src/HOL/Codatatype/Tools/bnf_util.ML
author blanchet
Tue Sep 11 18:39:47 2012 +0200 (2012-09-11)
changeset 49286 dde4967c9233
parent 49282 c057e1b39f16
child 49298 36e551d3af3b
permissions -rw-r--r--
added "defaults" option
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(*  Title:      HOL/Codatatype/Tools/bnf_util.ML
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    Author:     Dmitriy Traytel, TU Muenchen
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    Copyright   2012
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Library for bounded natural functors.
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*)
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signature BNF_UTIL =
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sig
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  val map3: ('a -> 'b -> 'c -> 'd) -> 'a list -> 'b list -> 'c list -> 'd list
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  val map4: ('a -> 'b -> 'c -> 'd -> 'e) -> 'a list -> 'b list -> 'c list -> 'd list -> 'e list
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  val map5: ('a -> 'b -> 'c -> 'd -> 'e -> 'f) ->
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    'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list
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  val map6: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g) ->
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    'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list
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  val map7: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h) ->
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    'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list -> 'h list
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  val map8: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h -> 'i) ->
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    'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list -> 'h list -> 'i list
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  val map9: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h -> 'i -> 'j) ->
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    'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list -> 'h list ->
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    'i list -> 'j list
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  val map10: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h -> 'i -> 'j -> 'k) ->
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    'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list -> 'h list ->
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    'i list -> 'j list -> 'k list
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  val map11: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h -> 'i -> 'j -> 'k -> 'l) ->
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    'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list -> 'h list ->
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    'i list -> 'j list -> 'k list -> 'l list
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  val map12: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h -> 'i -> 'j -> 'k -> 'l -> 'm) ->
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    'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list -> 'h list ->
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    'i list -> 'j list -> 'k list -> 'l list -> 'm list
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  val fold_map2: ('a -> 'b -> 'c -> 'd * 'c) -> 'a list -> 'b list -> 'c -> 'd list * 'c
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  val fold_map3: ('a -> 'b -> 'c -> 'd -> 'e * 'd) ->
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    'a list -> 'b list -> 'c list -> 'd -> 'e list * 'd
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  val fold_map4: ('a -> 'b -> 'c -> 'd -> 'e -> 'f * 'e) ->
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    'a list -> 'b list -> 'c list -> 'd list -> 'e -> 'f list * 'e
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  val fold_map5: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g * 'f) ->
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    'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f -> 'g list * 'f
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  val fold_map6: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h * 'g) ->
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    'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g -> 'h list * 'g
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  val fold_map7: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h -> 'i * 'h) ->
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    'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list -> 'h -> 'i list * 'h
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  val interleave: 'a list -> 'a list -> 'a list
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  val transpose: 'a list list -> 'a list list
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  val seq_conds: (bool -> 'a -> 'b) -> int -> int -> 'a list -> 'b list
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  val mk_fresh_names: Proof.context -> int -> string -> string list * Proof.context
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  val mk_TFrees: int -> Proof.context -> typ list * Proof.context
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  val mk_TFreess: int list -> Proof.context -> typ list list * Proof.context
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  val mk_Frees: string -> typ list -> Proof.context -> term list * Proof.context
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  val mk_Freess: string -> typ list list -> Proof.context -> term list list * Proof.context
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  val mk_Freesss: string -> typ list list list -> Proof.context ->
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    term list list list * Proof.context
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  val mk_Freessss: string -> typ list list list list -> Proof.context ->
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    term list list list list * Proof.context
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  val mk_Frees': string -> typ list -> Proof.context ->
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    (term list * (string * typ) list) * Proof.context
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  val mk_Freess': string -> typ list list -> Proof.context ->
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    (term list list * (string * typ) list list) * Proof.context
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  val mk_optionT: typ -> typ
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  val mk_relT: typ * typ -> typ
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  val dest_relT: typ -> typ * typ
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  val mk_sumT: typ * typ -> typ
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  val ctwo: term
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  val fst_const: typ -> term
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  val snd_const: typ -> term
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  val Id_const: typ -> term
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  val mk_Ball: term -> term -> term
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  val mk_Bex: term -> term -> term
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  val mk_Card_order: term -> term
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  val mk_Field: term -> term
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  val mk_Gr: term -> term -> term
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  val mk_IfN: typ -> term list -> term list -> term
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  val mk_Trueprop_eq: term * term -> term
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  val mk_UNION: term -> term -> term
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  val mk_Union: typ -> term
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  val mk_card_binop: string -> (typ * typ -> typ) -> term -> term -> term
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  val mk_card_of: term -> term
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  val mk_card_order: term -> term
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  val mk_ccexp: term -> term -> term
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  val mk_cexp: term -> term -> term
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  val mk_cinfinite: term -> term
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  val mk_collect: term list -> typ -> term
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  val mk_converse: term -> term
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  val mk_cprod: term -> term -> term
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  val mk_csum: term -> term -> term
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  val mk_dir_image: term -> term -> term
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  val mk_image: term -> term
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  val mk_in: term list -> term list -> typ -> term
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  val mk_ordLeq: term -> term -> term
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  val mk_rel_comp: term * term -> term
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  val mk_subset: term -> term -> term
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  val mk_wpull: term -> term -> term -> term -> term -> (term * term) option -> term -> term -> term
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  val list_all_free: term list -> term -> term
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  val list_exists_free: term list -> term -> term
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  (*parameterized terms*)
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  val mk_nthN: int -> term -> int -> term
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  (*parameterized thms*)
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  val mk_Un_upper: int -> int -> thm
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  val mk_conjIN: int -> thm
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  val mk_conjunctN: int -> int -> thm
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  val mk_disjIN: int -> int -> thm
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  val mk_nthI: int -> int -> thm
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  val mk_nth_conv: int -> int -> thm
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  val mk_ordLeq_csum: int -> int -> thm -> thm
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  val mk_UnN: int -> int -> thm
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  val ctrans: thm
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  val o_apply: thm
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  val mk_sym: thm -> thm
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  val mk_trans: thm -> thm -> thm
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  val mk_unabs_def: int -> thm -> thm
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  val mk_permute: ''a list -> ''a list -> 'b list -> 'b list
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  val find_indices: ''a list -> ''a list -> int list
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  val certifyT: Proof.context -> typ -> ctyp
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  val certify: Proof.context -> term -> cterm
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  val typedef: bool -> binding option -> binding * (string * sort) list * mixfix -> term ->
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    (binding * binding) option -> tactic -> local_theory -> (string * Typedef.info) * local_theory
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  val WRAP: ('a -> tactic) -> ('a -> tactic) -> 'a list -> tactic -> tactic
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  val WRAP': ('a -> int -> tactic) -> ('a -> int -> tactic) -> 'a list -> (int -> tactic) -> int ->
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    tactic
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  val CONJ_WRAP_GEN: tactic -> ('a -> tactic) -> 'a list -> tactic
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  val CONJ_WRAP_GEN': (int -> tactic) -> ('a -> int -> tactic) -> 'a list -> int -> tactic
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  val CONJ_WRAP: ('a -> tactic) -> 'a list -> tactic
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  val CONJ_WRAP': ('a -> int -> tactic) -> 'a list -> int -> tactic
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end;
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structure BNF_Util : BNF_UTIL =
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struct
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(* Library proper *)
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fun map3 _ [] [] [] = []
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  | map3 f (x1::x1s) (x2::x2s) (x3::x3s) = f x1 x2 x3 :: map3 f x1s x2s x3s
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  | map3 _ _ _ _ = raise ListPair.UnequalLengths;
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fun map4 _ [] [] [] [] = []
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  | map4 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) = f x1 x2 x3 x4 :: map4 f x1s x2s x3s x4s
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  | map4 _ _ _ _ _ = raise ListPair.UnequalLengths;
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fun map5 _ [] [] [] [] [] = []
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  | map5 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s) =
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    f x1 x2 x3 x4 x5 :: map5 f x1s x2s x3s x4s x5s
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  | map5 _ _ _ _ _ _ = raise ListPair.UnequalLengths;
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fun map6 _ [] [] [] [] [] [] = []
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  | map6 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s) (x6::x6s) =
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    f x1 x2 x3 x4 x5 x6 :: map6 f x1s x2s x3s x4s x5s x6s
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  | map6 _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
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fun map7 _ [] [] [] [] [] [] [] = []
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  | map7 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s) (x6::x6s) (x7::x7s) =
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    f x1 x2 x3 x4 x5 x6 x7 :: map7 f x1s x2s x3s x4s x5s x6s x7s
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  | map7 _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
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fun map8 _ [] [] [] [] [] [] [] [] = []
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  | map8 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s) (x6::x6s) (x7::x7s) (x8::x8s) =
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    f x1 x2 x3 x4 x5 x6 x7 x8 :: map8 f x1s x2s x3s x4s x5s x6s x7s x8s
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  | map8 _ _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
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fun map9 _ [] [] [] [] [] [] [] [] [] = []
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  | map9 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s)
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      (x6::x6s) (x7::x7s) (x8::x8s) (x9::x9s) =
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    f x1 x2 x3 x4 x5 x6 x7 x8 x9 :: map9 f x1s x2s x3s x4s x5s x6s x7s x8s x9s
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  | map9 _ _ _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
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fun map10 _ [] [] [] [] [] [] [] [] [] [] = []
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  | map10 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s)
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      (x6::x6s) (x7::x7s) (x8::x8s) (x9::x9s) (x10::x10s) =
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    f x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 :: map10 f x1s x2s x3s x4s x5s x6s x7s x8s x9s x10s
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  | map10 _ _ _ _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
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fun map11 _ [] [] [] [] [] [] [] [] [] [] [] = []
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  | map11 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s)
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      (x6::x6s) (x7::x7s) (x8::x8s) (x9::x9s) (x10::x10s) (x11::x11s) =
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    f x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 :: map11 f x1s x2s x3s x4s x5s x6s x7s x8s x9s x10s x11s
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  | map11 _ _ _ _ _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
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fun map12 _ [] [] [] [] [] [] [] [] [] [] [] [] = []
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  | map12 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s)
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      (x6::x6s) (x7::x7s) (x8::x8s) (x9::x9s) (x10::x10s) (x11::x11s) (x12::x12s) =
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    f x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 ::
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      map12 f x1s x2s x3s x4s x5s x6s x7s x8s x9s x10s x11s x12s
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  | map12 _ _ _ _ _ _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
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fun fold_map2 _ [] [] acc = ([], acc)
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  | fold_map2 f (x1::x1s) (x2::x2s) acc =
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    let
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      val (x, acc') = f x1 x2 acc;
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      val (xs, acc'') = fold_map2 f x1s x2s acc';
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    in (x :: xs, acc'') end
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  | fold_map2 _ _ _ _ = raise ListPair.UnequalLengths;
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fun fold_map3 _ [] [] [] acc = ([], acc)
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  | fold_map3 f (x1::x1s) (x2::x2s) (x3::x3s) acc =
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    let
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      val (x, acc') = f x1 x2 x3 acc;
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      val (xs, acc'') = fold_map3 f x1s x2s x3s acc';
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    in (x :: xs, acc'') end
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  | fold_map3 _ _ _ _ _ = raise ListPair.UnequalLengths;
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fun fold_map4 _ [] [] [] [] acc = ([], acc)
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  | fold_map4 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) acc =
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    let
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      val (x, acc') = f x1 x2 x3 x4 acc;
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      val (xs, acc'') = fold_map4 f x1s x2s x3s x4s acc';
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    in (x :: xs, acc'') end
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  | fold_map4 _ _ _ _ _ _ = raise ListPair.UnequalLengths;
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fun fold_map5 _ [] [] [] [] [] acc = ([], acc)
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  | fold_map5 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s) acc =
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    let
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      val (x, acc') = f x1 x2 x3 x4 x5 acc;
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      val (xs, acc'') = fold_map5 f x1s x2s x3s x4s x5s acc';
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    in (x :: xs, acc'') end
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  | fold_map5 _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
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fun fold_map6 _ [] [] [] [] [] [] acc = ([], acc)
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  | fold_map6 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s) (x6::x6s) acc =
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    let
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      val (x, acc') = f x1 x2 x3 x4 x5 x6 acc;
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      val (xs, acc'') = fold_map6 f x1s x2s x3s x4s x5s x6s acc';
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    in (x :: xs, acc'') end
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  | fold_map6 _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
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fun fold_map7 _ [] [] [] [] [] [] [] acc = ([], acc)
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  | fold_map7 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s) (x6::x6s) (x7::x7s) acc =
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    let
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      val (x, acc') = f x1 x2 x3 x4 x5 x6 x7 acc;
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      val (xs, acc'') = fold_map7 f x1s x2s x3s x4s x5s x6s x7s acc';
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    in (x :: xs, acc'') end
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  | fold_map7 _ _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
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(*stolen from ~~/src/HOL/Tools/SMT/smt_utils.ML*)
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fun certify ctxt = Thm.cterm_of (Proof_Context.theory_of ctxt);
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fun certifyT ctxt = Thm.ctyp_of (Proof_Context.theory_of ctxt);
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(*TODO: is this really different from Typedef.add_typedef_global?*)
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fun typedef def opt_name typ set opt_morphs tac lthy =
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   250
  let
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   251
    val ((name, info), (lthy, lthy_old)) =
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   252
      lthy
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   253
      |> Typedef.add_typedef def opt_name typ set opt_morphs tac
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   254
      ||> `Local_Theory.restore;
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   255
    val phi = Proof_Context.export_morphism lthy_old lthy;
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   256
  in
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   257
    ((name, Typedef.transform_info phi info), lthy)
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   258
  end;
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   259
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   260
(*Tactical WRAP surrounds a static given tactic (core) with two deterministic chains of tactics*)
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fun WRAP gen_before gen_after xs core_tac =
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   262
  fold_rev (fn x => fn tac => gen_before x THEN tac THEN gen_after x) xs core_tac;
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   263
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   264
fun WRAP' gen_before gen_after xs core_tac =
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   265
  fold_rev (fn x => fn tac => gen_before x THEN' tac THEN' gen_after x) xs core_tac;
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   266
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   267
fun CONJ_WRAP_GEN conj_tac gen_tac xs =
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   268
  let val (butlast, last) = split_last xs;
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   269
  in WRAP (fn thm => conj_tac THEN gen_tac thm) (K all_tac) butlast (gen_tac last) end;
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   270
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   271
fun CONJ_WRAP_GEN' conj_tac gen_tac xs =
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  let val (butlast, last) = split_last xs;
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   273
  in WRAP' (fn thm => conj_tac THEN' gen_tac thm) (K (K all_tac)) butlast (gen_tac last) end;
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   274
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   275
(*not eta-converted because of monotype restriction*)
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fun CONJ_WRAP gen_tac = CONJ_WRAP_GEN (rtac conjI 1) gen_tac;
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fun CONJ_WRAP' gen_tac = CONJ_WRAP_GEN' (rtac conjI) gen_tac;
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   278
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   279
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   280
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   281
(* Term construction *)
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   282
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   283
(** Fresh variables **)
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   284
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   285
fun mk_TFrees n = apfst (map TFree) o Variable.invent_types (replicate n (HOLogic.typeS));
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fun mk_TFreess ns = apfst (map (map TFree)) o
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   287
  fold_map Variable.invent_types (map (fn n => replicate n (HOLogic.typeS)) ns);
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   288
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   289
fun mk_names n x = if n = 1 then [x] else map (fn i => x ^ string_of_int i) (1 upto n);
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   290
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   291
fun mk_fresh_names ctxt = (fn xs => Variable.variant_fixes xs ctxt) oo mk_names;
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   292
fun mk_Frees x Ts ctxt = mk_fresh_names ctxt (length Ts) x |>> (fn xs => map2 (curry Free) xs Ts);
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   293
fun mk_Freess x Tss = fold_map2 mk_Frees (mk_names (length Tss) x) Tss;
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   294
fun mk_Freesss x Tsss = fold_map2 mk_Freess (mk_names (length Tsss) x) Tsss;
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   295
fun mk_Freessss x Tssss = fold_map2 mk_Freesss (mk_names (length Tssss) x) Tssss;
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   296
fun mk_Frees' x Ts ctxt = mk_fresh_names ctxt (length Ts) x |>> (fn xs => `(map Free) (xs ~~ Ts));
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   297
fun mk_Freess' x Tss = fold_map2 mk_Frees' (mk_names (length Tss) x) Tss #>> split_list;
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   298
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   299
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   300
(** Types **)
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   301
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   302
fun mk_optionT T = Type (@{type_name option}, [T]);
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   303
val mk_relT = HOLogic.mk_setT o HOLogic.mk_prodT;
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   304
val dest_relT = HOLogic.dest_prodT o HOLogic.dest_setT;
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   305
fun mk_sumT (LT, RT) = Type (@{type_name Sum_Type.sum}, [LT, RT]);
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fun mk_partial_funT (ranT, domT) = domT --> mk_optionT ranT;
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   307
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   308
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   309
(** Constants **)
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   310
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   311
fun fst_const T = Const (@{const_name fst}, T --> fst (HOLogic.dest_prodT T));
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   312
fun snd_const T = Const (@{const_name snd}, T --> snd (HOLogic.dest_prodT T));
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   313
fun Id_const T = Const (@{const_name Id}, mk_relT (T, T));
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   314
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   315
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   316
(** Operators **)
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   317
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   318
val mk_Trueprop_eq = HOLogic.mk_Trueprop o HOLogic.mk_eq;
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   319
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   320
fun mk_IfN _ _ [t] = t
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   321
  | mk_IfN T (c :: cs) (t :: ts) =
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   322
    Const (@{const_name If}, HOLogic.boolT --> T --> T --> T) $ c $ t $ mk_IfN T cs ts;
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   323
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   324
fun mk_converse R =
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   325
  let
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   326
    val RT = dest_relT (fastype_of R);
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   327
    val RST = mk_relT (snd RT, fst RT);
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   328
  in Const (@{const_name converse}, fastype_of R --> RST) $ R end;
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   329
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   330
fun mk_rel_comp (R, S) =
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   331
  let
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   332
    val RT = fastype_of R;
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   333
    val ST = fastype_of S;
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   334
    val RST = mk_relT (fst (dest_relT RT), snd (dest_relT ST));
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   335
  in Const (@{const_name relcomp}, RT --> ST --> RST) $ R $ S end;
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   336
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   337
fun mk_Gr A f =
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   338
  let val ((AT, BT), FT) = `dest_funT (fastype_of f);
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   339
  in Const (@{const_name Gr}, HOLogic.mk_setT AT --> FT --> mk_relT (AT, BT)) $ A $ f end;
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   340
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   341
fun mk_image f =
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   342
  let val (T, U) = dest_funT (fastype_of f);
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   343
  in Const (@{const_name image},
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   344
    (T --> U) --> (HOLogic.mk_setT T) --> (HOLogic.mk_setT U)) $ f end;
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   345
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   346
fun mk_Ball X f =
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   347
  Const (@{const_name Ball}, fastype_of X --> fastype_of f --> HOLogic.boolT) $ X $ f;
blanchet@48975
   348
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   349
fun mk_Bex X f =
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   350
  Const (@{const_name Bex}, fastype_of X --> fastype_of f --> HOLogic.boolT) $ X $ f;
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   351
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   352
fun mk_UNION X f =
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   353
  let val (T, U) = dest_funT (fastype_of f);
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   354
  in Const (@{const_name SUPR}, fastype_of X --> (T --> U) --> U) $ X $ f end;
blanchet@48975
   355
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   356
fun mk_Union T =
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   357
  Const (@{const_name Sup}, HOLogic.mk_setT (HOLogic.mk_setT T) --> HOLogic.mk_setT T);
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   358
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   359
fun mk_Field r =
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   360
  let val T = fst (dest_relT (fastype_of r));
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   361
  in Const (@{const_name Field}, mk_relT (T, T) --> HOLogic.mk_setT T) $ r end;
blanchet@48975
   362
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   363
fun mk_card_order bd =
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   364
  let
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   365
    val T = fastype_of bd;
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   366
    val AT = fst (dest_relT T);
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   367
  in
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   368
    Const (@{const_name card_order_on}, HOLogic.mk_setT AT --> T --> HOLogic.boolT) $
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   369
      (HOLogic.mk_UNIV AT) $ bd
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   370
  end;
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   371
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   372
fun mk_Card_order bd =
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   373
  let
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   374
    val T = fastype_of bd;
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   375
    val AT = fst (dest_relT T);
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   376
  in
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   377
    Const (@{const_name card_order_on}, HOLogic.mk_setT AT --> T --> HOLogic.boolT) $
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   378
      mk_Field bd $ bd
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   379
  end;
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   380
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   381
fun mk_cinfinite bd =
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   382
  Const (@{const_name cinfinite}, fastype_of bd --> HOLogic.boolT) $ bd;
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   383
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   384
fun mk_ordLeq t1 t2 =
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   385
  HOLogic.mk_mem (HOLogic.mk_prod (t1, t2),
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   386
    Const (@{const_name ordLeq}, mk_relT (fastype_of t1, fastype_of t2)));
blanchet@48975
   387
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   388
fun mk_card_of A =
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   389
  let
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   390
    val AT = fastype_of A;
blanchet@48975
   391
    val T = HOLogic.dest_setT AT;
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   392
  in
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   393
    Const (@{const_name card_of}, AT --> mk_relT (T, T)) $ A
blanchet@48975
   394
  end;
blanchet@48975
   395
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   396
fun mk_dir_image r f =
blanchet@48975
   397
  let val (T, U) = dest_funT (fastype_of f);
blanchet@48975
   398
  in Const (@{const_name dir_image}, mk_relT (T, T) --> (T --> U) --> mk_relT (U, U)) $ r $ f end;
blanchet@48975
   399
blanchet@48975
   400
(*FIXME: "x"?*)
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   401
(*(nth sets i) must be of type "T --> 'ai set"*)
blanchet@48975
   402
fun mk_in As sets T =
blanchet@48975
   403
  let
blanchet@48975
   404
    fun in_single set A =
blanchet@48975
   405
      let val AT = fastype_of A;
blanchet@48975
   406
      in Const (@{const_name less_eq},
blanchet@48975
   407
        AT --> AT --> HOLogic.boolT) $ (set $ Free ("x", T)) $ A end;
blanchet@48975
   408
  in
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   409
    if length sets > 0
blanchet@48975
   410
    then HOLogic.mk_Collect ("x", T, foldr1 (HOLogic.mk_conj) (map2 in_single sets As))
blanchet@48975
   411
    else HOLogic.mk_UNIV T
blanchet@48975
   412
  end;
blanchet@48975
   413
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   414
fun mk_wpull A B1 B2 f1 f2 pseudo p1 p2 =
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   415
  let
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   416
    val AT = fastype_of A;
blanchet@48975
   417
    val BT1 = fastype_of B1;
blanchet@48975
   418
    val BT2 = fastype_of B2;
blanchet@48975
   419
    val FT1 = fastype_of f1;
blanchet@48975
   420
    val FT2 = fastype_of f2;
blanchet@48975
   421
    val PT1 = fastype_of p1;
blanchet@48975
   422
    val PT2 = fastype_of p2;
blanchet@48975
   423
    val T1 = HOLogic.dest_setT BT1;
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   424
    val T2 = HOLogic.dest_setT BT2;
blanchet@48975
   425
    val domP = domain_type PT1;
blanchet@48975
   426
    val ranF = range_type FT1;
blanchet@48975
   427
    val _ = if is_some pseudo orelse
blanchet@48975
   428
               (HOLogic.dest_setT AT = domP andalso
blanchet@48975
   429
               domain_type FT1 = T1 andalso
blanchet@48975
   430
               domain_type FT2 = T2 andalso
blanchet@48975
   431
               domain_type PT2 = domP andalso
blanchet@48975
   432
               range_type PT1 = T1 andalso
blanchet@48975
   433
               range_type PT2 = T2 andalso
blanchet@48975
   434
               range_type FT2 = ranF)
blanchet@48975
   435
      then () else raise TYPE ("mk_wpull", [BT1, BT2, FT1, FT2, PT1, PT2], []);
blanchet@48975
   436
  in
blanchet@48975
   437
    (case pseudo of
blanchet@48975
   438
      NONE => Const (@{const_name wpull},
blanchet@48975
   439
        AT --> BT1 --> BT2 --> FT1 --> FT2 --> PT1 --> PT2 --> HOLogic.boolT) $
blanchet@48975
   440
        A $ B1 $ B2 $ f1 $ f2 $ p1 $ p2
blanchet@48975
   441
    | SOME (e1, e2) => Const (@{const_name wppull},
blanchet@48975
   442
        AT --> BT1 --> BT2 --> FT1 --> FT2 --> fastype_of e1 --> fastype_of e2 -->
blanchet@48975
   443
          PT1 --> PT2 --> HOLogic.boolT) $
blanchet@48975
   444
        A $ B1 $ B2 $ f1 $ f2 $ e1 $ e2 $ p1 $ p2)
blanchet@48975
   445
  end;
blanchet@48975
   446
blanchet@48975
   447
fun mk_subset t1 t2 =
blanchet@48975
   448
  Const (@{const_name less_eq}, (fastype_of t1) --> (fastype_of t2) --> HOLogic.boolT) $ t1 $ t2;
blanchet@48975
   449
blanchet@48975
   450
fun mk_card_binop binop typop t1 t2 =
blanchet@48975
   451
  let
blanchet@48975
   452
    val (T1, relT1) = `(fst o dest_relT) (fastype_of t1);
blanchet@48975
   453
    val (T2, relT2) = `(fst o dest_relT) (fastype_of t2);
blanchet@48975
   454
  in
blanchet@48975
   455
    Const (binop, relT1 --> relT2 --> mk_relT (typop (T1, T2), typop (T1, T2))) $ t1 $ t2
blanchet@48975
   456
  end;
blanchet@48975
   457
blanchet@48975
   458
val mk_csum = mk_card_binop @{const_name csum} mk_sumT;
blanchet@48975
   459
val mk_cprod = mk_card_binop @{const_name cprod} HOLogic.mk_prodT;
blanchet@48975
   460
val mk_cexp = mk_card_binop @{const_name cexp} mk_partial_funT;
blanchet@48975
   461
val mk_ccexp = mk_card_binop @{const_name ccexp} mk_partial_funT;
blanchet@48975
   462
val ctwo = @{term ctwo};
blanchet@48975
   463
blanchet@48975
   464
fun mk_collect xs defT =
blanchet@48975
   465
  let val T = (case xs of [] => defT | (x::_) => fastype_of x);
blanchet@48975
   466
  in Const (@{const_name collect}, HOLogic.mk_setT T --> T) $ (HOLogic.mk_set T xs) end;
blanchet@48975
   467
blanchet@48975
   468
fun mk_permute src dest xs = map (nth xs o (fn x => find_index ((curry op =) x) src)) dest;
blanchet@48975
   469
blanchet@49075
   470
val list_all_free =
blanchet@49075
   471
  fold_rev (fn free => fn P =>
blanchet@49075
   472
    let val (x, T) = Term.dest_Free free;
blanchet@49075
   473
    in HOLogic.all_const T $ Term.absfree (x, T) P end);
blanchet@49075
   474
blanchet@49075
   475
val list_exists_free =
blanchet@49075
   476
  fold_rev (fn free => fn P =>
blanchet@49075
   477
    let val (x, T) = Term.dest_Free free;
blanchet@49075
   478
    in HOLogic.exists_const T $ Term.absfree (x, T) P end);
blanchet@49075
   479
blanchet@48975
   480
fun find_indices xs ys = map_filter I
blanchet@48975
   481
  (map_index (fn (i, y) => if member (op =) xs y then SOME i else NONE) ys);
blanchet@48975
   482
blanchet@48975
   483
fun mk_trans thm1 thm2 = trans OF [thm1, thm2];
blanchet@48975
   484
fun mk_sym thm = sym OF [thm];
blanchet@48975
   485
blanchet@48975
   486
(*TODO: antiquote heavily used theorems once*)
blanchet@48975
   487
val ctrans = @{thm ordLeq_transitive};
blanchet@48975
   488
val o_apply = @{thm o_apply};
blanchet@48975
   489
blanchet@48975
   490
fun mk_nthN 1 t 1 = t
blanchet@48975
   491
  | mk_nthN _ t 1 = HOLogic.mk_fst t
blanchet@48975
   492
  | mk_nthN 2 t 2 = HOLogic.mk_snd t
blanchet@48975
   493
  | mk_nthN n t m = mk_nthN (n - 1) (HOLogic.mk_snd t) (m - 1);
blanchet@48975
   494
blanchet@48975
   495
fun mk_nth_conv n m =
blanchet@48975
   496
  let
blanchet@48975
   497
    fun thm b = if b then @{thm fst_snd} else @{thm snd_snd}
blanchet@48975
   498
    fun mk_nth_conv _ 1 1 = refl
blanchet@48975
   499
      | mk_nth_conv _ _ 1 = @{thm fst_conv}
blanchet@48975
   500
      | mk_nth_conv _ 2 2 = @{thm snd_conv}
blanchet@48975
   501
      | mk_nth_conv b _ 2 = @{thm snd_conv} RS thm b
blanchet@48975
   502
      | mk_nth_conv b n m = mk_nth_conv false (n - 1) (m - 1) RS thm b;
blanchet@48975
   503
  in mk_nth_conv (not (m = n)) n m end;
blanchet@48975
   504
blanchet@48975
   505
fun mk_nthI 1 1 = @{thm TrueE[OF TrueI]}
blanchet@48975
   506
  | mk_nthI n m = fold (curry op RS) (replicate (m - 1) @{thm sndI})
blanchet@48975
   507
    (if m = n then @{thm TrueE[OF TrueI]} else @{thm fstI});
blanchet@48975
   508
blanchet@48975
   509
fun mk_conjunctN 1 1 = @{thm TrueE[OF TrueI]}
blanchet@48975
   510
  | mk_conjunctN _ 1 = conjunct1
blanchet@48975
   511
  | mk_conjunctN 2 2 = conjunct2
blanchet@48975
   512
  | mk_conjunctN n m = conjunct2 RS (mk_conjunctN (n - 1) (m - 1));
blanchet@48975
   513
blanchet@48975
   514
fun mk_conjIN 1 = @{thm TrueE[OF TrueI]}
blanchet@48975
   515
  | mk_conjIN n = mk_conjIN (n - 1) RSN (2, conjI);
blanchet@48975
   516
blanchet@49075
   517
fun mk_disjIN 1 1 = @{thm TrueE[OF TrueI]}
blanchet@49075
   518
  | mk_disjIN _ 1 = disjI1
blanchet@49075
   519
  | mk_disjIN 2 2 = disjI2
blanchet@49075
   520
  | mk_disjIN n m = (mk_disjIN (n - 1) (m - 1)) RS disjI2;
blanchet@49075
   521
blanchet@48975
   522
fun mk_ordLeq_csum 1 1 thm = thm
blanchet@48975
   523
  | mk_ordLeq_csum _ 1 thm = @{thm ordLeq_transitive} OF [thm, @{thm ordLeq_csum1}]
blanchet@48975
   524
  | mk_ordLeq_csum 2 2 thm = @{thm ordLeq_transitive} OF [thm, @{thm ordLeq_csum2}]
blanchet@48975
   525
  | mk_ordLeq_csum n m thm = @{thm ordLeq_transitive} OF
blanchet@48975
   526
    [mk_ordLeq_csum (n - 1) (m - 1) thm, @{thm ordLeq_csum2[OF Card_order_csum]}];
blanchet@48975
   527
blanchet@48975
   528
local
blanchet@48975
   529
  fun mk_Un_upper' 0 = subset_refl
blanchet@48975
   530
    | mk_Un_upper' 1 = @{thm Un_upper1}
blanchet@48975
   531
    | mk_Un_upper' k = Library.foldr (op RS o swap)
blanchet@48975
   532
      (replicate (k - 1) @{thm subset_trans[OF Un_upper1]}, @{thm Un_upper1});
blanchet@48975
   533
in
blanchet@48975
   534
  fun mk_Un_upper 1 1 = subset_refl
blanchet@48975
   535
    | mk_Un_upper n 1 = mk_Un_upper' (n - 2) RS @{thm subset_trans[OF Un_upper1]}
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   536
    | mk_Un_upper n m = mk_Un_upper' (n - m) RS @{thm subset_trans[OF Un_upper2]};
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end;
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local
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  fun mk_UnN' 0 = @{thm UnI2}
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    | mk_UnN' m = mk_UnN' (m - 1) RS @{thm UnI1};
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in
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  fun mk_UnN 1 1 = @{thm TrueE[OF TrueI]}
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    | mk_UnN n 1 = Library.foldr1 (op RS o swap) (replicate (n - 1) @{thm UnI1})
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    | mk_UnN n m = mk_UnN' (n - m)
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end;
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fun interleave xs ys = flat (map2 (fn x => fn y => [x, y]) xs ys);
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fun transpose [] = []
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  | transpose ([] :: xss) = transpose xss
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  | transpose xss = map hd xss :: transpose (map tl xss);
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fun seq_conds f n k xs =
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  if k = n then
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    map (f false) (take (k - 1) xs)
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  else
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    let val (negs, pos) = split_last (take k xs) in
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      map (f false) negs @ [f true pos]
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    end;
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fun mk_unabs_def 0 thm = thm
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  | mk_unabs_def n thm = mk_unabs_def (n - 1) thm RS @{thm spec[OF iffD1[OF fun_eq_iff]]};
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end;