzero,
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    collect_set_map = Lazy.map f collect_set_map,
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    in_cong = Lazy.map f in_cong,
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    in_mono = Lazy.map f in_mono,
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    in_srel = Lazy.map f in_srel,
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    map_comp' = Lazy.map f map_comp',
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    map_cong = Lazy.map f map_cong,
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    map_id' = Lazy.map f map_id',
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    map_wppull = Lazy.map f map_wppull,
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    rel_eq = Lazy.map f rel_eq,
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    rel_flip = Lazy.map f rel_flip,
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    rel_srel = Lazy.map f rel_srel,
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    set_map' = map (Lazy.map f) set_map',
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    srel_cong = Lazy.map f srel_cong,
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    srel_mono = Lazy.map f srel_mono,
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    srel_Id = Lazy.map f srel_Id,
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    srel_Gr = Lazy.map f srel_Gr,
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    srel_converse = Lazy.map f srel_converse,
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    srel_O = Lazy.map f srel_O};
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val morph_facts = map_facts o Morphism.thm;
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type nonemptiness_witness = {
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  I: int list,
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  wit: term,
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  prop: thm list
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};
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fun mk_witness (I, wit) prop = {I = I, wit = wit, prop = prop};
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fun map_witness f g {I, wit, prop} = {I = I, wit = f wit, prop = map g prop};
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fun morph_witness phi = map_witness (Morphism.term phi) (Morphism.thm phi);
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datatype BNF = BNF of {
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  name: binding,
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  T: typ,
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  live: int,
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  lives: typ list, (*source type variables of map, only for composition*)
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  lives': typ list, (*target type variables of map, only for composition*)
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  dead: int,
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  deads: typ list, (*only for composition*)
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  map: term,
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  sets: term list,
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  bd: term,
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  axioms: axioms,
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  defs: defs,
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  facts: facts,
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  nwits: int,
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  wits: nonemptiness_witness list,
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  rel: term,
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  srel: term
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};
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(* getters *)
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fun rep_bnf (BNF bnf) = bnf;
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val name_of_bnf = #name o rep_bnf;
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val T_of_bnf = #T o rep_bnf;
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fun mk_T_of_bnf Ds Ts bnf =
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  let val bnf_rep = rep_bnf bnf
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  in Term.typ_subst_atomic ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts)) (#T bnf_rep) end;
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val live_of_bnf = #live o rep_bnf;
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   316
val lives_of_bnf = #lives o rep_bnf;
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   317
val dead_of_bnf = #dead o rep_bnf;
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   318
val deads_of_bnf = #deads o rep_bnf;
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   319
val axioms_of_bnf = #axioms o rep_bnf;
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   320
val facts_of_bnf = #facts o rep_bnf;
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   321
val nwits_of_bnf = #nwits o rep_bnf;
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   322
val wits_of_bnf = #wits o rep_bnf;
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   323
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   324
(*terms*)
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   325
val map_of_bnf = #map o rep_bnf;
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   326
val sets_of_bnf = #sets o rep_bnf;
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   327
fun mk_map_of_bnf Ds Ts Us bnf =
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   328
  let val bnf_rep = rep_bnf bnf;
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   329
  in
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   330
    Term.subst_atomic_types
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   331
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts) @ (#lives' bnf_rep ~~ Us)) (#map bnf_rep)
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   332
  end;
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   333
fun mk_sets_of_bnf Dss Tss bnf =
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   334
  let val bnf_rep = rep_bnf bnf;
blanchet@48975
   335
  in
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   336
    map2 (fn (Ds, Ts) => Term.subst_atomic_types
blanchet@48975
   337
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts))) (Dss ~~ Tss) (#sets bnf_rep)
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   338
  end;
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   339
val bd_of_bnf = #bd o rep_bnf;
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   340
fun mk_bd_of_bnf Ds Ts bnf =
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   341
  let val bnf_rep = rep_bnf bnf;
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   342
  in Term.subst_atomic_types ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts)) (#bd bnf_rep) end;
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   343
fun mk_wits_of_bnf Dss Tss bnf =
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   344
  let
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   345
    val bnf_rep = rep_bnf bnf;
blanchet@48975
   346
    val wits = map (fn x => (#I x, #wit x)) (#wits bnf_rep);
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   347
  in
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   348
    map2 (fn (Ds, Ts) => apsnd (Term.subst_atomic_types
blanchet@48975
   349
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts)))) (Dss ~~ Tss) wits
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   350
  end;
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   351
val rel_of_bnf = #rel o rep_bnf;
blanchet@49507
   352
fun mk_rel_of_bnf Ds Ts Us bnf =
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   353
  let val bnf_rep = rep_bnf bnf;
blanchet@49462
   354
  in
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   355
    Term.subst_atomic_types
blanchet@49507
   356
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts) @ (#lives' bnf_rep ~~ Us)) (#rel bnf_rep)
blanchet@49462
   357
  end;
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   358
val srel_of_bnf = #srel o rep_bnf;
blanchet@49506
   359
fun mk_srel_of_bnf Ds Ts Us bnf =
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   360
  let val bnf_rep = rep_bnf bnf;
blanchet@48975
   361
  in
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   362
    Term.subst_atomic_types
blanchet@49506
   363
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts) @ (#lives' bnf_rep ~~ Us)) (#srel bnf_rep)
blanchet@48975
   364
  end;
blanchet@48975
   365
blanchet@48975
   366
(*thms*)
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   367
val bd_card_order_of_bnf = #bd_card_order o #axioms o rep_bnf;
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   368
val bd_cinfinite_of_bnf = #bd_cinfinite o #axioms o rep_bnf;
blanchet@48975
   369
val bd_Card_order_of_bnf = #bd_Card_order o #facts o rep_bnf;
blanchet@48975
   370
val bd_Cinfinite_of_bnf = #bd_Cinfinite o #facts o rep_bnf;
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   371
val bd_Cnotzero_of_bnf = #bd_Cnotzero o #facts o rep_bnf;
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   372
val collect_set_map_of_bnf = Lazy.force o #collect_set_map o #facts o rep_bnf;
blanchet@48975
   373
val in_bd_of_bnf = #in_bd o #axioms o rep_bnf;
blanchet@48975
   374
val in_cong_of_bnf = Lazy.force o #in_cong o #facts o rep_bnf;
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   375
val in_mono_of_bnf = Lazy.force o #in_mono o #facts o rep_bnf;
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   376
val in_srel_of_bnf = Lazy.force o #in_srel o #facts o rep_bnf;
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   377
val map_def_of_bnf = #map_def o #defs o rep_bnf;
blanchet@48975
   378
val map_id_of_bnf = #map_id o #axioms o rep_bnf;
blanchet@48975
   379
val map_id'_of_bnf = Lazy.force o #map_id' o #facts o rep_bnf;
blanchet@48975
   380
val map_comp_of_bnf = #map_comp o #axioms o rep_bnf;
blanchet@48975
   381
val map_comp'_of_bnf = Lazy.force o #map_comp' o #facts o rep_bnf;
blanchet@51761
   382
val map_cong0_of_bnf = #map_cong0 o #axioms o rep_bnf;
blanchet@51762
   383
val map_cong_of_bnf = Lazy.force o #map_cong o #facts o rep_bnf;
blanchet@48975
   384
val map_wppull_of_bnf = Lazy.force o #map_wppull o #facts o rep_bnf;
blanchet@48975
   385
val map_wpull_of_bnf = #map_wpull o #axioms o rep_bnf;
blanchet@49507
   386
val rel_def_of_bnf = #rel_def o #defs o rep_bnf;
blanchet@49591
   387
val rel_eq_of_bnf = Lazy.force o #rel_eq o #facts o rep_bnf;
blanchet@49537
   388
val rel_flip_of_bnf = Lazy.force o #rel_flip o #facts o rep_bnf;
blanchet@49594
   389
val rel_srel_of_bnf = Lazy.force o #rel_srel o #facts o rep_bnf;
blanchet@48975
   390
val set_bd_of_bnf = #set_bd o #axioms o rep_bnf;
blanchet@48975
   391
val set_defs_of_bnf = #set_defs o #defs o rep_bnf;
blanchet@51766
   392
val set_map_of_bnf = #set_map o #axioms o rep_bnf;
blanchet@51766
   393
val set_map'_of_bnf = map Lazy.force o #set_map' o #facts o rep_bnf;
blanchet@49506
   394
val srel_cong_of_bnf = Lazy.force o #srel_cong o #facts o rep_bnf;
blanchet@49506
   395
val srel_mono_of_bnf = Lazy.force o #srel_mono o #facts o rep_bnf;
blanchet@49506
   396
val srel_def_of_bnf = #srel_def o #defs o rep_bnf;
blanchet@49506
   397
val srel_Id_of_bnf = Lazy.force o #srel_Id o #facts o rep_bnf;
blanchet@49506
   398
val srel_Gr_of_bnf = Lazy.force o #srel_Gr o #facts o rep_bnf;
blanchet@49506
   399
val srel_converse_of_bnf = Lazy.force o #srel_converse o #facts o rep_bnf;
blanchet@49506
   400
val srel_O_of_bnf = Lazy.force o #srel_O o #facts o rep_bnf;
blanchet@49506
   401
val srel_O_Gr_of_bnf = #srel_O_Gr o #axioms o rep_bnf;
blanchet@48975
   402
val wit_thms_of_bnf = maps #prop o wits_of_bnf;
blanchet@48975
   403
val wit_thmss_of_bnf = map #prop o wits_of_bnf;
blanchet@48975
   404
blanchet@49507
   405
fun mk_bnf name T live lives lives' dead deads map sets bd axioms defs facts wits rel srel =
blanchet@48975
   406
  BNF {name = name, T = T,
blanchet@48975
   407
       live = live, lives = lives, lives' = lives', dead = dead, deads = deads,
blanchet@48975
   408
       map = map, sets = sets, bd = bd,
blanchet@48975
   409
       axioms = axioms, defs = defs, facts = facts,
blanchet@49507
   410
       nwits = length wits, wits = wits, rel = rel, srel = srel};
blanchet@48975
   411
blanchet@48975
   412
fun morph_bnf phi (BNF {name = name, T = T, live = live, lives = lives, lives' = lives',
blanchet@48975
   413
  dead = dead, deads = deads, map = map, sets = sets, bd = bd,
blanchet@48975
   414
  axioms = axioms, defs = defs, facts = facts,
blanchet@49507
   415
  nwits = nwits, wits = wits, rel = rel, srel = srel}) =
blanchet@48975
   416
  BNF {name = Morphism.binding phi name, T = Morphism.typ phi T,
blanchet@48975
   417
    live = live, lives = List.map (Morphism.typ phi) lives,
blanchet@48975
   418
    lives' = List.map (Morphism.typ phi) lives',
blanchet@48975
   419
    dead = dead, deads = List.map (Morphism.typ phi) deads,
blanchet@48975
   420
    map = Morphism.term phi map, sets = List.map (Morphism.term phi) sets,
blanchet@48975
   421
    bd = Morphism.term phi bd,
blanchet@48975
   422
    axioms = morph_axioms phi axioms,
blanchet@48975
   423
    defs = morph_defs phi defs,
blanchet@48975
   424
    facts = morph_facts phi facts,
blanchet@48975
   425
    nwits = nwits,
blanchet@48975
   426
    wits = List.map (morph_witness phi) wits,
blanchet@49507
   427
    rel = Morphism.term phi rel, srel = Morphism.term phi srel};
blanchet@48975
   428
blanchet@48975
   429
fun eq_bnf (BNF {T = T1, live = live1, dead = dead1, ...},
blanchet@48975
   430
  BNF {T = T2, live = live2, dead = dead2, ...}) =
blanchet@48975
   431
  Type.could_unify (T1, T2) andalso live1 = live2 andalso dead1 = dead2;
blanchet@48975
   432
blanchet@48975
   433
structure Data = Generic_Data
blanchet@48975
   434
(
blanchet@48975
   435
  type T = BNF Symtab.table;
blanchet@48975
   436
  val empty = Symtab.empty;
blanchet@48975
   437
  val extend = I;
blanchet@49462
   438
  val merge = Symtab.merge eq_bnf;
blanchet@48975
   439
);
blanchet@48975
   440
blanchet@48975
   441
val bnf_of = Symtab.lookup o Data.get o Context.Proof;
blanchet@48975
   442
blanchet@48975
   443
blanchet@48975
   444
blanchet@48975
   445
(* Utilities *)
blanchet@48975
   446
blanchet@48975
   447
fun normalize_set insts instA set =
blanchet@48975
   448
  let
blanchet@48975
   449
    val (T, T') = dest_funT (fastype_of set);
blanchet@48975
   450
    val A = fst (Term.dest_TVar (HOLogic.dest_setT T'));
blanchet@48975
   451
    val params = Term.add_tvar_namesT T [];
blanchet@48975
   452
  in Term.subst_TVars ((A :: params) ~~ (instA :: insts)) set end;
blanchet@48975
   453
blanchet@49507
   454
fun normalize_rel ctxt instTs instA instB rel =
blanchet@49462
   455
  let
blanchet@49462
   456
    val thy = Proof_Context.theory_of ctxt;
blanchet@49462
   457
    val tyenv =
blanchet@49507
   458
      Sign.typ_match thy (fastype_of rel, Library.foldr (op -->) (instTs, mk_pred2T instA instB))
blanchet@49463
   459
        Vartab.empty;
blanchet@49507
   460
  in Envir.subst_term (tyenv, Vartab.empty) rel end
blanchet@49462
   461
  handle Type.TYPE_MATCH => error "Bad predicator";
blanchet@49462
   462
blanchet@49506
   463
fun normalize_srel ctxt instTs instA instB srel =
blanchet@48975
   464
  let
blanchet@48975
   465
    val thy = Proof_Context.theory_of ctxt;
blanchet@48975
   466
    val tyenv =
blanchet@49506
   467
      Sign.typ_match thy (fastype_of srel, Library.foldr (op -->) (instTs, mk_relT (instA, instB)))
blanchet@48975
   468
        Vartab.empty;
blanchet@49506
   469
  in Envir.subst_term (tyenv, Vartab.empty) srel end
blanchet@49453
   470
  handle Type.TYPE_MATCH => error "Bad relator";
blanchet@48975
   471
blanchet@48975
   472
fun normalize_wit insts CA As wit =
blanchet@48975
   473
  let
blanchet@48975
   474
    fun strip_param (Ts, T as Type (@{type_name fun}, [T1, T2])) =
blanchet@48975
   475
        if Type.raw_instance (CA, T) then (Ts, T) else strip_param (T1 :: Ts, T2)
blanchet@48975
   476
      | strip_param x = x;
blanchet@48975
   477
    val (Ts, T) = strip_param ([], fastype_of wit);
blanchet@48975
   478
    val subst = Term.add_tvar_namesT T [] ~~ insts;
blanchet@48975
   479
    fun find y = find_index (fn x => x = y) As;
blanchet@48975
   480
  in
blanchet@48975
   481
    (map (find o Term.typ_subst_TVars subst) (rev Ts), Term.subst_TVars subst wit)
blanchet@48975
   482
  end;
blanchet@48975
   483
blanchet@48975
   484
fun minimize_wits wits =
blanchet@48975
   485
 let
blanchet@48975
   486
   fun minimize done [] = done
traytel@49103
   487
     | minimize done ((I, wit) :: todo) =
blanchet@48975
   488
       if exists (fn (J, _) => subset (op =) (J, I)) (done @ todo)
blanchet@48975
   489
       then minimize done todo
blanchet@48975
   490
       else minimize ((I, wit) :: done) todo;
blanchet@48975
   491
 in minimize [] wits end;
blanchet@48975
   492
blanchet@48975
   493
blanchet@48975
   494
blanchet@48975
   495
(* Names *)
blanchet@48975
   496
blanchet@48975
   497
val mapN = "map";
blanchet@48975
   498
val setN = "set";
blanchet@48975
   499
fun mk_setN i = setN ^ nonzero_string_of_int i;
blanchet@48975
   500
val bdN = "bd";
blanchet@48975
   501
val witN = "wit";
blanchet@48975
   502
fun mk_witN i = witN ^ nonzero_string_of_int i;
blanchet@49507
   503
val relN = "rel";
blanchet@49506
   504
val srelN = "srel";
blanchet@48975
   505
blanchet@48975
   506
val bd_card_orderN = "bd_card_order";
blanchet@48975
   507
val bd_cinfiniteN = "bd_cinfinite";
blanchet@48975
   508
val bd_Card_orderN = "bd_Card_order";
blanchet@48975
   509
val bd_CinfiniteN = "bd_Cinfinite";
blanchet@48975
   510
val bd_CnotzeroN = "bd_Cnotzero";
blanchet@51766
   511
val collect_set_mapN = "collect_set_map";
blanchet@48975
   512
val in_bdN = "in_bd";
blanchet@48975
   513
val in_monoN = "in_mono";
blanchet@49506
   514
val in_srelN = "in_srel";
blanchet@48975
   515
val map_idN = "map_id";
blanchet@48975
   516
val map_id'N = "map_id'";
blanchet@48975
   517
val map_compN = "map_comp";
blanchet@48975
   518
val map_comp'N = "map_comp'";
blanchet@51761
   519
val map_cong0N = "map_cong0";
blanchet@51762
   520
val map_congN = "map_cong";
blanchet@48975
   521
val map_wpullN = "map_wpull";
blanchet@49591
   522
val rel_eqN = "rel_eq";
blanchet@49537
   523
val rel_flipN = "rel_flip";
blanchet@49594
   524
val rel_srelN = "rel_srel";
blanchet@51766
   525
val set_mapN = "set_map";
blanchet@51766
   526
val set_map'N = "set_map'";
blanchet@49537
   527
val set_bdN = "set_bd";
blanchet@49506
   528
val srel_IdN = "srel_Id";
blanchet@49506
   529
val srel_GrN = "srel_Gr";
blanchet@49506
   530
val srel_converseN = "srel_converse";
blanchet@49506
   531
val srel_monoN = "srel_mono"
blanchet@49506
   532
val srel_ON = "srel_comp";
blanchet@49506
   533
val srel_O_GrN = "srel_comp_Gr";
blanchet@48975
   534
blanchet@48975
   535
datatype const_policy = Dont_Inline | Hardly_Inline | Smart_Inline | Do_Inline;
blanchet@48975
   536
blanchet@49538
   537
datatype fact_policy = Dont_Note | Note_Some | Note_All;
blanchet@48975
   538
blanchet@48975
   539
val bnf_note_all = Attrib.setup_config_bool @{binding bnf_note_all} (K false);
blanchet@48975
   540
blanchet@49538
   541
fun user_policy policy ctxt = if Config.get ctxt bnf_note_all then Note_All else policy;
blanchet@48975
   542
blanchet@48975
   543
val smart_max_inline_size = 25; (*FUDGE*)
blanchet@48975
   544
blanchet@48975
   545
blanchet@48975
   546
(* Define new BNFs *)
blanchet@48975
   547
blanchet@51767
   548
fun prepare_def const_policy mk_fact_policy qualify prep_term Ds_opt map_b rel_b set_bs
blanchet@49507
   549
  (((((raw_b, raw_map), raw_sets), raw_bd_Abs), raw_wits), raw_rel_opt) no_defs_lthy =
blanchet@48975
   550
  let
blanchet@48975
   551
    val fact_policy = mk_fact_policy no_defs_lthy;
blanchet@48975
   552
    val b = qualify raw_b;
blanchet@48975
   553
    val live = length raw_sets;
blanchet@48975
   554
    val nwits = length raw_wits;
blanchet@48975
   555
blanchet@48975
   556
    val map_rhs = prep_term no_defs_lthy raw_map;
blanchet@48975
   557
    val set_rhss = map (prep_term no_defs_lthy) raw_sets;
blanchet@48975
   558
    val (bd_rhsT, bd_rhs) = (case prep_term no_defs_lthy raw_bd_Abs of
blanchet@48975
   559
      Abs (_, T, t) => (T, t)
blanchet@48975
   560
    | _ => error "Bad bound constant");
blanchet@48975
   561
    val wit_rhss = map (prep_term no_defs_lthy) raw_wits;
blanchet@48975
   562
traytel@49434
   563
    fun err T =
traytel@49434
   564
      error ("Trying to register the type " ^ quote (Syntax.string_of_typ no_defs_lthy T) ^
traytel@49434
   565
        " as unnamed BNF");
traytel@49434
   566
traytel@49434
   567
    val (b, key) =
traytel@49434
   568
      if Binding.eq_name (b, Binding.empty) then
traytel@49434
   569
        (case bd_rhsT of
traytel@49434
   570
          Type (C, Ts) => if forall (is_some o try dest_TFree) Ts
traytel@49434
   571
            then (Binding.qualified_name C, C) else err bd_rhsT
traytel@49434
   572
        | T => err T)
traytel@49434
   573
      else (b, Local_Theory.full_name no_defs_lthy b);
traytel@49434
   574
blanchet@49463
   575
    fun maybe_define user_specified (b, rhs) lthy =
blanchet@48975
   576
      let
blanchet@48975
   577
        val inline =
blanchet@49538
   578
          (user_specified orelse fact_policy = Dont_Note) andalso
blanchet@48975
   579
          (case const_policy of
blanchet@48975
   580
            Dont_Inline => false
blanchet@48975
   581
          | Hardly_Inline => Term.is_Free rhs orelse Term.is_Const rhs
blanchet@48975
   582
          | Smart_Inline => Term.size_of_term rhs <= smart_max_inline_size
blanchet@48975
   583
          | Do_Inline => true)
blanchet@48975
   584
      in
blanchet@48975
   585
        if inline then
blanchet@49460
   586
          ((rhs, Drule.reflexive_thm), lthy)
blanchet@48975
   587
        else
blanchet@48975
   588
          let val b = b () in
blanchet@48975
   589
            apfst (apsnd snd) (Local_Theory.define ((b, NoSyn), ((Thm.def_binding b, []), rhs))
blanchet@48975
   590
              lthy)
blanchet@48975
   591
          end
blanchet@48975
   592
      end;
blanchet@49459
   593
blanchet@49459
   594
    fun maybe_restore lthy_old lthy =
blanchet@49459
   595
      lthy |> not (pointer_eq (lthy_old, lthy)) ? Local_Theory.restore;
blanchet@48975
   596
blanchet@51758
   597
    val map_bind_def =
blanchet@51758
   598
      (fn () => if Binding.is_empty map_b then Binding.suffix_name ("_" ^ mapN) b else map_b,
blanchet@51758
   599
       map_rhs);
blanchet@49459
   600
    val set_binds_defs =
blanchet@49459
   601
      let
blanchet@51757
   602
        fun set_name i get_b =
blanchet@51757
   603
          (case try (nth set_bs) (i - 1) of
blanchet@51757
   604
            SOME b => if Binding.is_empty b then get_b else K b
blanchet@51757
   605
          | NONE => get_b);
blanchet@51757
   606
        val bs =
blanchet@51757
   607
          if live = 1 then
blanchet@51757
   608
            [set_name 1 (fn () => Binding.suffix_name ("_" ^ setN) b)]
blanchet@51757
   609
          else
blanchet@51757
   610
            map (fn i => set_name i (fn () => Binding.suffix_name ("_" ^ mk_setN i) b))
blanchet@51757
   611
              (1 upto live);
blanchet@51757
   612
      in bs ~~ set_rhss end;
blanchet@49459
   613
    val bd_bind_def = (fn () => Binding.suffix_name ("_" ^ bdN) b, bd_rhs);
blanchet@49459
   614
    val wit_binds_defs =
blanchet@49459
   615
      let
blanchet@49459
   616
        val bs = if nwits = 1 then [fn () => Binding.suffix_name ("_" ^ witN) b]
blanchet@49459
   617
          else map (fn i => fn () => Binding.suffix_name ("_" ^ mk_witN i) b) (1 upto nwits);
blanchet@51757
   618
      in bs ~~ wit_rhss end;
blanchet@49459
   619
blanchet@49459
   620
    val (((((bnf_map_term, raw_map_def),
blanchet@48975
   621
      (bnf_set_terms, raw_set_defs)),
blanchet@48975
   622
      (bnf_bd_term, raw_bd_def)),
blanchet@49459
   623
      (bnf_wit_terms, raw_wit_defs)), (lthy, lthy_old)) =
blanchet@48975
   624
        no_defs_lthy
blanchet@49463
   625
        |> maybe_define true map_bind_def
blanchet@49463
   626
        ||>> apfst split_list o fold_map (maybe_define true) set_binds_defs
blanchet@49463
   627
        ||>> maybe_define true bd_bind_def
blanchet@49463
   628
        ||>> apfst split_list o fold_map (maybe_define true) wit_binds_defs
blanchet@48975
   629
        ||> `(maybe_restore no_defs_lthy);
blanchet@48975
   630
blanchet@49459
   631
    val phi = Proof_Context.export_morphism lthy_old lthy;
blanchet@48975
   632
blanchet@48975
   633
    val bnf_map_def = Morphism.thm phi raw_map_def;
blanchet@48975
   634
    val bnf_set_defs = map (Morphism.thm phi) raw_set_defs;
blanchet@48975
   635
    val bnf_bd_def = Morphism.thm phi raw_bd_def;
blanchet@48975
   636
    val bnf_wit_defs = map (Morphism.thm phi) raw_wit_defs;
blanchet@48975
   637
blanchet@48975
   638
    val bnf_map = Morphism.term phi bnf_map_term;
blanchet@48975
   639
blanchet@48975
   640
    (*TODO: handle errors*)
blanchet@48975
   641
    (*simple shape analysis of a map function*)
traytel@49395
   642
    val ((alphas, betas), (CA, _)) =
traytel@49395
   643
      fastype_of bnf_map
traytel@49395
   644
      |> strip_typeN live
traytel@49395
   645
      |>> map_split dest_funT
traytel@49395
   646
      ||> dest_funT
traytel@49395
   647
      handle TYPE _ => error "Bad map function";
blanchet@48975
   648
blanchet@48975
   649
    val CA_params = map TVar (Term.add_tvarsT CA []);
blanchet@48975
   650
blanchet@48975
   651
    val bnf_sets = map2 (normalize_set CA_params) alphas (map (Morphism.term phi) bnf_set_terms);
blanchet@48975
   652
    val bdT = Morphism.typ phi bd_rhsT;
blanchet@48975
   653
    val bnf_bd =
blanchet@48975
   654
      Term.subst_TVars (Term.add_tvar_namesT bdT [] ~~ CA_params) (Morphism.term phi bnf_bd_term);
blanchet@48975
   655
    val bnf_wits = map (normalize_wit CA_params CA alphas o Morphism.term phi) bnf_wit_terms;
blanchet@48975
   656
blanchet@48975
   657
    (*TODO: assert Ds = (TVars of bnf_map) \ (alphas @ betas) as sets*)
blanchet@48975
   658
    val deads = (case Ds_opt of
blanchet@48975
   659
      NONE => subtract (op =) (alphas @ betas) (map TVar (Term.add_tvars bnf_map []))
blanchet@48975
   660
    | SOME Ds => map (Morphism.typ phi) Ds);
blanchet@48975
   661
    val dead = length deads;
blanchet@48975
   662
blanchet@48975
   663
    (*TODO: further checks of type of bnf_map*)
blanchet@48975
   664
    (*TODO: check types of bnf_sets*)
blanchet@48975
   665
    (*TODO: check type of bnf_bd*)
blanchet@49507
   666
    (*TODO: check type of bnf_rel*)
blanchet@48975
   667
blanchet@48975
   668
    val ((((((((((As', Bs'), Cs), Ds), B1Ts), B2Ts), domTs), ranTs), ranTs'), ranTs''),
blanchet@49459
   669
      (Ts, T)) = lthy
blanchet@48975
   670
      |> mk_TFrees live
blanchet@48975
   671
      ||>> mk_TFrees live
blanchet@48975
   672
      ||>> mk_TFrees live
blanchet@48975
   673
      ||>> mk_TFrees dead
blanchet@48975
   674
      ||>> mk_TFrees live
blanchet@48975
   675
      ||>> mk_TFrees live
blanchet@48975
   676
      ||>> mk_TFrees live
blanchet@48975
   677
      ||>> mk_TFrees live
blanchet@48975
   678
      ||>> mk_TFrees live
blanchet@48975
   679
      ||>> mk_TFrees live
blanchet@48975
   680
      ||> fst o mk_TFrees 1
blanchet@48975
   681
      ||> the_single
blanchet@48975
   682
      ||> `(replicate live);
blanchet@48975
   683
blanchet@48975
   684
    fun mk_bnf_map As' Bs' =
blanchet@48975
   685
      Term.subst_atomic_types ((deads ~~ Ds) @ (alphas ~~ As') @ (betas ~~ Bs')) bnf_map;
blanchet@49453
   686
    fun mk_bnf_t As' = Term.subst_atomic_types ((deads ~~ Ds) @ (alphas ~~ As'));
blanchet@49453
   687
    fun mk_bnf_T As' = Term.typ_subst_atomic ((deads ~~ Ds) @ (alphas ~~ As'));
blanchet@49453
   688
blanchet@48975
   689
    val (setRTs, RTs) = map_split (`HOLogic.mk_setT o HOLogic.mk_prodT) (As' ~~ Bs');
blanchet@48975
   690
    val setRTsAsCs = map (HOLogic.mk_setT o HOLogic.mk_prodT) (As' ~~ Cs);
blanchet@48975
   691
    val setRTsBsCs = map (HOLogic.mk_setT o HOLogic.mk_prodT) (Bs' ~~ Cs);
blanchet@48975
   692
    val setRT's = map (HOLogic.mk_setT o HOLogic.mk_prodT) (Bs' ~~ As');
blanchet@48975
   693
    val self_setRTs = map (HOLogic.mk_setT o HOLogic.mk_prodT) (As' ~~ As');
blanchet@49463
   694
    val QTs = map2 mk_pred2T As' Bs';
blanchet@48975
   695
blanchet@49453
   696
    val CA' = mk_bnf_T As' CA;
blanchet@49453
   697
    val CB' = mk_bnf_T Bs' CA;
blanchet@49453
   698
    val CC' = mk_bnf_T Cs CA;
blanchet@49453
   699
    val CRs' = mk_bnf_T RTs CA;
blanchet@49463
   700
    val CA'CB' = HOLogic.mk_prodT (CA', CB');
blanchet@49453
   701
blanchet@48975
   702
    val bnf_map_AsAs = mk_bnf_map As' As';
blanchet@48975
   703
    val bnf_map_AsBs = mk_bnf_map As' Bs';
blanchet@48975
   704
    val bnf_map_AsCs = mk_bnf_map As' Cs;
blanchet@48975
   705
    val bnf_map_BsCs = mk_bnf_map Bs' Cs;
blanchet@48975
   706
    val bnf_sets_As = map (mk_bnf_t As') bnf_sets;
blanchet@48975
   707
    val bnf_sets_Bs = map (mk_bnf_t Bs') bnf_sets;
blanchet@48975
   708
    val bnf_bd_As = mk_bnf_t As' bnf_bd;
blanchet@48975
   709
    val bnf_wit_As = map (apsnd (mk_bnf_t As')) bnf_wits;
blanchet@48975
   710
blanchet@49595
   711
    val pre_names_lthy = lthy;
blanchet@51762
   712
    val ((((((((((((((((((((((((fs, gs), hs), p), (x, x')), (y, y')), (z, z')), zs), As),
blanchet@49459
   713
      As_copy), Xs), B1s), B2s), f1s), f2s), e1s), e2s), p1s), p2s), bs), (Rs, Rs')), Rs_copy), Ss),
blanchet@49595
   714
      (Qs, Qs')), names_lthy) = pre_names_lthy
blanchet@48975
   715
      |> mk_Frees "f" (map2 (curry (op -->)) As' Bs')
blanchet@48975
   716
      ||>> mk_Frees "g" (map2 (curry (op -->)) Bs' Cs)
blanchet@48975
   717
      ||>> mk_Frees "h" (map2 (curry (op -->)) As' Ts)
blanchet@49463
   718
      ||>> yield_singleton (mk_Frees "p") CA'CB'
blanchet@48975
   719
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "x") CA'
blanchet@48975
   720
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "y") CB'
blanchet@48975
   721
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "z") CRs'
blanchet@48975
   722
      ||>> mk_Frees "z" As'
blanchet@48975
   723
      ||>> mk_Frees "A" (map HOLogic.mk_setT As')
blanchet@48975
   724
      ||>> mk_Frees "A" (map HOLogic.mk_setT As')
blanchet@48975
   725
      ||>> mk_Frees "A" (map HOLogic.mk_setT domTs)
blanchet@48975
   726
      ||>> mk_Frees "B1" (map HOLogic.mk_setT B1Ts)
blanchet@48975
   727
      ||>> mk_Frees "B2" (map HOLogic.mk_setT B2Ts)
blanchet@48975
   728
      ||>> mk_Frees "f1" (map2 (curry (op -->)) B1Ts ranTs)
blanchet@48975
   729
      ||>> mk_Frees "f2" (map2 (curry (op -->)) B2Ts ranTs)
blanchet@48975
   730
      ||>> mk_Frees "e1" (map2 (curry (op -->)) B1Ts ranTs')
blanchet@48975
   731
      ||>> mk_Frees "e2" (map2 (curry (op -->)) B2Ts ranTs'')
blanchet@48975
   732
      ||>> mk_Frees "p1" (map2 (curry (op -->)) domTs B1Ts)
blanchet@48975
   733
      ||>> mk_Frees "p2" (map2 (curry (op -->)) domTs B2Ts)
blanchet@48975
   734
      ||>> mk_Frees "b" As'
blanchet@49585
   735
      ||>> mk_Frees' "r" setRTs
blanchet@49585
   736
      ||>> mk_Frees "r" setRTs
blanchet@49585
   737
      ||>> mk_Frees "s" setRTsBsCs
blanchet@49592
   738
      ||>> mk_Frees' "P" QTs;
blanchet@48975
   739
blanchet@51762
   740
    val fs_copy = map2 (retype_free o fastype_of) fs gs;
blanchet@51762
   741
    val x_copy = retype_free CA' y;
blanchet@51762
   742
blanchet@49459
   743
    (*Gr (in R1 .. Rn) (map fst .. fst)^-1 O Gr (in R1 .. Rn) (map snd .. snd)*)
blanchet@49463
   744
    val O_Gr =
blanchet@49459
   745
      let
blanchet@49459
   746
        val map1 = Term.list_comb (mk_bnf_map RTs As', map fst_const RTs);
blanchet@49459
   747
        val map2 = Term.list_comb (mk_bnf_map RTs Bs', map snd_const RTs);
blanchet@49459
   748
        val bnf_in = mk_in (map Free Rs') (map (mk_bnf_t RTs) bnf_sets) CRs';
blanchet@49459
   749
      in
blanchet@49459
   750
        mk_rel_comp (mk_converse (mk_Gr bnf_in map1), mk_Gr bnf_in map2)
blanchet@49459
   751
      end;
blanchet@49459
   752
blanchet@49463
   753
    fun mk_predicate_of_set x_name y_name t =
blanchet@49463
   754
      let
blanchet@49463
   755
        val (T, U) = HOLogic.dest_prodT (HOLogic.dest_setT (fastype_of t));
blanchet@49463
   756
        val x = Free (x_name, T);
blanchet@49463
   757
        val y = Free (y_name, U);
blanchet@49463
   758
      in fold_rev Term.lambda [x, y] (HOLogic.mk_mem (HOLogic.mk_prod (x, y), t)) end;
blanchet@49463
   759
blanchet@49537
   760
    val sQs =
blanchet@49537
   761
      map3 (fn Q => fn T => fn U =>
blanchet@49537
   762
          HOLogic.Collect_const (HOLogic.mk_prodT (T, U)) $ HOLogic.mk_split Q) Qs As' Bs';
blanchet@49537
   763
blanchet@49507
   764
    val rel_rhs = (case raw_rel_opt of
blanchet@49463
   765
        NONE =>
blanchet@49463
   766
        fold_rev absfree Qs' (mk_predicate_of_set (fst x') (fst y')
blanchet@49537
   767
          (Term.list_comb (fold_rev Term.absfree Rs' O_Gr, sQs)))
blanchet@49507
   768
      | SOME raw_rel => prep_term no_defs_lthy raw_rel);
blanchet@49463
   769
blanchet@51767
   770
    val rel_bind_def =
blanchet@51767
   771
      (fn () => if Binding.is_empty rel_b then Binding.suffix_name ("_" ^ relN) b else rel_b,
blanchet@51767
   772
       rel_rhs);
blanchet@49463
   773
blanchet@49507
   774
    val ((bnf_rel_term, raw_rel_def), (lthy, lthy_old)) =
blanchet@49463
   775
      lthy
blanchet@49507
   776
      |> maybe_define (is_some raw_rel_opt) rel_bind_def
blanchet@49463
   777
      ||> `(maybe_restore lthy);
blanchet@49463
   778
blanchet@49463
   779
    val phi = Proof_Context.export_morphism lthy_old lthy;
blanchet@49507
   780
    val bnf_rel_def = Morphism.thm phi raw_rel_def;
blanchet@49507
   781
    val bnf_rel = Morphism.term phi bnf_rel_term;
blanchet@49463
   782
blanchet@49507
   783
    fun mk_bnf_rel QTs CA' CB' = normalize_rel lthy QTs CA' CB' bnf_rel;
blanchet@49463
   784
blanchet@49507
   785
    val rel = mk_bnf_rel QTs CA' CB';
blanchet@49463
   786
blanchet@49506
   787
    val srel_rhs =
blanchet@49463
   788
      fold_rev Term.absfree Rs' (HOLogic.Collect_const CA'CB' $
blanchet@49507
   789
        Term.lambda p (Term.list_comb (rel, map (mk_predicate_of_set (fst x') (fst y')) Rs) $
blanchet@49463
   790
        HOLogic.mk_fst p $ HOLogic.mk_snd p));
blanchet@49459
   791
blanchet@49506
   792
    val srel_bind_def = (fn () => Binding.suffix_name ("_" ^ srelN) b, srel_rhs);
blanchet@49459
   793
blanchet@49506
   794
    val ((bnf_srel_term, raw_srel_def), (lthy, lthy_old)) =
blanchet@49459
   795
      lthy
blanchet@49506
   796
      |> maybe_define false srel_bind_def
blanchet@49459
   797
      ||> `(maybe_restore lthy);
blanchet@49459
   798
blanchet@49459
   799
    val phi = Proof_Context.export_morphism lthy_old lthy;
blanchet@49506
   800
    val bnf_srel_def = Morphism.thm phi raw_srel_def;
blanchet@49506
   801
    val bnf_srel = Morphism.term phi bnf_srel_term;
blanchet@49459
   802
blanchet@49506
   803
    fun mk_bnf_srel setRTs CA' CB' = normalize_srel lthy setRTs CA' CB' bnf_srel;
blanchet@49459
   804
blanchet@49506
   805
    val srel = mk_bnf_srel setRTs CA' CB';
blanchet@49459
   806
blanchet@49460
   807
    val _ = case no_reflexive (raw_map_def :: raw_set_defs @ [raw_bd_def] @
blanchet@49507
   808
        raw_wit_defs @ [raw_rel_def, raw_srel_def]) of
blanchet@49459
   809
        [] => ()
blanchet@49459
   810
      | defs => Proof_Display.print_consts true lthy_old (K false)
blanchet@49459
   811
          (map (dest_Free o fst o Logic.dest_equals o prop_of) defs);
blanchet@49459
   812
blanchet@49458
   813
    val map_id_goal =
blanchet@51762
   814
      let val bnf_map_app_id = Term.list_comb (bnf_map_AsAs, map HOLogic.id_const As') in
blanchet@51762
   815
        mk_Trueprop_eq (bnf_map_app_id, HOLogic.id_const CA')
blanchet@48975
   816
      end;
blanchet@48975
   817
blanchet@49458
   818
    val map_comp_goal =
blanchet@48975
   819
      let
blanchet@49018
   820
        val bnf_map_app_comp = Term.list_comb (bnf_map_AsCs, map2 (curry HOLogic.mk_comp) gs fs);
blanchet@48975
   821
        val comp_bnf_map_app = HOLogic.mk_comp
blanchet@51762
   822
          (Term.list_comb (bnf_map_BsCs, gs), Term.list_comb (bnf_map_AsBs, fs));
blanchet@48975
   823
      in
blanchet@49123
   824
        fold_rev Logic.all (fs @ gs) (mk_Trueprop_eq (bnf_map_app_comp, comp_bnf_map_app))
blanchet@48975
   825
      end;
blanchet@48975
   826
blanchet@51762
   827
    fun mk_map_cong_prem x z set f f_copy =
blanchet@51762
   828
      Logic.all z (Logic.mk_implies
blanchet@51762
   829
        (HOLogic.mk_Trueprop (HOLogic.mk_mem (z, set $ x)),
blanchet@51762
   830
        mk_Trueprop_eq (f $ z, f_copy $ z)));
blanchet@51762
   831
blanchet@51761
   832
    val map_cong0_goal =
blanchet@48975
   833
      let
blanchet@51762
   834
        val prems = map4 (mk_map_cong_prem x) zs bnf_sets_As fs fs_copy;
blanchet@51762
   835
        val eq = mk_Trueprop_eq (Term.list_comb (bnf_map_AsBs, fs) $ x,
blanchet@48975
   836
          Term.list_comb (bnf_map_AsBs, fs_copy) $ x);
blanchet@48975
   837
      in
blanchet@51762
   838
        fold_rev Logic.all (x :: fs @ fs_copy) (Logic.list_implies (prems, eq))
blanchet@48975
   839
      end;
blanchet@48975
   840
blanchet@51766
   841
    val set_maps_goal =
blanchet@48975
   842
      let
blanchet@48975
   843
        fun mk_goal setA setB f =
blanchet@48975
   844
          let
blanchet@48975
   845
            val set_comp_map =
blanchet@48975
   846
              HOLogic.mk_comp (setB, Term.list_comb (bnf_map_AsBs, fs));
blanchet@48975
   847
            val image_comp_set = HOLogic.mk_comp (mk_image f, setA);
blanchet@48975
   848
          in
blanchet@49123
   849
            fold_rev Logic.all fs (mk_Trueprop_eq (set_comp_map, image_comp_set))
blanchet@48975
   850
          end;
blanchet@48975
   851
      in
blanchet@48975
   852
        map3 mk_goal bnf_sets_As bnf_sets_Bs fs
blanchet@48975
   853
      end;
blanchet@48975
   854
blanchet@49458
   855
    val card_order_bd_goal = HOLogic.mk_Trueprop (mk_card_order bnf_bd_As);
blanchet@48975
   856
blanchet@49458
   857
    val cinfinite_bd_goal = HOLogic.mk_Trueprop (mk_cinfinite bnf_bd_As);
blanchet@48975
   858
blanchet@49458
   859
    val set_bds_goal =
blanchet@48975
   860
      let
blanchet@48975
   861
        fun mk_goal set =
blanchet@48975
   862
          Logic.all x (HOLogic.mk_Trueprop (mk_ordLeq (mk_card_of (set $ x)) bnf_bd_As));
blanchet@48975
   863
      in
blanchet@48975
   864
        map mk_goal bnf_sets_As
blanchet@48975
   865
      end;
blanchet@48975
   866
blanchet@49458
   867
    val in_bd_goal =
blanchet@48975
   868
      let
blanchet@48975
   869
        val bd = mk_cexp
blanchet@48975
   870
          (if live = 0 then ctwo
blanchet@48975
   871
            else mk_csum (Library.foldr1 (uncurry mk_csum) (map mk_card_of As)) ctwo)
blanchet@48975
   872
          bnf_bd_As;
blanchet@48975
   873
      in
blanchet@48975
   874
        fold_rev Logic.all As
blanchet@48975
   875
          (HOLogic.mk_Trueprop (mk_ordLeq (mk_card_of (mk_in As bnf_sets_As CA')) bd))
blanchet@48975
   876
      end;
blanchet@48975
   877
blanchet@49458
   878
    val map_wpull_goal =
blanchet@48975
   879
      let
blanchet@48975
   880
        val prems = map HOLogic.mk_Trueprop
blanchet@48975
   881
          (map8 mk_wpull Xs B1s B2s f1s f2s (replicate live NONE) p1s p2s);
blanchet@48975
   882
        val CX = mk_bnf_T domTs CA;
blanchet@48975
   883
        val CB1 = mk_bnf_T B1Ts CA;
blanchet@48975
   884
        val CB2 = mk_bnf_T B2Ts CA;
blanchet@48975
   885
        val bnf_sets_CX = map2 (normalize_set (map (mk_bnf_T domTs) CA_params)) domTs bnf_sets;
blanchet@48975
   886
        val bnf_sets_CB1 = map2 (normalize_set (map (mk_bnf_T B1Ts) CA_params)) B1Ts bnf_sets;
blanchet@48975
   887
        val bnf_sets_CB2 = map2 (normalize_set (map (mk_bnf_T B2Ts) CA_params)) B2Ts bnf_sets;
blanchet@48975
   888
        val bnf_map_app_f1 = Term.list_comb (mk_bnf_map B1Ts ranTs, f1s);
blanchet@48975
   889
        val bnf_map_app_f2 = Term.list_comb (mk_bnf_map B2Ts ranTs, f2s);
blanchet@48975
   890
        val bnf_map_app_p1 = Term.list_comb (mk_bnf_map domTs B1Ts, p1s);
blanchet@48975
   891
        val bnf_map_app_p2 = Term.list_comb (mk_bnf_map domTs B2Ts, p2s);
blanchet@48975
   892
blanchet@48975
   893
        val map_wpull = mk_wpull (mk_in Xs bnf_sets_CX CX)
blanchet@48975
   894
          (mk_in B1s bnf_sets_CB1 CB1) (mk_in B2s bnf_sets_CB2 CB2)
blanchet@48975
   895
          bnf_map_app_f1 bnf_map_app_f2 NONE bnf_map_app_p1 bnf_map_app_p2;
blanchet@48975
   896
      in
blanchet@48975
   897
        fold_rev Logic.all (Xs @ B1s @ B2s @ f1s @ f2s @ p1s @ p2s)
blanchet@48975
   898
          (Logic.list_implies (prems, HOLogic.mk_Trueprop map_wpull))
blanchet@48975
   899
      end;
blanchet@48975
   900
blanchet@49506
   901
    val srel_O_Gr_goal = fold_rev Logic.all Rs (mk_Trueprop_eq (Term.list_comb (srel, Rs), O_Gr));
blanchet@49453
   902
blanchet@51766
   903
    val goals = zip_axioms map_id_goal map_comp_goal map_cong0_goal set_maps_goal card_order_bd_goal
blanchet@51766
   904
      cinfinite_bd_goal set_bds_goal in_bd_goal map_wpull_goal srel_O_Gr_goal;
blanchet@48975
   905
blanchet@48975
   906
    fun mk_wit_goals (I, wit) =
blanchet@48975
   907
      let
blanchet@48975
   908
        val xs = map (nth bs) I;
blanchet@48975
   909
        fun wit_goal i =
blanchet@48975
   910
          let
blanchet@48975
   911
            val z = nth zs i;
blanchet@48975
   912
            val set_wit = nth bnf_sets_As i $ Term.list_comb (wit, xs);
blanchet@48975
   913
            val concl = HOLogic.mk_Trueprop
blanchet@48975
   914
              (if member (op =) I i then HOLogic.mk_eq (z, nth bs i)
blanchet@48975
   915
              else @{term False});
blanchet@48975
   916
          in
blanchet@48975
   917
            fold_rev Logic.all (z :: xs)
blanchet@48975
   918
              (Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (z, set_wit)), concl))
blanchet@48975
   919
          end;
blanchet@48975
   920
      in
blanchet@48975
   921
        map wit_goal (0 upto live - 1)
blanchet@48975
   922
      end;
blanchet@48975
   923
blanchet@48975
   924
    val wit_goalss = map mk_wit_goals bnf_wit_As;
blanchet@48975
   925
blanchet@48975
   926
    fun after_qed thms lthy =
blanchet@48975
   927
      let
blanchet@48975
   928
        val (axioms, wit_thms) = apfst (mk_axioms live) (chop (length goals) thms);
blanchet@48975
   929
traytel@49109
   930
        val bd_Card_order = #bd_card_order axioms RS @{thm conjunct2[OF card_order_on_Card_order]};
blanchet@48975
   931
        val bd_Cinfinite = @{thm conjI} OF [#bd_cinfinite axioms, bd_Card_order];
blanchet@48975
   932
        val bd_Cnotzero = bd_Cinfinite RS @{thm Cinfinite_Cnotzero};
blanchet@48975
   933
blanchet@51766
   934
        fun mk_collect_set_map () =
blanchet@48975
   935
          let
blanchet@48975
   936
            val defT = mk_bnf_T Ts CA --> HOLogic.mk_setT T;
blanchet@48975
   937
            val collect_map = HOLogic.mk_comp
blanchet@48975
   938
              (mk_collect (map (mk_bnf_t Ts) bnf_sets) defT,
blanchet@48975
   939
              Term.list_comb (mk_bnf_map As' Ts, hs));
blanchet@48975
   940
            val image_collect = mk_collect
blanchet@48975
   941
              (map2 (fn h => fn set => HOLogic.mk_comp (mk_image h, set)) hs bnf_sets_As)
blanchet@48975
   942
              defT;
blanchet@48975
   943
            (*collect {set1 ... setm} o map f1 ... fm = collect {f1` o set1 ... fm` o setm}*)
blanchet@49123
   944
            val goal = fold_rev Logic.all hs (mk_Trueprop_eq (collect_map, image_collect));
blanchet@48975
   945
          in
blanchet@51766
   946
            Goal.prove_sorry lthy [] [] goal (K (mk_collect_set_map_tac (#set_map axioms)))
traytel@49109
   947
            |> Thm.close_derivation
blanchet@48975
   948
          end;
blanchet@48975
   949
blanchet@51766
   950
        val collect_set_map = Lazy.lazy mk_collect_set_map;
blanchet@48975
   951
blanchet@48975
   952
        fun mk_in_mono () =
blanchet@48975
   953
          let
blanchet@48975
   954
            val prems_mono = map2 (HOLogic.mk_Trueprop oo mk_subset) As As_copy;
blanchet@49458
   955
            val in_mono_goal =
blanchet@48975
   956
              fold_rev Logic.all (As @ As_copy)
blanchet@48975
   957
                (Logic.list_implies (prems_mono, HOLogic.mk_Trueprop
blanchet@48975
   958
                  (mk_subset (mk_in As bnf_sets_As CA') (mk_in As_copy bnf_sets_As CA'))));
blanchet@48975
   959
          in
wenzelm@51551
   960
            Goal.prove_sorry lthy [] [] in_mono_goal (K (mk_in_mono_tac live))
traytel@49109
   961
            |> Thm.close_derivation
blanchet@48975
   962
          end;
blanchet@48975
   963
blanchet@49538
   964
        val in_mono = Lazy.lazy mk_in_mono;
blanchet@48975
   965
blanchet@48975
   966
        fun mk_in_cong () =
blanchet@48975
   967
          let
blanchet@51762
   968
            val prems_cong = map2 (curry mk_Trueprop_eq) As As_copy;
blanchet@49458
   969
            val in_cong_goal =
blanchet@48975
   970
              fold_rev Logic.all (As @ As_copy)
blanchet@51762
   971
                (Logic.list_implies (prems_cong,
blanchet@51762
   972
                  mk_Trueprop_eq (mk_in As bnf_sets_As CA', mk_in As_copy bnf_sets_As CA')));
blanchet@48975
   973
          in
wenzelm@51551
   974
            Goal.prove_sorry lthy [] [] in_cong_goal (K ((TRY o hyp_subst_tac THEN' rtac refl) 1))
traytel@49109
   975
            |> Thm.close_derivation
blanchet@48975
   976
          end;
blanchet@48975
   977
blanchet@49538
   978
        val in_cong = Lazy.lazy mk_in_cong;
blanchet@48975
   979
blanchet@51762
   980
        val map_id' = Lazy.lazy (fn () => mk_map_id' (#map_id axioms));
blanchet@51762
   981
        val map_comp' = Lazy.lazy (fn () => mk_map_comp' (#map_comp axioms));
blanchet@51762
   982
blanchet@51762
   983
        fun mk_map_cong () =
blanchet@51762
   984
          let
blanchet@51762
   985
            val prem0 = mk_Trueprop_eq (x, x_copy);
blanchet@51762
   986
            val prems = map4 (mk_map_cong_prem x_copy) zs bnf_sets_As fs fs_copy;
blanchet@51762
   987
            val eq = mk_Trueprop_eq (Term.list_comb (bnf_map_AsBs, fs) $ x,
blanchet@51762
   988
              Term.list_comb (bnf_map_AsBs, fs_copy) $ x_copy);
blanchet@51762
   989
            val goal = fold_rev Logic.all (x :: x_copy :: fs @ fs_copy)
blanchet@51762
   990
              (Logic.list_implies (prem0 :: prems, eq));
blanchet@51762
   991
          in
blanchet@51762
   992
            Goal.prove_sorry lthy [] [] goal (fn _ => mk_map_cong_tac (#map_cong0 axioms))
blanchet@51762
   993
            |> Thm.close_derivation
blanchet@51762
   994
          end;
blanchet@51762
   995
blanchet@51762
   996
        val map_cong = Lazy.lazy mk_map_cong;
blanchet@48975
   997
blanchet@51766
   998
        val set_map' = map (fn thm => Lazy.lazy (fn () => mk_set_map' thm)) (#set_map axioms);
blanchet@48975
   999
blanchet@48975
  1000
        fun mk_map_wppull () =
blanchet@48975
  1001
          let
blanchet@48975
  1002
            val prems = if live = 0 then [] else
blanchet@48975
  1003
              [HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@48975
  1004
                (map8 mk_wpull Xs B1s B2s f1s f2s (map SOME (e1s ~~ e2s)) p1s p2s))];
blanchet@48975
  1005
            val CX = mk_bnf_T domTs CA;
blanchet@48975
  1006
            val CB1 = mk_bnf_T B1Ts CA;
blanchet@48975
  1007
            val CB2 = mk_bnf_T B2Ts CA;
blanchet@48975
  1008
            val bnf_sets_CX =
blanchet@48975
  1009
              map2 (normalize_set (map (mk_bnf_T domTs) CA_params)) domTs bnf_sets;
blanchet@48975
  1010
            val bnf_sets_CB1 =
blanchet@48975
  1011
              map2 (normalize_set (map (mk_bnf_T B1Ts) CA_params)) B1Ts bnf_sets;
blanchet@48975
  1012
            val bnf_sets_CB2 =
blanchet@48975
  1013
              map2 (normalize_set (map (mk_bnf_T B2Ts) CA_params)) B2Ts bnf_sets;
blanchet@48975
  1014
            val bnf_map_app_f1 = Term.list_comb (mk_bnf_map B1Ts ranTs, f1s);
blanchet@48975
  1015
            val bnf_map_app_f2 = Term.list_comb (mk_bnf_map B2Ts ranTs, f2s);
blanchet@48975
  1016
            val bnf_map_app_e1 = Term.list_comb (mk_bnf_map B1Ts ranTs', e1s);
blanchet@48975
  1017
            val bnf_map_app_e2 = Term.list_comb (mk_bnf_map B2Ts ranTs'', e2s);
blanchet@48975
  1018
            val bnf_map_app_p1 = Term.list_comb (mk_bnf_map domTs B1Ts, p1s);
blanchet@48975
  1019
            val bnf_map_app_p2 = Term.list_comb (mk_bnf_map domTs B2Ts, p2s);
blanchet@48975
  1020
blanchet@48975
  1021
            val concl = mk_wpull (mk_in Xs bnf_sets_CX CX)
blanchet@48975
  1022
              (mk_in B1s bnf_sets_CB1 CB1) (mk_in B2s bnf_sets_CB2 CB2)
blanchet@48975
  1023
              bnf_map_app_f1 bnf_map_app_f2 (SOME (bnf_map_app_e1, bnf_map_app_e2))
blanchet@48975
  1024
              bnf_map_app_p1 bnf_map_app_p2;
blanchet@48975
  1025
blanchet@48975
  1026
            val goal =
blanchet@48975
  1027
              fold_rev Logic.all (Xs @ B1s @ B2s @ f1s @ f2s @ e1s @ e2s @ p1s @ p2s)
blanchet@48975
  1028
                (Logic.list_implies (prems, HOLogic.mk_Trueprop concl))
blanchet@48975
  1029
          in
wenzelm@51551
  1030
            Goal.prove_sorry lthy [] [] goal
blanchet@51761
  1031
              (fn _ => mk_map_wppull_tac (#map_id axioms) (#map_cong0 axioms)
blanchet@51766
  1032
                (#map_wpull axioms) (Lazy.force map_comp') (map Lazy.force set_map'))
traytel@49109
  1033
            |> Thm.close_derivation
blanchet@48975
  1034
          end;
blanchet@48975
  1035
blanchet@51762
  1036
        val map_wppull = Lazy.lazy mk_map_wppull;
blanchet@49453
  1037
blanchet@51762
  1038
        val srel_O_Grs = no_refl [#srel_O_Gr axioms];
blanchet@48975
  1039
blanchet@49506
  1040
        fun mk_srel_Gr () =
blanchet@48975
  1041
          let
blanchet@49506
  1042
            val lhs = Term.list_comb (srel, map2 mk_Gr As fs);
blanchet@48975
  1043
            val rhs = mk_Gr (mk_in As bnf_sets_As CA') (Term.list_comb (bnf_map_AsBs, fs));
blanchet@49123
  1044
            val goal = fold_rev Logic.all (As @ fs) (mk_Trueprop_eq (lhs, rhs));
blanchet@48975
  1045
          in
wenzelm@51551
  1046
            Goal.prove_sorry lthy [] [] goal
blanchet@51761
  1047
              (mk_srel_Gr_tac srel_O_Grs (#map_id axioms) (#map_cong0 axioms) (Lazy.force map_id')
blanchet@51766
  1048
                (Lazy.force map_comp') (map Lazy.force set_map'))
traytel@49109
  1049
            |> Thm.close_derivation
blanchet@48975
  1050
          end;
blanchet@48975
  1051
blanchet@49538
  1052
        val srel_Gr = Lazy.lazy mk_srel_Gr;
blanchet@48975
  1053
blanchet@49506
  1054
        fun mk_srel_prems f = map2 (HOLogic.mk_Trueprop oo f) Rs Rs_copy
blanchet@49506
  1055
        fun mk_srel_concl f = HOLogic.mk_Trueprop
blanchet@49506
  1056
          (f (Term.list_comb (srel, Rs), Term.list_comb (srel, Rs_copy)));
blanchet@48975
  1057
blanchet@49506
  1058
        fun mk_srel_mono () =
blanchet@48975
  1059
          let
blanchet@49506
  1060
            val mono_prems = mk_srel_prems mk_subset;
blanchet@49506
  1061
            val mono_concl = mk_srel_concl (uncurry mk_subset);
blanchet@48975
  1062
          in
wenzelm@51551
  1063
            Goal.prove_sorry lthy [] []
blanchet@48975
  1064
              (fold_rev Logic.all (Rs @ Rs_copy) (Logic.list_implies (mono_prems, mono_concl)))
blanchet@49506
  1065
              (mk_srel_mono_tac srel_O_Grs (Lazy.force in_mono))
traytel@49109
  1066
            |> Thm.close_derivation
blanchet@48975
  1067
          end;
blanchet@48975
  1068
blanchet@49506
  1069
        fun mk_srel_cong () =
blanchet@48975
  1070
          let
blanchet@49506
  1071
            val cong_prems = mk_srel_prems (curry HOLogic.mk_eq);
blanchet@49506
  1072
            val cong_concl = mk_srel_concl HOLogic.mk_eq;
blanchet@48975
  1073
          in
wenzelm@51551
  1074
            Goal.prove_sorry lthy [] []
blanchet@48975
  1075
              (fold_rev Logic.all (Rs @ Rs_copy) (Logic.list_implies (cong_prems, cong_concl)))
blanchet@48975
  1076
              (fn _ => (TRY o hyp_subst_tac THEN' rtac refl) 1)
traytel@49109
  1077
            |> Thm.close_derivation
blanchet@48975
  1078
          end;
blanchet@48975
  1079
blanchet@49538
  1080
        val srel_mono = Lazy.lazy mk_srel_mono;
blanchet@49538
  1081
        val srel_cong = Lazy.lazy mk_srel_cong;
blanchet@48975
  1082
blanchet@49506
  1083
        fun mk_srel_Id () =
blanchet@49515
  1084
          let val srelAsAs = mk_bnf_srel self_setRTs CA' CA' in
wenzelm@51551
  1085
            Goal.prove_sorry lthy [] []
blanchet@51762
  1086
              (mk_Trueprop_eq (Term.list_comb (srelAsAs, map Id_const As'), Id_const CA'))
blanchet@49506
  1087
              (mk_srel_Id_tac live (Lazy.force srel_Gr) (#map_id axioms))
traytel@49109
  1088
            |> Thm.close_derivation
blanchet@48975
  1089
          end;
blanchet@48975
  1090
blanchet@49538
  1091
        val srel_Id = Lazy.lazy mk_srel_Id;
blanchet@48975
  1092
blanchet@49506
  1093
        fun mk_srel_converse () =
blanchet@48975
  1094
          let
blanchet@49515
  1095
            val srelBsAs = mk_bnf_srel setRT's CB' CA';
blanchet@49515
  1096
            val lhs = Term.list_comb (srelBsAs, map mk_converse Rs);
blanchet@49506
  1097
            val rhs = mk_converse (Term.list_comb (srel, Rs));
blanchet@48975
  1098
            val le_goal = fold_rev Logic.all Rs (HOLogic.mk_Trueprop (mk_subset lhs rhs));
wenzelm@51551
  1099
            val le_thm = Goal.prove_sorry lthy [] [] le_goal
blanchet@51761
  1100
              (mk_srel_converse_le_tac srel_O_Grs (Lazy.force srel_Id) (#map_cong0 axioms)
blanchet@51766
  1101
                (Lazy.force map_comp') (map Lazy.force set_map'))
traytel@49109
  1102
              |> Thm.close_derivation
blanchet@49123
  1103
            val goal = fold_rev Logic.all Rs (mk_Trueprop_eq (lhs, rhs));
blanchet@48975
  1104
          in
wenzelm@51551
  1105
            Goal.prove_sorry lthy [] [] goal (fn _ => mk_srel_converse_tac le_thm)
traytel@49109
  1106
            |> Thm.close_derivation
blanchet@48975
  1107
          end;
blanchet@48975
  1108
blanchet@49538
  1109
        val srel_converse = Lazy.lazy mk_srel_converse;
blanchet@48975
  1110
blanchet@49506
  1111
        fun mk_srel_O () =
blanchet@48975
  1112
          let
blanchet@49515
  1113
            val srelAsCs = mk_bnf_srel setRTsAsCs CA' CC';
blanchet@49515
  1114
            val srelBsCs = mk_bnf_srel setRTsBsCs CB' CC';
blanchet@49515
  1115
            val lhs = Term.list_comb (srelAsCs, map2 (curry mk_rel_comp) Rs Ss);
blanchet@49515
  1116
            val rhs = mk_rel_comp (Term.list_comb (srel, Rs), Term.list_comb (srelBsCs, Ss));
blanchet@49123
  1117
            val goal = fold_rev Logic.all (Rs @ Ss) (mk_Trueprop_eq (lhs, rhs));
blanchet@48975
  1118
          in
wenzelm@51551
  1119
            Goal.prove_sorry lthy [] [] goal
blanchet@51761
  1120
              (mk_srel_O_tac srel_O_Grs (Lazy.force srel_Id) (#map_cong0 axioms)
blanchet@51766
  1121
                (Lazy.force map_wppull) (Lazy.force map_comp') (map Lazy.force set_map'))
traytel@49109
  1122
            |> Thm.close_derivation
blanchet@48975
  1123
          end;
blanchet@48975
  1124
blanchet@49538
  1125
        val srel_O = Lazy.lazy mk_srel_O;
blanchet@48975
  1126
blanchet@49506
  1127
        fun mk_in_srel () =
blanchet@48975
  1128
          let
blanchet@48975
  1129
            val bnf_in = mk_in Rs (map (mk_bnf_t RTs) bnf_sets) CRs';
blanchet@48975
  1130
            val map1 = Term.list_comb (mk_bnf_map RTs As', map fst_const RTs);
blanchet@48975
  1131
            val map2 = Term.list_comb (mk_bnf_map RTs Bs', map snd_const RTs);
blanchet@48975
  1132
            val map_fst_eq = HOLogic.mk_eq (map1 $ z, x);
blanchet@48975
  1133
            val map_snd_eq = HOLogic.mk_eq (map2 $ z, y);
blanchet@49506
  1134
            val lhs = HOLogic.mk_mem (HOLogic.mk_prod (x, y), Term.list_comb (srel, Rs));
blanchet@48975
  1135
            val rhs =
blanchet@48975
  1136
              HOLogic.mk_exists (fst z', snd z', HOLogic.mk_conj (HOLogic.mk_mem (z, bnf_in),
blanchet@48975
  1137
                HOLogic.mk_conj (map_fst_eq, map_snd_eq)));
blanchet@48975
  1138
            val goal =
blanchet@49123
  1139
              fold_rev Logic.all (x :: y :: Rs) (mk_Trueprop_eq (lhs, rhs));
blanchet@48975
  1140
          in
wenzelm@51551
  1141
            Goal.prove_sorry lthy [] [] goal (mk_in_srel_tac srel_O_Grs (length bnf_sets))
traytel@49109
  1142
            |> Thm.close_derivation
blanchet@48975
  1143
          end;
blanchet@48975
  1144
blanchet@49538
  1145
        val in_srel = Lazy.lazy mk_in_srel;
blanchet@48975
  1146
blanchet@49537
  1147
        val eqset_imp_iff_pair = @{thm eqset_imp_iff_pair};
blanchet@49591
  1148
        val mem_Collect_etc = @{thms fst_conv mem_Collect_eq prod.cases snd_conv};
blanchet@49591
  1149
        val mem_Collect_etc' = @{thms fst_conv mem_Collect_eq pair_in_Id_conv snd_conv};
blanchet@49537
  1150
blanchet@49594
  1151
        fun mk_rel_srel () =
blanchet@49537
  1152
          unfold_thms lthy mem_Collect_etc
blanchet@49537
  1153
            (funpow live (fn thm => thm RS @{thm fun_cong_pair}) (bnf_srel_def RS meta_eq_to_obj_eq)
blanchet@49537
  1154
               RS eqset_imp_iff_pair RS sym)
blanchet@49537
  1155
          |> Drule.zero_var_indexes;
blanchet@49537
  1156
blanchet@49594
  1157
        val rel_srel = Lazy.lazy mk_rel_srel;
blanchet@49537
  1158
blanchet@49591
  1159
        fun mk_rel_eq () =
blanchet@49591
  1160
          unfold_thms lthy (bnf_srel_def :: mem_Collect_etc')
blanchet@49631
  1161
            (Lazy.force srel_Id RS @{thm arg_cong[of _ _ "%A x y. (x, y) : A"]})
blanchet@49631
  1162
          |> Drule.eta_contraction_rule;
blanchet@49591
  1163
blanchet@49591
  1164
        val rel_eq = Lazy.lazy mk_rel_eq;
blanchet@49591
  1165
blanchet@49537
  1166
        fun mk_rel_flip () =
blanchet@49537
  1167
          let
blanchet@49537
  1168
            val srel_converse_thm = Lazy.force srel_converse;
blanchet@49585
  1169
            val cts = map (SOME o certify lthy) sQs;
blanchet@49585
  1170
            val srel_converse_thm' = cterm_instantiate_pos cts srel_converse_thm;
blanchet@49537
  1171
          in
blanchet@49537
  1172
            unfold_thms lthy (bnf_srel_def :: @{thm converse_iff} :: mem_Collect_etc)
blanchet@49537
  1173
              (srel_converse_thm' RS eqset_imp_iff_pair)
blanchet@49595
  1174
            |> singleton (Proof_Context.export names_lthy pre_names_lthy)
blanchet@49537
  1175
          end;
blanchet@49537
  1176
blanchet@49538
  1177
        val rel_flip = Lazy.lazy mk_rel_flip;
blanchet@49537
  1178
blanchet@49507
  1179
        val defs = mk_defs bnf_map_def bnf_set_defs bnf_rel_def bnf_srel_def;
blanchet@48975
  1180
blanchet@51766
  1181
        val facts = mk_facts bd_Card_order bd_Cinfinite bd_Cnotzero collect_set_map in_cong in_mono
blanchet@51766
  1182
          in_srel map_comp' map_cong map_id' map_wppull rel_eq rel_flip rel_srel set_map'
blanchet@51766
  1183
          srel_cong srel_mono srel_Id srel_Gr srel_converse srel_O;
blanchet@48975
  1184
blanchet@48975
  1185
        val wits = map2 mk_witness bnf_wits wit_thms;
blanchet@48975
  1186
blanchet@49507
  1187
        val bnf_rel =
blanchet@49507
  1188
          Term.subst_atomic_types ((Ds ~~ deads) @ (As' ~~ alphas) @ (Bs' ~~ betas)) rel;
blanchet@49506
  1189
        val bnf_srel =
blanchet@49506
  1190
          Term.subst_atomic_types ((Ds ~~ deads) @ (As' ~~ alphas) @ (Bs' ~~ betas)) srel;
blanchet@48975
  1191
blanchet@48975
  1192
        val bnf = mk_bnf b CA live alphas betas dead deads bnf_map bnf_sets bnf_bd axioms defs facts
blanchet@49507
  1193
          wits bnf_rel bnf_srel;
blanchet@48975
  1194
      in
blanchet@48975
  1195
        (bnf, lthy
blanchet@49538
  1196
          |> (if fact_policy = Note_All then
blanchet@48975
  1197
                let
blanchet@48975
  1198
                  val witNs = if length wits = 1 then [witN] else map mk_witN (1 upto length wits);
traytel@49109
  1199
                  val notes =
traytel@49109
  1200
                    [(bd_card_orderN, [#bd_card_order axioms]),
traytel@49109
  1201
                    (bd_cinfiniteN, [#bd_cinfinite axioms]),
traytel@49109
  1202
                    (bd_Card_orderN, [#bd_Card_order facts]),
traytel@49109
  1203
                    (bd_CinfiniteN, [#bd_Cinfinite facts]),
traytel@49109
  1204
                    (bd_CnotzeroN, [#bd_Cnotzero facts]),
blanchet@51766
  1205
                    (collect_set_mapN, [Lazy.force (#collect_set_map facts)]),
traytel@49109
  1206
                    (in_bdN, [#in_bd axioms]),
traytel@49109
  1207
                    (in_monoN, [Lazy.force (#in_mono facts)]),
blanchet@49506
  1208
                    (in_srelN, [Lazy.force (#in_srel facts)]),
traytel@49109
  1209
                    (map_compN, [#map_comp axioms]),
traytel@49109
  1210
                    (map_idN, [#map_id axioms]),
traytel@49109
  1211
                    (map_wpullN, [#map_wpull axioms]),
blanchet@51766
  1212
                    (set_mapN, #set_map axioms),
traytel@49109
  1213
                    (set_bdN, #set_bd axioms)] @
blanchet@51757
  1214
                    (witNs ~~ wit_thms)
traytel@49109
  1215
                    |> map (fn (thmN, thms) =>
traytel@49109
  1216
                      ((qualify (Binding.qualify true (Binding.name_of b) (Binding.name thmN)), []),
traytel@49109
  1217
                      [(thms, [])]));
blanchet@48975
  1218
                in
traytel@49109
  1219
                  Local_Theory.notes notes #> snd
blanchet@48975
  1220
                end
blanchet@48975
  1221
              else
blanchet@48975
  1222
                I)
blanchet@49538
  1223
          |> (if fact_policy <> Dont_Note then
traytel@49109
  1224
                let
traytel@49109
  1225
                  val notes =
blanchet@51765
  1226
                    [(map_comp'N, [Lazy.force (#map_comp' facts)], []),
blanchet@51765
  1227
                    (map_cong0N, [#map_cong0 axioms], []),
blanchet@51765
  1228
                    (map_congN, [Lazy.force (#map_cong facts)], fundef_cong_attrs),
blanchet@51765
  1229
                    (map_id'N, [Lazy.force (#map_id' facts)], []),
blanchet@51765
  1230
                    (rel_eqN, [Lazy.force (#rel_eq facts)], []),
blanchet@51765
  1231
                    (rel_flipN, [Lazy.force (#rel_flip facts)], []),
blanchet@51765
  1232
                    (rel_srelN, [Lazy.force (#rel_srel facts)], []),
blanchet@51766
  1233
                    (set_map'N, map Lazy.force (#set_map' facts), []),
blanchet@51765
  1234
                    (srel_O_GrN, srel_O_Grs, []),
blanchet@51765
  1235
                    (srel_IdN, [Lazy.force (#srel_Id facts)], []),
blanchet@51765
  1236
                    (srel_GrN, [Lazy.force (#srel_Gr facts)], []),
blanchet@51765
  1237
                    (srel_converseN, [Lazy.force (#srel_converse facts)], []),
blanchet@51765
  1238
                    (srel_monoN, [Lazy.force (#srel_mono facts)], []),
blanchet@51765
  1239
                    (srel_ON, [Lazy.force (#srel_O facts)], [])]
blanchet@49460
  1240
                    |> filter_out (null o #2)
blanchet@51765
  1241
                    |> map (fn (thmN, thms, attrs) =>
blanchet@51765
  1242
                      ((qualify (Binding.qualify true (Binding.name_of b) (Binding.name thmN)),
blanchet@51765
  1243
                        attrs), [(thms, [])]));
traytel@49109
  1244
                in
traytel@49109
  1245
                  Local_Theory.notes notes #> snd
traytel@49109
  1246
                end
blanchet@48975
  1247
              else
blanchet@48975
  1248
                I))
blanchet@48975
  1249
      end;
blanchet@49459
  1250
blanchet@49459
  1251
    val one_step_defs =
blanchet@49507
  1252
      no_reflexive (bnf_map_def :: bnf_bd_def :: bnf_set_defs @ bnf_wit_defs @ [bnf_rel_def,
blanchet@49506
  1253
        bnf_srel_def]);
blanchet@48975
  1254
  in
blanchet@49459
  1255
    (key, goals, wit_goalss, after_qed, lthy, one_step_defs)
blanchet@48975
  1256
  end;
blanchet@48975
  1257
traytel@49434
  1258
fun register_bnf key (bnf, lthy) =
traytel@49434
  1259
  (bnf, Local_Theory.declaration {syntax = false, pervasive = true}
traytel@49434
  1260
    (fn phi => Data.map (Symtab.update_new (key, morph_bnf phi bnf))) lthy);
traytel@49434
  1261
blanchet@49456
  1262
(* TODO: Once the invariant "nwits > 0" holds, remove "mk_conjunction_balanced'" and "rtac TrueI"
blanchet@49456
  1263
   below *)
blanchet@49456
  1264
fun mk_conjunction_balanced' [] = @{prop True}
blanchet@49456
  1265
  | mk_conjunction_balanced' ts = Logic.mk_conjunction_balanced ts;
blanchet@49456
  1266
blanchet@51767
  1267
fun bnf_def const_policy fact_policy qualify tacs wit_tac Ds map_b rel_b set_bs =
blanchet@49463
  1268
  (fn (_, goals, wit_goalss, after_qed, lthy, one_step_defs) =>
blanchet@48975
  1269
  let
blanchet@49456
  1270
    val wits_tac =
blanchet@49456
  1271
      K (TRYALL Goal.conjunction_tac) THEN' K (TRYALL (rtac TrueI)) THEN'
blanchet@49504
  1272
      mk_unfold_thms_then_tac lthy one_step_defs wit_tac;
blanchet@49456
  1273
    val wit_goals = map mk_conjunction_balanced' wit_goalss;
blanchet@48975
  1274
    val wit_thms =
wenzelm@51551
  1275
      Goal.prove_sorry lthy [] [] (mk_conjunction_balanced' wit_goals) wits_tac
blanchet@48975
  1276
      |> Conjunction.elim_balanced (length wit_goals)
blanchet@48975
  1277
      |> map2 (Conjunction.elim_balanced o length) wit_goalss
blanchet@49456
  1278
      |> map (map (Thm.close_derivation o Thm.forall_elim_vars 0));
blanchet@48975
  1279
  in
wenzelm@51551
  1280
    map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])
blanchet@49504
  1281
      goals (map (mk_unfold_thms_then_tac lthy one_step_defs) tacs)
blanchet@48975
  1282
    |> (fn thms => after_qed (map single thms @ wit_thms) lthy)
blanchet@51767
  1283
  end) oo prepare_def const_policy fact_policy qualify (K I) Ds map_b rel_b set_bs;
blanchet@48975
  1284
traytel@49434
  1285
val bnf_def_cmd = (fn (key, goals, wit_goals, after_qed, lthy, defs) =>
blanchet@48975
  1286
  Proof.unfolding ([[(defs, [])]])
traytel@49434
  1287
    (Proof.theorem NONE (snd o register_bnf key oo after_qed)
blanchet@48975
  1288
      (map (single o rpair []) goals @ map (map (rpair [])) wit_goals) lthy)) oo
blanchet@51767
  1289
  prepare_def Do_Inline (user_policy Note_Some) I Syntax.read_term NONE Binding.empty Binding.empty
blanchet@51767
  1290
    [];
blanchet@48975
  1291
blanchet@48975
  1292
fun print_bnfs ctxt =
blanchet@48975
  1293
  let
blanchet@48975
  1294
    fun pretty_set sets i = Pretty.block
blanchet@48975
  1295
      [Pretty.str (mk_setN (i + 1) ^ ":"), Pretty.brk 1,
blanchet@48975
  1296
          Pretty.quote (Syntax.pretty_term ctxt (nth sets i))];
blanchet@48975
  1297
blanchet@48975
  1298
    fun pretty_bnf (key, BNF {T = T, map = map, sets = sets, bd = bd,
blanchet@48975
  1299
      live = live, lives = lives, dead = dead, deads = deads, ...}) =
blanchet@48975
  1300
      Pretty.big_list
blanchet@48975
  1301
        (Pretty.string_of (Pretty.block [Pretty.str key, Pretty.str ":", Pretty.brk 1,
blanchet@48975
  1302
          Pretty.quote (Syntax.pretty_typ ctxt T)]))
blanchet@48975
  1303
        ([Pretty.block [Pretty.str "live:", Pretty.brk 1, Pretty.str (string_of_int live),
blanchet@48975
  1304
            Pretty.brk 3, Pretty.list "[" "]" (List.map (Syntax.pretty_typ ctxt) lives)],
blanchet@48975
  1305
          Pretty.block [Pretty.str "dead:", Pretty.brk 1, Pretty.str (string_of_int dead),
blanchet@48975
  1306
            Pretty.brk 3, Pretty.list "[" "]" (List.map (Syntax.pretty_typ ctxt) deads)],
blanchet@48975
  1307
          Pretty.block [Pretty.str (mapN ^ ":"), Pretty.brk 1,
blanchet@48975
  1308
            Pretty.quote (Syntax.pretty_term ctxt map)]] @
blanchet@48975
  1309
          List.map (pretty_set sets) (0 upto length sets - 1) @
blanchet@48975
  1310
          [Pretty.block [Pretty.str (bdN ^ ":"), Pretty.brk 1,
blanchet@48975
  1311
            Pretty.quote (Syntax.pretty_term ctxt bd)]]);
blanchet@48975
  1312
  in
blanchet@48975
  1313
    Pretty.big_list "BNFs:" (map pretty_bnf (Symtab.dest (Data.get (Context.Proof ctxt))))
blanchet@48975
  1314
    |> Pretty.writeln
blanchet@48975
  1315
  end;
blanchet@48975
  1316
blanchet@48975
  1317
val _ =
blanchet@48975
  1318
  Outer_Syntax.improper_command @{command_spec "print_bnfs"} "print all BNFs"
blanchet@48975
  1319
    (Scan.succeed (Toplevel.keep (print_bnfs o Toplevel.context_of)));
blanchet@48975
  1320
blanchet@48975
  1321
val _ =
blanchet@48975
  1322
  Outer_Syntax.local_theory_to_proof @{command_spec "bnf_def"} "define a BNF for an existing type"
traytel@49434
  1323
    ((parse_opt_binding_colon -- Parse.term --
blanchet@49277
  1324
       (@{keyword "["} |-- Parse.list Parse.term --| @{keyword "]"}) -- Parse.term --
blanchet@49459
  1325
       (@{keyword "["} |-- Parse.list Parse.term --| @{keyword "]"}) -- Scan.option Parse.term)
blanchet@49459
  1326
       >> bnf_def_cmd);
blanchet@48975
  1327
blanchet@48975
  1328
end;