src/HOL/BNF/Tools/bnf_def.ML
author blanchet
Sun Sep 23 14:52:53 2012 +0200 (2012-09-23)
changeset 49537 fe1deee434b6
parent 49536 898aea2e7a94
child 49538 c90818b63599
permissions -rw-r--r--
generate "rel_as_srel" and "rel_flip" properties
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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 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_natural_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_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_as_srel_of_bnf: BNF -> thm
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  val rel_def_of_bnf: BNF -> thm
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  val rel_flip_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_natural'_of_bnf: BNF -> thm list
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  val set_natural_of_bnf: BNF -> thm list
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  val sets_of_bnf: BNF -> term 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 =
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    Derive_Few_Facts | Derive_All_Facts | Derive_All_Facts_Note_Most | Note_All_Facts_and_Axioms
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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 ->
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    ((((binding * term) * term list) * term) * term list) * term option -> local_theory ->
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    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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type axioms = {
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  map_id: thm,
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  map_comp: thm,
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  map_cong: thm,
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  set_natural: 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_cong = cong, set_natural = 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_cong, set_natural, bd_card_order, bd_cinfinite, set_bd,
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  in_bd, map_wpull, srel_O_Gr} =
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  zip_axioms map_id map_comp map_cong set_natural 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_cong, set_natural, 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_cong = f map_cong,
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    set_natural = map f set_natural,
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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_natural: 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_id': thm lazy,
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  map_wppull: thm lazy,
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  rel_as_srel: thm lazy,
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  rel_flip: thm lazy,
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  set_natural': 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_natural in_cong in_mono in_srel
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    map_comp' map_id' map_wppull rel_as_srel rel_flip set_natural' srel_cong srel_mono srel_Id
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    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_natural = collect_set_natural,
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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_id' = map_id',
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  map_wppull = map_wppull,
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  rel_as_srel = rel_as_srel,
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  rel_flip = rel_flip,
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  set_natural' = set_natural',
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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_natural,
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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_id',
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  map_wppull,
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  rel_as_srel,
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  rel_flip,
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  set_natural',
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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_natural = Lazy.map f collect_set_natural,
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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_id' = Lazy.map f map_id',
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    map_wppull = Lazy.map f map_wppull,
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    rel_as_srel = Lazy.map f rel_as_srel,
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    rel_flip = Lazy.map f rel_flip,
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    set_natural' = map (Lazy.map f) set_natural',
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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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val lives_of_bnf = #lives o rep_bnf;
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val dead_of_bnf = #dead o rep_bnf;
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val deads_of_bnf = #deads o rep_bnf;
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val axioms_of_bnf = #axioms o rep_bnf;
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val facts_of_bnf = #facts o rep_bnf;
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val nwits_of_bnf = #nwits o rep_bnf;
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val wits_of_bnf = #wits o rep_bnf;
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(*terms*)
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val map_of_bnf = #map o rep_bnf;
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   312
val sets_of_bnf = #sets o rep_bnf;
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   313
fun mk_map_of_bnf Ds Ts Us bnf =
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   314
  let val bnf_rep = rep_bnf bnf;
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   315
  in
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   316
    Term.subst_atomic_types
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   317
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts) @ (#lives' bnf_rep ~~ Us)) (#map bnf_rep)
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   318
  end;
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   319
fun mk_sets_of_bnf Dss Tss bnf =
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   320
  let val bnf_rep = rep_bnf bnf;
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   321
  in
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   322
    map2 (fn (Ds, Ts) => Term.subst_atomic_types
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   323
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts))) (Dss ~~ Tss) (#sets bnf_rep)
blanchet@48975
   324
  end;
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   325
val bd_of_bnf = #bd o rep_bnf;
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   326
fun mk_bd_of_bnf Ds Ts bnf =
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   327
  let val bnf_rep = rep_bnf bnf;
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   328
  in Term.subst_atomic_types ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts)) (#bd bnf_rep) end;
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   329
fun mk_wits_of_bnf Dss Tss bnf =
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   330
  let
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   331
    val bnf_rep = rep_bnf bnf;
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   332
    val wits = map (fn x => (#I x, #wit x)) (#wits bnf_rep);
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   333
  in
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   334
    map2 (fn (Ds, Ts) => apsnd (Term.subst_atomic_types
blanchet@48975
   335
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts)))) (Dss ~~ Tss) wits
blanchet@48975
   336
  end;
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   337
val rel_of_bnf = #rel o rep_bnf;
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   338
fun mk_rel_of_bnf Ds Ts Us bnf =
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   339
  let val bnf_rep = rep_bnf bnf;
blanchet@49462
   340
  in
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   341
    Term.subst_atomic_types
blanchet@49507
   342
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts) @ (#lives' bnf_rep ~~ Us)) (#rel bnf_rep)
blanchet@49462
   343
  end;
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   344
val srel_of_bnf = #srel o rep_bnf;
blanchet@49506
   345
fun mk_srel_of_bnf Ds Ts Us bnf =
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   346
  let val bnf_rep = rep_bnf bnf;
blanchet@48975
   347
  in
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   348
    Term.subst_atomic_types
blanchet@49506
   349
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts) @ (#lives' bnf_rep ~~ Us)) (#srel bnf_rep)
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   350
  end;
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   351
blanchet@48975
   352
(*thms*)
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   353
val bd_card_order_of_bnf = #bd_card_order o #axioms o rep_bnf;
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   354
val bd_cinfinite_of_bnf = #bd_cinfinite o #axioms o rep_bnf;
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   355
val bd_Card_order_of_bnf = #bd_Card_order o #facts o rep_bnf;
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   356
val bd_Cinfinite_of_bnf = #bd_Cinfinite o #facts o rep_bnf;
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   357
val bd_Cnotzero_of_bnf = #bd_Cnotzero o #facts o rep_bnf;
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   358
val collect_set_natural_of_bnf = Lazy.force o #collect_set_natural o #facts o rep_bnf;
blanchet@48975
   359
val in_bd_of_bnf = #in_bd o #axioms o rep_bnf;
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   360
val in_cong_of_bnf = Lazy.force o #in_cong o #facts o rep_bnf;
blanchet@48975
   361
val in_mono_of_bnf = Lazy.force o #in_mono o #facts o rep_bnf;
blanchet@49506
   362
val in_srel_of_bnf = Lazy.force o #in_srel o #facts o rep_bnf;
blanchet@48975
   363
val map_def_of_bnf = #map_def o #defs o rep_bnf;
blanchet@48975
   364
val map_id_of_bnf = #map_id o #axioms o rep_bnf;
blanchet@48975
   365
val map_id'_of_bnf = Lazy.force o #map_id' o #facts o rep_bnf;
blanchet@48975
   366
val map_comp_of_bnf = #map_comp o #axioms o rep_bnf;
blanchet@48975
   367
val map_comp'_of_bnf = Lazy.force o #map_comp' o #facts o rep_bnf;
blanchet@48975
   368
val map_cong_of_bnf = #map_cong o #axioms o rep_bnf;
blanchet@48975
   369
val map_wppull_of_bnf = Lazy.force o #map_wppull o #facts o rep_bnf;
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   370
val map_wpull_of_bnf = #map_wpull o #axioms o rep_bnf;
blanchet@49537
   371
val rel_as_srel_of_bnf = Lazy.force o #rel_as_srel o #facts o rep_bnf;
blanchet@49507
   372
val rel_def_of_bnf = #rel_def o #defs o rep_bnf;
blanchet@49537
   373
val rel_flip_of_bnf = Lazy.force o #rel_flip o #facts o rep_bnf;
blanchet@48975
   374
val set_bd_of_bnf = #set_bd o #axioms o rep_bnf;
blanchet@48975
   375
val set_defs_of_bnf = #set_defs o #defs o rep_bnf;
blanchet@48975
   376
val set_natural_of_bnf = #set_natural o #axioms o rep_bnf;
blanchet@48975
   377
val set_natural'_of_bnf = map Lazy.force o #set_natural' o #facts o rep_bnf;
blanchet@49506
   378
val srel_cong_of_bnf = Lazy.force o #srel_cong o #facts o rep_bnf;
blanchet@49506
   379
val srel_mono_of_bnf = Lazy.force o #srel_mono o #facts o rep_bnf;
blanchet@49506
   380
val srel_def_of_bnf = #srel_def o #defs o rep_bnf;
blanchet@49506
   381
val srel_Id_of_bnf = Lazy.force o #srel_Id o #facts o rep_bnf;
blanchet@49506
   382
val srel_Gr_of_bnf = Lazy.force o #srel_Gr o #facts o rep_bnf;
blanchet@49506
   383
val srel_converse_of_bnf = Lazy.force o #srel_converse o #facts o rep_bnf;
blanchet@49506
   384
val srel_O_of_bnf = Lazy.force o #srel_O o #facts o rep_bnf;
blanchet@49506
   385
val srel_O_Gr_of_bnf = #srel_O_Gr o #axioms o rep_bnf;
blanchet@48975
   386
val wit_thms_of_bnf = maps #prop o wits_of_bnf;
blanchet@48975
   387
val wit_thmss_of_bnf = map #prop o wits_of_bnf;
blanchet@48975
   388
blanchet@49507
   389
fun mk_bnf name T live lives lives' dead deads map sets bd axioms defs facts wits rel srel =
blanchet@48975
   390
  BNF {name = name, T = T,
blanchet@48975
   391
       live = live, lives = lives, lives' = lives', dead = dead, deads = deads,
blanchet@48975
   392
       map = map, sets = sets, bd = bd,
blanchet@48975
   393
       axioms = axioms, defs = defs, facts = facts,
blanchet@49507
   394
       nwits = length wits, wits = wits, rel = rel, srel = srel};
blanchet@48975
   395
blanchet@48975
   396
fun morph_bnf phi (BNF {name = name, T = T, live = live, lives = lives, lives' = lives',
blanchet@48975
   397
  dead = dead, deads = deads, map = map, sets = sets, bd = bd,
blanchet@48975
   398
  axioms = axioms, defs = defs, facts = facts,
blanchet@49507
   399
  nwits = nwits, wits = wits, rel = rel, srel = srel}) =
blanchet@48975
   400
  BNF {name = Morphism.binding phi name, T = Morphism.typ phi T,
blanchet@48975
   401
    live = live, lives = List.map (Morphism.typ phi) lives,
blanchet@48975
   402
    lives' = List.map (Morphism.typ phi) lives',
blanchet@48975
   403
    dead = dead, deads = List.map (Morphism.typ phi) deads,
blanchet@48975
   404
    map = Morphism.term phi map, sets = List.map (Morphism.term phi) sets,
blanchet@48975
   405
    bd = Morphism.term phi bd,
blanchet@48975
   406
    axioms = morph_axioms phi axioms,
blanchet@48975
   407
    defs = morph_defs phi defs,
blanchet@48975
   408
    facts = morph_facts phi facts,
blanchet@48975
   409
    nwits = nwits,
blanchet@48975
   410
    wits = List.map (morph_witness phi) wits,
blanchet@49507
   411
    rel = Morphism.term phi rel, srel = Morphism.term phi srel};
blanchet@48975
   412
blanchet@48975
   413
fun eq_bnf (BNF {T = T1, live = live1, dead = dead1, ...},
blanchet@48975
   414
  BNF {T = T2, live = live2, dead = dead2, ...}) =
blanchet@48975
   415
  Type.could_unify (T1, T2) andalso live1 = live2 andalso dead1 = dead2;
blanchet@48975
   416
blanchet@48975
   417
structure Data = Generic_Data
blanchet@48975
   418
(
blanchet@48975
   419
  type T = BNF Symtab.table;
blanchet@48975
   420
  val empty = Symtab.empty;
blanchet@48975
   421
  val extend = I;
blanchet@49462
   422
  val merge = Symtab.merge eq_bnf;
blanchet@48975
   423
);
blanchet@48975
   424
blanchet@48975
   425
val bnf_of = Symtab.lookup o Data.get o Context.Proof;
blanchet@48975
   426
blanchet@48975
   427
blanchet@48975
   428
blanchet@48975
   429
(* Utilities *)
blanchet@48975
   430
blanchet@48975
   431
fun normalize_set insts instA set =
blanchet@48975
   432
  let
blanchet@48975
   433
    val (T, T') = dest_funT (fastype_of set);
blanchet@48975
   434
    val A = fst (Term.dest_TVar (HOLogic.dest_setT T'));
blanchet@48975
   435
    val params = Term.add_tvar_namesT T [];
blanchet@48975
   436
  in Term.subst_TVars ((A :: params) ~~ (instA :: insts)) set end;
blanchet@48975
   437
blanchet@49507
   438
fun normalize_rel ctxt instTs instA instB rel =
blanchet@49462
   439
  let
blanchet@49462
   440
    val thy = Proof_Context.theory_of ctxt;
blanchet@49462
   441
    val tyenv =
blanchet@49507
   442
      Sign.typ_match thy (fastype_of rel, Library.foldr (op -->) (instTs, mk_pred2T instA instB))
blanchet@49463
   443
        Vartab.empty;
blanchet@49507
   444
  in Envir.subst_term (tyenv, Vartab.empty) rel end
blanchet@49462
   445
  handle Type.TYPE_MATCH => error "Bad predicator";
blanchet@49462
   446
blanchet@49506
   447
fun normalize_srel ctxt instTs instA instB srel =
blanchet@48975
   448
  let
blanchet@48975
   449
    val thy = Proof_Context.theory_of ctxt;
blanchet@48975
   450
    val tyenv =
blanchet@49506
   451
      Sign.typ_match thy (fastype_of srel, Library.foldr (op -->) (instTs, mk_relT (instA, instB)))
blanchet@48975
   452
        Vartab.empty;
blanchet@49506
   453
  in Envir.subst_term (tyenv, Vartab.empty) srel end
blanchet@49453
   454
  handle Type.TYPE_MATCH => error "Bad relator";
blanchet@48975
   455
blanchet@48975
   456
fun normalize_wit insts CA As wit =
blanchet@48975
   457
  let
blanchet@48975
   458
    fun strip_param (Ts, T as Type (@{type_name fun}, [T1, T2])) =
blanchet@48975
   459
        if Type.raw_instance (CA, T) then (Ts, T) else strip_param (T1 :: Ts, T2)
blanchet@48975
   460
      | strip_param x = x;
blanchet@48975
   461
    val (Ts, T) = strip_param ([], fastype_of wit);
blanchet@48975
   462
    val subst = Term.add_tvar_namesT T [] ~~ insts;
blanchet@48975
   463
    fun find y = find_index (fn x => x = y) As;
blanchet@48975
   464
  in
blanchet@48975
   465
    (map (find o Term.typ_subst_TVars subst) (rev Ts), Term.subst_TVars subst wit)
blanchet@48975
   466
  end;
blanchet@48975
   467
blanchet@48975
   468
fun minimize_wits wits =
blanchet@48975
   469
 let
blanchet@48975
   470
   fun minimize done [] = done
traytel@49103
   471
     | minimize done ((I, wit) :: todo) =
blanchet@48975
   472
       if exists (fn (J, _) => subset (op =) (J, I)) (done @ todo)
blanchet@48975
   473
       then minimize done todo
blanchet@48975
   474
       else minimize ((I, wit) :: done) todo;
blanchet@48975
   475
 in minimize [] wits end;
blanchet@48975
   476
blanchet@48975
   477
blanchet@48975
   478
blanchet@48975
   479
(* Names *)
blanchet@48975
   480
blanchet@48975
   481
val mapN = "map";
blanchet@48975
   482
val setN = "set";
blanchet@48975
   483
fun mk_setN i = setN ^ nonzero_string_of_int i;
blanchet@48975
   484
val bdN = "bd";
blanchet@48975
   485
val witN = "wit";
blanchet@48975
   486
fun mk_witN i = witN ^ nonzero_string_of_int i;
blanchet@49507
   487
val relN = "rel";
blanchet@49506
   488
val srelN = "srel";
blanchet@48975
   489
blanchet@48975
   490
val bd_card_orderN = "bd_card_order";
blanchet@48975
   491
val bd_cinfiniteN = "bd_cinfinite";
blanchet@48975
   492
val bd_Card_orderN = "bd_Card_order";
blanchet@48975
   493
val bd_CinfiniteN = "bd_Cinfinite";
blanchet@48975
   494
val bd_CnotzeroN = "bd_Cnotzero";
blanchet@48975
   495
val collect_set_naturalN = "collect_set_natural";
blanchet@48975
   496
val in_bdN = "in_bd";
blanchet@48975
   497
val in_monoN = "in_mono";
blanchet@49506
   498
val in_srelN = "in_srel";
blanchet@48975
   499
val map_idN = "map_id";
blanchet@48975
   500
val map_id'N = "map_id'";
blanchet@48975
   501
val map_compN = "map_comp";
blanchet@48975
   502
val map_comp'N = "map_comp'";
blanchet@48975
   503
val map_congN = "map_cong";
blanchet@48975
   504
val map_wpullN = "map_wpull";
blanchet@49537
   505
val rel_as_srelN = "rel_as_srel";
blanchet@49537
   506
val rel_flipN = "rel_flip";
blanchet@49537
   507
val set_naturalN = "set_natural";
blanchet@49537
   508
val set_natural'N = "set_natural'";
blanchet@49537
   509
val set_bdN = "set_bd";
blanchet@49506
   510
val srel_IdN = "srel_Id";
blanchet@49506
   511
val srel_GrN = "srel_Gr";
blanchet@49506
   512
val srel_converseN = "srel_converse";
blanchet@49506
   513
val srel_monoN = "srel_mono"
blanchet@49506
   514
val srel_ON = "srel_comp";
blanchet@49506
   515
val srel_O_GrN = "srel_comp_Gr";
blanchet@48975
   516
blanchet@48975
   517
datatype const_policy = Dont_Inline | Hardly_Inline | Smart_Inline | Do_Inline;
blanchet@48975
   518
blanchet@48975
   519
datatype fact_policy =
blanchet@49461
   520
  Derive_Few_Facts | Derive_All_Facts | Derive_All_Facts_Note_Most | Note_All_Facts_and_Axioms;
blanchet@48975
   521
blanchet@48975
   522
val bnf_note_all = Attrib.setup_config_bool @{binding bnf_note_all} (K false);
blanchet@48975
   523
traytel@49435
   524
fun user_policy policy ctxt =
traytel@49435
   525
  if Config.get ctxt bnf_note_all then Note_All_Facts_and_Axioms else policy;
blanchet@48975
   526
blanchet@48975
   527
val smart_max_inline_size = 25; (*FUDGE*)
blanchet@48975
   528
blanchet@48975
   529
blanchet@48975
   530
(* Define new BNFs *)
blanchet@48975
   531
blanchet@49019
   532
fun prepare_def const_policy mk_fact_policy qualify prep_term Ds_opt
blanchet@49507
   533
  (((((raw_b, raw_map), raw_sets), raw_bd_Abs), raw_wits), raw_rel_opt) no_defs_lthy =
blanchet@48975
   534
  let
blanchet@48975
   535
    val fact_policy = mk_fact_policy no_defs_lthy;
blanchet@48975
   536
    val b = qualify raw_b;
blanchet@48975
   537
    val live = length raw_sets;
blanchet@48975
   538
    val nwits = length raw_wits;
blanchet@48975
   539
blanchet@48975
   540
    val map_rhs = prep_term no_defs_lthy raw_map;
blanchet@48975
   541
    val set_rhss = map (prep_term no_defs_lthy) raw_sets;
blanchet@48975
   542
    val (bd_rhsT, bd_rhs) = (case prep_term no_defs_lthy raw_bd_Abs of
blanchet@48975
   543
      Abs (_, T, t) => (T, t)
blanchet@48975
   544
    | _ => error "Bad bound constant");
blanchet@48975
   545
    val wit_rhss = map (prep_term no_defs_lthy) raw_wits;
blanchet@48975
   546
traytel@49434
   547
    fun err T =
traytel@49434
   548
      error ("Trying to register the type " ^ quote (Syntax.string_of_typ no_defs_lthy T) ^
traytel@49434
   549
        " as unnamed BNF");
traytel@49434
   550
traytel@49434
   551
    val (b, key) =
traytel@49434
   552
      if Binding.eq_name (b, Binding.empty) then
traytel@49434
   553
        (case bd_rhsT of
traytel@49434
   554
          Type (C, Ts) => if forall (is_some o try dest_TFree) Ts
traytel@49434
   555
            then (Binding.qualified_name C, C) else err bd_rhsT
traytel@49434
   556
        | T => err T)
traytel@49434
   557
      else (b, Local_Theory.full_name no_defs_lthy b);
traytel@49434
   558
blanchet@49463
   559
    fun maybe_define user_specified (b, rhs) lthy =
blanchet@48975
   560
      let
blanchet@48975
   561
        val inline =
blanchet@49463
   562
          (user_specified orelse fact_policy = Derive_Few_Facts) andalso
blanchet@48975
   563
          (case const_policy of
blanchet@48975
   564
            Dont_Inline => false
blanchet@48975
   565
          | Hardly_Inline => Term.is_Free rhs orelse Term.is_Const rhs
blanchet@48975
   566
          | Smart_Inline => Term.size_of_term rhs <= smart_max_inline_size
blanchet@48975
   567
          | Do_Inline => true)
blanchet@48975
   568
      in
blanchet@48975
   569
        if inline then
blanchet@49460
   570
          ((rhs, Drule.reflexive_thm), lthy)
blanchet@48975
   571
        else
blanchet@48975
   572
          let val b = b () in
blanchet@48975
   573
            apfst (apsnd snd) (Local_Theory.define ((b, NoSyn), ((Thm.def_binding b, []), rhs))
blanchet@48975
   574
              lthy)
blanchet@48975
   575
          end
blanchet@48975
   576
      end;
blanchet@49459
   577
blanchet@49459
   578
    fun maybe_restore lthy_old lthy =
blanchet@49459
   579
      lthy |> not (pointer_eq (lthy_old, lthy)) ? Local_Theory.restore;
blanchet@48975
   580
blanchet@49459
   581
    val map_bind_def = (fn () => Binding.suffix_name ("_" ^ mapN) b, map_rhs);
blanchet@49459
   582
    val set_binds_defs =
blanchet@49459
   583
      let
blanchet@49459
   584
        val bs = if live = 1 then [fn () => Binding.suffix_name ("_" ^ setN) b]
blanchet@49459
   585
          else map (fn i => fn () => Binding.suffix_name ("_" ^ mk_setN i) b) (1 upto live)
blanchet@49459
   586
      in map2 pair bs set_rhss end;
blanchet@49459
   587
    val bd_bind_def = (fn () => Binding.suffix_name ("_" ^ bdN) b, bd_rhs);
blanchet@49459
   588
    val wit_binds_defs =
blanchet@49459
   589
      let
blanchet@49459
   590
        val bs = if nwits = 1 then [fn () => Binding.suffix_name ("_" ^ witN) b]
blanchet@49459
   591
          else map (fn i => fn () => Binding.suffix_name ("_" ^ mk_witN i) b) (1 upto nwits);
blanchet@49459
   592
      in map2 pair bs wit_rhss end;
blanchet@49459
   593
blanchet@49459
   594
    val (((((bnf_map_term, raw_map_def),
blanchet@48975
   595
      (bnf_set_terms, raw_set_defs)),
blanchet@48975
   596
      (bnf_bd_term, raw_bd_def)),
blanchet@49459
   597
      (bnf_wit_terms, raw_wit_defs)), (lthy, lthy_old)) =
blanchet@48975
   598
        no_defs_lthy
blanchet@49463
   599
        |> maybe_define true map_bind_def
blanchet@49463
   600
        ||>> apfst split_list o fold_map (maybe_define true) set_binds_defs
blanchet@49463
   601
        ||>> maybe_define true bd_bind_def
blanchet@49463
   602
        ||>> apfst split_list o fold_map (maybe_define true) wit_binds_defs
blanchet@48975
   603
        ||> `(maybe_restore no_defs_lthy);
blanchet@48975
   604
blanchet@49459
   605
    val phi = Proof_Context.export_morphism lthy_old lthy;
blanchet@48975
   606
blanchet@48975
   607
    val bnf_map_def = Morphism.thm phi raw_map_def;
blanchet@48975
   608
    val bnf_set_defs = map (Morphism.thm phi) raw_set_defs;
blanchet@48975
   609
    val bnf_bd_def = Morphism.thm phi raw_bd_def;
blanchet@48975
   610
    val bnf_wit_defs = map (Morphism.thm phi) raw_wit_defs;
blanchet@48975
   611
blanchet@48975
   612
    val bnf_map = Morphism.term phi bnf_map_term;
blanchet@48975
   613
blanchet@48975
   614
    (*TODO: handle errors*)
blanchet@48975
   615
    (*simple shape analysis of a map function*)
traytel@49395
   616
    val ((alphas, betas), (CA, _)) =
traytel@49395
   617
      fastype_of bnf_map
traytel@49395
   618
      |> strip_typeN live
traytel@49395
   619
      |>> map_split dest_funT
traytel@49395
   620
      ||> dest_funT
traytel@49395
   621
      handle TYPE _ => error "Bad map function";
blanchet@48975
   622
blanchet@48975
   623
    val CA_params = map TVar (Term.add_tvarsT CA []);
blanchet@48975
   624
blanchet@48975
   625
    val bnf_sets = map2 (normalize_set CA_params) alphas (map (Morphism.term phi) bnf_set_terms);
blanchet@48975
   626
    val bdT = Morphism.typ phi bd_rhsT;
blanchet@48975
   627
    val bnf_bd =
blanchet@48975
   628
      Term.subst_TVars (Term.add_tvar_namesT bdT [] ~~ CA_params) (Morphism.term phi bnf_bd_term);
blanchet@48975
   629
    val bnf_wits = map (normalize_wit CA_params CA alphas o Morphism.term phi) bnf_wit_terms;
blanchet@48975
   630
blanchet@48975
   631
    (*TODO: assert Ds = (TVars of bnf_map) \ (alphas @ betas) as sets*)
blanchet@48975
   632
    val deads = (case Ds_opt of
blanchet@48975
   633
      NONE => subtract (op =) (alphas @ betas) (map TVar (Term.add_tvars bnf_map []))
blanchet@48975
   634
    | SOME Ds => map (Morphism.typ phi) Ds);
blanchet@48975
   635
    val dead = length deads;
blanchet@48975
   636
blanchet@48975
   637
    (*TODO: further checks of type of bnf_map*)
blanchet@48975
   638
    (*TODO: check types of bnf_sets*)
blanchet@48975
   639
    (*TODO: check type of bnf_bd*)
blanchet@49507
   640
    (*TODO: check type of bnf_rel*)
blanchet@48975
   641
blanchet@48975
   642
    val ((((((((((As', Bs'), Cs), Ds), B1Ts), B2Ts), domTs), ranTs), ranTs'), ranTs''),
blanchet@49459
   643
      (Ts, T)) = lthy
blanchet@48975
   644
      |> mk_TFrees live
blanchet@48975
   645
      ||>> mk_TFrees live
blanchet@48975
   646
      ||>> mk_TFrees live
blanchet@48975
   647
      ||>> mk_TFrees dead
blanchet@48975
   648
      ||>> mk_TFrees live
blanchet@48975
   649
      ||>> mk_TFrees live
blanchet@48975
   650
      ||>> mk_TFrees live
blanchet@48975
   651
      ||>> mk_TFrees live
blanchet@48975
   652
      ||>> mk_TFrees live
blanchet@48975
   653
      ||>> mk_TFrees live
blanchet@48975
   654
      ||> fst o mk_TFrees 1
blanchet@48975
   655
      ||> the_single
blanchet@48975
   656
      ||> `(replicate live);
blanchet@48975
   657
blanchet@48975
   658
    fun mk_bnf_map As' Bs' =
blanchet@48975
   659
      Term.subst_atomic_types ((deads ~~ Ds) @ (alphas ~~ As') @ (betas ~~ Bs')) bnf_map;
blanchet@49453
   660
    fun mk_bnf_t As' = Term.subst_atomic_types ((deads ~~ Ds) @ (alphas ~~ As'));
blanchet@49453
   661
    fun mk_bnf_T As' = Term.typ_subst_atomic ((deads ~~ Ds) @ (alphas ~~ As'));
blanchet@49453
   662
blanchet@48975
   663
    val (setRTs, RTs) = map_split (`HOLogic.mk_setT o HOLogic.mk_prodT) (As' ~~ Bs');
blanchet@48975
   664
    val setRTsAsCs = map (HOLogic.mk_setT o HOLogic.mk_prodT) (As' ~~ Cs);
blanchet@48975
   665
    val setRTsBsCs = map (HOLogic.mk_setT o HOLogic.mk_prodT) (Bs' ~~ Cs);
blanchet@48975
   666
    val setRT's = map (HOLogic.mk_setT o HOLogic.mk_prodT) (Bs' ~~ As');
blanchet@48975
   667
    val self_setRTs = map (HOLogic.mk_setT o HOLogic.mk_prodT) (As' ~~ As');
blanchet@49463
   668
    val QTs = map2 mk_pred2T As' Bs';
blanchet@48975
   669
blanchet@49453
   670
    val CA' = mk_bnf_T As' CA;
blanchet@49453
   671
    val CB' = mk_bnf_T Bs' CA;
blanchet@49453
   672
    val CC' = mk_bnf_T Cs CA;
blanchet@49453
   673
    val CRs' = mk_bnf_T RTs CA;
blanchet@49463
   674
    val CA'CB' = HOLogic.mk_prodT (CA', CB');
blanchet@49453
   675
blanchet@48975
   676
    val bnf_map_AsAs = mk_bnf_map As' As';
blanchet@48975
   677
    val bnf_map_AsBs = mk_bnf_map As' Bs';
blanchet@48975
   678
    val bnf_map_AsCs = mk_bnf_map As' Cs;
blanchet@48975
   679
    val bnf_map_BsCs = mk_bnf_map Bs' Cs;
blanchet@48975
   680
    val bnf_sets_As = map (mk_bnf_t As') bnf_sets;
blanchet@48975
   681
    val bnf_sets_Bs = map (mk_bnf_t Bs') bnf_sets;
blanchet@48975
   682
    val bnf_bd_As = mk_bnf_t As' bnf_bd;
blanchet@48975
   683
    val bnf_wit_As = map (apsnd (mk_bnf_t As')) bnf_wits;
blanchet@48975
   684
blanchet@49463
   685
    val (((((((((((((((((((((((((fs, fs_copy), gs), hs), p), (x, x')), (y, y')), (z, z')), zs), As),
blanchet@49459
   686
      As_copy), Xs), B1s), B2s), f1s), f2s), e1s), e2s), p1s), p2s), bs), (Rs, Rs')), Rs_copy), Ss),
blanchet@49459
   687
      (Qs, Qs')), _) = lthy
blanchet@48975
   688
      |> mk_Frees "f" (map2 (curry (op -->)) As' Bs')
blanchet@48975
   689
      ||>> mk_Frees "f" (map2 (curry (op -->)) As' Bs')
blanchet@48975
   690
      ||>> mk_Frees "g" (map2 (curry (op -->)) Bs' Cs)
blanchet@48975
   691
      ||>> mk_Frees "h" (map2 (curry (op -->)) As' Ts)
blanchet@49463
   692
      ||>> yield_singleton (mk_Frees "p") CA'CB'
blanchet@48975
   693
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "x") CA'
blanchet@48975
   694
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "y") CB'
blanchet@48975
   695
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "z") CRs'
blanchet@48975
   696
      ||>> mk_Frees "z" As'
blanchet@48975
   697
      ||>> mk_Frees "A" (map HOLogic.mk_setT As')
blanchet@48975
   698
      ||>> mk_Frees "A" (map HOLogic.mk_setT As')
blanchet@48975
   699
      ||>> mk_Frees "A" (map HOLogic.mk_setT domTs)
blanchet@48975
   700
      ||>> mk_Frees "B1" (map HOLogic.mk_setT B1Ts)
blanchet@48975
   701
      ||>> mk_Frees "B2" (map HOLogic.mk_setT B2Ts)
blanchet@48975
   702
      ||>> mk_Frees "f1" (map2 (curry (op -->)) B1Ts ranTs)
blanchet@48975
   703
      ||>> mk_Frees "f2" (map2 (curry (op -->)) B2Ts ranTs)
blanchet@48975
   704
      ||>> mk_Frees "e1" (map2 (curry (op -->)) B1Ts ranTs')
blanchet@48975
   705
      ||>> mk_Frees "e2" (map2 (curry (op -->)) B2Ts ranTs'')
blanchet@48975
   706
      ||>> mk_Frees "p1" (map2 (curry (op -->)) domTs B1Ts)
blanchet@48975
   707
      ||>> mk_Frees "p2" (map2 (curry (op -->)) domTs B2Ts)
blanchet@48975
   708
      ||>> mk_Frees "b" As'
blanchet@49536
   709
      ||>> mk_Frees' "S" setRTs
blanchet@49536
   710
      ||>> mk_Frees "S" setRTs
blanchet@49536
   711
      ||>> mk_Frees "T" setRTsBsCs
blanchet@49537
   712
      ||>> mk_Frees' "R" QTs;
blanchet@48975
   713
blanchet@49459
   714
    (*Gr (in R1 .. Rn) (map fst .. fst)^-1 O Gr (in R1 .. Rn) (map snd .. snd)*)
blanchet@49463
   715
    val O_Gr =
blanchet@49459
   716
      let
blanchet@49459
   717
        val map1 = Term.list_comb (mk_bnf_map RTs As', map fst_const RTs);
blanchet@49459
   718
        val map2 = Term.list_comb (mk_bnf_map RTs Bs', map snd_const RTs);
blanchet@49459
   719
        val bnf_in = mk_in (map Free Rs') (map (mk_bnf_t RTs) bnf_sets) CRs';
blanchet@49459
   720
      in
blanchet@49459
   721
        mk_rel_comp (mk_converse (mk_Gr bnf_in map1), mk_Gr bnf_in map2)
blanchet@49459
   722
      end;
blanchet@49459
   723
blanchet@49463
   724
    fun mk_predicate_of_set x_name y_name t =
blanchet@49463
   725
      let
blanchet@49463
   726
        val (T, U) = HOLogic.dest_prodT (HOLogic.dest_setT (fastype_of t));
blanchet@49463
   727
        val x = Free (x_name, T);
blanchet@49463
   728
        val y = Free (y_name, U);
blanchet@49463
   729
      in fold_rev Term.lambda [x, y] (HOLogic.mk_mem (HOLogic.mk_prod (x, y), t)) end;
blanchet@49463
   730
blanchet@49537
   731
    val sQs =
blanchet@49537
   732
      map3 (fn Q => fn T => fn U =>
blanchet@49537
   733
          HOLogic.Collect_const (HOLogic.mk_prodT (T, U)) $ HOLogic.mk_split Q) Qs As' Bs';
blanchet@49537
   734
blanchet@49507
   735
    val rel_rhs = (case raw_rel_opt of
blanchet@49463
   736
        NONE =>
blanchet@49463
   737
        fold_rev absfree Qs' (mk_predicate_of_set (fst x') (fst y')
blanchet@49537
   738
          (Term.list_comb (fold_rev Term.absfree Rs' O_Gr, sQs)))
blanchet@49507
   739
      | SOME raw_rel => prep_term no_defs_lthy raw_rel);
blanchet@49463
   740
blanchet@49507
   741
    val rel_bind_def = (fn () => Binding.suffix_name ("_" ^ relN) b, rel_rhs);
blanchet@49463
   742
blanchet@49507
   743
    val ((bnf_rel_term, raw_rel_def), (lthy, lthy_old)) =
blanchet@49463
   744
      lthy
blanchet@49507
   745
      |> maybe_define (is_some raw_rel_opt) rel_bind_def
blanchet@49463
   746
      ||> `(maybe_restore lthy);
blanchet@49463
   747
blanchet@49463
   748
    val phi = Proof_Context.export_morphism lthy_old lthy;
blanchet@49507
   749
    val bnf_rel_def = Morphism.thm phi raw_rel_def;
blanchet@49507
   750
    val bnf_rel = Morphism.term phi bnf_rel_term;
blanchet@49463
   751
blanchet@49507
   752
    fun mk_bnf_rel QTs CA' CB' = normalize_rel lthy QTs CA' CB' bnf_rel;
blanchet@49463
   753
blanchet@49507
   754
    val rel = mk_bnf_rel QTs CA' CB';
blanchet@49463
   755
blanchet@49506
   756
    val srel_rhs =
blanchet@49463
   757
      fold_rev Term.absfree Rs' (HOLogic.Collect_const CA'CB' $
blanchet@49507
   758
        Term.lambda p (Term.list_comb (rel, map (mk_predicate_of_set (fst x') (fst y')) Rs) $
blanchet@49463
   759
        HOLogic.mk_fst p $ HOLogic.mk_snd p));
blanchet@49459
   760
blanchet@49506
   761
    val srel_bind_def = (fn () => Binding.suffix_name ("_" ^ srelN) b, srel_rhs);
blanchet@49459
   762
blanchet@49506
   763
    val ((bnf_srel_term, raw_srel_def), (lthy, lthy_old)) =
blanchet@49459
   764
      lthy
blanchet@49506
   765
      |> maybe_define false srel_bind_def
blanchet@49459
   766
      ||> `(maybe_restore lthy);
blanchet@49459
   767
blanchet@49459
   768
    val phi = Proof_Context.export_morphism lthy_old lthy;
blanchet@49506
   769
    val bnf_srel_def = Morphism.thm phi raw_srel_def;
blanchet@49506
   770
    val bnf_srel = Morphism.term phi bnf_srel_term;
blanchet@49459
   771
blanchet@49506
   772
    fun mk_bnf_srel setRTs CA' CB' = normalize_srel lthy setRTs CA' CB' bnf_srel;
blanchet@49459
   773
blanchet@49506
   774
    val srel = mk_bnf_srel setRTs CA' CB';
blanchet@49459
   775
blanchet@49460
   776
    val _ = case no_reflexive (raw_map_def :: raw_set_defs @ [raw_bd_def] @
blanchet@49507
   777
        raw_wit_defs @ [raw_rel_def, raw_srel_def]) of
blanchet@49459
   778
        [] => ()
blanchet@49459
   779
      | defs => Proof_Display.print_consts true lthy_old (K false)
blanchet@49459
   780
          (map (dest_Free o fst o Logic.dest_equals o prop_of) defs);
blanchet@49459
   781
blanchet@49458
   782
    val map_id_goal =
blanchet@48975
   783
      let
blanchet@49018
   784
        val bnf_map_app_id = Term.list_comb (bnf_map_AsAs, map HOLogic.id_const As');
blanchet@48975
   785
      in
blanchet@48975
   786
        HOLogic.mk_Trueprop
blanchet@48975
   787
          (HOLogic.mk_eq (bnf_map_app_id, HOLogic.id_const CA'))
blanchet@48975
   788
      end;
blanchet@48975
   789
blanchet@49458
   790
    val map_comp_goal =
blanchet@48975
   791
      let
blanchet@49018
   792
        val bnf_map_app_comp = Term.list_comb (bnf_map_AsCs, map2 (curry HOLogic.mk_comp) gs fs);
blanchet@48975
   793
        val comp_bnf_map_app = HOLogic.mk_comp
blanchet@48975
   794
          (Term.list_comb (bnf_map_BsCs, gs),
blanchet@48975
   795
           Term.list_comb (bnf_map_AsBs, fs));
blanchet@48975
   796
      in
blanchet@49123
   797
        fold_rev Logic.all (fs @ gs) (mk_Trueprop_eq (bnf_map_app_comp, comp_bnf_map_app))
blanchet@48975
   798
      end;
blanchet@48975
   799
blanchet@49458
   800
    val map_cong_goal =
blanchet@48975
   801
      let
blanchet@48975
   802
        fun mk_prem z set f f_copy =
blanchet@48975
   803
          Logic.all z (Logic.mk_implies
blanchet@48975
   804
            (HOLogic.mk_Trueprop (HOLogic.mk_mem (z, set $ x)),
blanchet@49123
   805
            mk_Trueprop_eq (f $ z, f_copy $ z)));
blanchet@48975
   806
        val prems = map4 mk_prem zs bnf_sets_As fs fs_copy;
blanchet@48975
   807
        val eq = HOLogic.mk_eq (Term.list_comb (bnf_map_AsBs, fs) $ x,
blanchet@48975
   808
          Term.list_comb (bnf_map_AsBs, fs_copy) $ x);
blanchet@48975
   809
      in
blanchet@48975
   810
        fold_rev Logic.all (x :: fs @ fs_copy)
blanchet@48975
   811
          (Logic.list_implies (prems, HOLogic.mk_Trueprop eq))
blanchet@48975
   812
      end;
blanchet@48975
   813
blanchet@49458
   814
    val set_naturals_goal =
blanchet@48975
   815
      let
blanchet@48975
   816
        fun mk_goal setA setB f =
blanchet@48975
   817
          let
blanchet@48975
   818
            val set_comp_map =
blanchet@48975
   819
              HOLogic.mk_comp (setB, Term.list_comb (bnf_map_AsBs, fs));
blanchet@48975
   820
            val image_comp_set = HOLogic.mk_comp (mk_image f, setA);
blanchet@48975
   821
          in
blanchet@49123
   822
            fold_rev Logic.all fs (mk_Trueprop_eq (set_comp_map, image_comp_set))
blanchet@48975
   823
          end;
blanchet@48975
   824
      in
blanchet@48975
   825
        map3 mk_goal bnf_sets_As bnf_sets_Bs fs
blanchet@48975
   826
      end;
blanchet@48975
   827
blanchet@49458
   828
    val card_order_bd_goal = HOLogic.mk_Trueprop (mk_card_order bnf_bd_As);
blanchet@48975
   829
blanchet@49458
   830
    val cinfinite_bd_goal = HOLogic.mk_Trueprop (mk_cinfinite bnf_bd_As);
blanchet@48975
   831
blanchet@49458
   832
    val set_bds_goal =
blanchet@48975
   833
      let
blanchet@48975
   834
        fun mk_goal set =
blanchet@48975
   835
          Logic.all x (HOLogic.mk_Trueprop (mk_ordLeq (mk_card_of (set $ x)) bnf_bd_As));
blanchet@48975
   836
      in
blanchet@48975
   837
        map mk_goal bnf_sets_As
blanchet@48975
   838
      end;
blanchet@48975
   839
blanchet@49458
   840
    val in_bd_goal =
blanchet@48975
   841
      let
blanchet@48975
   842
        val bd = mk_cexp
blanchet@48975
   843
          (if live = 0 then ctwo
blanchet@48975
   844
            else mk_csum (Library.foldr1 (uncurry mk_csum) (map mk_card_of As)) ctwo)
blanchet@48975
   845
          bnf_bd_As;
blanchet@48975
   846
      in
blanchet@48975
   847
        fold_rev Logic.all As
blanchet@48975
   848
          (HOLogic.mk_Trueprop (mk_ordLeq (mk_card_of (mk_in As bnf_sets_As CA')) bd))
blanchet@48975
   849
      end;
blanchet@48975
   850
blanchet@49458
   851
    val map_wpull_goal =
blanchet@48975
   852
      let
blanchet@48975
   853
        val prems = map HOLogic.mk_Trueprop
blanchet@48975
   854
          (map8 mk_wpull Xs B1s B2s f1s f2s (replicate live NONE) p1s p2s);
blanchet@48975
   855
        val CX = mk_bnf_T domTs CA;
blanchet@48975
   856
        val CB1 = mk_bnf_T B1Ts CA;
blanchet@48975
   857
        val CB2 = mk_bnf_T B2Ts CA;
blanchet@48975
   858
        val bnf_sets_CX = map2 (normalize_set (map (mk_bnf_T domTs) CA_params)) domTs bnf_sets;
blanchet@48975
   859
        val bnf_sets_CB1 = map2 (normalize_set (map (mk_bnf_T B1Ts) CA_params)) B1Ts bnf_sets;
blanchet@48975
   860
        val bnf_sets_CB2 = map2 (normalize_set (map (mk_bnf_T B2Ts) CA_params)) B2Ts bnf_sets;
blanchet@48975
   861
        val bnf_map_app_f1 = Term.list_comb (mk_bnf_map B1Ts ranTs, f1s);
blanchet@48975
   862
        val bnf_map_app_f2 = Term.list_comb (mk_bnf_map B2Ts ranTs, f2s);
blanchet@48975
   863
        val bnf_map_app_p1 = Term.list_comb (mk_bnf_map domTs B1Ts, p1s);
blanchet@48975
   864
        val bnf_map_app_p2 = Term.list_comb (mk_bnf_map domTs B2Ts, p2s);
blanchet@48975
   865
blanchet@48975
   866
        val map_wpull = mk_wpull (mk_in Xs bnf_sets_CX CX)
blanchet@48975
   867
          (mk_in B1s bnf_sets_CB1 CB1) (mk_in B2s bnf_sets_CB2 CB2)
blanchet@48975
   868
          bnf_map_app_f1 bnf_map_app_f2 NONE bnf_map_app_p1 bnf_map_app_p2;
blanchet@48975
   869
      in
blanchet@48975
   870
        fold_rev Logic.all (Xs @ B1s @ B2s @ f1s @ f2s @ p1s @ p2s)
blanchet@48975
   871
          (Logic.list_implies (prems, HOLogic.mk_Trueprop map_wpull))
blanchet@48975
   872
      end;
blanchet@48975
   873
blanchet@49506
   874
    val srel_O_Gr_goal = fold_rev Logic.all Rs (mk_Trueprop_eq (Term.list_comb (srel, Rs), O_Gr));
blanchet@49453
   875
blanchet@49460
   876
    val goals = zip_axioms map_id_goal map_comp_goal map_cong_goal set_naturals_goal
blanchet@49506
   877
      card_order_bd_goal cinfinite_bd_goal set_bds_goal in_bd_goal map_wpull_goal srel_O_Gr_goal;
blanchet@48975
   878
blanchet@48975
   879
    fun mk_wit_goals (I, wit) =
blanchet@48975
   880
      let
blanchet@48975
   881
        val xs = map (nth bs) I;
blanchet@48975
   882
        fun wit_goal i =
blanchet@48975
   883
          let
blanchet@48975
   884
            val z = nth zs i;
blanchet@48975
   885
            val set_wit = nth bnf_sets_As i $ Term.list_comb (wit, xs);
blanchet@48975
   886
            val concl = HOLogic.mk_Trueprop
blanchet@48975
   887
              (if member (op =) I i then HOLogic.mk_eq (z, nth bs i)
blanchet@48975
   888
              else @{term False});
blanchet@48975
   889
          in
blanchet@48975
   890
            fold_rev Logic.all (z :: xs)
blanchet@48975
   891
              (Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (z, set_wit)), concl))
blanchet@48975
   892
          end;
blanchet@48975
   893
      in
blanchet@48975
   894
        map wit_goal (0 upto live - 1)
blanchet@48975
   895
      end;
blanchet@48975
   896
blanchet@48975
   897
    val wit_goalss = map mk_wit_goals bnf_wit_As;
blanchet@48975
   898
blanchet@48975
   899
    fun after_qed thms lthy =
blanchet@48975
   900
      let
blanchet@48975
   901
        val (axioms, wit_thms) = apfst (mk_axioms live) (chop (length goals) thms);
blanchet@48975
   902
traytel@49109
   903
        val bd_Card_order = #bd_card_order axioms RS @{thm conjunct2[OF card_order_on_Card_order]};
blanchet@48975
   904
        val bd_Cinfinite = @{thm conjI} OF [#bd_cinfinite axioms, bd_Card_order];
blanchet@48975
   905
        val bd_Cnotzero = bd_Cinfinite RS @{thm Cinfinite_Cnotzero};
blanchet@48975
   906
blanchet@49461
   907
        fun mk_lazy f = if fact_policy <> Derive_Few_Facts then Lazy.value (f ()) else Lazy.lazy f;
blanchet@48975
   908
blanchet@48975
   909
        fun mk_collect_set_natural () =
blanchet@48975
   910
          let
blanchet@48975
   911
            val defT = mk_bnf_T Ts CA --> HOLogic.mk_setT T;
blanchet@48975
   912
            val collect_map = HOLogic.mk_comp
blanchet@48975
   913
              (mk_collect (map (mk_bnf_t Ts) bnf_sets) defT,
blanchet@48975
   914
              Term.list_comb (mk_bnf_map As' Ts, hs));
blanchet@48975
   915
            val image_collect = mk_collect
blanchet@48975
   916
              (map2 (fn h => fn set => HOLogic.mk_comp (mk_image h, set)) hs bnf_sets_As)
blanchet@48975
   917
              defT;
blanchet@48975
   918
            (*collect {set1 ... setm} o map f1 ... fm = collect {f1` o set1 ... fm` o setm}*)
blanchet@49123
   919
            val goal = fold_rev Logic.all hs (mk_Trueprop_eq (collect_map, image_collect));
blanchet@48975
   920
          in
blanchet@48975
   921
            Skip_Proof.prove lthy [] [] goal
blanchet@48975
   922
              (fn {context = ctxt, ...} => mk_collect_set_natural_tac ctxt (#set_natural axioms))
traytel@49109
   923
            |> Thm.close_derivation
blanchet@48975
   924
          end;
blanchet@48975
   925
blanchet@48975
   926
        val collect_set_natural = mk_lazy mk_collect_set_natural;
blanchet@48975
   927
blanchet@48975
   928
        fun mk_in_mono () =
blanchet@48975
   929
          let
blanchet@48975
   930
            val prems_mono = map2 (HOLogic.mk_Trueprop oo mk_subset) As As_copy;
blanchet@49458
   931
            val in_mono_goal =
blanchet@48975
   932
              fold_rev Logic.all (As @ As_copy)
blanchet@48975
   933
                (Logic.list_implies (prems_mono, HOLogic.mk_Trueprop
blanchet@48975
   934
                  (mk_subset (mk_in As bnf_sets_As CA') (mk_in As_copy bnf_sets_As CA'))));
blanchet@48975
   935
          in
blanchet@49458
   936
            Skip_Proof.prove lthy [] [] in_mono_goal (K (mk_in_mono_tac live))
traytel@49109
   937
            |> Thm.close_derivation
blanchet@48975
   938
          end;
blanchet@48975
   939
blanchet@48975
   940
        val in_mono = mk_lazy mk_in_mono;
blanchet@48975
   941
blanchet@48975
   942
        fun mk_in_cong () =
blanchet@48975
   943
          let
blanchet@48975
   944
            val prems_cong = map2 (HOLogic.mk_Trueprop oo curry HOLogic.mk_eq) As As_copy;
blanchet@49458
   945
            val in_cong_goal =
blanchet@48975
   946
              fold_rev Logic.all (As @ As_copy)
blanchet@48975
   947
                (Logic.list_implies (prems_cong, HOLogic.mk_Trueprop
blanchet@48975
   948
                  (HOLogic.mk_eq (mk_in As bnf_sets_As CA', mk_in As_copy bnf_sets_As CA'))));
blanchet@48975
   949
          in
blanchet@49458
   950
            Skip_Proof.prove lthy [] [] in_cong_goal (K ((TRY o hyp_subst_tac THEN' rtac refl) 1))
traytel@49109
   951
            |> Thm.close_derivation
blanchet@48975
   952
          end;
blanchet@48975
   953
blanchet@48975
   954
        val in_cong = mk_lazy mk_in_cong;
blanchet@48975
   955
blanchet@48975
   956
        val map_id' = mk_lazy (fn () => mk_id' (#map_id axioms));
blanchet@48975
   957
        val map_comp' = mk_lazy (fn () => mk_comp' (#map_comp axioms));
blanchet@48975
   958
blanchet@48975
   959
        val set_natural' =
blanchet@48975
   960
          map (fn thm => mk_lazy (fn () => mk_set_natural' thm)) (#set_natural axioms);
blanchet@48975
   961
blanchet@48975
   962
        fun mk_map_wppull () =
blanchet@48975
   963
          let
blanchet@48975
   964
            val prems = if live = 0 then [] else
blanchet@48975
   965
              [HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@48975
   966
                (map8 mk_wpull Xs B1s B2s f1s f2s (map SOME (e1s ~~ e2s)) p1s p2s))];
blanchet@48975
   967
            val CX = mk_bnf_T domTs CA;
blanchet@48975
   968
            val CB1 = mk_bnf_T B1Ts CA;
blanchet@48975
   969
            val CB2 = mk_bnf_T B2Ts CA;
blanchet@48975
   970
            val bnf_sets_CX =
blanchet@48975
   971
              map2 (normalize_set (map (mk_bnf_T domTs) CA_params)) domTs bnf_sets;
blanchet@48975
   972
            val bnf_sets_CB1 =
blanchet@48975
   973
              map2 (normalize_set (map (mk_bnf_T B1Ts) CA_params)) B1Ts bnf_sets;
blanchet@48975
   974
            val bnf_sets_CB2 =
blanchet@48975
   975
              map2 (normalize_set (map (mk_bnf_T B2Ts) CA_params)) B2Ts bnf_sets;
blanchet@48975
   976
            val bnf_map_app_f1 = Term.list_comb (mk_bnf_map B1Ts ranTs, f1s);
blanchet@48975
   977
            val bnf_map_app_f2 = Term.list_comb (mk_bnf_map B2Ts ranTs, f2s);
blanchet@48975
   978
            val bnf_map_app_e1 = Term.list_comb (mk_bnf_map B1Ts ranTs', e1s);
blanchet@48975
   979
            val bnf_map_app_e2 = Term.list_comb (mk_bnf_map B2Ts ranTs'', e2s);
blanchet@48975
   980
            val bnf_map_app_p1 = Term.list_comb (mk_bnf_map domTs B1Ts, p1s);
blanchet@48975
   981
            val bnf_map_app_p2 = Term.list_comb (mk_bnf_map domTs B2Ts, p2s);
blanchet@48975
   982
blanchet@48975
   983
            val concl = mk_wpull (mk_in Xs bnf_sets_CX CX)
blanchet@48975
   984
              (mk_in B1s bnf_sets_CB1 CB1) (mk_in B2s bnf_sets_CB2 CB2)
blanchet@48975
   985
              bnf_map_app_f1 bnf_map_app_f2 (SOME (bnf_map_app_e1, bnf_map_app_e2))
blanchet@48975
   986
              bnf_map_app_p1 bnf_map_app_p2;
blanchet@48975
   987
blanchet@48975
   988
            val goal =
blanchet@48975
   989
              fold_rev Logic.all (Xs @ B1s @ B2s @ f1s @ f2s @ e1s @ e2s @ p1s @ p2s)
blanchet@48975
   990
                (Logic.list_implies (prems, HOLogic.mk_Trueprop concl))
blanchet@48975
   991
          in
blanchet@48975
   992
            Skip_Proof.prove lthy [] [] goal
blanchet@48975
   993
              (fn _ => mk_map_wppull_tac (#map_id axioms) (#map_cong axioms)
blanchet@48975
   994
                (#map_wpull axioms) (Lazy.force map_comp') (map Lazy.force set_natural'))
traytel@49109
   995
            |> Thm.close_derivation
blanchet@48975
   996
          end;
blanchet@48975
   997
blanchet@49506
   998
        val srel_O_Grs = no_refl [#srel_O_Gr axioms];
blanchet@49453
   999
blanchet@48975
  1000
        val map_wppull = mk_lazy mk_map_wppull;
blanchet@48975
  1001
blanchet@49506
  1002
        fun mk_srel_Gr () =
blanchet@48975
  1003
          let
blanchet@49506
  1004
            val lhs = Term.list_comb (srel, map2 mk_Gr As fs);
blanchet@48975
  1005
            val rhs = mk_Gr (mk_in As bnf_sets_As CA') (Term.list_comb (bnf_map_AsBs, fs));
blanchet@49123
  1006
            val goal = fold_rev Logic.all (As @ fs) (mk_Trueprop_eq (lhs, rhs));
blanchet@48975
  1007
          in
blanchet@48975
  1008
            Skip_Proof.prove lthy [] [] goal
blanchet@49506
  1009
              (mk_srel_Gr_tac srel_O_Grs (#map_id axioms) (#map_cong axioms) (Lazy.force map_id')
blanchet@48975
  1010
                (Lazy.force map_comp') (map Lazy.force set_natural'))
traytel@49109
  1011
            |> Thm.close_derivation
blanchet@48975
  1012
          end;
blanchet@48975
  1013
blanchet@49506
  1014
        val srel_Gr = mk_lazy mk_srel_Gr;
blanchet@48975
  1015
blanchet@49506
  1016
        fun mk_srel_prems f = map2 (HOLogic.mk_Trueprop oo f) Rs Rs_copy
blanchet@49506
  1017
        fun mk_srel_concl f = HOLogic.mk_Trueprop
blanchet@49506
  1018
          (f (Term.list_comb (srel, Rs), Term.list_comb (srel, Rs_copy)));
blanchet@48975
  1019
blanchet@49506
  1020
        fun mk_srel_mono () =
blanchet@48975
  1021
          let
blanchet@49506
  1022
            val mono_prems = mk_srel_prems mk_subset;
blanchet@49506
  1023
            val mono_concl = mk_srel_concl (uncurry mk_subset);
blanchet@48975
  1024
          in
blanchet@48975
  1025
            Skip_Proof.prove lthy [] []
blanchet@48975
  1026
              (fold_rev Logic.all (Rs @ Rs_copy) (Logic.list_implies (mono_prems, mono_concl)))
blanchet@49506
  1027
              (mk_srel_mono_tac srel_O_Grs (Lazy.force in_mono))
traytel@49109
  1028
            |> Thm.close_derivation
blanchet@48975
  1029
          end;
blanchet@48975
  1030
blanchet@49506
  1031
        fun mk_srel_cong () =
blanchet@48975
  1032
          let
blanchet@49506
  1033
            val cong_prems = mk_srel_prems (curry HOLogic.mk_eq);
blanchet@49506
  1034
            val cong_concl = mk_srel_concl HOLogic.mk_eq;
blanchet@48975
  1035
          in
blanchet@48975
  1036
            Skip_Proof.prove lthy [] []
blanchet@48975
  1037
              (fold_rev Logic.all (Rs @ Rs_copy) (Logic.list_implies (cong_prems, cong_concl)))
blanchet@48975
  1038
              (fn _ => (TRY o hyp_subst_tac THEN' rtac refl) 1)
traytel@49109
  1039
            |> Thm.close_derivation
blanchet@48975
  1040
          end;
blanchet@48975
  1041
blanchet@49506
  1042
        val srel_mono = mk_lazy mk_srel_mono;
blanchet@49506
  1043
        val srel_cong = mk_lazy mk_srel_cong;
blanchet@48975
  1044
blanchet@49506
  1045
        fun mk_srel_Id () =
blanchet@49515
  1046
          let val srelAsAs = mk_bnf_srel self_setRTs CA' CA' in
blanchet@48975
  1047
            Skip_Proof.prove lthy [] []
blanchet@48975
  1048
              (HOLogic.mk_Trueprop
blanchet@49515
  1049
                (HOLogic.mk_eq (Term.list_comb (srelAsAs, map Id_const As'), Id_const CA')))
blanchet@49506
  1050
              (mk_srel_Id_tac live (Lazy.force srel_Gr) (#map_id axioms))
traytel@49109
  1051
            |> Thm.close_derivation
blanchet@48975
  1052
          end;
blanchet@48975
  1053
blanchet@49506
  1054
        val srel_Id = mk_lazy mk_srel_Id;
blanchet@48975
  1055
blanchet@49506
  1056
        fun mk_srel_converse () =
blanchet@48975
  1057
          let
blanchet@49515
  1058
            val srelBsAs = mk_bnf_srel setRT's CB' CA';
blanchet@49515
  1059
            val lhs = Term.list_comb (srelBsAs, map mk_converse Rs);
blanchet@49506
  1060
            val rhs = mk_converse (Term.list_comb (srel, Rs));
blanchet@48975
  1061
            val le_goal = fold_rev Logic.all Rs (HOLogic.mk_Trueprop (mk_subset lhs rhs));
blanchet@48975
  1062
            val le_thm = Skip_Proof.prove lthy [] [] le_goal
blanchet@49506
  1063
              (mk_srel_converse_le_tac srel_O_Grs (Lazy.force srel_Id) (#map_cong axioms)
blanchet@48975
  1064
                (Lazy.force map_comp') (map Lazy.force set_natural'))
traytel@49109
  1065
              |> Thm.close_derivation
blanchet@49123
  1066
            val goal = fold_rev Logic.all Rs (mk_Trueprop_eq (lhs, rhs));
blanchet@48975
  1067
          in
blanchet@49506
  1068
            Skip_Proof.prove lthy [] [] goal (fn _ => mk_srel_converse_tac le_thm)
traytel@49109
  1069
            |> Thm.close_derivation
blanchet@48975
  1070
          end;
blanchet@48975
  1071
blanchet@49506
  1072
        val srel_converse = mk_lazy mk_srel_converse;
blanchet@48975
  1073
blanchet@49506
  1074
        fun mk_srel_O () =
blanchet@48975
  1075
          let
blanchet@49515
  1076
            val srelAsCs = mk_bnf_srel setRTsAsCs CA' CC';
blanchet@49515
  1077
            val srelBsCs = mk_bnf_srel setRTsBsCs CB' CC';
blanchet@49515
  1078
            val lhs = Term.list_comb (srelAsCs, map2 (curry mk_rel_comp) Rs Ss);
blanchet@49515
  1079
            val rhs = mk_rel_comp (Term.list_comb (srel, Rs), Term.list_comb (srelBsCs, Ss));
blanchet@49123
  1080
            val goal = fold_rev Logic.all (Rs @ Ss) (mk_Trueprop_eq (lhs, rhs));
blanchet@48975
  1081
          in
blanchet@48975
  1082
            Skip_Proof.prove lthy [] [] goal
blanchet@49506
  1083
              (mk_srel_O_tac srel_O_Grs (Lazy.force srel_Id) (#map_cong axioms)
blanchet@48975
  1084
                (Lazy.force map_wppull) (Lazy.force map_comp') (map Lazy.force set_natural'))
traytel@49109
  1085
            |> Thm.close_derivation
blanchet@48975
  1086
          end;
blanchet@48975
  1087
blanchet@49506
  1088
        val srel_O = mk_lazy mk_srel_O;
blanchet@48975
  1089
blanchet@49506
  1090
        fun mk_in_srel () =
blanchet@48975
  1091
          let
blanchet@48975
  1092
            val bnf_in = mk_in Rs (map (mk_bnf_t RTs) bnf_sets) CRs';
blanchet@48975
  1093
            val map1 = Term.list_comb (mk_bnf_map RTs As', map fst_const RTs);
blanchet@48975
  1094
            val map2 = Term.list_comb (mk_bnf_map RTs Bs', map snd_const RTs);
blanchet@48975
  1095
            val map_fst_eq = HOLogic.mk_eq (map1 $ z, x);
blanchet@48975
  1096
            val map_snd_eq = HOLogic.mk_eq (map2 $ z, y);
blanchet@49506
  1097
            val lhs = HOLogic.mk_mem (HOLogic.mk_prod (x, y), Term.list_comb (srel, Rs));
blanchet@48975
  1098
            val rhs =
blanchet@48975
  1099
              HOLogic.mk_exists (fst z', snd z', HOLogic.mk_conj (HOLogic.mk_mem (z, bnf_in),
blanchet@48975
  1100
                HOLogic.mk_conj (map_fst_eq, map_snd_eq)));
blanchet@48975
  1101
            val goal =
blanchet@49123
  1102
              fold_rev Logic.all (x :: y :: Rs) (mk_Trueprop_eq (lhs, rhs));
blanchet@48975
  1103
          in
blanchet@49506
  1104
            Skip_Proof.prove lthy [] [] goal (mk_in_srel_tac srel_O_Grs (length bnf_sets))
traytel@49109
  1105
            |> Thm.close_derivation
blanchet@48975
  1106
          end;
blanchet@48975
  1107
blanchet@49506
  1108
        val in_srel = mk_lazy mk_in_srel;
blanchet@48975
  1109
blanchet@49537
  1110
        val eqset_imp_iff_pair = @{thm eqset_imp_iff_pair};
blanchet@49537
  1111
        val mem_Collect_etc = @{thms mem_Collect_eq fst_conv snd_conv prod.cases};
blanchet@49537
  1112
blanchet@49537
  1113
        fun mk_rel_as_srel () =
blanchet@49537
  1114
          unfold_thms lthy mem_Collect_etc
blanchet@49537
  1115
            (funpow live (fn thm => thm RS @{thm fun_cong_pair}) (bnf_srel_def RS meta_eq_to_obj_eq)
blanchet@49537
  1116
               RS eqset_imp_iff_pair RS sym)
blanchet@49537
  1117
          |> Drule.zero_var_indexes;
blanchet@49537
  1118
blanchet@49537
  1119
        val rel_as_srel = mk_lazy mk_rel_as_srel;
blanchet@49537
  1120
blanchet@49537
  1121
        fun mk_rel_flip () =
blanchet@49537
  1122
          let
blanchet@49537
  1123
            val srel_converse_thm = Lazy.force srel_converse;
blanchet@49537
  1124
            val Rs' = Term.add_vars (prop_of srel_converse_thm) [];
blanchet@49537
  1125
            val cts = map (pairself (certify lthy)) (map Var Rs' ~~ sQs);
blanchet@49537
  1126
            val srel_converse_thm' = Drule.cterm_instantiate cts srel_converse_thm;
blanchet@49537
  1127
          in
blanchet@49537
  1128
            unfold_thms lthy (bnf_srel_def :: @{thm converse_iff} :: mem_Collect_etc)
blanchet@49537
  1129
              (srel_converse_thm' RS eqset_imp_iff_pair)
blanchet@49537
  1130
            |> Drule.zero_var_indexes |> Thm.generalize ([], map fst Qs') 1
blanchet@49537
  1131
          end;
blanchet@49537
  1132
blanchet@49537
  1133
        val rel_flip = mk_lazy mk_rel_flip;
blanchet@49537
  1134
blanchet@49507
  1135
        val defs = mk_defs bnf_map_def bnf_set_defs bnf_rel_def bnf_srel_def;
blanchet@48975
  1136
blanchet@49506
  1137
        val facts = mk_facts bd_Card_order bd_Cinfinite bd_Cnotzero collect_set_natural in_cong
blanchet@49537
  1138
          in_mono in_srel map_comp' map_id' map_wppull rel_as_srel rel_flip set_natural' srel_cong
blanchet@49537
  1139
          srel_mono srel_Id srel_Gr srel_converse srel_O;
blanchet@48975
  1140
blanchet@48975
  1141
        val wits = map2 mk_witness bnf_wits wit_thms;
blanchet@48975
  1142
blanchet@49507
  1143
        val bnf_rel =
blanchet@49507
  1144
          Term.subst_atomic_types ((Ds ~~ deads) @ (As' ~~ alphas) @ (Bs' ~~ betas)) rel;
blanchet@49506
  1145
        val bnf_srel =
blanchet@49506
  1146
          Term.subst_atomic_types ((Ds ~~ deads) @ (As' ~~ alphas) @ (Bs' ~~ betas)) srel;
blanchet@48975
  1147
blanchet@48975
  1148
        val bnf = mk_bnf b CA live alphas betas dead deads bnf_map bnf_sets bnf_bd axioms defs facts
blanchet@49507
  1149
          wits bnf_rel bnf_srel;
blanchet@48975
  1150
      in
blanchet@48975
  1151
        (bnf, lthy
blanchet@48975
  1152
          |> (if fact_policy = Note_All_Facts_and_Axioms then
blanchet@48975
  1153
                let
blanchet@48975
  1154
                  val witNs = if length wits = 1 then [witN] else map mk_witN (1 upto length wits);
traytel@49109
  1155
                  val notes =
traytel@49109
  1156
                    [(bd_card_orderN, [#bd_card_order axioms]),
traytel@49109
  1157
                    (bd_cinfiniteN, [#bd_cinfinite axioms]),
traytel@49109
  1158
                    (bd_Card_orderN, [#bd_Card_order facts]),
traytel@49109
  1159
                    (bd_CinfiniteN, [#bd_Cinfinite facts]),
traytel@49109
  1160
                    (bd_CnotzeroN, [#bd_Cnotzero facts]),
traytel@49109
  1161
                    (collect_set_naturalN, [Lazy.force (#collect_set_natural facts)]),
traytel@49109
  1162
                    (in_bdN, [#in_bd axioms]),
traytel@49109
  1163
                    (in_monoN, [Lazy.force (#in_mono facts)]),
blanchet@49506
  1164
                    (in_srelN, [Lazy.force (#in_srel facts)]),
traytel@49109
  1165
                    (map_compN, [#map_comp axioms]),
traytel@49109
  1166
                    (map_idN, [#map_id axioms]),
traytel@49109
  1167
                    (map_wpullN, [#map_wpull axioms]),
traytel@49109
  1168
                    (set_naturalN, #set_natural axioms),
traytel@49109
  1169
                    (set_bdN, #set_bd axioms)] @
traytel@49109
  1170
                    map2 pair witNs wit_thms
traytel@49109
  1171
                    |> map (fn (thmN, thms) =>
traytel@49109
  1172
                      ((qualify (Binding.qualify true (Binding.name_of b) (Binding.name thmN)), []),
traytel@49109
  1173
                      [(thms, [])]));
blanchet@48975
  1174
                in
traytel@49109
  1175
                  Local_Theory.notes notes #> snd
blanchet@48975
  1176
                end
blanchet@48975
  1177
              else
blanchet@48975
  1178
                I)
blanchet@48975
  1179
          |> (if fact_policy = Note_All_Facts_and_Axioms orelse
blanchet@48975
  1180
                 fact_policy = Derive_All_Facts_Note_Most then
traytel@49109
  1181
                let
traytel@49109
  1182
                  val notes =
blanchet@49506
  1183
                    [(map_comp'N, [Lazy.force (#map_comp' facts)]),
blanchet@49506
  1184
                    (map_congN, [#map_cong axioms]),
traytel@49109
  1185
                    (map_id'N, [Lazy.force (#map_id' facts)]),
blanchet@49537
  1186
                    (rel_as_srelN, [Lazy.force (#rel_as_srel facts)]),
blanchet@49537
  1187
                    (rel_flipN, [Lazy.force (#rel_flip facts)]),
blanchet@49506
  1188
                    (set_natural'N, map Lazy.force (#set_natural' facts)),
blanchet@49506
  1189
                    (srel_O_GrN, srel_O_Grs),
blanchet@49506
  1190
                    (srel_IdN, [Lazy.force (#srel_Id facts)]),
blanchet@49506
  1191
                    (srel_GrN, [Lazy.force (#srel_Gr facts)]),
blanchet@49506
  1192
                    (srel_converseN, [Lazy.force (#srel_converse facts)]),
blanchet@49506
  1193
                    (srel_monoN, [Lazy.force (#srel_mono facts)]),
blanchet@49506
  1194
                    (srel_ON, [Lazy.force (#srel_O facts)])]
blanchet@49460
  1195
                    |> filter_out (null o #2)
traytel@49109
  1196
                    |> map (fn (thmN, thms) =>
traytel@49109
  1197
                      ((qualify (Binding.qualify true (Binding.name_of b) (Binding.name thmN)), []),
traytel@49109
  1198
                      [(thms, [])]));
traytel@49109
  1199
                in
traytel@49109
  1200
                  Local_Theory.notes notes #> snd
traytel@49109
  1201
                end
blanchet@48975
  1202
              else
blanchet@48975
  1203
                I))
blanchet@48975
  1204
      end;
blanchet@49459
  1205
blanchet@49459
  1206
    val one_step_defs =
blanchet@49507
  1207
      no_reflexive (bnf_map_def :: bnf_bd_def :: bnf_set_defs @ bnf_wit_defs @ [bnf_rel_def,
blanchet@49506
  1208
        bnf_srel_def]);
blanchet@48975
  1209
  in
blanchet@49459
  1210
    (key, goals, wit_goalss, after_qed, lthy, one_step_defs)
blanchet@48975
  1211
  end;
blanchet@48975
  1212
traytel@49434
  1213
fun register_bnf key (bnf, lthy) =
traytel@49434
  1214
  (bnf, Local_Theory.declaration {syntax = false, pervasive = true}
traytel@49434
  1215
    (fn phi => Data.map (Symtab.update_new (key, morph_bnf phi bnf))) lthy);
traytel@49434
  1216
blanchet@49456
  1217
(* TODO: Once the invariant "nwits > 0" holds, remove "mk_conjunction_balanced'" and "rtac TrueI"
blanchet@49456
  1218
   below *)
blanchet@49456
  1219
fun mk_conjunction_balanced' [] = @{prop True}
blanchet@49456
  1220
  | mk_conjunction_balanced' ts = Logic.mk_conjunction_balanced ts;
blanchet@49456
  1221
blanchet@49018
  1222
fun bnf_def const_policy fact_policy qualify tacs wit_tac Ds =
blanchet@49463
  1223
  (fn (_, goals, wit_goalss, after_qed, lthy, one_step_defs) =>
blanchet@48975
  1224
  let
blanchet@49456
  1225
    val wits_tac =
blanchet@49456
  1226
      K (TRYALL Goal.conjunction_tac) THEN' K (TRYALL (rtac TrueI)) THEN'
blanchet@49504
  1227
      mk_unfold_thms_then_tac lthy one_step_defs wit_tac;
blanchet@49456
  1228
    val wit_goals = map mk_conjunction_balanced' wit_goalss;
blanchet@48975
  1229
    val wit_thms =
blanchet@49456
  1230
      Skip_Proof.prove lthy [] [] (mk_conjunction_balanced' wit_goals) wits_tac
blanchet@48975
  1231
      |> Conjunction.elim_balanced (length wit_goals)
blanchet@48975
  1232
      |> map2 (Conjunction.elim_balanced o length) wit_goalss
blanchet@49456
  1233
      |> map (map (Thm.close_derivation o Thm.forall_elim_vars 0));
blanchet@48975
  1234
  in
blanchet@49111
  1235
    map2 (Thm.close_derivation oo Skip_Proof.prove lthy [] [])
blanchet@49504
  1236
      goals (map (mk_unfold_thms_then_tac lthy one_step_defs) tacs)
blanchet@48975
  1237
    |> (fn thms => after_qed (map single thms @ wit_thms) lthy)
blanchet@49279
  1238
  end) oo prepare_def const_policy fact_policy qualify (K I) Ds;
blanchet@48975
  1239
traytel@49434
  1240
val bnf_def_cmd = (fn (key, goals, wit_goals, after_qed, lthy, defs) =>
blanchet@48975
  1241
  Proof.unfolding ([[(defs, [])]])
traytel@49434
  1242
    (Proof.theorem NONE (snd o register_bnf key oo after_qed)
blanchet@48975
  1243
      (map (single o rpair []) goals @ map (map (rpair [])) wit_goals) lthy)) oo
traytel@49435
  1244
  prepare_def Do_Inline (user_policy Derive_All_Facts_Note_Most) I Syntax.read_term NONE;
blanchet@48975
  1245
blanchet@48975
  1246
fun print_bnfs ctxt =
blanchet@48975
  1247
  let
blanchet@48975
  1248
    fun pretty_set sets i = Pretty.block
blanchet@48975
  1249
      [Pretty.str (mk_setN (i + 1) ^ ":"), Pretty.brk 1,
blanchet@48975
  1250
          Pretty.quote (Syntax.pretty_term ctxt (nth sets i))];
blanchet@48975
  1251
blanchet@48975
  1252
    fun pretty_bnf (key, BNF {T = T, map = map, sets = sets, bd = bd,
blanchet@48975
  1253
      live = live, lives = lives, dead = dead, deads = deads, ...}) =
blanchet@48975
  1254
      Pretty.big_list
blanchet@48975
  1255
        (Pretty.string_of (Pretty.block [Pretty.str key, Pretty.str ":", Pretty.brk 1,
blanchet@48975
  1256
          Pretty.quote (Syntax.pretty_typ ctxt T)]))
blanchet@48975
  1257
        ([Pretty.block [Pretty.str "live:", Pretty.brk 1, Pretty.str (string_of_int live),
blanchet@48975
  1258
            Pretty.brk 3, Pretty.list "[" "]" (List.map (Syntax.pretty_typ ctxt) lives)],
blanchet@48975
  1259
          Pretty.block [Pretty.str "dead:", Pretty.brk 1, Pretty.str (string_of_int dead),
blanchet@48975
  1260
            Pretty.brk 3, Pretty.list "[" "]" (List.map (Syntax.pretty_typ ctxt) deads)],
blanchet@48975
  1261
          Pretty.block [Pretty.str (mapN ^ ":"), Pretty.brk 1,
blanchet@48975
  1262
            Pretty.quote (Syntax.pretty_term ctxt map)]] @
blanchet@48975
  1263
          List.map (pretty_set sets) (0 upto length sets - 1) @
blanchet@48975
  1264
          [Pretty.block [Pretty.str (bdN ^ ":"), Pretty.brk 1,
blanchet@48975
  1265
            Pretty.quote (Syntax.pretty_term ctxt bd)]]);
blanchet@48975
  1266
  in
blanchet@48975
  1267
    Pretty.big_list "BNFs:" (map pretty_bnf (Symtab.dest (Data.get (Context.Proof ctxt))))
blanchet@48975
  1268
    |> Pretty.writeln
blanchet@48975
  1269
  end;
blanchet@48975
  1270
blanchet@48975
  1271
val _ =
blanchet@48975
  1272
  Outer_Syntax.improper_command @{command_spec "print_bnfs"} "print all BNFs"
blanchet@48975
  1273
    (Scan.succeed (Toplevel.keep (print_bnfs o Toplevel.context_of)));
blanchet@48975
  1274
blanchet@48975
  1275
val _ =
blanchet@48975
  1276
  Outer_Syntax.local_theory_to_proof @{command_spec "bnf_def"} "define a BNF for an existing type"
traytel@49434
  1277
    ((parse_opt_binding_colon -- Parse.term --
blanchet@49277
  1278
       (@{keyword "["} |-- Parse.list Parse.term --| @{keyword "]"}) -- Parse.term --
blanchet@49459
  1279
       (@{keyword "["} |-- Parse.list Parse.term --| @{keyword "]"}) -- Scan.option Parse.term)
blanchet@49459
  1280
       >> bnf_def_cmd);
blanchet@48975
  1281
blanchet@48975
  1282
end;