src/HOL/BNF/Tools/bnf_def.ML
author blanchet
Wed Apr 24 13:16:21 2013 +0200 (2013-04-24)
changeset 51758 55963309557b
parent 51757 7babcb61aa5c
child 51761 4c9f08836d87
permissions -rw-r--r--
honor user-specified name for map function
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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_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_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_natural'_of_bnf: BNF -> thm list
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  val set_natural_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 list -> ((((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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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_eq: thm lazy,
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  rel_flip: thm lazy,
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  rel_srel: 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_eq rel_flip rel_srel set_natural' 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_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_eq = rel_eq,
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  rel_flip = rel_flip,
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  rel_srel = rel_srel,
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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_eq,
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  rel_flip,
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  rel_srel,
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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_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_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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   314
val wits_of_bnf = #wits o rep_bnf;
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   315
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   316
(*terms*)
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   317
val map_of_bnf = #map o rep_bnf;
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   318
val sets_of_bnf = #sets o rep_bnf;
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   319
fun mk_map_of_bnf Ds Ts Us bnf =
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   320
  let val bnf_rep = rep_bnf bnf;
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   321
  in
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   322
    Term.subst_atomic_types
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   323
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts) @ (#lives' bnf_rep ~~ Us)) (#map bnf_rep)
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   324
  end;
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   325
fun mk_sets_of_bnf Dss Tss bnf =
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   326
  let val bnf_rep = rep_bnf bnf;
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   327
  in
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   328
    map2 (fn (Ds, Ts) => Term.subst_atomic_types
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   329
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts))) (Dss ~~ Tss) (#sets bnf_rep)
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   330
  end;
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   331
val bd_of_bnf = #bd o rep_bnf;
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   332
fun mk_bd_of_bnf Ds Ts bnf =
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   333
  let val bnf_rep = rep_bnf bnf;
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   334
  in Term.subst_atomic_types ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts)) (#bd bnf_rep) end;
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   335
fun mk_wits_of_bnf Dss Tss bnf =
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   336
  let
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   337
    val bnf_rep = rep_bnf bnf;
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   338
    val wits = map (fn x => (#I x, #wit x)) (#wits bnf_rep);
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   339
  in
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   340
    map2 (fn (Ds, Ts) => apsnd (Term.subst_atomic_types
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   341
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts)))) (Dss ~~ Tss) wits
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   342
  end;
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   343
val rel_of_bnf = #rel o rep_bnf;
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   344
fun mk_rel_of_bnf Ds Ts Us bnf =
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   345
  let val bnf_rep = rep_bnf bnf;
blanchet@49462
   346
  in
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   347
    Term.subst_atomic_types
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   348
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts) @ (#lives' bnf_rep ~~ Us)) (#rel bnf_rep)
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   349
  end;
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   350
val srel_of_bnf = #srel o rep_bnf;
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   351
fun mk_srel_of_bnf Ds Ts Us bnf =
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   352
  let val bnf_rep = rep_bnf bnf;
blanchet@48975
   353
  in
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   354
    Term.subst_atomic_types
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   355
      ((#deads bnf_rep ~~ Ds) @ (#lives bnf_rep ~~ Ts) @ (#lives' bnf_rep ~~ Us)) (#srel bnf_rep)
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   356
  end;
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   357
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   358
(*thms*)
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   359
val bd_card_order_of_bnf = #bd_card_order o #axioms o rep_bnf;
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   360
val bd_cinfinite_of_bnf = #bd_cinfinite o #axioms o rep_bnf;
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   361
val bd_Card_order_of_bnf = #bd_Card_order o #facts o rep_bnf;
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   362
val bd_Cinfinite_of_bnf = #bd_Cinfinite o #facts o rep_bnf;
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   363
val bd_Cnotzero_of_bnf = #bd_Cnotzero o #facts o rep_bnf;
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   364
val collect_set_natural_of_bnf = Lazy.force o #collect_set_natural o #facts o rep_bnf;
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   365
val in_bd_of_bnf = #in_bd o #axioms o rep_bnf;
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   366
val in_cong_of_bnf = Lazy.force o #in_cong o #facts o rep_bnf;
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   367
val in_mono_of_bnf = Lazy.force o #in_mono o #facts o rep_bnf;
blanchet@49506
   368
val in_srel_of_bnf = Lazy.force o #in_srel o #facts o rep_bnf;
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   369
val map_def_of_bnf = #map_def o #defs o rep_bnf;
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   370
val map_id_of_bnf = #map_id o #axioms o rep_bnf;
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   371
val map_id'_of_bnf = Lazy.force o #map_id' o #facts o rep_bnf;
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   372
val map_comp_of_bnf = #map_comp o #axioms o rep_bnf;
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   373
val map_comp'_of_bnf = Lazy.force o #map_comp' o #facts o rep_bnf;
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   374
val map_cong_of_bnf = #map_cong o #axioms o rep_bnf;
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   375
val map_wppull_of_bnf = Lazy.force o #map_wppull o #facts o rep_bnf;
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   376
val map_wpull_of_bnf = #map_wpull o #axioms o rep_bnf;
blanchet@49507
   377
val rel_def_of_bnf = #rel_def o #defs o rep_bnf;
blanchet@49591
   378
val rel_eq_of_bnf = Lazy.force o #rel_eq o #facts o rep_bnf;
blanchet@49537
   379
val rel_flip_of_bnf = Lazy.force o #rel_flip o #facts o rep_bnf;
blanchet@49594
   380
val rel_srel_of_bnf = Lazy.force o #rel_srel o #facts o rep_bnf;
blanchet@48975
   381
val set_bd_of_bnf = #set_bd o #axioms o rep_bnf;
blanchet@48975
   382
val set_defs_of_bnf = #set_defs o #defs o rep_bnf;
blanchet@48975
   383
val set_natural_of_bnf = #set_natural o #axioms o rep_bnf;
blanchet@48975
   384
val set_natural'_of_bnf = map Lazy.force o #set_natural' o #facts o rep_bnf;
blanchet@49506
   385
val srel_cong_of_bnf = Lazy.force o #srel_cong o #facts o rep_bnf;
blanchet@49506
   386
val srel_mono_of_bnf = Lazy.force o #srel_mono o #facts o rep_bnf;
blanchet@49506
   387
val srel_def_of_bnf = #srel_def o #defs o rep_bnf;
blanchet@49506
   388
val srel_Id_of_bnf = Lazy.force o #srel_Id o #facts o rep_bnf;
blanchet@49506
   389
val srel_Gr_of_bnf = Lazy.force o #srel_Gr o #facts o rep_bnf;
blanchet@49506
   390
val srel_converse_of_bnf = Lazy.force o #srel_converse o #facts o rep_bnf;
blanchet@49506
   391
val srel_O_of_bnf = Lazy.force o #srel_O o #facts o rep_bnf;
blanchet@49506
   392
val srel_O_Gr_of_bnf = #srel_O_Gr o #axioms o rep_bnf;
blanchet@48975
   393
val wit_thms_of_bnf = maps #prop o wits_of_bnf;
blanchet@48975
   394
val wit_thmss_of_bnf = map #prop o wits_of_bnf;
blanchet@48975
   395
blanchet@49507
   396
fun mk_bnf name T live lives lives' dead deads map sets bd axioms defs facts wits rel srel =
blanchet@48975
   397
  BNF {name = name, T = T,
blanchet@48975
   398
       live = live, lives = lives, lives' = lives', dead = dead, deads = deads,
blanchet@48975
   399
       map = map, sets = sets, bd = bd,
blanchet@48975
   400
       axioms = axioms, defs = defs, facts = facts,
blanchet@49507
   401
       nwits = length wits, wits = wits, rel = rel, srel = srel};
blanchet@48975
   402
blanchet@48975
   403
fun morph_bnf phi (BNF {name = name, T = T, live = live, lives = lives, lives' = lives',
blanchet@48975
   404
  dead = dead, deads = deads, map = map, sets = sets, bd = bd,
blanchet@48975
   405
  axioms = axioms, defs = defs, facts = facts,
blanchet@49507
   406
  nwits = nwits, wits = wits, rel = rel, srel = srel}) =
blanchet@48975
   407
  BNF {name = Morphism.binding phi name, T = Morphism.typ phi T,
blanchet@48975
   408
    live = live, lives = List.map (Morphism.typ phi) lives,
blanchet@48975
   409
    lives' = List.map (Morphism.typ phi) lives',
blanchet@48975
   410
    dead = dead, deads = List.map (Morphism.typ phi) deads,
blanchet@48975
   411
    map = Morphism.term phi map, sets = List.map (Morphism.term phi) sets,
blanchet@48975
   412
    bd = Morphism.term phi bd,
blanchet@48975
   413
    axioms = morph_axioms phi axioms,
blanchet@48975
   414
    defs = morph_defs phi defs,
blanchet@48975
   415
    facts = morph_facts phi facts,
blanchet@48975
   416
    nwits = nwits,
blanchet@48975
   417
    wits = List.map (morph_witness phi) wits,
blanchet@49507
   418
    rel = Morphism.term phi rel, srel = Morphism.term phi srel};
blanchet@48975
   419
blanchet@48975
   420
fun eq_bnf (BNF {T = T1, live = live1, dead = dead1, ...},
blanchet@48975
   421
  BNF {T = T2, live = live2, dead = dead2, ...}) =
blanchet@48975
   422
  Type.could_unify (T1, T2) andalso live1 = live2 andalso dead1 = dead2;
blanchet@48975
   423
blanchet@48975
   424
structure Data = Generic_Data
blanchet@48975
   425
(
blanchet@48975
   426
  type T = BNF Symtab.table;
blanchet@48975
   427
  val empty = Symtab.empty;
blanchet@48975
   428
  val extend = I;
blanchet@49462
   429
  val merge = Symtab.merge eq_bnf;
blanchet@48975
   430
);
blanchet@48975
   431
blanchet@48975
   432
val bnf_of = Symtab.lookup o Data.get o Context.Proof;
blanchet@48975
   433
blanchet@48975
   434
blanchet@48975
   435
blanchet@48975
   436
(* Utilities *)
blanchet@48975
   437
blanchet@48975
   438
fun normalize_set insts instA set =
blanchet@48975
   439
  let
blanchet@48975
   440
    val (T, T') = dest_funT (fastype_of set);
blanchet@48975
   441
    val A = fst (Term.dest_TVar (HOLogic.dest_setT T'));
blanchet@48975
   442
    val params = Term.add_tvar_namesT T [];
blanchet@48975
   443
  in Term.subst_TVars ((A :: params) ~~ (instA :: insts)) set end;
blanchet@48975
   444
blanchet@49507
   445
fun normalize_rel ctxt instTs instA instB rel =
blanchet@49462
   446
  let
blanchet@49462
   447
    val thy = Proof_Context.theory_of ctxt;
blanchet@49462
   448
    val tyenv =
blanchet@49507
   449
      Sign.typ_match thy (fastype_of rel, Library.foldr (op -->) (instTs, mk_pred2T instA instB))
blanchet@49463
   450
        Vartab.empty;
blanchet@49507
   451
  in Envir.subst_term (tyenv, Vartab.empty) rel end
blanchet@49462
   452
  handle Type.TYPE_MATCH => error "Bad predicator";
blanchet@49462
   453
blanchet@49506
   454
fun normalize_srel ctxt instTs instA instB srel =
blanchet@48975
   455
  let
blanchet@48975
   456
    val thy = Proof_Context.theory_of ctxt;
blanchet@48975
   457
    val tyenv =
blanchet@49506
   458
      Sign.typ_match thy (fastype_of srel, Library.foldr (op -->) (instTs, mk_relT (instA, instB)))
blanchet@48975
   459
        Vartab.empty;
blanchet@49506
   460
  in Envir.subst_term (tyenv, Vartab.empty) srel end
blanchet@49453
   461
  handle Type.TYPE_MATCH => error "Bad relator";
blanchet@48975
   462
blanchet@48975
   463
fun normalize_wit insts CA As wit =
blanchet@48975
   464
  let
blanchet@48975
   465
    fun strip_param (Ts, T as Type (@{type_name fun}, [T1, T2])) =
blanchet@48975
   466
        if Type.raw_instance (CA, T) then (Ts, T) else strip_param (T1 :: Ts, T2)
blanchet@48975
   467
      | strip_param x = x;
blanchet@48975
   468
    val (Ts, T) = strip_param ([], fastype_of wit);
blanchet@48975
   469
    val subst = Term.add_tvar_namesT T [] ~~ insts;
blanchet@48975
   470
    fun find y = find_index (fn x => x = y) As;
blanchet@48975
   471
  in
blanchet@48975
   472
    (map (find o Term.typ_subst_TVars subst) (rev Ts), Term.subst_TVars subst wit)
blanchet@48975
   473
  end;
blanchet@48975
   474
blanchet@48975
   475
fun minimize_wits wits =
blanchet@48975
   476
 let
blanchet@48975
   477
   fun minimize done [] = done
traytel@49103
   478
     | minimize done ((I, wit) :: todo) =
blanchet@48975
   479
       if exists (fn (J, _) => subset (op =) (J, I)) (done @ todo)
blanchet@48975
   480
       then minimize done todo
blanchet@48975
   481
       else minimize ((I, wit) :: done) todo;
blanchet@48975
   482
 in minimize [] wits end;
blanchet@48975
   483
blanchet@48975
   484
blanchet@48975
   485
blanchet@48975
   486
(* Names *)
blanchet@48975
   487
blanchet@48975
   488
val mapN = "map";
blanchet@48975
   489
val setN = "set";
blanchet@48975
   490
fun mk_setN i = setN ^ nonzero_string_of_int i;
blanchet@48975
   491
val bdN = "bd";
blanchet@48975
   492
val witN = "wit";
blanchet@48975
   493
fun mk_witN i = witN ^ nonzero_string_of_int i;
blanchet@49507
   494
val relN = "rel";
blanchet@49506
   495
val srelN = "srel";
blanchet@48975
   496
blanchet@48975
   497
val bd_card_orderN = "bd_card_order";
blanchet@48975
   498
val bd_cinfiniteN = "bd_cinfinite";
blanchet@48975
   499
val bd_Card_orderN = "bd_Card_order";
blanchet@48975
   500
val bd_CinfiniteN = "bd_Cinfinite";
blanchet@48975
   501
val bd_CnotzeroN = "bd_Cnotzero";
blanchet@48975
   502
val collect_set_naturalN = "collect_set_natural";
blanchet@48975
   503
val in_bdN = "in_bd";
blanchet@48975
   504
val in_monoN = "in_mono";
blanchet@49506
   505
val in_srelN = "in_srel";
blanchet@48975
   506
val map_idN = "map_id";
blanchet@48975
   507
val map_id'N = "map_id'";
blanchet@48975
   508
val map_compN = "map_comp";
blanchet@48975
   509
val map_comp'N = "map_comp'";
blanchet@48975
   510
val map_congN = "map_cong";
blanchet@48975
   511
val map_wpullN = "map_wpull";
blanchet@49591
   512
val rel_eqN = "rel_eq";
blanchet@49537
   513
val rel_flipN = "rel_flip";
blanchet@49594
   514
val rel_srelN = "rel_srel";
blanchet@49537
   515
val set_naturalN = "set_natural";
blanchet@49537
   516
val set_natural'N = "set_natural'";
blanchet@49537
   517
val set_bdN = "set_bd";
blanchet@49506
   518
val srel_IdN = "srel_Id";
blanchet@49506
   519
val srel_GrN = "srel_Gr";
blanchet@49506
   520
val srel_converseN = "srel_converse";
blanchet@49506
   521
val srel_monoN = "srel_mono"
blanchet@49506
   522
val srel_ON = "srel_comp";
blanchet@49506
   523
val srel_O_GrN = "srel_comp_Gr";
blanchet@48975
   524
blanchet@48975
   525
datatype const_policy = Dont_Inline | Hardly_Inline | Smart_Inline | Do_Inline;
blanchet@48975
   526
blanchet@49538
   527
datatype fact_policy = Dont_Note | Note_Some | Note_All;
blanchet@48975
   528
blanchet@48975
   529
val bnf_note_all = Attrib.setup_config_bool @{binding bnf_note_all} (K false);
blanchet@48975
   530
blanchet@49538
   531
fun user_policy policy ctxt = if Config.get ctxt bnf_note_all then Note_All else policy;
blanchet@48975
   532
blanchet@48975
   533
val smart_max_inline_size = 25; (*FUDGE*)
blanchet@48975
   534
blanchet@48975
   535
blanchet@48975
   536
(* Define new BNFs *)
blanchet@48975
   537
blanchet@51758
   538
fun prepare_def const_policy mk_fact_policy qualify prep_term Ds_opt map_b set_bs
blanchet@49507
   539
  (((((raw_b, raw_map), raw_sets), raw_bd_Abs), raw_wits), raw_rel_opt) no_defs_lthy =
blanchet@48975
   540
  let
blanchet@48975
   541
    val fact_policy = mk_fact_policy no_defs_lthy;
blanchet@48975
   542
    val b = qualify raw_b;
blanchet@48975
   543
    val live = length raw_sets;
blanchet@48975
   544
    val nwits = length raw_wits;
blanchet@48975
   545
blanchet@48975
   546
    val map_rhs = prep_term no_defs_lthy raw_map;
blanchet@48975
   547
    val set_rhss = map (prep_term no_defs_lthy) raw_sets;
blanchet@48975
   548
    val (bd_rhsT, bd_rhs) = (case prep_term no_defs_lthy raw_bd_Abs of
blanchet@48975
   549
      Abs (_, T, t) => (T, t)
blanchet@48975
   550
    | _ => error "Bad bound constant");
blanchet@48975
   551
    val wit_rhss = map (prep_term no_defs_lthy) raw_wits;
blanchet@48975
   552
traytel@49434
   553
    fun err T =
traytel@49434
   554
      error ("Trying to register the type " ^ quote (Syntax.string_of_typ no_defs_lthy T) ^
traytel@49434
   555
        " as unnamed BNF");
traytel@49434
   556
traytel@49434
   557
    val (b, key) =
traytel@49434
   558
      if Binding.eq_name (b, Binding.empty) then
traytel@49434
   559
        (case bd_rhsT of
traytel@49434
   560
          Type (C, Ts) => if forall (is_some o try dest_TFree) Ts
traytel@49434
   561
            then (Binding.qualified_name C, C) else err bd_rhsT
traytel@49434
   562
        | T => err T)
traytel@49434
   563
      else (b, Local_Theory.full_name no_defs_lthy b);
traytel@49434
   564
blanchet@49463
   565
    fun maybe_define user_specified (b, rhs) lthy =
blanchet@48975
   566
      let
blanchet@48975
   567
        val inline =
blanchet@49538
   568
          (user_specified orelse fact_policy = Dont_Note) andalso
blanchet@48975
   569
          (case const_policy of
blanchet@48975
   570
            Dont_Inline => false
blanchet@48975
   571
          | Hardly_Inline => Term.is_Free rhs orelse Term.is_Const rhs
blanchet@48975
   572
          | Smart_Inline => Term.size_of_term rhs <= smart_max_inline_size
blanchet@48975
   573
          | Do_Inline => true)
blanchet@48975
   574
      in
blanchet@48975
   575
        if inline then
blanchet@49460
   576
          ((rhs, Drule.reflexive_thm), lthy)
blanchet@48975
   577
        else
blanchet@48975
   578
          let val b = b () in
blanchet@48975
   579
            apfst (apsnd snd) (Local_Theory.define ((b, NoSyn), ((Thm.def_binding b, []), rhs))
blanchet@48975
   580
              lthy)
blanchet@48975
   581
          end
blanchet@48975
   582
      end;
blanchet@49459
   583
blanchet@49459
   584
    fun maybe_restore lthy_old lthy =
blanchet@49459
   585
      lthy |> not (pointer_eq (lthy_old, lthy)) ? Local_Theory.restore;
blanchet@48975
   586
blanchet@51758
   587
    val map_bind_def =
blanchet@51758
   588
      (fn () => if Binding.is_empty map_b then Binding.suffix_name ("_" ^ mapN) b else map_b,
blanchet@51758
   589
       map_rhs);
blanchet@49459
   590
    val set_binds_defs =
blanchet@49459
   591
      let
blanchet@51757
   592
        fun set_name i get_b =
blanchet@51757
   593
          (case try (nth set_bs) (i - 1) of
blanchet@51757
   594
            SOME b => if Binding.is_empty b then get_b else K b
blanchet@51757
   595
          | NONE => get_b);
blanchet@51757
   596
        val bs =
blanchet@51757
   597
          if live = 1 then
blanchet@51757
   598
            [set_name 1 (fn () => Binding.suffix_name ("_" ^ setN) b)]
blanchet@51757
   599
          else
blanchet@51757
   600
            map (fn i => set_name i (fn () => Binding.suffix_name ("_" ^ mk_setN i) b))
blanchet@51757
   601
              (1 upto live);
blanchet@51757
   602
      in bs ~~ set_rhss end;
blanchet@49459
   603
    val bd_bind_def = (fn () => Binding.suffix_name ("_" ^ bdN) b, bd_rhs);
blanchet@49459
   604
    val wit_binds_defs =
blanchet@49459
   605
      let
blanchet@49459
   606
        val bs = if nwits = 1 then [fn () => Binding.suffix_name ("_" ^ witN) b]
blanchet@49459
   607
          else map (fn i => fn () => Binding.suffix_name ("_" ^ mk_witN i) b) (1 upto nwits);
blanchet@51757
   608
      in bs ~~ wit_rhss end;
blanchet@49459
   609
blanchet@49459
   610
    val (((((bnf_map_term, raw_map_def),
blanchet@48975
   611
      (bnf_set_terms, raw_set_defs)),
blanchet@48975
   612
      (bnf_bd_term, raw_bd_def)),
blanchet@49459
   613
      (bnf_wit_terms, raw_wit_defs)), (lthy, lthy_old)) =
blanchet@48975
   614
        no_defs_lthy
blanchet@49463
   615
        |> maybe_define true map_bind_def
blanchet@49463
   616
        ||>> apfst split_list o fold_map (maybe_define true) set_binds_defs
blanchet@49463
   617
        ||>> maybe_define true bd_bind_def
blanchet@49463
   618
        ||>> apfst split_list o fold_map (maybe_define true) wit_binds_defs
blanchet@48975
   619
        ||> `(maybe_restore no_defs_lthy);
blanchet@48975
   620
blanchet@49459
   621
    val phi = Proof_Context.export_morphism lthy_old lthy;
blanchet@48975
   622
blanchet@48975
   623
    val bnf_map_def = Morphism.thm phi raw_map_def;
blanchet@48975
   624
    val bnf_set_defs = map (Morphism.thm phi) raw_set_defs;
blanchet@48975
   625
    val bnf_bd_def = Morphism.thm phi raw_bd_def;
blanchet@48975
   626
    val bnf_wit_defs = map (Morphism.thm phi) raw_wit_defs;
blanchet@48975
   627
blanchet@48975
   628
    val bnf_map = Morphism.term phi bnf_map_term;
blanchet@48975
   629
blanchet@48975
   630
    (*TODO: handle errors*)
blanchet@48975
   631
    (*simple shape analysis of a map function*)
traytel@49395
   632
    val ((alphas, betas), (CA, _)) =
traytel@49395
   633
      fastype_of bnf_map
traytel@49395
   634
      |> strip_typeN live
traytel@49395
   635
      |>> map_split dest_funT
traytel@49395
   636
      ||> dest_funT
traytel@49395
   637
      handle TYPE _ => error "Bad map function";
blanchet@48975
   638
blanchet@48975
   639
    val CA_params = map TVar (Term.add_tvarsT CA []);
blanchet@48975
   640
blanchet@48975
   641
    val bnf_sets = map2 (normalize_set CA_params) alphas (map (Morphism.term phi) bnf_set_terms);
blanchet@48975
   642
    val bdT = Morphism.typ phi bd_rhsT;
blanchet@48975
   643
    val bnf_bd =
blanchet@48975
   644
      Term.subst_TVars (Term.add_tvar_namesT bdT [] ~~ CA_params) (Morphism.term phi bnf_bd_term);
blanchet@48975
   645
    val bnf_wits = map (normalize_wit CA_params CA alphas o Morphism.term phi) bnf_wit_terms;
blanchet@48975
   646
blanchet@48975
   647
    (*TODO: assert Ds = (TVars of bnf_map) \ (alphas @ betas) as sets*)
blanchet@48975
   648
    val deads = (case Ds_opt of
blanchet@48975
   649
      NONE => subtract (op =) (alphas @ betas) (map TVar (Term.add_tvars bnf_map []))
blanchet@48975
   650
    | SOME Ds => map (Morphism.typ phi) Ds);
blanchet@48975
   651
    val dead = length deads;
blanchet@48975
   652
blanchet@48975
   653
    (*TODO: further checks of type of bnf_map*)
blanchet@48975
   654
    (*TODO: check types of bnf_sets*)
blanchet@48975
   655
    (*TODO: check type of bnf_bd*)
blanchet@49507
   656
    (*TODO: check type of bnf_rel*)
blanchet@48975
   657
blanchet@48975
   658
    val ((((((((((As', Bs'), Cs), Ds), B1Ts), B2Ts), domTs), ranTs), ranTs'), ranTs''),
blanchet@49459
   659
      (Ts, T)) = lthy
blanchet@48975
   660
      |> mk_TFrees live
blanchet@48975
   661
      ||>> mk_TFrees live
blanchet@48975
   662
      ||>> mk_TFrees live
blanchet@48975
   663
      ||>> mk_TFrees dead
blanchet@48975
   664
      ||>> mk_TFrees live
blanchet@48975
   665
      ||>> mk_TFrees live
blanchet@48975
   666
      ||>> mk_TFrees live
blanchet@48975
   667
      ||>> mk_TFrees live
blanchet@48975
   668
      ||>> mk_TFrees live
blanchet@48975
   669
      ||>> mk_TFrees live
blanchet@48975
   670
      ||> fst o mk_TFrees 1
blanchet@48975
   671
      ||> the_single
blanchet@48975
   672
      ||> `(replicate live);
blanchet@48975
   673
blanchet@48975
   674
    fun mk_bnf_map As' Bs' =
blanchet@48975
   675
      Term.subst_atomic_types ((deads ~~ Ds) @ (alphas ~~ As') @ (betas ~~ Bs')) bnf_map;
blanchet@49453
   676
    fun mk_bnf_t As' = Term.subst_atomic_types ((deads ~~ Ds) @ (alphas ~~ As'));
blanchet@49453
   677
    fun mk_bnf_T As' = Term.typ_subst_atomic ((deads ~~ Ds) @ (alphas ~~ As'));
blanchet@49453
   678
blanchet@48975
   679
    val (setRTs, RTs) = map_split (`HOLogic.mk_setT o HOLogic.mk_prodT) (As' ~~ Bs');
blanchet@48975
   680
    val setRTsAsCs = map (HOLogic.mk_setT o HOLogic.mk_prodT) (As' ~~ Cs);
blanchet@48975
   681
    val setRTsBsCs = map (HOLogic.mk_setT o HOLogic.mk_prodT) (Bs' ~~ Cs);
blanchet@48975
   682
    val setRT's = map (HOLogic.mk_setT o HOLogic.mk_prodT) (Bs' ~~ As');
blanchet@48975
   683
    val self_setRTs = map (HOLogic.mk_setT o HOLogic.mk_prodT) (As' ~~ As');
blanchet@49463
   684
    val QTs = map2 mk_pred2T As' Bs';
blanchet@48975
   685
blanchet@49453
   686
    val CA' = mk_bnf_T As' CA;
blanchet@49453
   687
    val CB' = mk_bnf_T Bs' CA;
blanchet@49453
   688
    val CC' = mk_bnf_T Cs CA;
blanchet@49453
   689
    val CRs' = mk_bnf_T RTs CA;
blanchet@49463
   690
    val CA'CB' = HOLogic.mk_prodT (CA', CB');
blanchet@49453
   691
blanchet@48975
   692
    val bnf_map_AsAs = mk_bnf_map As' As';
blanchet@48975
   693
    val bnf_map_AsBs = mk_bnf_map As' Bs';
blanchet@48975
   694
    val bnf_map_AsCs = mk_bnf_map As' Cs;
blanchet@48975
   695
    val bnf_map_BsCs = mk_bnf_map Bs' Cs;
blanchet@48975
   696
    val bnf_sets_As = map (mk_bnf_t As') bnf_sets;
blanchet@48975
   697
    val bnf_sets_Bs = map (mk_bnf_t Bs') bnf_sets;
blanchet@48975
   698
    val bnf_bd_As = mk_bnf_t As' bnf_bd;
blanchet@48975
   699
    val bnf_wit_As = map (apsnd (mk_bnf_t As')) bnf_wits;
blanchet@48975
   700
blanchet@49595
   701
    val pre_names_lthy = lthy;
blanchet@49463
   702
    val (((((((((((((((((((((((((fs, fs_copy), gs), hs), p), (x, x')), (y, y')), (z, z')), zs), As),
blanchet@49459
   703
      As_copy), Xs), B1s), B2s), f1s), f2s), e1s), e2s), p1s), p2s), bs), (Rs, Rs')), Rs_copy), Ss),
blanchet@49595
   704
      (Qs, Qs')), names_lthy) = pre_names_lthy
blanchet@48975
   705
      |> mk_Frees "f" (map2 (curry (op -->)) As' Bs')
blanchet@48975
   706
      ||>> mk_Frees "f" (map2 (curry (op -->)) As' Bs')
blanchet@48975
   707
      ||>> mk_Frees "g" (map2 (curry (op -->)) Bs' Cs)
blanchet@48975
   708
      ||>> mk_Frees "h" (map2 (curry (op -->)) As' Ts)
blanchet@49463
   709
      ||>> yield_singleton (mk_Frees "p") CA'CB'
blanchet@48975
   710
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "x") CA'
blanchet@48975
   711
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "y") CB'
blanchet@48975
   712
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "z") CRs'
blanchet@48975
   713
      ||>> mk_Frees "z" As'
blanchet@48975
   714
      ||>> mk_Frees "A" (map HOLogic.mk_setT As')
blanchet@48975
   715
      ||>> mk_Frees "A" (map HOLogic.mk_setT As')
blanchet@48975
   716
      ||>> mk_Frees "A" (map HOLogic.mk_setT domTs)
blanchet@48975
   717
      ||>> mk_Frees "B1" (map HOLogic.mk_setT B1Ts)
blanchet@48975
   718
      ||>> mk_Frees "B2" (map HOLogic.mk_setT B2Ts)
blanchet@48975
   719
      ||>> mk_Frees "f1" (map2 (curry (op -->)) B1Ts ranTs)
blanchet@48975
   720
      ||>> mk_Frees "f2" (map2 (curry (op -->)) B2Ts ranTs)
blanchet@48975
   721
      ||>> mk_Frees "e1" (map2 (curry (op -->)) B1Ts ranTs')
blanchet@48975
   722
      ||>> mk_Frees "e2" (map2 (curry (op -->)) B2Ts ranTs'')
blanchet@48975
   723
      ||>> mk_Frees "p1" (map2 (curry (op -->)) domTs B1Ts)
blanchet@48975
   724
      ||>> mk_Frees "p2" (map2 (curry (op -->)) domTs B2Ts)
blanchet@48975
   725
      ||>> mk_Frees "b" As'
blanchet@49585
   726
      ||>> mk_Frees' "r" setRTs
blanchet@49585
   727
      ||>> mk_Frees "r" setRTs
blanchet@49585
   728
      ||>> mk_Frees "s" setRTsBsCs
blanchet@49592
   729
      ||>> mk_Frees' "P" QTs;
blanchet@48975
   730
blanchet@49459
   731
    (*Gr (in R1 .. Rn) (map fst .. fst)^-1 O Gr (in R1 .. Rn) (map snd .. snd)*)
blanchet@49463
   732
    val O_Gr =
blanchet@49459
   733
      let
blanchet@49459
   734
        val map1 = Term.list_comb (mk_bnf_map RTs As', map fst_const RTs);
blanchet@49459
   735
        val map2 = Term.list_comb (mk_bnf_map RTs Bs', map snd_const RTs);
blanchet@49459
   736
        val bnf_in = mk_in (map Free Rs') (map (mk_bnf_t RTs) bnf_sets) CRs';
blanchet@49459
   737
      in
blanchet@49459
   738
        mk_rel_comp (mk_converse (mk_Gr bnf_in map1), mk_Gr bnf_in map2)
blanchet@49459
   739
      end;
blanchet@49459
   740
blanchet@49463
   741
    fun mk_predicate_of_set x_name y_name t =
blanchet@49463
   742
      let
blanchet@49463
   743
        val (T, U) = HOLogic.dest_prodT (HOLogic.dest_setT (fastype_of t));
blanchet@49463
   744
        val x = Free (x_name, T);
blanchet@49463
   745
        val y = Free (y_name, U);
blanchet@49463
   746
      in fold_rev Term.lambda [x, y] (HOLogic.mk_mem (HOLogic.mk_prod (x, y), t)) end;
blanchet@49463
   747
blanchet@49537
   748
    val sQs =
blanchet@49537
   749
      map3 (fn Q => fn T => fn U =>
blanchet@49537
   750
          HOLogic.Collect_const (HOLogic.mk_prodT (T, U)) $ HOLogic.mk_split Q) Qs As' Bs';
blanchet@49537
   751
blanchet@49507
   752
    val rel_rhs = (case raw_rel_opt of
blanchet@49463
   753
        NONE =>
blanchet@49463
   754
        fold_rev absfree Qs' (mk_predicate_of_set (fst x') (fst y')
blanchet@49537
   755
          (Term.list_comb (fold_rev Term.absfree Rs' O_Gr, sQs)))
blanchet@49507
   756
      | SOME raw_rel => prep_term no_defs_lthy raw_rel);
blanchet@49463
   757
blanchet@49507
   758
    val rel_bind_def = (fn () => Binding.suffix_name ("_" ^ relN) b, rel_rhs);
blanchet@49463
   759
blanchet@49507
   760
    val ((bnf_rel_term, raw_rel_def), (lthy, lthy_old)) =
blanchet@49463
   761
      lthy
blanchet@49507
   762
      |> maybe_define (is_some raw_rel_opt) rel_bind_def
blanchet@49463
   763
      ||> `(maybe_restore lthy);
blanchet@49463
   764
blanchet@49463
   765
    val phi = Proof_Context.export_morphism lthy_old lthy;
blanchet@49507
   766
    val bnf_rel_def = Morphism.thm phi raw_rel_def;
blanchet@49507
   767
    val bnf_rel = Morphism.term phi bnf_rel_term;
blanchet@49463
   768
blanchet@49507
   769
    fun mk_bnf_rel QTs CA' CB' = normalize_rel lthy QTs CA' CB' bnf_rel;
blanchet@49463
   770
blanchet@49507
   771
    val rel = mk_bnf_rel QTs CA' CB';
blanchet@49463
   772
blanchet@49506
   773
    val srel_rhs =
blanchet@49463
   774
      fold_rev Term.absfree Rs' (HOLogic.Collect_const CA'CB' $
blanchet@49507
   775
        Term.lambda p (Term.list_comb (rel, map (mk_predicate_of_set (fst x') (fst y')) Rs) $
blanchet@49463
   776
        HOLogic.mk_fst p $ HOLogic.mk_snd p));
blanchet@49459
   777
blanchet@49506
   778
    val srel_bind_def = (fn () => Binding.suffix_name ("_" ^ srelN) b, srel_rhs);
blanchet@49459
   779
blanchet@49506
   780
    val ((bnf_srel_term, raw_srel_def), (lthy, lthy_old)) =
blanchet@49459
   781
      lthy
blanchet@49506
   782
      |> maybe_define false srel_bind_def
blanchet@49459
   783
      ||> `(maybe_restore lthy);
blanchet@49459
   784
blanchet@49459
   785
    val phi = Proof_Context.export_morphism lthy_old lthy;
blanchet@49506
   786
    val bnf_srel_def = Morphism.thm phi raw_srel_def;
blanchet@49506
   787
    val bnf_srel = Morphism.term phi bnf_srel_term;
blanchet@49459
   788
blanchet@49506
   789
    fun mk_bnf_srel setRTs CA' CB' = normalize_srel lthy setRTs CA' CB' bnf_srel;
blanchet@49459
   790
blanchet@49506
   791
    val srel = mk_bnf_srel setRTs CA' CB';
blanchet@49459
   792
blanchet@49460
   793
    val _ = case no_reflexive (raw_map_def :: raw_set_defs @ [raw_bd_def] @
blanchet@49507
   794
        raw_wit_defs @ [raw_rel_def, raw_srel_def]) of
blanchet@49459
   795
        [] => ()
blanchet@49459
   796
      | defs => Proof_Display.print_consts true lthy_old (K false)
blanchet@49459
   797
          (map (dest_Free o fst o Logic.dest_equals o prop_of) defs);
blanchet@49459
   798
blanchet@49458
   799
    val map_id_goal =
blanchet@48975
   800
      let
blanchet@49018
   801
        val bnf_map_app_id = Term.list_comb (bnf_map_AsAs, map HOLogic.id_const As');
blanchet@48975
   802
      in
blanchet@48975
   803
        HOLogic.mk_Trueprop
blanchet@48975
   804
          (HOLogic.mk_eq (bnf_map_app_id, HOLogic.id_const CA'))
blanchet@48975
   805
      end;
blanchet@48975
   806
blanchet@49458
   807
    val map_comp_goal =
blanchet@48975
   808
      let
blanchet@49018
   809
        val bnf_map_app_comp = Term.list_comb (bnf_map_AsCs, map2 (curry HOLogic.mk_comp) gs fs);
blanchet@48975
   810
        val comp_bnf_map_app = HOLogic.mk_comp
blanchet@48975
   811
          (Term.list_comb (bnf_map_BsCs, gs),
blanchet@48975
   812
           Term.list_comb (bnf_map_AsBs, fs));
blanchet@48975
   813
      in
blanchet@49123
   814
        fold_rev Logic.all (fs @ gs) (mk_Trueprop_eq (bnf_map_app_comp, comp_bnf_map_app))
blanchet@48975
   815
      end;
blanchet@48975
   816
blanchet@49458
   817
    val map_cong_goal =
blanchet@48975
   818
      let
blanchet@48975
   819
        fun mk_prem z set f f_copy =
blanchet@48975
   820
          Logic.all z (Logic.mk_implies
blanchet@48975
   821
            (HOLogic.mk_Trueprop (HOLogic.mk_mem (z, set $ x)),
blanchet@49123
   822
            mk_Trueprop_eq (f $ z, f_copy $ z)));
blanchet@48975
   823
        val prems = map4 mk_prem zs bnf_sets_As fs fs_copy;
blanchet@48975
   824
        val eq = HOLogic.mk_eq (Term.list_comb (bnf_map_AsBs, fs) $ x,
blanchet@48975
   825
          Term.list_comb (bnf_map_AsBs, fs_copy) $ x);
blanchet@48975
   826
      in
blanchet@48975
   827
        fold_rev Logic.all (x :: fs @ fs_copy)
blanchet@48975
   828
          (Logic.list_implies (prems, HOLogic.mk_Trueprop eq))
blanchet@48975
   829
      end;
blanchet@48975
   830
blanchet@49458
   831
    val set_naturals_goal =
blanchet@48975
   832
      let
blanchet@48975
   833
        fun mk_goal setA setB f =
blanchet@48975
   834
          let
blanchet@48975
   835
            val set_comp_map =
blanchet@48975
   836
              HOLogic.mk_comp (setB, Term.list_comb (bnf_map_AsBs, fs));
blanchet@48975
   837
            val image_comp_set = HOLogic.mk_comp (mk_image f, setA);
blanchet@48975
   838
          in
blanchet@49123
   839
            fold_rev Logic.all fs (mk_Trueprop_eq (set_comp_map, image_comp_set))
blanchet@48975
   840
          end;
blanchet@48975
   841
      in
blanchet@48975
   842
        map3 mk_goal bnf_sets_As bnf_sets_Bs fs
blanchet@48975
   843
      end;
blanchet@48975
   844
blanchet@49458
   845
    val card_order_bd_goal = HOLogic.mk_Trueprop (mk_card_order bnf_bd_As);
blanchet@48975
   846
blanchet@49458
   847
    val cinfinite_bd_goal = HOLogic.mk_Trueprop (mk_cinfinite bnf_bd_As);
blanchet@48975
   848
blanchet@49458
   849
    val set_bds_goal =
blanchet@48975
   850
      let
blanchet@48975
   851
        fun mk_goal set =
blanchet@48975
   852
          Logic.all x (HOLogic.mk_Trueprop (mk_ordLeq (mk_card_of (set $ x)) bnf_bd_As));
blanchet@48975
   853
      in
blanchet@48975
   854
        map mk_goal bnf_sets_As
blanchet@48975
   855
      end;
blanchet@48975
   856
blanchet@49458
   857
    val in_bd_goal =
blanchet@48975
   858
      let
blanchet@48975
   859
        val bd = mk_cexp
blanchet@48975
   860
          (if live = 0 then ctwo
blanchet@48975
   861
            else mk_csum (Library.foldr1 (uncurry mk_csum) (map mk_card_of As)) ctwo)
blanchet@48975
   862
          bnf_bd_As;
blanchet@48975
   863
      in
blanchet@48975
   864
        fold_rev Logic.all As
blanchet@48975
   865
          (HOLogic.mk_Trueprop (mk_ordLeq (mk_card_of (mk_in As bnf_sets_As CA')) bd))
blanchet@48975
   866
      end;
blanchet@48975
   867
blanchet@49458
   868
    val map_wpull_goal =
blanchet@48975
   869
      let
blanchet@48975
   870
        val prems = map HOLogic.mk_Trueprop
blanchet@48975
   871
          (map8 mk_wpull Xs B1s B2s f1s f2s (replicate live NONE) p1s p2s);
blanchet@48975
   872
        val CX = mk_bnf_T domTs CA;
blanchet@48975
   873
        val CB1 = mk_bnf_T B1Ts CA;
blanchet@48975
   874
        val CB2 = mk_bnf_T B2Ts CA;
blanchet@48975
   875
        val bnf_sets_CX = map2 (normalize_set (map (mk_bnf_T domTs) CA_params)) domTs bnf_sets;
blanchet@48975
   876
        val bnf_sets_CB1 = map2 (normalize_set (map (mk_bnf_T B1Ts) CA_params)) B1Ts bnf_sets;
blanchet@48975
   877
        val bnf_sets_CB2 = map2 (normalize_set (map (mk_bnf_T B2Ts) CA_params)) B2Ts bnf_sets;
blanchet@48975
   878
        val bnf_map_app_f1 = Term.list_comb (mk_bnf_map B1Ts ranTs, f1s);
blanchet@48975
   879
        val bnf_map_app_f2 = Term.list_comb (mk_bnf_map B2Ts ranTs, f2s);
blanchet@48975
   880
        val bnf_map_app_p1 = Term.list_comb (mk_bnf_map domTs B1Ts, p1s);
blanchet@48975
   881
        val bnf_map_app_p2 = Term.list_comb (mk_bnf_map domTs B2Ts, p2s);
blanchet@48975
   882
blanchet@48975
   883
        val map_wpull = mk_wpull (mk_in Xs bnf_sets_CX CX)
blanchet@48975
   884
          (mk_in B1s bnf_sets_CB1 CB1) (mk_in B2s bnf_sets_CB2 CB2)
blanchet@48975
   885
          bnf_map_app_f1 bnf_map_app_f2 NONE bnf_map_app_p1 bnf_map_app_p2;
blanchet@48975
   886
      in
blanchet@48975
   887
        fold_rev Logic.all (Xs @ B1s @ B2s @ f1s @ f2s @ p1s @ p2s)
blanchet@48975
   888
          (Logic.list_implies (prems, HOLogic.mk_Trueprop map_wpull))
blanchet@48975
   889
      end;
blanchet@48975
   890
blanchet@49506
   891
    val srel_O_Gr_goal = fold_rev Logic.all Rs (mk_Trueprop_eq (Term.list_comb (srel, Rs), O_Gr));
blanchet@49453
   892
blanchet@49460
   893
    val goals = zip_axioms map_id_goal map_comp_goal map_cong_goal set_naturals_goal
blanchet@49506
   894
      card_order_bd_goal cinfinite_bd_goal set_bds_goal in_bd_goal map_wpull_goal srel_O_Gr_goal;
blanchet@48975
   895
blanchet@48975
   896
    fun mk_wit_goals (I, wit) =
blanchet@48975
   897
      let
blanchet@48975
   898
        val xs = map (nth bs) I;
blanchet@48975
   899
        fun wit_goal i =
blanchet@48975
   900
          let
blanchet@48975
   901
            val z = nth zs i;
blanchet@48975
   902
            val set_wit = nth bnf_sets_As i $ Term.list_comb (wit, xs);
blanchet@48975
   903
            val concl = HOLogic.mk_Trueprop
blanchet@48975
   904
              (if member (op =) I i then HOLogic.mk_eq (z, nth bs i)
blanchet@48975
   905
              else @{term False});
blanchet@48975
   906
          in
blanchet@48975
   907
            fold_rev Logic.all (z :: xs)
blanchet@48975
   908
              (Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (z, set_wit)), concl))
blanchet@48975
   909
          end;
blanchet@48975
   910
      in
blanchet@48975
   911
        map wit_goal (0 upto live - 1)
blanchet@48975
   912
      end;
blanchet@48975
   913
blanchet@48975
   914
    val wit_goalss = map mk_wit_goals bnf_wit_As;
blanchet@48975
   915
blanchet@48975
   916
    fun after_qed thms lthy =
blanchet@48975
   917
      let
blanchet@48975
   918
        val (axioms, wit_thms) = apfst (mk_axioms live) (chop (length goals) thms);
blanchet@48975
   919
traytel@49109
   920
        val bd_Card_order = #bd_card_order axioms RS @{thm conjunct2[OF card_order_on_Card_order]};
blanchet@48975
   921
        val bd_Cinfinite = @{thm conjI} OF [#bd_cinfinite axioms, bd_Card_order];
blanchet@48975
   922
        val bd_Cnotzero = bd_Cinfinite RS @{thm Cinfinite_Cnotzero};
blanchet@48975
   923
blanchet@48975
   924
        fun mk_collect_set_natural () =
blanchet@48975
   925
          let
blanchet@48975
   926
            val defT = mk_bnf_T Ts CA --> HOLogic.mk_setT T;
blanchet@48975
   927
            val collect_map = HOLogic.mk_comp
blanchet@48975
   928
              (mk_collect (map (mk_bnf_t Ts) bnf_sets) defT,
blanchet@48975
   929
              Term.list_comb (mk_bnf_map As' Ts, hs));
blanchet@48975
   930
            val image_collect = mk_collect
blanchet@48975
   931
              (map2 (fn h => fn set => HOLogic.mk_comp (mk_image h, set)) hs bnf_sets_As)
blanchet@48975
   932
              defT;
blanchet@48975
   933
            (*collect {set1 ... setm} o map f1 ... fm = collect {f1` o set1 ... fm` o setm}*)
blanchet@49123
   934
            val goal = fold_rev Logic.all hs (mk_Trueprop_eq (collect_map, image_collect));
blanchet@48975
   935
          in
wenzelm@51551
   936
            Goal.prove_sorry lthy [] [] goal (K (mk_collect_set_natural_tac (#set_natural axioms)))
traytel@49109
   937
            |> Thm.close_derivation
blanchet@48975
   938
          end;
blanchet@48975
   939
blanchet@49538
   940
        val collect_set_natural = Lazy.lazy mk_collect_set_natural;
blanchet@48975
   941
blanchet@48975
   942
        fun mk_in_mono () =
blanchet@48975
   943
          let
blanchet@48975
   944
            val prems_mono = map2 (HOLogic.mk_Trueprop oo mk_subset) As As_copy;
blanchet@49458
   945
            val in_mono_goal =
blanchet@48975
   946
              fold_rev Logic.all (As @ As_copy)
blanchet@48975
   947
                (Logic.list_implies (prems_mono, HOLogic.mk_Trueprop
blanchet@48975
   948
                  (mk_subset (mk_in As bnf_sets_As CA') (mk_in As_copy bnf_sets_As CA'))));
blanchet@48975
   949
          in
wenzelm@51551
   950
            Goal.prove_sorry lthy [] [] in_mono_goal (K (mk_in_mono_tac live))
traytel@49109
   951
            |> Thm.close_derivation
blanchet@48975
   952
          end;
blanchet@48975
   953
blanchet@49538
   954
        val in_mono = Lazy.lazy mk_in_mono;
blanchet@48975
   955
blanchet@48975
   956
        fun mk_in_cong () =
blanchet@48975
   957
          let
blanchet@48975
   958
            val prems_cong = map2 (HOLogic.mk_Trueprop oo curry HOLogic.mk_eq) As As_copy;
blanchet@49458
   959
            val in_cong_goal =
blanchet@48975
   960
              fold_rev Logic.all (As @ As_copy)
blanchet@48975
   961
                (Logic.list_implies (prems_cong, HOLogic.mk_Trueprop
blanchet@48975
   962
                  (HOLogic.mk_eq (mk_in As bnf_sets_As CA', mk_in As_copy bnf_sets_As CA'))));
blanchet@48975
   963
          in
wenzelm@51551
   964
            Goal.prove_sorry lthy [] [] in_cong_goal (K ((TRY o hyp_subst_tac THEN' rtac refl) 1))
traytel@49109
   965
            |> Thm.close_derivation
blanchet@48975
   966
          end;
blanchet@48975
   967
blanchet@49538
   968
        val in_cong = Lazy.lazy mk_in_cong;
blanchet@48975
   969
blanchet@49538
   970
        val map_id' = Lazy.lazy (fn () => mk_id' (#map_id axioms));
blanchet@49538
   971
        val map_comp' = Lazy.lazy (fn () => mk_comp' (#map_comp axioms));
blanchet@48975
   972
blanchet@48975
   973
        val set_natural' =
blanchet@49538
   974
          map (fn thm => Lazy.lazy (fn () => mk_set_natural' thm)) (#set_natural axioms);
blanchet@48975
   975
blanchet@48975
   976
        fun mk_map_wppull () =
blanchet@48975
   977
          let
blanchet@48975
   978
            val prems = if live = 0 then [] else
blanchet@48975
   979
              [HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@48975
   980
                (map8 mk_wpull Xs B1s B2s f1s f2s (map SOME (e1s ~~ e2s)) p1s p2s))];
blanchet@48975
   981
            val CX = mk_bnf_T domTs CA;
blanchet@48975
   982
            val CB1 = mk_bnf_T B1Ts CA;
blanchet@48975
   983
            val CB2 = mk_bnf_T B2Ts CA;
blanchet@48975
   984
            val bnf_sets_CX =
blanchet@48975
   985
              map2 (normalize_set (map (mk_bnf_T domTs) CA_params)) domTs bnf_sets;
blanchet@48975
   986
            val bnf_sets_CB1 =
blanchet@48975
   987
              map2 (normalize_set (map (mk_bnf_T B1Ts) CA_params)) B1Ts bnf_sets;
blanchet@48975
   988
            val bnf_sets_CB2 =
blanchet@48975
   989
              map2 (normalize_set (map (mk_bnf_T B2Ts) CA_params)) B2Ts bnf_sets;
blanchet@48975
   990
            val bnf_map_app_f1 = Term.list_comb (mk_bnf_map B1Ts ranTs, f1s);
blanchet@48975
   991
            val bnf_map_app_f2 = Term.list_comb (mk_bnf_map B2Ts ranTs, f2s);
blanchet@48975
   992
            val bnf_map_app_e1 = Term.list_comb (mk_bnf_map B1Ts ranTs', e1s);
blanchet@48975
   993
            val bnf_map_app_e2 = Term.list_comb (mk_bnf_map B2Ts ranTs'', e2s);
blanchet@48975
   994
            val bnf_map_app_p1 = Term.list_comb (mk_bnf_map domTs B1Ts, p1s);
blanchet@48975
   995
            val bnf_map_app_p2 = Term.list_comb (mk_bnf_map domTs B2Ts, p2s);
blanchet@48975
   996
blanchet@48975
   997
            val concl = mk_wpull (mk_in Xs bnf_sets_CX CX)
blanchet@48975
   998
              (mk_in B1s bnf_sets_CB1 CB1) (mk_in B2s bnf_sets_CB2 CB2)
blanchet@48975
   999
              bnf_map_app_f1 bnf_map_app_f2 (SOME (bnf_map_app_e1, bnf_map_app_e2))
blanchet@48975
  1000
              bnf_map_app_p1 bnf_map_app_p2;
blanchet@48975
  1001
blanchet@48975
  1002
            val goal =
blanchet@48975
  1003
              fold_rev Logic.all (Xs @ B1s @ B2s @ f1s @ f2s @ e1s @ e2s @ p1s @ p2s)
blanchet@48975
  1004
                (Logic.list_implies (prems, HOLogic.mk_Trueprop concl))
blanchet@48975
  1005
          in
wenzelm@51551
  1006
            Goal.prove_sorry lthy [] [] goal
blanchet@48975
  1007
              (fn _ => mk_map_wppull_tac (#map_id axioms) (#map_cong axioms)
blanchet@48975
  1008
                (#map_wpull axioms) (Lazy.force map_comp') (map Lazy.force set_natural'))
traytel@49109
  1009
            |> Thm.close_derivation
blanchet@48975
  1010
          end;
blanchet@48975
  1011
blanchet@49506
  1012
        val srel_O_Grs = no_refl [#srel_O_Gr axioms];
blanchet@49453
  1013
blanchet@49538
  1014
        val map_wppull = Lazy.lazy mk_map_wppull;
blanchet@48975
  1015
blanchet@49506
  1016
        fun mk_srel_Gr () =
blanchet@48975
  1017
          let
blanchet@49506
  1018
            val lhs = Term.list_comb (srel, map2 mk_Gr As fs);
blanchet@48975
  1019
            val rhs = mk_Gr (mk_in As bnf_sets_As CA') (Term.list_comb (bnf_map_AsBs, fs));
blanchet@49123
  1020
            val goal = fold_rev Logic.all (As @ fs) (mk_Trueprop_eq (lhs, rhs));
blanchet@48975
  1021
          in
wenzelm@51551
  1022
            Goal.prove_sorry lthy [] [] goal
blanchet@49506
  1023
              (mk_srel_Gr_tac srel_O_Grs (#map_id axioms) (#map_cong axioms) (Lazy.force map_id')
blanchet@48975
  1024
                (Lazy.force map_comp') (map Lazy.force set_natural'))
traytel@49109
  1025
            |> Thm.close_derivation
blanchet@48975
  1026
          end;
blanchet@48975
  1027
blanchet@49538
  1028
        val srel_Gr = Lazy.lazy mk_srel_Gr;
blanchet@48975
  1029
blanchet@49506
  1030
        fun mk_srel_prems f = map2 (HOLogic.mk_Trueprop oo f) Rs Rs_copy
blanchet@49506
  1031
        fun mk_srel_concl f = HOLogic.mk_Trueprop
blanchet@49506
  1032
          (f (Term.list_comb (srel, Rs), Term.list_comb (srel, Rs_copy)));
blanchet@48975
  1033
blanchet@49506
  1034
        fun mk_srel_mono () =
blanchet@48975
  1035
          let
blanchet@49506
  1036
            val mono_prems = mk_srel_prems mk_subset;
blanchet@49506
  1037
            val mono_concl = mk_srel_concl (uncurry mk_subset);
blanchet@48975
  1038
          in
wenzelm@51551
  1039
            Goal.prove_sorry lthy [] []
blanchet@48975
  1040
              (fold_rev Logic.all (Rs @ Rs_copy) (Logic.list_implies (mono_prems, mono_concl)))
blanchet@49506
  1041
              (mk_srel_mono_tac srel_O_Grs (Lazy.force in_mono))
traytel@49109
  1042
            |> Thm.close_derivation
blanchet@48975
  1043
          end;
blanchet@48975
  1044
blanchet@49506
  1045
        fun mk_srel_cong () =
blanchet@48975
  1046
          let
blanchet@49506
  1047
            val cong_prems = mk_srel_prems (curry HOLogic.mk_eq);
blanchet@49506
  1048
            val cong_concl = mk_srel_concl HOLogic.mk_eq;
blanchet@48975
  1049
          in
wenzelm@51551
  1050
            Goal.prove_sorry lthy [] []
blanchet@48975
  1051
              (fold_rev Logic.all (Rs @ Rs_copy) (Logic.list_implies (cong_prems, cong_concl)))
blanchet@48975
  1052
              (fn _ => (TRY o hyp_subst_tac THEN' rtac refl) 1)
traytel@49109
  1053
            |> Thm.close_derivation
blanchet@48975
  1054
          end;
blanchet@48975
  1055
blanchet@49538
  1056
        val srel_mono = Lazy.lazy mk_srel_mono;
blanchet@49538
  1057
        val srel_cong = Lazy.lazy mk_srel_cong;
blanchet@48975
  1058
blanchet@49506
  1059
        fun mk_srel_Id () =
blanchet@49515
  1060
          let val srelAsAs = mk_bnf_srel self_setRTs CA' CA' in
wenzelm@51551
  1061
            Goal.prove_sorry lthy [] []
blanchet@48975
  1062
              (HOLogic.mk_Trueprop
blanchet@49515
  1063
                (HOLogic.mk_eq (Term.list_comb (srelAsAs, map Id_const As'), Id_const CA')))
blanchet@49506
  1064
              (mk_srel_Id_tac live (Lazy.force srel_Gr) (#map_id axioms))
traytel@49109
  1065
            |> Thm.close_derivation
blanchet@48975
  1066
          end;
blanchet@48975
  1067
blanchet@49538
  1068
        val srel_Id = Lazy.lazy mk_srel_Id;
blanchet@48975
  1069
blanchet@49506
  1070
        fun mk_srel_converse () =
blanchet@48975
  1071
          let
blanchet@49515
  1072
            val srelBsAs = mk_bnf_srel setRT's CB' CA';
blanchet@49515
  1073
            val lhs = Term.list_comb (srelBsAs, map mk_converse Rs);
blanchet@49506
  1074
            val rhs = mk_converse (Term.list_comb (srel, Rs));
blanchet@48975
  1075
            val le_goal = fold_rev Logic.all Rs (HOLogic.mk_Trueprop (mk_subset lhs rhs));
wenzelm@51551
  1076
            val le_thm = Goal.prove_sorry lthy [] [] le_goal
blanchet@49506
  1077
              (mk_srel_converse_le_tac srel_O_Grs (Lazy.force srel_Id) (#map_cong axioms)
blanchet@48975
  1078
                (Lazy.force map_comp') (map Lazy.force set_natural'))
traytel@49109
  1079
              |> Thm.close_derivation
blanchet@49123
  1080
            val goal = fold_rev Logic.all Rs (mk_Trueprop_eq (lhs, rhs));
blanchet@48975
  1081
          in
wenzelm@51551
  1082
            Goal.prove_sorry lthy [] [] goal (fn _ => mk_srel_converse_tac le_thm)
traytel@49109
  1083
            |> Thm.close_derivation
blanchet@48975
  1084
          end;
blanchet@48975
  1085
blanchet@49538
  1086
        val srel_converse = Lazy.lazy mk_srel_converse;
blanchet@48975
  1087
blanchet@49506
  1088
        fun mk_srel_O () =
blanchet@48975
  1089
          let
blanchet@49515
  1090
            val srelAsCs = mk_bnf_srel setRTsAsCs CA' CC';
blanchet@49515
  1091
            val srelBsCs = mk_bnf_srel setRTsBsCs CB' CC';
blanchet@49515
  1092
            val lhs = Term.list_comb (srelAsCs, map2 (curry mk_rel_comp) Rs Ss);
blanchet@49515
  1093
            val rhs = mk_rel_comp (Term.list_comb (srel, Rs), Term.list_comb (srelBsCs, Ss));
blanchet@49123
  1094
            val goal = fold_rev Logic.all (Rs @ Ss) (mk_Trueprop_eq (lhs, rhs));
blanchet@48975
  1095
          in
wenzelm@51551
  1096
            Goal.prove_sorry lthy [] [] goal
blanchet@49506
  1097
              (mk_srel_O_tac srel_O_Grs (Lazy.force srel_Id) (#map_cong axioms)
blanchet@48975
  1098
                (Lazy.force map_wppull) (Lazy.force map_comp') (map Lazy.force set_natural'))
traytel@49109
  1099
            |> Thm.close_derivation
blanchet@48975
  1100
          end;
blanchet@48975
  1101
blanchet@49538
  1102
        val srel_O = Lazy.lazy mk_srel_O;
blanchet@48975
  1103
blanchet@49506
  1104
        fun mk_in_srel () =
blanchet@48975
  1105
          let
blanchet@48975
  1106
            val bnf_in = mk_in Rs (map (mk_bnf_t RTs) bnf_sets) CRs';
blanchet@48975
  1107
            val map1 = Term.list_comb (mk_bnf_map RTs As', map fst_const RTs);
blanchet@48975
  1108
            val map2 = Term.list_comb (mk_bnf_map RTs Bs', map snd_const RTs);
blanchet@48975
  1109
            val map_fst_eq = HOLogic.mk_eq (map1 $ z, x);
blanchet@48975
  1110
            val map_snd_eq = HOLogic.mk_eq (map2 $ z, y);
blanchet@49506
  1111
            val lhs = HOLogic.mk_mem (HOLogic.mk_prod (x, y), Term.list_comb (srel, Rs));
blanchet@48975
  1112
            val rhs =
blanchet@48975
  1113
              HOLogic.mk_exists (fst z', snd z', HOLogic.mk_conj (HOLogic.mk_mem (z, bnf_in),
blanchet@48975
  1114
                HOLogic.mk_conj (map_fst_eq, map_snd_eq)));
blanchet@48975
  1115
            val goal =
blanchet@49123
  1116
              fold_rev Logic.all (x :: y :: Rs) (mk_Trueprop_eq (lhs, rhs));
blanchet@48975
  1117
          in
wenzelm@51551
  1118
            Goal.prove_sorry lthy [] [] goal (mk_in_srel_tac srel_O_Grs (length bnf_sets))
traytel@49109
  1119
            |> Thm.close_derivation
blanchet@48975
  1120
          end;
blanchet@48975
  1121
blanchet@49538
  1122
        val in_srel = Lazy.lazy mk_in_srel;
blanchet@48975
  1123
blanchet@49537
  1124
        val eqset_imp_iff_pair = @{thm eqset_imp_iff_pair};
blanchet@49591
  1125
        val mem_Collect_etc = @{thms fst_conv mem_Collect_eq prod.cases snd_conv};
blanchet@49591
  1126
        val mem_Collect_etc' = @{thms fst_conv mem_Collect_eq pair_in_Id_conv snd_conv};
blanchet@49537
  1127
blanchet@49594
  1128
        fun mk_rel_srel () =
blanchet@49537
  1129
          unfold_thms lthy mem_Collect_etc
blanchet@49537
  1130
            (funpow live (fn thm => thm RS @{thm fun_cong_pair}) (bnf_srel_def RS meta_eq_to_obj_eq)
blanchet@49537
  1131
               RS eqset_imp_iff_pair RS sym)
blanchet@49537
  1132
          |> Drule.zero_var_indexes;
blanchet@49537
  1133
blanchet@49594
  1134
        val rel_srel = Lazy.lazy mk_rel_srel;
blanchet@49537
  1135
blanchet@49591
  1136
        fun mk_rel_eq () =
blanchet@49591
  1137
          unfold_thms lthy (bnf_srel_def :: mem_Collect_etc')
blanchet@49631
  1138
            (Lazy.force srel_Id RS @{thm arg_cong[of _ _ "%A x y. (x, y) : A"]})
blanchet@49631
  1139
          |> Drule.eta_contraction_rule;
blanchet@49591
  1140
blanchet@49591
  1141
        val rel_eq = Lazy.lazy mk_rel_eq;
blanchet@49591
  1142
blanchet@49537
  1143
        fun mk_rel_flip () =
blanchet@49537
  1144
          let
blanchet@49537
  1145
            val srel_converse_thm = Lazy.force srel_converse;
blanchet@49585
  1146
            val cts = map (SOME o certify lthy) sQs;
blanchet@49585
  1147
            val srel_converse_thm' = cterm_instantiate_pos cts srel_converse_thm;
blanchet@49537
  1148
          in
blanchet@49537
  1149
            unfold_thms lthy (bnf_srel_def :: @{thm converse_iff} :: mem_Collect_etc)
blanchet@49537
  1150
              (srel_converse_thm' RS eqset_imp_iff_pair)
blanchet@49595
  1151
            |> singleton (Proof_Context.export names_lthy pre_names_lthy)
blanchet@49537
  1152
          end;
blanchet@49537
  1153
blanchet@49538
  1154
        val rel_flip = Lazy.lazy mk_rel_flip;
blanchet@49537
  1155
blanchet@49507
  1156
        val defs = mk_defs bnf_map_def bnf_set_defs bnf_rel_def bnf_srel_def;
blanchet@48975
  1157
blanchet@49506
  1158
        val facts = mk_facts bd_Card_order bd_Cinfinite bd_Cnotzero collect_set_natural in_cong
blanchet@49594
  1159
          in_mono in_srel map_comp' map_id' map_wppull rel_eq rel_flip rel_srel set_natural'
blanchet@49591
  1160
          srel_cong srel_mono srel_Id srel_Gr srel_converse srel_O;
blanchet@48975
  1161
blanchet@48975
  1162
        val wits = map2 mk_witness bnf_wits wit_thms;
blanchet@48975
  1163
blanchet@49507
  1164
        val bnf_rel =
blanchet@49507
  1165
          Term.subst_atomic_types ((Ds ~~ deads) @ (As' ~~ alphas) @ (Bs' ~~ betas)) rel;
blanchet@49506
  1166
        val bnf_srel =
blanchet@49506
  1167
          Term.subst_atomic_types ((Ds ~~ deads) @ (As' ~~ alphas) @ (Bs' ~~ betas)) srel;
blanchet@48975
  1168
blanchet@48975
  1169
        val bnf = mk_bnf b CA live alphas betas dead deads bnf_map bnf_sets bnf_bd axioms defs facts
blanchet@49507
  1170
          wits bnf_rel bnf_srel;
blanchet@48975
  1171
      in
blanchet@48975
  1172
        (bnf, lthy
blanchet@49538
  1173
          |> (if fact_policy = Note_All then
blanchet@48975
  1174
                let
blanchet@48975
  1175
                  val witNs = if length wits = 1 then [witN] else map mk_witN (1 upto length wits);
traytel@49109
  1176
                  val notes =
traytel@49109
  1177
                    [(bd_card_orderN, [#bd_card_order axioms]),
traytel@49109
  1178
                    (bd_cinfiniteN, [#bd_cinfinite axioms]),
traytel@49109
  1179
                    (bd_Card_orderN, [#bd_Card_order facts]),
traytel@49109
  1180
                    (bd_CinfiniteN, [#bd_Cinfinite facts]),
traytel@49109
  1181
                    (bd_CnotzeroN, [#bd_Cnotzero facts]),
traytel@49109
  1182
                    (collect_set_naturalN, [Lazy.force (#collect_set_natural facts)]),
traytel@49109
  1183
                    (in_bdN, [#in_bd axioms]),
traytel@49109
  1184
                    (in_monoN, [Lazy.force (#in_mono facts)]),
blanchet@49506
  1185
                    (in_srelN, [Lazy.force (#in_srel facts)]),
traytel@49109
  1186
                    (map_compN, [#map_comp axioms]),
traytel@49109
  1187
                    (map_idN, [#map_id axioms]),
traytel@49109
  1188
                    (map_wpullN, [#map_wpull axioms]),
traytel@49109
  1189
                    (set_naturalN, #set_natural axioms),
traytel@49109
  1190
                    (set_bdN, #set_bd axioms)] @
blanchet@51757
  1191
                    (witNs ~~ wit_thms)
traytel@49109
  1192
                    |> map (fn (thmN, thms) =>
traytel@49109
  1193
                      ((qualify (Binding.qualify true (Binding.name_of b) (Binding.name thmN)), []),
traytel@49109
  1194
                      [(thms, [])]));
blanchet@48975
  1195
                in
traytel@49109
  1196
                  Local_Theory.notes notes #> snd
blanchet@48975
  1197
                end
blanchet@48975
  1198
              else
blanchet@48975
  1199
                I)
blanchet@49538
  1200
          |> (if fact_policy <> Dont_Note then
traytel@49109
  1201
                let
traytel@49109
  1202
                  val notes =
blanchet@49506
  1203
                    [(map_comp'N, [Lazy.force (#map_comp' facts)]),
blanchet@49506
  1204
                    (map_congN, [#map_cong axioms]),
traytel@49109
  1205
                    (map_id'N, [Lazy.force (#map_id' facts)]),
blanchet@49591
  1206
                    (rel_eqN, [Lazy.force (#rel_eq facts)]),
blanchet@49537
  1207
                    (rel_flipN, [Lazy.force (#rel_flip facts)]),
blanchet@49594
  1208
                    (rel_srelN, [Lazy.force (#rel_srel facts)]),
blanchet@49506
  1209
                    (set_natural'N, map Lazy.force (#set_natural' facts)),
blanchet@49506
  1210
                    (srel_O_GrN, srel_O_Grs),
blanchet@49506
  1211
                    (srel_IdN, [Lazy.force (#srel_Id facts)]),
blanchet@49506
  1212
                    (srel_GrN, [Lazy.force (#srel_Gr facts)]),
blanchet@49506
  1213
                    (srel_converseN, [Lazy.force (#srel_converse facts)]),
blanchet@49506
  1214
                    (srel_monoN, [Lazy.force (#srel_mono facts)]),
blanchet@49506
  1215
                    (srel_ON, [Lazy.force (#srel_O facts)])]
blanchet@49460
  1216
                    |> filter_out (null o #2)
traytel@49109
  1217
                    |> map (fn (thmN, thms) =>
traytel@49109
  1218
                      ((qualify (Binding.qualify true (Binding.name_of b) (Binding.name thmN)), []),
traytel@49109
  1219
                      [(thms, [])]));
traytel@49109
  1220
                in
traytel@49109
  1221
                  Local_Theory.notes notes #> snd
traytel@49109
  1222
                end
blanchet@48975
  1223
              else
blanchet@48975
  1224
                I))
blanchet@48975
  1225
      end;
blanchet@49459
  1226
blanchet@49459
  1227
    val one_step_defs =
blanchet@49507
  1228
      no_reflexive (bnf_map_def :: bnf_bd_def :: bnf_set_defs @ bnf_wit_defs @ [bnf_rel_def,
blanchet@49506
  1229
        bnf_srel_def]);
blanchet@48975
  1230
  in
blanchet@49459
  1231
    (key, goals, wit_goalss, after_qed, lthy, one_step_defs)
blanchet@48975
  1232
  end;
blanchet@48975
  1233
traytel@49434
  1234
fun register_bnf key (bnf, lthy) =
traytel@49434
  1235
  (bnf, Local_Theory.declaration {syntax = false, pervasive = true}
traytel@49434
  1236
    (fn phi => Data.map (Symtab.update_new (key, morph_bnf phi bnf))) lthy);
traytel@49434
  1237
blanchet@49456
  1238
(* TODO: Once the invariant "nwits > 0" holds, remove "mk_conjunction_balanced'" and "rtac TrueI"
blanchet@49456
  1239
   below *)
blanchet@49456
  1240
fun mk_conjunction_balanced' [] = @{prop True}
blanchet@49456
  1241
  | mk_conjunction_balanced' ts = Logic.mk_conjunction_balanced ts;
blanchet@49456
  1242
blanchet@49018
  1243
fun bnf_def const_policy fact_policy qualify tacs wit_tac Ds =
blanchet@49463
  1244
  (fn (_, goals, wit_goalss, after_qed, lthy, one_step_defs) =>
blanchet@48975
  1245
  let
blanchet@49456
  1246
    val wits_tac =
blanchet@49456
  1247
      K (TRYALL Goal.conjunction_tac) THEN' K (TRYALL (rtac TrueI)) THEN'
blanchet@49504
  1248
      mk_unfold_thms_then_tac lthy one_step_defs wit_tac;
blanchet@49456
  1249
    val wit_goals = map mk_conjunction_balanced' wit_goalss;
blanchet@48975
  1250
    val wit_thms =
wenzelm@51551
  1251
      Goal.prove_sorry lthy [] [] (mk_conjunction_balanced' wit_goals) wits_tac
blanchet@48975
  1252
      |> Conjunction.elim_balanced (length wit_goals)
blanchet@48975
  1253
      |> map2 (Conjunction.elim_balanced o length) wit_goalss
blanchet@49456
  1254
      |> map (map (Thm.close_derivation o Thm.forall_elim_vars 0));
blanchet@48975
  1255
  in
wenzelm@51551
  1256
    map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])
blanchet@49504
  1257
      goals (map (mk_unfold_thms_then_tac lthy one_step_defs) tacs)
blanchet@48975
  1258
    |> (fn thms => after_qed (map single thms @ wit_thms) lthy)
blanchet@51758
  1259
  end) oooo prepare_def const_policy fact_policy qualify (K I) Ds;
blanchet@48975
  1260
traytel@49434
  1261
val bnf_def_cmd = (fn (key, goals, wit_goals, after_qed, lthy, defs) =>
blanchet@48975
  1262
  Proof.unfolding ([[(defs, [])]])
traytel@49434
  1263
    (Proof.theorem NONE (snd o register_bnf key oo after_qed)
blanchet@48975
  1264
      (map (single o rpair []) goals @ map (map (rpair [])) wit_goals) lthy)) oo
blanchet@51758
  1265
  prepare_def Do_Inline (user_policy Note_Some) I Syntax.read_term NONE Binding.empty [];
blanchet@48975
  1266
blanchet@48975
  1267
fun print_bnfs ctxt =
blanchet@48975
  1268
  let
blanchet@48975
  1269
    fun pretty_set sets i = Pretty.block
blanchet@48975
  1270
      [Pretty.str (mk_setN (i + 1) ^ ":"), Pretty.brk 1,
blanchet@48975
  1271
          Pretty.quote (Syntax.pretty_term ctxt (nth sets i))];
blanchet@48975
  1272
blanchet@48975
  1273
    fun pretty_bnf (key, BNF {T = T, map = map, sets = sets, bd = bd,
blanchet@48975
  1274
      live = live, lives = lives, dead = dead, deads = deads, ...}) =
blanchet@48975
  1275
      Pretty.big_list
blanchet@48975
  1276
        (Pretty.string_of (Pretty.block [Pretty.str key, Pretty.str ":", Pretty.brk 1,
blanchet@48975
  1277
          Pretty.quote (Syntax.pretty_typ ctxt T)]))
blanchet@48975
  1278
        ([Pretty.block [Pretty.str "live:", Pretty.brk 1, Pretty.str (string_of_int live),
blanchet@48975
  1279
            Pretty.brk 3, Pretty.list "[" "]" (List.map (Syntax.pretty_typ ctxt) lives)],
blanchet@48975
  1280
          Pretty.block [Pretty.str "dead:", Pretty.brk 1, Pretty.str (string_of_int dead),
blanchet@48975
  1281
            Pretty.brk 3, Pretty.list "[" "]" (List.map (Syntax.pretty_typ ctxt) deads)],
blanchet@48975
  1282
          Pretty.block [Pretty.str (mapN ^ ":"), Pretty.brk 1,
blanchet@48975
  1283
            Pretty.quote (Syntax.pretty_term ctxt map)]] @
blanchet@48975
  1284
          List.map (pretty_set sets) (0 upto length sets - 1) @
blanchet@48975
  1285
          [Pretty.block [Pretty.str (bdN ^ ":"), Pretty.brk 1,
blanchet@48975
  1286
            Pretty.quote (Syntax.pretty_term ctxt bd)]]);
blanchet@48975
  1287
  in
blanchet@48975
  1288
    Pretty.big_list "BNFs:" (map pretty_bnf (Symtab.dest (Data.get (Context.Proof ctxt))))
blanchet@48975
  1289
    |> Pretty.writeln
blanchet@48975
  1290
  end;
blanchet@48975
  1291
blanchet@48975
  1292
val _ =
blanchet@48975
  1293
  Outer_Syntax.improper_command @{command_spec "print_bnfs"} "print all BNFs"
blanchet@48975
  1294
    (Scan.succeed (Toplevel.keep (print_bnfs o Toplevel.context_of)));
blanchet@48975
  1295
blanchet@48975
  1296
val _ =
blanchet@48975
  1297
  Outer_Syntax.local_theory_to_proof @{command_spec "bnf_def"} "define a BNF for an existing type"
traytel@49434
  1298
    ((parse_opt_binding_colon -- Parse.term --
blanchet@49277
  1299
       (@{keyword "["} |-- Parse.list Parse.term --| @{keyword "]"}) -- Parse.term --
blanchet@49459
  1300
       (@{keyword "["} |-- Parse.list Parse.term --| @{keyword "]"}) -- Scan.option Parse.term)
blanchet@49459
  1301
       >> bnf_def_cmd);
blanchet@48975
  1302
blanchet@48975
  1303
end;