src/HOL/Tools/Nitpick/nitpick_model.ML
author blanchet
Thu Mar 11 15:33:45 2010 +0100 (2010-03-11)
changeset 35712 77aa29bf14ee
parent 35711 548d3f16404b
child 35718 eee1a5e0d334
permissions -rw-r--r--
added a mechanism to Nitpick to support custom rendering of terms, and used it for multisets
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(*  Title:      HOL/Tools/Nitpick/nitpick_model.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2009, 2010
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Model reconstruction for Nitpick.
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*)
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signature NITPICK_MODEL =
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sig
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  type styp = Nitpick_Util.styp
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  type scope = Nitpick_Scope.scope
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  type rep = Nitpick_Rep.rep
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  type nut = Nitpick_Nut.nut
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  type params = {
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    show_skolems: bool,
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    show_datatypes: bool,
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    show_consts: bool}
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  type term_postprocessor =
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    Proof.context -> string -> (typ -> term list) -> typ -> term -> term
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  structure NameTable : TABLE
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  val irrelevant : string
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  val unknown : string
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  val unrep : string
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  val register_term_postprocessor :
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    typ -> term_postprocessor -> theory -> theory
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  val unregister_term_postprocessor : typ -> theory -> theory
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  val tuple_list_for_name :
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    nut NameTable.table -> Kodkod.raw_bound list -> nut -> int list list
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  val dest_plain_fun : term -> bool * (term list * term list)
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  val reconstruct_hol_model :
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    params -> scope -> (term option * int list) list -> styp list -> nut list
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    -> nut list -> nut list -> nut NameTable.table -> Kodkod.raw_bound list
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    -> Pretty.T * bool
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  val prove_hol_model :
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    scope -> Time.time option -> nut list -> nut list -> nut NameTable.table
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    -> Kodkod.raw_bound list -> term -> bool option
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end;
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structure Nitpick_Model : NITPICK_MODEL =
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struct
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open Nitpick_Util
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open Nitpick_HOL
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open Nitpick_Scope
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open Nitpick_Peephole
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open Nitpick_Rep
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open Nitpick_Nut
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structure KK = Kodkod
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type params = {
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  show_skolems: bool,
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  show_datatypes: bool,
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  show_consts: bool}
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type term_postprocessor =
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  Proof.context -> string -> (typ -> term list) -> typ -> term -> term
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structure Data = Theory_Data(
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  type T = (typ * term_postprocessor) list
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  val empty = []
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  val extend = I
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  fun merge (ps1, ps2) = AList.merge (op =) (K true) (ps1, ps2))
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val irrelevant = "_"
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val unknown = "?"
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val unrep = "\<dots>"
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val maybe_mixfix = "_\<^sup>?"
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val base_mixfix = "_\<^bsub>base\<^esub>"
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val step_mixfix = "_\<^bsub>step\<^esub>"
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val abs_mixfix = "\<guillemotleft>_\<guillemotright>"
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val cyclic_co_val_name = "\<omega>"
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val cyclic_const_prefix = "\<xi>"
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val cyclic_type_name = nitpick_prefix ^ cyclic_const_prefix
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val opt_flag = nitpick_prefix ^ "opt"
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val non_opt_flag = nitpick_prefix ^ "non_opt"
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type atom_pool = ((string * int) * int list) list
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(* atom_pool Unsynchronized.ref -> string -> int -> int -> string *)
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fun nth_atom_suffix pool s j k =
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  (case AList.lookup (op =) (!pool) (s, k) of
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     SOME js =>
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     (case find_index (curry (op =) j) js of
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        ~1 => (Unsynchronized.change pool (cons ((s, k), j :: js));
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               length js + 1)
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      | n => length js - n)
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   | NONE => (Unsynchronized.change pool (cons ((s, k), [j])); 1))
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  |> nat_subscript
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  |> (s <> "" andalso Symbol.is_ascii_digit (List.last (explode s)))
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     ? prefix "\<^isub>,"
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(* atom_pool Unsynchronized.ref -> string -> typ -> int -> int -> string *)
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fun nth_atom_name pool prefix (Type (s, _)) j k =
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    let val s' = shortest_name s in
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      prefix ^ (if String.isPrefix "\\" s' then s' else substring (s', 0, 1)) ^
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      nth_atom_suffix pool s j k
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    end
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  | nth_atom_name pool prefix (TFree (s, _)) j k =
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    prefix ^ perhaps (try (unprefix "'")) s ^ nth_atom_suffix pool s j k
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  | nth_atom_name _ _ T _ _ =
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    raise TYPE ("Nitpick_Model.nth_atom_name", [T], [])
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(* atom_pool Unsynchronized.ref -> bool -> typ -> int -> int -> term *)
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fun nth_atom pool for_auto T j k =
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  if for_auto then
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    Free (nth_atom_name pool (hd (space_explode "." nitpick_prefix)) T j k, T)
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  else
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    Const (nth_atom_name pool "" T j k, T)
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(* term -> real *)
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fun extract_real_number (Const (@{const_name divide}, _) $ t1 $ t2) =
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    real (snd (HOLogic.dest_number t1)) / real (snd (HOLogic.dest_number t2))
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  | extract_real_number t = real (snd (HOLogic.dest_number t))
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(* term * term -> order *)
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fun nice_term_ord (Abs (_, _, t1), Abs (_, _, t2)) = nice_term_ord (t1, t2)
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  | nice_term_ord tp = Real.compare (pairself extract_real_number tp)
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    handle TERM ("dest_number", _) =>
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           case tp of
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             (t11 $ t12, t21 $ t22) =>
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             (case nice_term_ord (t11, t21) of
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                EQUAL => nice_term_ord (t12, t22)
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              | ord => ord)
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           | _ => Term_Ord.fast_term_ord tp
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(* typ -> term_postprocessor -> theory -> theory *)
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fun register_term_postprocessor T p = Data.map (cons (T, p))
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(* typ -> theory -> theory *)
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fun unregister_term_postprocessor T = Data.map (AList.delete (op =) T)
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(* nut NameTable.table -> KK.raw_bound list -> nut -> int list list *)
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fun tuple_list_for_name rel_table bounds name =
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  the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]
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(* term -> term *)
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fun unarize_unbox_etc_term (Const (@{const_name FinFun}, _) $ t1) =
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    unarize_unbox_etc_term t1
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  | unarize_unbox_etc_term (Const (@{const_name FunBox}, _) $ t1) =
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    unarize_unbox_etc_term t1
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  | unarize_unbox_etc_term
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        (Const (@{const_name PairBox},
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                Type (@{type_name fun}, [T1, Type (@{type_name fun}, [T2, _])]))
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         $ t1 $ t2) =
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    let val Ts = map uniterize_unarize_unbox_etc_type [T1, T2] in
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      Const (@{const_name Pair}, Ts ---> Type (@{type_name "*"}, Ts))
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      $ unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
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    end
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  | unarize_unbox_etc_term (Const (s, T)) =
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    Const (s, uniterize_unarize_unbox_etc_type T)
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  | unarize_unbox_etc_term (t1 $ t2) =
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    unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
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  | unarize_unbox_etc_term (Free (s, T)) =
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    Free (s, uniterize_unarize_unbox_etc_type T)
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  | unarize_unbox_etc_term (Var (x, T)) =
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    Var (x, uniterize_unarize_unbox_etc_type T)
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  | unarize_unbox_etc_term (Bound j) = Bound j
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  | unarize_unbox_etc_term (Abs (s, T, t')) =
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    Abs (s, uniterize_unarize_unbox_etc_type T, unarize_unbox_etc_term t')
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(* typ -> typ -> (typ * typ) * (typ * typ) *)
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fun factor_out_types (T1 as Type (@{type_name "*"}, [T11, T12]))
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                     (T2 as Type (@{type_name "*"}, [T21, T22])) =
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    let val (n1, n2) = pairself num_factors_in_type (T11, T21) in
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      if n1 = n2 then
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        let
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          val ((T11', opt_T12'), (T21', opt_T22')) = factor_out_types T12 T22
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        in
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          ((Type (@{type_name "*"}, [T11, T11']), opt_T12'),
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           (Type (@{type_name "*"}, [T21, T21']), opt_T22'))
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        end
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      else if n1 < n2 then
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        case factor_out_types T1 T21 of
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          (p1, (T21', NONE)) => (p1, (T21', SOME T22))
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        | (p1, (T21', SOME T22')) =>
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          (p1, (T21', SOME (Type (@{type_name "*"}, [T22', T22]))))
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      else
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        swap (factor_out_types T2 T1)
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    end
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  | factor_out_types (Type (@{type_name "*"}, [T11, T12])) T2 =
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    ((T11, SOME T12), (T2, NONE))
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  | factor_out_types T1 (Type (@{type_name "*"}, [T21, T22])) =
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    ((T1, NONE), (T21, SOME T22))
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  | factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))
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(* bool -> typ -> typ -> (term * term) list -> term *)
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fun make_plain_fun maybe_opt T1 T2 =
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  let
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    (* typ -> typ -> (term * term) list -> term *)
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    fun aux T1 T2 [] =
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        Const (if maybe_opt then opt_flag else non_opt_flag, T1 --> T2)
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      | aux T1 T2 ((t1, t2) :: tps) =
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        Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
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        $ aux T1 T2 tps $ t1 $ t2
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  in aux T1 T2 o rev end
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(* term -> bool *)
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fun is_plain_fun (Const (s, _)) = (s = opt_flag orelse s = non_opt_flag)
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  | is_plain_fun (Const (@{const_name fun_upd}, _) $ t0 $ _ $ _) =
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    is_plain_fun t0
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  | is_plain_fun _ = false
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(* term -> bool * (term list * term list) *)
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val dest_plain_fun =
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  let
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    (* term -> bool * (term list * term list) *)
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    fun aux (Abs (_, _, Const (s, _))) = (s <> irrelevant, ([], []))
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      | aux (Const (s, _)) = (s <> non_opt_flag, ([], []))
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      | aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
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        let val (maybe_opt, (ts1, ts2)) = aux t0 in
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          (maybe_opt, (t1 :: ts1, t2 :: ts2))
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        end
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      | aux t = raise TERM ("Nitpick_Model.dest_plain_fun", [t])
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  in apsnd (pairself rev) o aux end
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(* typ -> typ -> typ -> term -> term * term *)
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fun break_in_two T T1 T2 t =
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  let
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    val ps = HOLogic.flat_tupleT_paths T
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    val cut = length (HOLogic.strip_tupleT T1)
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    val (ps1, ps2) = pairself HOLogic.flat_tupleT_paths (T1, T2)
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    val (ts1, ts2) = t |> HOLogic.strip_ptuple ps |> chop cut
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  in (HOLogic.mk_ptuple ps1 T1 ts1, HOLogic.mk_ptuple ps2 T2 ts2) end
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(* typ -> term -> term -> term *)
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fun pair_up (Type (@{type_name "*"}, [T1', T2']))
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            (t1 as Const (@{const_name Pair},
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                          Type (@{type_name fun},
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                                [_, Type (@{type_name fun}, [_, T1])]))
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             $ t11 $ t12) t2 =
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    if T1 = T1' then HOLogic.mk_prod (t1, t2)
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    else HOLogic.mk_prod (t11, pair_up T2' t12 t2)
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  | pair_up _ t1 t2 = HOLogic.mk_prod (t1, t2)
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(* typ -> term -> term list * term list -> (term * term) list*)
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fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3
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(* typ -> typ -> typ -> term -> term *)
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fun typecast_fun (Type (@{type_name fun}, [T1', T2'])) T1 T2 t =
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    let
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      (* typ -> typ -> typ -> typ -> term -> term *)
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      fun do_curry T1 T1a T1b T2 t =
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        let
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          val (maybe_opt, tsp) = dest_plain_fun t
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          val tps =
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            tsp |>> map (break_in_two T1 T1a T1b)
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                |> uncurry (map2 (fn (t1a, t1b) => fn t2 => (t1a, (t1b, t2))))
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                |> AList.coalesce (op =)
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                |> map (apsnd (make_plain_fun maybe_opt T1b T2))
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        in make_plain_fun maybe_opt T1a (T1b --> T2) tps end
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      (* typ -> typ -> term -> term *)
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      and do_uncurry T1 T2 t =
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        let
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          val (maybe_opt, tsp) = dest_plain_fun t
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          val tps =
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            tsp |> op ~~
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                |> maps (fn (t1, t2) =>
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                            multi_pair_up T1 t1 (snd (dest_plain_fun t2)))
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        in make_plain_fun maybe_opt T1 T2 tps end
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      (* typ -> typ -> typ -> typ -> term -> term *)
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      and do_arrow T1' T2' _ _ (Const (s, _)) = Const (s, T1' --> T2')
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        | do_arrow T1' T2' T1 T2
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                   (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
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          Const (@{const_name fun_upd},
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                 (T1' --> T2') --> T1' --> T2' --> T1' --> T2')
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          $ do_arrow T1' T2' T1 T2 t0 $ do_term T1' T1 t1 $ do_term T2' T2 t2
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        | do_arrow _ _ _ _ t =
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          raise TERM ("Nitpick_Model.typecast_fun.do_arrow", [t])
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      and do_fun T1' T2' T1 T2 t =
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        case factor_out_types T1' T1 of
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          ((_, NONE), (_, NONE)) => t |> do_arrow T1' T2' T1 T2
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        | ((_, NONE), (T1a, SOME T1b)) =>
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          t |> do_curry T1 T1a T1b T2 |> do_arrow T1' T2' T1a (T1b --> T2)
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        | ((T1a', SOME T1b'), (_, NONE)) =>
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          t |> do_arrow T1a' (T1b' --> T2') T1 T2 |> do_uncurry T1' T2'
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        | _ => raise TYPE ("Nitpick_Model.typecast_fun.do_fun", [T1, T1'], [])
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      (* typ -> typ -> term -> term *)
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      and do_term (Type (@{type_name fun}, [T1', T2']))
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                  (Type (@{type_name fun}, [T1, T2])) t =
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          do_fun T1' T2' T1 T2 t
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        | do_term (T' as Type (@{type_name "*"}, Ts' as [T1', T2']))
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                  (Type (@{type_name "*"}, [T1, T2]))
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                  (Const (@{const_name Pair}, _) $ t1 $ t2) =
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          Const (@{const_name Pair}, Ts' ---> T')
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          $ do_term T1' T1 t1 $ do_term T2' T2 t2
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        | do_term T' T t =
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          if T = T' then t
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          else raise TYPE ("Nitpick_Model.typecast_fun.do_term", [T, T'], [])
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    in if T1' = T1 andalso T2' = T2 then t else do_fun T1' T2' T1 T2 t end
blanchet@34998
   286
  | typecast_fun T' _ _ _ =
blanchet@34998
   287
    raise TYPE ("Nitpick_Model.typecast_fun", [T'], [])
blanchet@33192
   288
blanchet@33192
   289
(* term -> string *)
blanchet@33192
   290
fun truth_const_sort_key @{const True} = "0"
blanchet@33192
   291
  | truth_const_sort_key @{const False} = "2"
blanchet@33192
   292
  | truth_const_sort_key _ = "1"
blanchet@33192
   293
blanchet@33192
   294
(* typ -> term list -> term *)
blanchet@35665
   295
fun mk_tuple (Type (@{type_name "*"}, [T1, T2])) ts =
blanchet@33192
   296
    HOLogic.mk_prod (mk_tuple T1 ts,
blanchet@33192
   297
        mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))
blanchet@33192
   298
  | mk_tuple _ (t :: _) = t
blanchet@34124
   299
  | mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])
blanchet@33192
   300
blanchet@35711
   301
(* theory -> typ * typ -> bool *)
blanchet@35711
   302
fun varified_type_match thy (candid_T, pat_T) =
blanchet@35711
   303
  strict_type_match thy (candid_T, Logic.varifyT pat_T)
blanchet@35711
   304
blanchet@35712
   305
(* atom_pool -> (string * string) * (string * string) -> scope -> nut list
blanchet@35712
   306
   -> nut list -> nut list -> nut NameTable.table -> KK.raw_bound list -> typ
blanchet@35712
   307
   -> term list *)
blanchet@35712
   308
fun all_values_of_type pool wacky_names (scope as {card_assigns, ...} : scope)
blanchet@35712
   309
                       sel_names rel_table bounds card T =
blanchet@35712
   310
  let
blanchet@35712
   311
    val card = if card = 0 then card_of_type card_assigns T else card
blanchet@35712
   312
    (* nat -> term *)
blanchet@35712
   313
    fun nth_value_of_type n =
blanchet@35712
   314
      let
blanchet@35712
   315
        (* bool -> term *)
blanchet@35712
   316
        fun term unfold =
blanchet@35712
   317
          reconstruct_term unfold pool wacky_names scope sel_names rel_table
blanchet@35712
   318
                           bounds T T (Atom (card, 0)) [[n]]
blanchet@35712
   319
      in
blanchet@35712
   320
        case term false of
blanchet@35712
   321
          t as Const (s, _) =>
blanchet@35712
   322
          if String.isPrefix cyclic_const_prefix s then
blanchet@35712
   323
            HOLogic.mk_eq (t, term true)
blanchet@35712
   324
          else
blanchet@35712
   325
            t
blanchet@35712
   326
        | t => t
blanchet@35712
   327
      end
blanchet@35712
   328
  in index_seq 0 card |> map nth_value_of_type |> sort nice_term_ord end
blanchet@35280
   329
(* bool -> atom_pool -> (string * string) * (string * string) -> scope
blanchet@35280
   330
   -> nut list -> nut list -> nut list -> nut NameTable.table
blanchet@35280
   331
   -> KK.raw_bound list -> typ -> typ -> rep -> int list list -> term *)
blanchet@35712
   332
and reconstruct_term unfold pool (wacky_names as ((maybe_name, abs_name), _))
blanchet@35712
   333
        (scope as {hol_ctxt as {ctxt, thy, stds, ...}, binarize, card_assigns,
blanchet@35712
   334
                   bits, datatypes, ofs, ...}) sel_names rel_table bounds =
blanchet@33192
   335
  let
blanchet@33192
   336
    val for_auto = (maybe_name = "")
blanchet@34124
   337
    (* int list list -> int *)
blanchet@34124
   338
    fun value_of_bits jss =
blanchet@34124
   339
      let
blanchet@34124
   340
        val j0 = offset_of_type ofs @{typ unsigned_bit}
blanchet@34124
   341
        val js = map (Integer.add (~ j0) o the_single) jss
blanchet@34124
   342
      in
blanchet@34124
   343
        fold (fn j => Integer.add (reasonable_power 2 j |> j = bits ? op ~))
blanchet@34124
   344
             js 0
blanchet@34124
   345
      end
blanchet@35712
   346
    (* typ -> term list *)
blanchet@35712
   347
    val all_values =
blanchet@35712
   348
      all_values_of_type pool wacky_names scope sel_names rel_table bounds 0
blanchet@35712
   349
    (* typ -> term -> term *)
blanchet@35712
   350
    fun postprocess_term (Type (@{type_name fun}, _)) = I
blanchet@35712
   351
      | postprocess_term T =
blanchet@35712
   352
        if null (Data.get thy) then
blanchet@35712
   353
          I
blanchet@35712
   354
        else case AList.lookup (varified_type_match thy) (Data.get thy) T of
blanchet@35712
   355
          SOME postproc => postproc ctxt maybe_name all_values T
blanchet@35712
   356
        | NONE => I
blanchet@35712
   357
    (* typ list -> term -> term *)
blanchet@35712
   358
    fun postprocess_subterms Ts (t1 $ t2) =
blanchet@35712
   359
        let val t = postprocess_subterms Ts t1 $ postprocess_subterms Ts t2 in
blanchet@35712
   360
          postprocess_term (fastype_of1 (Ts, t)) t
blanchet@35712
   361
        end
blanchet@35712
   362
      | postprocess_subterms Ts (Abs (s, T, t')) =
blanchet@35712
   363
        Abs (s, T, postprocess_subterms (T :: Ts) t')
blanchet@35712
   364
      | postprocess_subterms Ts t = postprocess_term (fastype_of1 (Ts, t)) t
blanchet@33192
   365
    (* bool -> typ -> typ -> (term * term) list -> term *)
blanchet@35388
   366
    fun make_set maybe_opt T1 T2 tps =
blanchet@33192
   367
      let
wenzelm@35402
   368
        val empty_const = Const (@{const_abbrev Set.empty}, T1 --> T2)
blanchet@33192
   369
        val insert_const = Const (@{const_name insert},
blanchet@34124
   370
                                  T1 --> (T1 --> T2) --> T1 --> T2)
blanchet@33192
   371
        (* (term * term) list -> term *)
blanchet@33192
   372
        fun aux [] =
blanchet@35385
   373
            if maybe_opt andalso not (is_complete_type datatypes false T1) then
blanchet@33192
   374
              insert_const $ Const (unrep, T1) $ empty_const
blanchet@33192
   375
            else
blanchet@33192
   376
              empty_const
blanchet@33192
   377
          | aux ((t1, t2) :: zs) =
blanchet@35388
   378
            aux zs
blanchet@35388
   379
            |> t2 <> @{const False}
blanchet@35388
   380
               ? curry (op $)
blanchet@35388
   381
                       (insert_const
blanchet@35388
   382
                        $ (t1 |> t2 <> @{const True}
blanchet@35388
   383
                                 ? curry (op $)
blanchet@35388
   384
                                         (Const (maybe_name, T1 --> T1))))
blanchet@35388
   385
      in
blanchet@35388
   386
        if forall (fn (_, t) => t <> @{const True} andalso t <> @{const False})
blanchet@35388
   387
                  tps then
blanchet@35388
   388
          Const (unknown, T1 --> T2)
blanchet@35388
   389
        else
blanchet@35388
   390
          aux tps
blanchet@35388
   391
      end
blanchet@35665
   392
    (* bool -> typ -> typ -> typ -> (term * term) list -> term *)
blanchet@35665
   393
    fun make_map maybe_opt T1 T2 T2' =
blanchet@33192
   394
      let
blanchet@33192
   395
        val update_const = Const (@{const_name fun_upd},
blanchet@34124
   396
                                  (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
blanchet@33192
   397
        (* (term * term) list -> term *)
wenzelm@35402
   398
        fun aux' [] = Const (@{const_abbrev Map.empty}, T1 --> T2)
blanchet@35712
   399
          | aux' ((t1, t2) :: tps) =
blanchet@33192
   400
            (case t2 of
blanchet@35712
   401
               Const (@{const_name None}, _) => aux' tps
blanchet@35712
   402
             | _ => update_const $ aux' tps $ t1 $ t2)
blanchet@35712
   403
        fun aux tps =
blanchet@35665
   404
          if maybe_opt andalso not (is_complete_type datatypes false T1) then
blanchet@35712
   405
            update_const $ aux' tps $ Const (unrep, T1)
blanchet@33192
   406
            $ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))
blanchet@33192
   407
          else
blanchet@35712
   408
            aux' tps
blanchet@33192
   409
      in aux end
blanchet@33192
   410
    (* typ list -> term -> term *)
blanchet@34982
   411
    fun polish_funs Ts t =
blanchet@33192
   412
      (case fastype_of1 (Ts, t) of
blanchet@35665
   413
         Type (@{type_name fun}, [T1, T2]) =>
blanchet@33192
   414
         if is_plain_fun t then
blanchet@33192
   415
           case T2 of
blanchet@33192
   416
             @{typ bool} =>
blanchet@33192
   417
             let
blanchet@33192
   418
               val (maybe_opt, ts_pair) =
blanchet@34982
   419
                 dest_plain_fun t ||> pairself (map (polish_funs Ts))
blanchet@33192
   420
             in
blanchet@33192
   421
               make_set maybe_opt T1 T2
blanchet@33192
   422
                        (sort_wrt (truth_const_sort_key o snd) (op ~~ ts_pair))
blanchet@33192
   423
             end
blanchet@33192
   424
           | Type (@{type_name option}, [T2']) =>
blanchet@33192
   425
             let
blanchet@35665
   426
               val (maybe_opt, ts_pair) =
blanchet@35665
   427
                 dest_plain_fun t ||> pairself (map (polish_funs Ts))
blanchet@35665
   428
             in make_map maybe_opt T1 T2 T2' (rev (op ~~ ts_pair)) end
blanchet@33192
   429
           | _ => raise SAME ()
blanchet@33192
   430
         else
blanchet@33192
   431
           raise SAME ()
blanchet@33192
   432
       | _ => raise SAME ())
blanchet@33192
   433
      handle SAME () =>
blanchet@33192
   434
             case t of
blanchet@34982
   435
               (t1 as Const (@{const_name fun_upd}, _) $ t11 $ _)
blanchet@34982
   436
               $ (t2 as Const (s, _)) =>
blanchet@34982
   437
               if s = unknown then polish_funs Ts t11
blanchet@34982
   438
               else polish_funs Ts t1 $ polish_funs Ts t2
blanchet@34982
   439
             | t1 $ t2 => polish_funs Ts t1 $ polish_funs Ts t2
blanchet@34982
   440
             | Abs (s, T, t') => Abs (s, T, polish_funs (T :: Ts) t')
blanchet@35665
   441
             | Const (s, Type (@{type_name fun}, [T1, T2])) =>
blanchet@34982
   442
               if s = opt_flag orelse s = non_opt_flag then
blanchet@35712
   443
                 Abs ("x", T1,
blanchet@35712
   444
                      Const (if is_complete_type datatypes false T1 then
blanchet@35712
   445
                               irrelevant
blanchet@35712
   446
                             else
blanchet@35712
   447
                               unknown, T2))
blanchet@34982
   448
               else
blanchet@34982
   449
                 t
blanchet@34982
   450
             | t => t
blanchet@33192
   451
    (* bool -> typ -> typ -> typ -> term list -> term list -> term *)
blanchet@33192
   452
    fun make_fun maybe_opt T1 T2 T' ts1 ts2 =
blanchet@34126
   453
      ts1 ~~ ts2 |> sort (nice_term_ord o pairself fst)
blanchet@34998
   454
                 |> make_plain_fun maybe_opt T1 T2
blanchet@35665
   455
                 |> unarize_unbox_etc_term
blanchet@35665
   456
                 |> typecast_fun (uniterize_unarize_unbox_etc_type T')
blanchet@35665
   457
                                 (uniterize_unarize_unbox_etc_type T1)
blanchet@35665
   458
                                 (uniterize_unarize_unbox_etc_type T2)
blanchet@33192
   459
    (* (typ * int) list -> typ -> typ -> int -> term *)
blanchet@35665
   460
    fun term_for_atom seen (T as Type (@{type_name fun}, [T1, T2])) T' j _ =
blanchet@33192
   461
        let
blanchet@33192
   462
          val k1 = card_of_type card_assigns T1
blanchet@33192
   463
          val k2 = card_of_type card_assigns T2
blanchet@33192
   464
        in
blanchet@35665
   465
          term_for_rep true seen T T' (Vect (k1, Atom (k2, 0)))
blanchet@33192
   466
                       [nth_combination (replicate k1 (k2, 0)) j]
blanchet@33192
   467
          handle General.Subscript =>
blanchet@33232
   468
                 raise ARG ("Nitpick_Model.reconstruct_term.term_for_atom",
blanchet@33192
   469
                            signed_string_of_int j ^ " for " ^
blanchet@33192
   470
                            string_for_rep (Vect (k1, Atom (k2, 0))))
blanchet@33192
   471
        end
blanchet@35665
   472
      | term_for_atom seen (Type (@{type_name "*"}, [T1, T2])) _ j k =
blanchet@35075
   473
        let
blanchet@35075
   474
          val k1 = card_of_type card_assigns T1
blanchet@35075
   475
          val k2 = k div k1
blanchet@35075
   476
        in
blanchet@33192
   477
          list_comb (HOLogic.pair_const T1 T2,
blanchet@35075
   478
                     map3 (fn T => term_for_atom seen T T) [T1, T2]
blanchet@35075
   479
                          [j div k2, j mod k2] [k1, k2]) (* ### k2 or k1? FIXME *)
blanchet@33192
   480
        end
blanchet@35075
   481
      | term_for_atom seen @{typ prop} _ j k =
blanchet@35075
   482
        HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j k)
blanchet@35075
   483
      | term_for_atom _ @{typ bool} _ j _ =
blanchet@33192
   484
        if j = 0 then @{const False} else @{const True}
blanchet@35075
   485
      | term_for_atom _ @{typ unit} _ _ _ = @{const Unity}
blanchet@35075
   486
      | term_for_atom seen T _ j k =
blanchet@35220
   487
        if T = nat_T andalso is_standard_datatype thy stds nat_T then
blanchet@33192
   488
          HOLogic.mk_number nat_T j
blanchet@33192
   489
        else if T = int_T then
blanchet@35075
   490
          HOLogic.mk_number int_T (int_for_atom (k, 0) j)
blanchet@33192
   491
        else if is_fp_iterator_type T then
blanchet@35075
   492
          HOLogic.mk_number nat_T (k - j - 1)
blanchet@33192
   493
        else if T = @{typ bisim_iterator} then
blanchet@33192
   494
          HOLogic.mk_number nat_T j
blanchet@33192
   495
        else case datatype_spec datatypes T of
blanchet@35076
   496
          NONE => nth_atom pool for_auto T j k
blanchet@35076
   497
        | SOME {deep = false, ...} => nth_atom pool for_auto T j k
blanchet@35179
   498
        | SOME {co, standard, constrs, ...} =>
blanchet@33192
   499
          let
blanchet@33192
   500
            (* styp -> int list *)
blanchet@33192
   501
            fun tuples_for_const (s, T) =
blanchet@33192
   502
              tuple_list_for_name rel_table bounds (ConstName (s, T, Any))
blanchet@35180
   503
            (* unit -> term *)
blanchet@35180
   504
            fun cyclic_atom () =
blanchet@35180
   505
              nth_atom pool for_auto (Type (cyclic_type_name, [])) j k
blanchet@35180
   506
            fun cyclic_var () = Var ((nth_atom_name pool "" T j k, 0), T)
blanchet@35180
   507
blanchet@33192
   508
            val discr_jsss = map (tuples_for_const o discr_for_constr o #const)
blanchet@33192
   509
                                 constrs
blanchet@33192
   510
            val real_j = j + offset_of_type ofs T
blanchet@33192
   511
            val constr_x as (constr_s, constr_T) =
blanchet@33192
   512
              get_first (fn (jss, {const, ...}) =>
blanchet@34121
   513
                            if member (op =) jss [real_j] then SOME const
blanchet@34121
   514
                            else NONE)
blanchet@33192
   515
                        (discr_jsss ~~ constrs) |> the
blanchet@33192
   516
            val arg_Ts = curried_binder_types constr_T
blanchet@35190
   517
            val sel_xs =
blanchet@35190
   518
              map (binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize
blanchet@35190
   519
                                                          constr_x)
blanchet@35190
   520
                  (index_seq 0 (length arg_Ts))
blanchet@33192
   521
            val sel_Rs =
blanchet@33192
   522
              map (fn x => get_first
blanchet@33192
   523
                               (fn ConstName (s', T', R) =>
blanchet@33192
   524
                                   if (s', T') = x then SOME R else NONE
blanchet@33232
   525
                                 | u => raise NUT ("Nitpick_Model.reconstruct_\
blanchet@33192
   526
                                                   \term.term_for_atom", [u]))
blanchet@33192
   527
                               sel_names |> the) sel_xs
blanchet@33192
   528
            val arg_Rs = map (snd o dest_Func) sel_Rs
blanchet@33192
   529
            val sel_jsss = map tuples_for_const sel_xs
blanchet@33192
   530
            val arg_jsss =
blanchet@33192
   531
              map (map_filter (fn js => if hd js = real_j then SOME (tl js)
blanchet@33192
   532
                                        else NONE)) sel_jsss
blanchet@33192
   533
            val uncur_arg_Ts = binder_types constr_T
blanchet@35179
   534
            val maybe_cyclic = co orelse not standard
blanchet@33192
   535
          in
blanchet@35180
   536
            if maybe_cyclic andalso not (null seen) andalso
blanchet@35188
   537
               member (op =) (seen |> unfold ? (fst o split_last)) (T, j) then
blanchet@35180
   538
              cyclic_var ()
blanchet@34124
   539
            else if constr_s = @{const_name Word} then
blanchet@34124
   540
              HOLogic.mk_number
blanchet@34124
   541
                  (if T = @{typ "unsigned_bit word"} then nat_T else int_T)
blanchet@34124
   542
                  (value_of_bits (the_single arg_jsss))
blanchet@33192
   543
            else
blanchet@33192
   544
              let
blanchet@35179
   545
                val seen = seen |> maybe_cyclic ? cons (T, j)
blanchet@33192
   546
                val ts =
blanchet@33192
   547
                  if length arg_Ts = 0 then
blanchet@33192
   548
                    []
blanchet@33192
   549
                  else
blanchet@35665
   550
                    map3 (fn Ts =>
blanchet@35665
   551
                             term_for_rep (constr_s <> @{const_name FinFun})
blanchet@35665
   552
                                          seen Ts Ts) arg_Ts arg_Rs arg_jsss
blanchet@33192
   553
                    |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)
blanchet@33192
   554
                    |> dest_n_tuple (length uncur_arg_Ts)
blanchet@33192
   555
                val t =
blanchet@33192
   556
                  if constr_s = @{const_name Abs_Frac} then
blanchet@35711
   557
                    case ts of
blanchet@35711
   558
                      [Const (@{const_name Pair}, _) $ t1 $ t2] =>
blanchet@35711
   559
                      frac_from_term_pair (body_type T) t1 t2
blanchet@35711
   560
                    | _ => raise TERM ("Nitpick_Model.reconstruct_term.\
blanchet@35711
   561
                                       \term_for_atom (Abs_Frac)", ts)
blanchet@34936
   562
                  else if not for_auto andalso
blanchet@34936
   563
                          (is_abs_fun thy constr_x orelse
blanchet@34936
   564
                           constr_s = @{const_name Quot}) then
blanchet@33192
   565
                    Const (abs_name, constr_T) $ the_single ts
blanchet@33192
   566
                  else
blanchet@33192
   567
                    list_comb (Const constr_x, ts)
blanchet@33192
   568
              in
blanchet@35179
   569
                if maybe_cyclic then
blanchet@35180
   570
                  let val var = cyclic_var () in
blanchet@35188
   571
                    if unfold andalso not standard andalso
blanchet@35180
   572
                       length seen = 1 andalso
blanchet@35180
   573
                       exists_subterm (fn Const (s, _) =>
blanchet@35188
   574
                                          String.isPrefix cyclic_const_prefix s
blanchet@35180
   575
                                        | t' => t' = var) t then
blanchet@35188
   576
                      subst_atomic [(var, cyclic_atom ())] t
blanchet@35180
   577
                    else if exists_subterm (curry (op =) var) t then
blanchet@35179
   578
                      if co then
blanchet@35179
   579
                        Const (@{const_name The}, (T --> bool_T) --> T)
blanchet@35179
   580
                        $ Abs (cyclic_co_val_name, T,
blanchet@35179
   581
                               Const (@{const_name "op ="}, T --> T --> bool_T)
blanchet@35180
   582
                               $ Bound 0 $ abstract_over (var, t))
blanchet@35179
   583
                      else
blanchet@35180
   584
                        cyclic_atom ()
blanchet@33192
   585
                    else
blanchet@33192
   586
                      t
blanchet@33192
   587
                  end
blanchet@33192
   588
                else
blanchet@33192
   589
                  t
blanchet@33192
   590
              end
blanchet@33192
   591
          end
blanchet@33192
   592
    (* (typ * int) list -> int -> rep -> typ -> typ -> typ -> int list
blanchet@33192
   593
       -> term *)
blanchet@33192
   594
    and term_for_vect seen k R T1 T2 T' js =
blanchet@35075
   595
      make_fun true T1 T2 T'
blanchet@35075
   596
               (map (fn j => term_for_atom seen T1 T1 j k) (index_seq 0 k))
blanchet@35665
   597
               (map (term_for_rep true seen T2 T2 R o single)
blanchet@33192
   598
                    (batch_list (arity_of_rep R) js))
blanchet@35665
   599
    (* bool -> (typ * int) list -> typ -> typ -> rep -> int list list -> term *)
blanchet@35665
   600
    and term_for_rep _ seen T T' Unit [[]] = term_for_atom seen T T' 0 1
blanchet@35665
   601
      | term_for_rep _ seen T T' (R as Atom (k, j0)) [[j]] =
blanchet@35075
   602
        if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0) k
blanchet@33232
   603
        else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])
blanchet@35665
   604
      | term_for_rep _ seen (Type (@{type_name "*"}, [T1, T2])) _
blanchet@35665
   605
                     (Struct [R1, R2]) [js] =
blanchet@33192
   606
        let
blanchet@33192
   607
          val arity1 = arity_of_rep R1
blanchet@33192
   608
          val (js1, js2) = chop arity1 js
blanchet@33192
   609
        in
blanchet@33192
   610
          list_comb (HOLogic.pair_const T1 T2,
blanchet@35665
   611
                     map3 (fn T => term_for_rep true seen T T) [T1, T2] [R1, R2]
blanchet@33192
   612
                          [[js1], [js2]])
blanchet@33192
   613
        end
blanchet@35665
   614
      | term_for_rep _ seen (Type (@{type_name fun}, [T1, T2])) T'
blanchet@35665
   615
                     (Vect (k, R')) [js] =
blanchet@33192
   616
        term_for_vect seen k R' T1 T2 T' js
blanchet@35665
   617
      | term_for_rep _ seen (Type (@{type_name fun}, [T1, T2])) T'
blanchet@35665
   618
                     (Func (R1, Formula Neut)) jss =
blanchet@33192
   619
        let
blanchet@33192
   620
          val jss1 = all_combinations_for_rep R1
blanchet@35665
   621
          val ts1 = map (term_for_rep true seen T1 T1 R1 o single) jss1
blanchet@33192
   622
          val ts2 =
blanchet@35665
   623
            map (fn js => term_for_rep true seen T2 T2 (Atom (2, 0))
blanchet@35385
   624
                                       [[int_from_bool (member (op =) jss js)]])
blanchet@34121
   625
                jss1
blanchet@33192
   626
        in make_fun false T1 T2 T' ts1 ts2 end
blanchet@35665
   627
      | term_for_rep maybe_opt seen (Type (@{type_name fun}, [T1, T2])) T'
blanchet@35665
   628
                     (Func (R1, R2)) jss =
blanchet@33192
   629
        let
blanchet@33192
   630
          val arity1 = arity_of_rep R1
blanchet@33192
   631
          val jss1 = all_combinations_for_rep R1
blanchet@35665
   632
          val ts1 = map (term_for_rep false seen T1 T1 R1 o single) jss1
blanchet@33192
   633
          val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)
blanchet@35665
   634
          val ts2 = map (term_for_rep false seen T2 T2 R2 o the_default []
blanchet@33192
   635
                         o AList.lookup (op =) grouped_jss2) jss1
blanchet@35665
   636
        in make_fun maybe_opt T1 T2 T' ts1 ts2 end
blanchet@35665
   637
      | term_for_rep _ seen T T' (Opt R) jss =
blanchet@35665
   638
        if null jss then Const (unknown, T)
blanchet@35665
   639
        else term_for_rep true seen T T' R jss
blanchet@35665
   640
      | term_for_rep _ _ T _ R jss =
blanchet@33232
   641
        raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",
blanchet@33192
   642
                   Refute.string_of_typ T ^ " " ^ string_for_rep R ^ " " ^
blanchet@33192
   643
                   string_of_int (length jss))
blanchet@35712
   644
  in
blanchet@35712
   645
    postprocess_subterms [] o polish_funs [] o unarize_unbox_etc_term
blanchet@35712
   646
    oooo term_for_rep true []
blanchet@35712
   647
  end
blanchet@33192
   648
blanchet@35180
   649
(* atom_pool -> scope -> nut list -> nut NameTable.table -> KK.raw_bound list
blanchet@35180
   650
   -> nut -> term *)
blanchet@35180
   651
fun term_for_name pool scope sel_names rel_table bounds name =
blanchet@33192
   652
  let val T = type_of name in
blanchet@33192
   653
    tuple_list_for_name rel_table bounds name
blanchet@35280
   654
    |> reconstruct_term false pool (("", ""), ("", "")) scope sel_names
blanchet@35280
   655
                        rel_table bounds T T (rep_of name)
blanchet@33192
   656
  end
blanchet@33192
   657
blanchet@35280
   658
(* Proof.context -> ((string * string) * (string * string)) * Proof.context *)
blanchet@33192
   659
fun add_wacky_syntax ctxt =
blanchet@33192
   660
  let
blanchet@33192
   661
    (* term -> string *)
blanchet@33192
   662
    val name_of = fst o dest_Const
blanchet@33192
   663
    val thy = ProofContext.theory_of ctxt |> Context.reject_draft
blanchet@33192
   664
    val (maybe_t, thy) =
blanchet@33202
   665
      Sign.declare_const ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),
blanchet@33202
   666
                          Mixfix (maybe_mixfix, [1000], 1000)) thy
blanchet@35280
   667
    val (abs_t, thy) =
blanchet@35280
   668
      Sign.declare_const ((@{binding nitpick_abs}, @{typ "'a => 'b"}),
blanchet@35280
   669
                          Mixfix (abs_mixfix, [40], 40)) thy
blanchet@33192
   670
    val (base_t, thy) =
blanchet@33202
   671
      Sign.declare_const ((@{binding nitpick_base}, @{typ "'a => 'a"}),
blanchet@33202
   672
                          Mixfix (base_mixfix, [1000], 1000)) thy
blanchet@33192
   673
    val (step_t, thy) =
blanchet@33202
   674
      Sign.declare_const ((@{binding nitpick_step}, @{typ "'a => 'a"}),
blanchet@33202
   675
                          Mixfix (step_mixfix, [1000], 1000)) thy
blanchet@33192
   676
  in
blanchet@35280
   677
    (pairself (pairself name_of) ((maybe_t, abs_t), (base_t, step_t)),
blanchet@33192
   678
     ProofContext.transfer_syntax thy ctxt)
blanchet@33192
   679
  end
blanchet@33192
   680
blanchet@33192
   681
(* term -> term *)
blanchet@33192
   682
fun unfold_outer_the_binders (t as Const (@{const_name The}, _)
blanchet@33192
   683
                                   $ Abs (s, T, Const (@{const_name "op ="}, _)
blanchet@33192
   684
                                                $ Bound 0 $ t')) =
blanchet@33192
   685
    betapply (Abs (s, T, t'), t) |> unfold_outer_the_binders
blanchet@33192
   686
  | unfold_outer_the_binders t = t
blanchet@33192
   687
(* typ list -> int -> term * term -> bool *)
blanchet@33192
   688
fun bisimilar_values _ 0 _ = true
blanchet@33192
   689
  | bisimilar_values coTs max_depth (t1, t2) =
blanchet@33192
   690
    let val T = fastype_of t1 in
blanchet@33192
   691
      if exists_subtype (member (op =) coTs) T then
blanchet@33192
   692
        let
blanchet@33192
   693
          val ((head1, args1), (head2, args2)) =
blanchet@33192
   694
            pairself (strip_comb o unfold_outer_the_binders) (t1, t2)
blanchet@34121
   695
          val max_depth = max_depth - (if member (op =) coTs T then 1 else 0)
blanchet@33192
   696
        in
blanchet@34936
   697
          head1 = head2 andalso
blanchet@34936
   698
          forall (bisimilar_values coTs max_depth) (args1 ~~ args2)
blanchet@33192
   699
        end
blanchet@33192
   700
      else
blanchet@33192
   701
        t1 = t2
blanchet@33192
   702
    end
blanchet@33192
   703
blanchet@33192
   704
(* params -> scope -> (term option * int list) list -> styp list -> nut list
blanchet@34126
   705
  -> nut list -> nut list -> nut NameTable.table -> KK.raw_bound list
blanchet@33192
   706
  -> Pretty.T * bool *)
blanchet@33192
   707
fun reconstruct_hol_model {show_skolems, show_datatypes, show_consts}
blanchet@35280
   708
        ({hol_ctxt = {thy, ctxt, max_bisim_depth, boxes, stds, wfs, user_axioms,
blanchet@35280
   709
                      debug, binary_ints, destroy_constrs, specialize,
blanchet@35280
   710
                      skolemize, star_linear_preds, uncurry, fast_descrs,
blanchet@35280
   711
                      tac_timeout, evals, case_names, def_table, nondef_table,
blanchet@35280
   712
                      user_nondefs, simp_table, psimp_table, intro_table,
blanchet@35280
   713
                      ground_thm_table, ersatz_table, skolems, special_funs,
blanchet@35280
   714
                      unrolled_preds, wf_cache, constr_cache},
blanchet@35190
   715
         binarize, card_assigns, bits, bisim_depth, datatypes, ofs} : scope)
blanchet@34124
   716
        formats all_frees free_names sel_names nonsel_names rel_table bounds =
blanchet@33192
   717
  let
blanchet@35180
   718
    val pool = Unsynchronized.ref []
blanchet@35280
   719
    val (wacky_names as (_, base_step_names), ctxt) =
blanchet@33192
   720
      add_wacky_syntax ctxt
blanchet@35070
   721
    val hol_ctxt =
blanchet@33192
   722
      {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
blanchet@34982
   723
       stds = stds, wfs = wfs, user_axioms = user_axioms, debug = debug,
blanchet@34124
   724
       binary_ints = binary_ints, destroy_constrs = destroy_constrs,
blanchet@34124
   725
       specialize = specialize, skolemize = skolemize,
blanchet@34124
   726
       star_linear_preds = star_linear_preds, uncurry = uncurry,
blanchet@34124
   727
       fast_descrs = fast_descrs, tac_timeout = tac_timeout, evals = evals,
blanchet@34124
   728
       case_names = case_names, def_table = def_table,
blanchet@33192
   729
       nondef_table = nondef_table, user_nondefs = user_nondefs,
blanchet@33192
   730
       simp_table = simp_table, psimp_table = psimp_table,
blanchet@33192
   731
       intro_table = intro_table, ground_thm_table = ground_thm_table,
blanchet@33192
   732
       ersatz_table = ersatz_table, skolems = skolems,
blanchet@33192
   733
       special_funs = special_funs, unrolled_preds = unrolled_preds,
blanchet@33580
   734
       wf_cache = wf_cache, constr_cache = constr_cache}
blanchet@35190
   735
    val scope = {hol_ctxt = hol_ctxt, binarize = binarize,
blanchet@35190
   736
                 card_assigns = card_assigns, bits = bits,
blanchet@35190
   737
                 bisim_depth = bisim_depth, datatypes = datatypes, ofs = ofs}
blanchet@35180
   738
    (* bool -> typ -> typ -> rep -> int list list -> term *)
blanchet@35188
   739
    fun term_for_rep unfold =
blanchet@35188
   740
      reconstruct_term unfold pool wacky_names scope sel_names rel_table bounds
blanchet@35188
   741
    (* nat -> typ -> nat -> term *)
blanchet@35180
   742
    fun nth_value_of_type card T n =
blanchet@35188
   743
      let
blanchet@35188
   744
        (* bool -> term *)
blanchet@35188
   745
        fun aux unfold = term_for_rep unfold T T (Atom (card, 0)) [[n]]
blanchet@35188
   746
      in
blanchet@35188
   747
        case aux false of
blanchet@35188
   748
          t as Const (s, _) =>
blanchet@35188
   749
          if String.isPrefix cyclic_const_prefix s then
blanchet@35188
   750
            HOLogic.mk_eq (t, aux true)
blanchet@35188
   751
          else
blanchet@35188
   752
            t
blanchet@35188
   753
        | t => t
blanchet@35188
   754
      end
blanchet@35712
   755
    (* nat -> typ -> term list *)
blanchet@35712
   756
    val all_values =
blanchet@35712
   757
      all_values_of_type pool wacky_names scope sel_names rel_table bounds
blanchet@33192
   758
    (* dtype_spec list -> dtype_spec -> bool *)
blanchet@33192
   759
    fun is_codatatype_wellformed (cos : dtype_spec list)
blanchet@33192
   760
                                 ({typ, card, ...} : dtype_spec) =
blanchet@33192
   761
      let
blanchet@35712
   762
        val ts = all_values card typ
blanchet@33192
   763
        val max_depth = Integer.sum (map #card cos)
blanchet@33192
   764
      in
blanchet@33192
   765
        forall (not o bisimilar_values (map #typ cos) max_depth)
blanchet@33192
   766
               (all_distinct_unordered_pairs_of ts)
blanchet@33192
   767
      end
blanchet@33192
   768
    (* string -> Pretty.T *)
blanchet@33192
   769
    fun pretty_for_assign name =
blanchet@33192
   770
      let
blanchet@33192
   771
        val (oper, (t1, T'), T) =
blanchet@33192
   772
          case name of
blanchet@33192
   773
            FreeName (s, T, _) =>
blanchet@35665
   774
            let val t = Free (s, uniterize_unarize_unbox_etc_type T) in
blanchet@33192
   775
              ("=", (t, format_term_type thy def_table formats t), T)
blanchet@33192
   776
            end
blanchet@33192
   777
          | ConstName (s, T, _) =>
blanchet@33192
   778
            (assign_operator_for_const (s, T),
blanchet@35280
   779
             user_friendly_const hol_ctxt base_step_names formats (s, T), T)
blanchet@33232
   780
          | _ => raise NUT ("Nitpick_Model.reconstruct_hol_model.\
blanchet@33192
   781
                            \pretty_for_assign", [name])
blanchet@33192
   782
        val t2 = if rep_of name = Any then
blanchet@33192
   783
                   Const (@{const_name undefined}, T')
blanchet@33192
   784
                 else
blanchet@33192
   785
                   tuple_list_for_name rel_table bounds name
blanchet@35180
   786
                   |> term_for_rep false T T' (rep_of name)
blanchet@33192
   787
      in
blanchet@33192
   788
        Pretty.block (Pretty.breaks
blanchet@33571
   789
            [setmp_show_all_types (Syntax.pretty_term ctxt) t1,
blanchet@33192
   790
             Pretty.str oper, Syntax.pretty_term ctxt t2])
blanchet@33192
   791
      end
blanchet@33192
   792
    (* dtype_spec -> Pretty.T *)
blanchet@34123
   793
    fun pretty_for_datatype ({typ, card, complete, ...} : dtype_spec) =
blanchet@33192
   794
      Pretty.block (Pretty.breaks
blanchet@35665
   795
          (Syntax.pretty_typ ctxt (uniterize_unarize_unbox_etc_type typ) ::
blanchet@35665
   796
           (case typ of
blanchet@35665
   797
              Type (@{type_name fin_fun}, _) => [Pretty.str "[finite]"]
blanchet@35665
   798
            | Type (@{type_name fun_box}, _) => [Pretty.str "[boxed]"]
blanchet@35665
   799
            | Type (@{type_name pair_box}, _) => [Pretty.str "[boxed]"]
blanchet@35665
   800
            | _ => []) @
blanchet@35665
   801
           [Pretty.str "=",
blanchet@35665
   802
            Pretty.enum "," "{" "}"
blanchet@35712
   803
                (map (Syntax.pretty_term ctxt) (all_values card typ) @
blanchet@35665
   804
                 (if fun_from_pair complete false then []
blanchet@35665
   805
                  else [Pretty.str unrep]))]))
blanchet@33192
   806
    (* typ -> dtype_spec list *)
blanchet@33192
   807
    fun integer_datatype T =
blanchet@33192
   808
      [{typ = T, card = card_of_type card_assigns T, co = false,
blanchet@35385
   809
        standard = true, complete = (false, false), concrete = (true, true),
blanchet@35385
   810
        deep = true, constrs = []}]
blanchet@33232
   811
      handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []
blanchet@33192
   812
    val (codatatypes, datatypes) =
blanchet@34982
   813
      datatypes |> filter #deep |> List.partition #co
blanchet@35220
   814
                ||> append (integer_datatype int_T
blanchet@35220
   815
                            |> is_standard_datatype thy stds nat_T
blanchet@35220
   816
                               ? append (integer_datatype nat_T))
blanchet@33192
   817
    val block_of_datatypes =
blanchet@33192
   818
      if show_datatypes andalso not (null datatypes) then
blanchet@33192
   819
        [Pretty.big_list ("Datatype" ^ plural_s_for_list datatypes ^ ":")
blanchet@33192
   820
                         (map pretty_for_datatype datatypes)]
blanchet@33192
   821
      else
blanchet@33192
   822
        []
blanchet@33192
   823
    val block_of_codatatypes =
blanchet@33192
   824
      if show_datatypes andalso not (null codatatypes) then
blanchet@33192
   825
        [Pretty.big_list ("Codatatype" ^ plural_s_for_list codatatypes ^ ":")
blanchet@33192
   826
                         (map pretty_for_datatype codatatypes)]
blanchet@33192
   827
      else
blanchet@33192
   828
        []
blanchet@33192
   829
    (* bool -> string -> nut list -> Pretty.T list *)
blanchet@33192
   830
    fun block_of_names show title names =
blanchet@33192
   831
      if show andalso not (null names) then
blanchet@33192
   832
        Pretty.str (title ^ plural_s_for_list names ^ ":")
blanchet@33192
   833
        :: map (Pretty.indent indent_size o pretty_for_assign)
blanchet@33192
   834
               (sort_wrt (original_name o nickname_of) names)
blanchet@33192
   835
      else
blanchet@33192
   836
        []
blanchet@33192
   837
    val (skolem_names, nonskolem_nonsel_names) =
blanchet@33192
   838
      List.partition is_skolem_name nonsel_names
blanchet@33192
   839
    val (eval_names, noneval_nonskolem_nonsel_names) =
blanchet@33192
   840
      List.partition (String.isPrefix eval_prefix o nickname_of)
blanchet@33192
   841
                     nonskolem_nonsel_names
blanchet@35665
   842
      ||> filter_out (member (op =) [@{const_name bisim},
blanchet@35665
   843
                                     @{const_name bisim_iterator_max}]
blanchet@34121
   844
                      o nickname_of)
blanchet@33192
   845
    val free_names =
blanchet@33192
   846
      map (fn x as (s, T) =>
blanchet@34121
   847
              case filter (curry (op =) x
blanchet@35280
   848
                       o pairf nickname_of
blanchet@35665
   849
                               (uniterize_unarize_unbox_etc_type o type_of))
blanchet@35190
   850
                       free_names of
blanchet@33192
   851
                [name] => name
blanchet@33192
   852
              | [] => FreeName (s, T, Any)
blanchet@33232
   853
              | _ => raise TERM ("Nitpick_Model.reconstruct_hol_model",
blanchet@33192
   854
                                 [Const x])) all_frees
blanchet@33192
   855
    val chunks = block_of_names true "Free variable" free_names @
blanchet@33192
   856
                 block_of_names show_skolems "Skolem constant" skolem_names @
blanchet@33192
   857
                 block_of_names true "Evaluated term" eval_names @
blanchet@33192
   858
                 block_of_datatypes @ block_of_codatatypes @
blanchet@33192
   859
                 block_of_names show_consts "Constant"
blanchet@33192
   860
                                noneval_nonskolem_nonsel_names
blanchet@33192
   861
  in
blanchet@33192
   862
    (Pretty.chunks (if null chunks then [Pretty.str "Empty assignment"]
blanchet@33192
   863
                    else chunks),
blanchet@34936
   864
     bisim_depth >= 0 orelse
blanchet@34936
   865
     forall (is_codatatype_wellformed codatatypes) codatatypes)
blanchet@33192
   866
  end
blanchet@33192
   867
blanchet@33192
   868
(* scope -> Time.time option -> nut list -> nut list -> nut NameTable.table
blanchet@34126
   869
   -> KK.raw_bound list -> term -> bool option *)
blanchet@35280
   870
fun prove_hol_model (scope as {hol_ctxt = {thy, ctxt, debug, ...},
blanchet@34998
   871
                               card_assigns, ...})
blanchet@33192
   872
                    auto_timeout free_names sel_names rel_table bounds prop =
blanchet@33192
   873
  let
blanchet@35076
   874
    val pool = Unsynchronized.ref []
blanchet@33192
   875
    (* typ * int -> term *)
blanchet@33192
   876
    fun free_type_assm (T, k) =
blanchet@33192
   877
      let
blanchet@33192
   878
        (* int -> term *)
blanchet@35076
   879
        fun atom j = nth_atom pool true T j k
blanchet@33192
   880
        fun equation_for_atom j = HOLogic.eq_const T $ Bound 0 $ atom j
blanchet@33192
   881
        val eqs = map equation_for_atom (index_seq 0 k)
blanchet@33192
   882
        val compreh_assm =
blanchet@33192
   883
          Const (@{const_name All}, (T --> bool_T) --> bool_T)
blanchet@33192
   884
              $ Abs ("x", T, foldl1 HOLogic.mk_disj eqs)
blanchet@33192
   885
        val distinct_assm = distinctness_formula T (map atom (index_seq 0 k))
blanchet@34998
   886
      in s_conj (compreh_assm, distinct_assm) end
blanchet@33192
   887
    (* nut -> term *)
blanchet@33192
   888
    fun free_name_assm name =
blanchet@33192
   889
      HOLogic.mk_eq (Free (nickname_of name, type_of name),
blanchet@35180
   890
                     term_for_name pool scope sel_names rel_table bounds name)
blanchet@33192
   891
    val freeT_assms = map free_type_assm (filter (is_TFree o fst) card_assigns)
blanchet@33192
   892
    val model_assms = map free_name_assm free_names
blanchet@34998
   893
    val assm = foldr1 s_conj (freeT_assms @ model_assms)
blanchet@33192
   894
    (* bool -> bool *)
blanchet@33192
   895
    fun try_out negate =
blanchet@33192
   896
      let
blanchet@33192
   897
        val concl = (negate ? curry (op $) @{const Not})
wenzelm@35625
   898
                    (Object_Logic.atomize_term thy prop)
blanchet@34998
   899
        val prop = HOLogic.mk_Trueprop (HOLogic.mk_imp (assm, concl))
blanchet@33192
   900
                   |> map_types (map_type_tfree
blanchet@34998
   901
                                     (fn (s, []) => TFree (s, HOLogic.typeS)
blanchet@34998
   902
                                       | x => TFree x))
blanchet@34998
   903
       val _ = if debug then
blanchet@34998
   904
                 priority ((if negate then "Genuineness" else "Spuriousness") ^
blanchet@34998
   905
                           " goal: " ^ Syntax.string_of_term ctxt prop ^ ".")
blanchet@34998
   906
               else
blanchet@34998
   907
                 ()
blanchet@34998
   908
        val goal = prop |> cterm_of thy |> Goal.init
blanchet@33192
   909
      in
blanchet@33192
   910
        (goal |> SINGLE (DETERM_TIMEOUT auto_timeout
blanchet@33192
   911
                                        (auto_tac (clasimpset_of ctxt)))
blanchet@33192
   912
              |> the |> Goal.finish ctxt; true)
blanchet@33192
   913
        handle THM _ => false
blanchet@33192
   914
             | TimeLimit.TimeOut => false
blanchet@33192
   915
      end
blanchet@33192
   916
  in
blanchet@33705
   917
    if try_out false then SOME true
blanchet@33705
   918
    else if try_out true then SOME false
blanchet@33192
   919
    else NONE
blanchet@33192
   920
  end
blanchet@33192
   921
blanchet@33192
   922
end;