src/HOL/Tools/Nitpick/nitpick_model.ML
author blanchet
Fri Dec 18 12:00:29 2009 +0100 (2009-12-18)
changeset 34126 8a2c5d7aff51
parent 34124 c4628a1dcf75
child 34936 c4f04bee79f3
permissions -rw-r--r--
polished Nitpick's binary integer support etc.;
etc. = improve inconsistent scope correction + sort values nicely in output
+ handle "mod" using the characterization "x mod y = x - x div y * y"
(instead of explicit code in Nitpick)
+ introduce KK = Kodkod as abbreviation
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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
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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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  structure NameTable : TABLE
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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 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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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 non_opt_name = nitpick_prefix ^ "non_opt"
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(* string -> int -> string *)
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fun atom_suffix s j =
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  nat_subscript (j + 1)
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  |> (s <> "" andalso Symbol.is_ascii_digit (List.last (explode s)))
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     ? prefix "\<^isub>,"
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(* string -> typ -> int -> string *)
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fun atom_name prefix (T as Type (s, _)) j =
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    prefix ^ substring (shortest_name s, 0, 1) ^ atom_suffix s j
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  | atom_name prefix (T as TFree (s, _)) j =
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    prefix ^ perhaps (try (unprefix "'")) s ^ atom_suffix s j
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  | atom_name _ T _ = raise TYPE ("Nitpick_Model.atom_name", [T], [])
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(* bool -> typ -> int -> term *)
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fun atom for_auto T j =
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  if for_auto then
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    Free (atom_name (hd (space_explode "." nitpick_prefix)) T j, T)
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  else
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    Const (atom_name "" T j, T)
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(* term -> real *)
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fun extract_real_number (Const (@{const_name HOL.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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           | _ => TermOrd.fast_term_ord tp
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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 unbit_and_unbox_term (Const (@{const_name FunBox}, _) $ t1) =
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    unbit_and_unbox_term t1
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  | unbit_and_unbox_term (Const (@{const_name PairBox},
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                          Type ("fun", [T1, Type ("fun", [T2, T3])]))
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                          $ t1 $ t2) =
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    let val Ts = map unbit_and_unbox_type [T1, T2] in
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      Const (@{const_name Pair}, Ts ---> Type ("*", Ts))
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      $ unbit_and_unbox_term t1 $ unbit_and_unbox_term t2
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    end
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  | unbit_and_unbox_term (Const (s, T)) = Const (s, unbit_and_unbox_type T)
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  | unbit_and_unbox_term (t1 $ t2) =
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    unbit_and_unbox_term t1 $ unbit_and_unbox_term t2
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  | unbit_and_unbox_term (Free (s, T)) = Free (s, unbit_and_unbox_type T)
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  | unbit_and_unbox_term (Var (x, T)) = Var (x, unbit_and_unbox_type T)
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  | unbit_and_unbox_term (Bound j) = Bound j
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  | unbit_and_unbox_term (Abs (s, T, t')) =
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    Abs (s, unbit_and_unbox_type T, unbit_and_unbox_term t')
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(* typ -> typ -> (typ * typ) * (typ * typ) *)
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fun factor_out_types (T1 as Type ("*", [T11, T12]))
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                     (T2 as Type ("*", [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 ("*", [T11, T11']), opt_T12'),
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           (Type ("*", [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 ("*", [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 ("*", [T11, T12])) T2 = ((T11, SOME T12), (T2, NONE))
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  | factor_out_types T1 (Type ("*", [T21, T22])) = ((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 orelse T2 <> bool_T then @{const_name undefined}
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               else non_opt_name, T1 --> T2)
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      | aux T1 T2 ((t1, t2) :: ps) =
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        Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
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        $ aux T1 T2 ps $ 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, _)) =
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    (s = @{const_name undefined} orelse s = non_opt_name)
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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 -> term list * term list *)
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    fun aux (Const (s, _)) = (s <> non_opt_name, ([], []))
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      | aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
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        let val (s, (ts1, ts2)) = aux t0 in (s, (t1 :: ts1, t2 :: ts2)) 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 ("*", [T1', T2']))
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            (t1 as Const (@{const_name Pair},
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                          Type ("fun", [_, Type ("fun", [_, T1])])) $ t11 $ t12)
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            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 ("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, ps) = dest_plain_fun t
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          val ps =
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            ps |>> 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) ps 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 ps =
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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 ps 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 ("fun", [T1', T2'])) (Type ("fun", [T1, T2])) t =
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          do_fun T1' T2' T1 T2 t
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        | do_term (T' as Type ("*", Ts' as [T1', T2'])) (Type ("*", [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
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  | typecast_fun T' _ _ _ = raise TYPE ("Nitpick_Model.typecast_fun", [T'], [])
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(* term -> string *)
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fun truth_const_sort_key @{const True} = "0"
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  | truth_const_sort_key @{const False} = "2"
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  | truth_const_sort_key _ = "1"
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(* typ -> term list -> term *)
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fun mk_tuple (Type ("*", [T1, T2])) ts =
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    HOLogic.mk_prod (mk_tuple T1 ts,
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        mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))
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  | mk_tuple _ (t :: _) = t
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  | mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])
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(* string * string * string * string -> scope -> nut list -> nut list
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   -> nut list -> nut NameTable.table -> KK.raw_bound list -> typ -> typ -> rep
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   -> int list list -> term *)
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fun reconstruct_term (maybe_name, base_name, step_name, abs_name)
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        ({ext_ctxt as {thy, ctxt, ...}, card_assigns, bits, datatypes, ofs, ...}
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         : scope) sel_names rel_table bounds =
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  let
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    val for_auto = (maybe_name = "")
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    (* int list list -> int *)
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    fun value_of_bits jss =
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      let
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        val j0 = offset_of_type ofs @{typ unsigned_bit}
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        val js = map (Integer.add (~ j0) o the_single) jss
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      in
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        fold (fn j => Integer.add (reasonable_power 2 j |> j = bits ? op ~))
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             js 0
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      end
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    (* bool -> typ -> typ -> (term * term) list -> term *)
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    fun make_set maybe_opt T1 T2 =
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      let
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        val empty_const = Const (@{const_name Set.empty}, T1 --> T2)
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        val insert_const = Const (@{const_name insert},
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                                  T1 --> (T1 --> T2) --> T1 --> T2)
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        (* (term * term) list -> term *)
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        fun aux [] =
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            if maybe_opt andalso not (is_complete_type datatypes T1) then
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              insert_const $ Const (unrep, T1) $ empty_const
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            else
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              empty_const
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          | aux ((t1, t2) :: zs) =
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            aux zs |> t2 <> @{const False}
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                      ? curry (op $) (insert_const
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                                      $ (t1 |> t2 <> @{const True}
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                                               ? curry (op $)
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                                                       (Const (maybe_name,
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                                                               T1 --> T1))))
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      in aux end
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   284
    (* typ -> typ -> typ -> (term * term) list -> term *)
blanchet@33192
   285
    fun make_map T1 T2 T2' =
blanchet@33192
   286
      let
blanchet@33192
   287
        val update_const = Const (@{const_name fun_upd},
blanchet@34124
   288
                                  (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
blanchet@33192
   289
        (* (term * term) list -> term *)
blanchet@33192
   290
        fun aux' [] = Const (@{const_name Map.empty}, T1 --> T2)
blanchet@33192
   291
          | aux' ((t1, t2) :: ps) =
blanchet@33192
   292
            (case t2 of
blanchet@33192
   293
               Const (@{const_name None}, _) => aux' ps
blanchet@33192
   294
             | _ => update_const $ aux' ps $ t1 $ t2)
blanchet@33192
   295
        fun aux ps =
blanchet@34123
   296
          if not (is_complete_type datatypes T1) then
blanchet@33192
   297
            update_const $ aux' ps $ Const (unrep, T1)
blanchet@33192
   298
            $ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))
blanchet@33192
   299
          else
blanchet@33192
   300
            aux' ps
blanchet@33192
   301
      in aux end
blanchet@33192
   302
    (* typ list -> term -> term *)
blanchet@33192
   303
    fun setify_mapify_funs Ts t =
blanchet@33192
   304
      (case fastype_of1 (Ts, t) of
blanchet@33192
   305
         Type ("fun", [T1, T2]) =>
blanchet@33192
   306
         if is_plain_fun t then
blanchet@33192
   307
           case T2 of
blanchet@33192
   308
             @{typ bool} =>
blanchet@33192
   309
             let
blanchet@33192
   310
               val (maybe_opt, ts_pair) =
blanchet@33192
   311
                 dest_plain_fun t ||> pairself (map (setify_mapify_funs Ts))
blanchet@33192
   312
             in
blanchet@33192
   313
               make_set maybe_opt T1 T2
blanchet@33192
   314
                        (sort_wrt (truth_const_sort_key o snd) (op ~~ ts_pair))
blanchet@33192
   315
             end
blanchet@33192
   316
           | Type (@{type_name option}, [T2']) =>
blanchet@33192
   317
             let
blanchet@33192
   318
               val ts_pair = snd (dest_plain_fun t)
blanchet@33192
   319
                             |> pairself (map (setify_mapify_funs Ts))
blanchet@33192
   320
             in make_map T1 T2 T2' (rev (op ~~ ts_pair)) end
blanchet@33192
   321
           | _ => raise SAME ()
blanchet@33192
   322
         else
blanchet@33192
   323
           raise SAME ()
blanchet@33192
   324
       | _ => raise SAME ())
blanchet@33192
   325
      handle SAME () =>
blanchet@33192
   326
             case t of
blanchet@33192
   327
               t1 $ t2 => setify_mapify_funs Ts t1 $ setify_mapify_funs Ts t2
blanchet@33192
   328
             | Abs (s, T, t') => Abs (s, T, setify_mapify_funs (T :: Ts) t')
blanchet@33192
   329
             | _ => t
blanchet@33192
   330
    (* bool -> typ -> typ -> typ -> term list -> term list -> term *)
blanchet@33192
   331
    fun make_fun maybe_opt T1 T2 T' ts1 ts2 =
blanchet@34126
   332
      ts1 ~~ ts2 |> sort (nice_term_ord o pairself fst)
blanchet@33192
   333
                 |> make_plain_fun (maybe_opt andalso not for_auto) T1 T2
blanchet@34124
   334
                 |> unbit_and_unbox_term
blanchet@34124
   335
                 |> typecast_fun (unbit_and_unbox_type T')
blanchet@34124
   336
                                 (unbit_and_unbox_type T1)
blanchet@34124
   337
                                 (unbit_and_unbox_type T2)
blanchet@33192
   338
    (* (typ * int) list -> typ -> typ -> int -> term *)
blanchet@33192
   339
    fun term_for_atom seen (T as Type ("fun", [T1, T2])) T' j =
blanchet@33192
   340
        let
blanchet@33192
   341
          val k1 = card_of_type card_assigns T1
blanchet@33192
   342
          val k2 = card_of_type card_assigns T2
blanchet@33192
   343
        in
blanchet@33192
   344
          term_for_rep seen T T' (Vect (k1, Atom (k2, 0)))
blanchet@33192
   345
                       [nth_combination (replicate k1 (k2, 0)) j]
blanchet@33192
   346
          handle General.Subscript =>
blanchet@33232
   347
                 raise ARG ("Nitpick_Model.reconstruct_term.term_for_atom",
blanchet@33192
   348
                            signed_string_of_int j ^ " for " ^
blanchet@33192
   349
                            string_for_rep (Vect (k1, Atom (k2, 0))))
blanchet@33192
   350
        end
blanchet@33192
   351
      | term_for_atom seen (Type ("*", [T1, T2])) _ j =
blanchet@33192
   352
        let val k1 = card_of_type card_assigns T1 in
blanchet@33192
   353
          list_comb (HOLogic.pair_const T1 T2,
blanchet@33192
   354
                     map2 (fn T => term_for_atom seen T T) [T1, T2]
blanchet@33192
   355
                          [j div k1, j mod k1])
blanchet@33192
   356
        end
blanchet@33192
   357
      | term_for_atom seen @{typ prop} _ j =
blanchet@33192
   358
        HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j)
blanchet@33192
   359
      | term_for_atom _ @{typ bool} _ j =
blanchet@33192
   360
        if j = 0 then @{const False} else @{const True}
blanchet@33192
   361
      | term_for_atom _ @{typ unit} _ _ = @{const Unity}
blanchet@33192
   362
      | term_for_atom seen T _ j =
blanchet@33192
   363
        if T = nat_T then
blanchet@33192
   364
          HOLogic.mk_number nat_T j
blanchet@33192
   365
        else if T = int_T then
blanchet@33192
   366
          HOLogic.mk_number int_T
blanchet@33192
   367
              (int_for_atom (card_of_type card_assigns int_T, 0) j)
blanchet@33192
   368
        else if is_fp_iterator_type T then
blanchet@33192
   369
          HOLogic.mk_number nat_T (card_of_type card_assigns T - j - 1)
blanchet@33192
   370
        else if T = @{typ bisim_iterator} then
blanchet@33192
   371
          HOLogic.mk_number nat_T j
blanchet@33192
   372
        else case datatype_spec datatypes T of
blanchet@33192
   373
          NONE => atom for_auto T j
blanchet@33558
   374
        | SOME {shallow = true, ...} => atom for_auto T j
blanchet@33558
   375
        | SOME {co, constrs, ...} =>
blanchet@33192
   376
          let
blanchet@33192
   377
            (* styp -> int list *)
blanchet@33192
   378
            fun tuples_for_const (s, T) =
blanchet@33192
   379
              tuple_list_for_name rel_table bounds (ConstName (s, T, Any))
blanchet@33192
   380
            (* unit -> indexname * typ *)
blanchet@33192
   381
            fun var () = ((atom_name "" T j, 0), T)
blanchet@33192
   382
            val discr_jsss = map (tuples_for_const o discr_for_constr o #const)
blanchet@33192
   383
                                 constrs
blanchet@33192
   384
            val real_j = j + offset_of_type ofs T
blanchet@33192
   385
            val constr_x as (constr_s, constr_T) =
blanchet@33192
   386
              get_first (fn (jss, {const, ...}) =>
blanchet@34121
   387
                            if member (op =) jss [real_j] then SOME const
blanchet@34121
   388
                            else NONE)
blanchet@33192
   389
                        (discr_jsss ~~ constrs) |> the
blanchet@33192
   390
            val arg_Ts = curried_binder_types constr_T
blanchet@33192
   391
            val sel_xs = map (boxed_nth_sel_for_constr ext_ctxt constr_x)
blanchet@33192
   392
                             (index_seq 0 (length arg_Ts))
blanchet@33192
   393
            val sel_Rs =
blanchet@33192
   394
              map (fn x => get_first
blanchet@33192
   395
                               (fn ConstName (s', T', R) =>
blanchet@33192
   396
                                   if (s', T') = x then SOME R else NONE
blanchet@33232
   397
                                 | u => raise NUT ("Nitpick_Model.reconstruct_\
blanchet@33192
   398
                                                   \term.term_for_atom", [u]))
blanchet@33192
   399
                               sel_names |> the) sel_xs
blanchet@33192
   400
            val arg_Rs = map (snd o dest_Func) sel_Rs
blanchet@33192
   401
            val sel_jsss = map tuples_for_const sel_xs
blanchet@33192
   402
            val arg_jsss =
blanchet@33192
   403
              map (map_filter (fn js => if hd js = real_j then SOME (tl js)
blanchet@33192
   404
                                        else NONE)) sel_jsss
blanchet@33192
   405
            val uncur_arg_Ts = binder_types constr_T
blanchet@33192
   406
          in
blanchet@34121
   407
            if co andalso member (op =) seen (T, j) then
blanchet@33192
   408
              Var (var ())
blanchet@34124
   409
            else if constr_s = @{const_name Word} then
blanchet@34124
   410
              HOLogic.mk_number
blanchet@34124
   411
                  (if T = @{typ "unsigned_bit word"} then nat_T else int_T)
blanchet@34124
   412
                  (value_of_bits (the_single arg_jsss))
blanchet@33192
   413
            else
blanchet@33192
   414
              let
blanchet@33192
   415
                val seen = seen |> co ? cons (T, j)
blanchet@33192
   416
                val ts =
blanchet@33192
   417
                  if length arg_Ts = 0 then
blanchet@33192
   418
                    []
blanchet@33192
   419
                  else
blanchet@33192
   420
                    map3 (fn Ts => term_for_rep seen Ts Ts) arg_Ts arg_Rs
blanchet@33192
   421
                         arg_jsss
blanchet@33192
   422
                    |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)
blanchet@33192
   423
                    |> dest_n_tuple (length uncur_arg_Ts)
blanchet@33192
   424
                val t =
blanchet@33192
   425
                  if constr_s = @{const_name Abs_Frac} then
blanchet@33192
   426
                    let
blanchet@33192
   427
                      val num_T = body_type T
blanchet@33192
   428
                      (* int -> term *)
blanchet@33192
   429
                      val mk_num = HOLogic.mk_number num_T
blanchet@33192
   430
                    in
blanchet@33192
   431
                      case ts of
blanchet@33192
   432
                        [Const (@{const_name Pair}, _) $ t1 $ t2] =>
blanchet@33192
   433
                        (case snd (HOLogic.dest_number t1) of
blanchet@33192
   434
                           0 => mk_num 0
blanchet@33192
   435
                         | n1 => case HOLogic.dest_number t2 |> snd of
blanchet@33192
   436
                                   1 => mk_num n1
blanchet@33192
   437
                                 | n2 => Const (@{const_name HOL.divide},
blanchet@34124
   438
                                                num_T --> num_T --> num_T)
blanchet@33192
   439
                                         $ mk_num n1 $ mk_num n2)
blanchet@33232
   440
                      | _ => raise TERM ("Nitpick_Model.reconstruct_term.term_\
blanchet@33192
   441
                                         \for_atom (Abs_Frac)", ts)
blanchet@33192
   442
                    end
blanchet@33192
   443
                  else if not for_auto andalso is_abs_fun thy constr_x then
blanchet@33192
   444
                    Const (abs_name, constr_T) $ the_single ts
blanchet@33192
   445
                  else
blanchet@33192
   446
                    list_comb (Const constr_x, ts)
blanchet@33192
   447
              in
blanchet@33192
   448
                if co then
blanchet@33192
   449
                  let val var = var () in
blanchet@34121
   450
                    if exists_subterm (curry (op =) (Var var)) t then
blanchet@33192
   451
                      Const (@{const_name The}, (T --> bool_T) --> T)
blanchet@33192
   452
                      $ Abs ("\<omega>", T,
blanchet@34124
   453
                             Const (@{const_name "op ="}, T --> T --> bool_T)
blanchet@33192
   454
                             $ Bound 0 $ abstract_over (Var var, t))
blanchet@33192
   455
                    else
blanchet@33192
   456
                      t
blanchet@33192
   457
                  end
blanchet@33192
   458
                else
blanchet@33192
   459
                  t
blanchet@33192
   460
              end
blanchet@33192
   461
          end
blanchet@33192
   462
    (* (typ * int) list -> int -> rep -> typ -> typ -> typ -> int list
blanchet@33192
   463
       -> term *)
blanchet@33192
   464
    and term_for_vect seen k R T1 T2 T' js =
blanchet@33192
   465
      make_fun true T1 T2 T' (map (term_for_atom seen T1 T1) (index_seq 0 k))
blanchet@33192
   466
               (map (term_for_rep seen T2 T2 R o single)
blanchet@33192
   467
                    (batch_list (arity_of_rep R) js))
blanchet@33192
   468
    (* (typ * int) list -> typ -> typ -> rep -> int list list -> term *)
blanchet@33192
   469
    and term_for_rep seen T T' Unit [[]] = term_for_atom seen T T' 0
blanchet@33192
   470
      | term_for_rep seen T T' (R as Atom (k, j0)) [[j]] =
blanchet@33192
   471
        if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0)
blanchet@33232
   472
        else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])
blanchet@33192
   473
      | term_for_rep seen (Type ("*", [T1, T2])) _ (Struct [R1, R2]) [js] =
blanchet@33192
   474
        let
blanchet@33192
   475
          val arity1 = arity_of_rep R1
blanchet@33192
   476
          val (js1, js2) = chop arity1 js
blanchet@33192
   477
        in
blanchet@33192
   478
          list_comb (HOLogic.pair_const T1 T2,
blanchet@33192
   479
                     map3 (fn T => term_for_rep seen T T) [T1, T2] [R1, R2]
blanchet@33192
   480
                          [[js1], [js2]])
blanchet@33192
   481
        end
blanchet@33192
   482
      | term_for_rep seen (Type ("fun", [T1, T2])) T' (R as Vect (k, R')) [js] =
blanchet@33192
   483
        term_for_vect seen k R' T1 T2 T' js
blanchet@33192
   484
      | term_for_rep seen (Type ("fun", [T1, T2])) T' (Func (R1, Formula Neut))
blanchet@33192
   485
                     jss =
blanchet@33192
   486
        let
blanchet@33192
   487
          val jss1 = all_combinations_for_rep R1
blanchet@33192
   488
          val ts1 = map (term_for_rep seen T1 T1 R1 o single) jss1
blanchet@33192
   489
          val ts2 =
blanchet@33192
   490
            map (fn js => term_for_rep seen T2 T2 (Atom (2, 0))
blanchet@34121
   491
                                       [[int_for_bool (member (op =) jss js)]])
blanchet@34121
   492
                jss1
blanchet@33192
   493
        in make_fun false T1 T2 T' ts1 ts2 end
blanchet@33192
   494
      | term_for_rep seen (Type ("fun", [T1, T2])) T' (Func (R1, R2)) jss =
blanchet@33192
   495
        let
blanchet@33192
   496
          val arity1 = arity_of_rep R1
blanchet@33192
   497
          val jss1 = all_combinations_for_rep R1
blanchet@33192
   498
          val ts1 = map (term_for_rep seen T1 T1 R1 o single) jss1
blanchet@33192
   499
          val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)
blanchet@33192
   500
          val ts2 = map (term_for_rep seen T2 T2 R2 o the_default []
blanchet@33192
   501
                         o AList.lookup (op =) grouped_jss2) jss1
blanchet@33192
   502
        in make_fun true T1 T2 T' ts1 ts2 end
blanchet@33192
   503
      | term_for_rep seen T T' (Opt R) jss =
blanchet@33192
   504
        if null jss then Const (unknown, T) else term_for_rep seen T T' R jss
blanchet@33192
   505
      | term_for_rep seen T _ R jss =
blanchet@33232
   506
        raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",
blanchet@33192
   507
                   Refute.string_of_typ T ^ " " ^ string_for_rep R ^ " " ^
blanchet@33192
   508
                   string_of_int (length jss))
blanchet@33192
   509
  in
blanchet@34124
   510
    (not for_auto ? setify_mapify_funs []) o unbit_and_unbox_term
blanchet@34124
   511
    oooo term_for_rep []
blanchet@33192
   512
  end
blanchet@33192
   513
blanchet@34126
   514
(* scope -> nut list -> nut NameTable.table -> KK.raw_bound list -> nut
blanchet@33192
   515
   -> term *)
blanchet@33192
   516
fun term_for_name scope sel_names rel_table bounds name =
blanchet@33192
   517
  let val T = type_of name in
blanchet@33192
   518
    tuple_list_for_name rel_table bounds name
blanchet@33192
   519
    |> reconstruct_term ("", "", "", "") scope sel_names rel_table bounds T T
blanchet@33192
   520
                        (rep_of name)
blanchet@33192
   521
  end
blanchet@33192
   522
blanchet@33192
   523
(* Proof.context
blanchet@33192
   524
   -> (string * string * string * string * string) * Proof.context *)
blanchet@33192
   525
fun add_wacky_syntax ctxt =
blanchet@33192
   526
  let
blanchet@33192
   527
    (* term -> string *)
blanchet@33192
   528
    val name_of = fst o dest_Const
blanchet@33192
   529
    val thy = ProofContext.theory_of ctxt |> Context.reject_draft
blanchet@33192
   530
    val (maybe_t, thy) =
blanchet@33202
   531
      Sign.declare_const ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),
blanchet@33202
   532
                          Mixfix (maybe_mixfix, [1000], 1000)) thy
blanchet@33192
   533
    val (base_t, thy) =
blanchet@33202
   534
      Sign.declare_const ((@{binding nitpick_base}, @{typ "'a => 'a"}),
blanchet@33202
   535
                          Mixfix (base_mixfix, [1000], 1000)) thy
blanchet@33192
   536
    val (step_t, thy) =
blanchet@33202
   537
      Sign.declare_const ((@{binding nitpick_step}, @{typ "'a => 'a"}),
blanchet@33202
   538
                          Mixfix (step_mixfix, [1000], 1000)) thy
blanchet@33192
   539
    val (abs_t, thy) =
blanchet@33202
   540
      Sign.declare_const ((@{binding nitpick_abs}, @{typ "'a => 'b"}),
blanchet@33202
   541
                          Mixfix (abs_mixfix, [40], 40)) thy
blanchet@33192
   542
  in
blanchet@33192
   543
    ((name_of maybe_t, name_of base_t, name_of step_t, name_of abs_t),
blanchet@33192
   544
     ProofContext.transfer_syntax thy ctxt)
blanchet@33192
   545
  end
blanchet@33192
   546
blanchet@33192
   547
(* term -> term *)
blanchet@33192
   548
fun unfold_outer_the_binders (t as Const (@{const_name The}, _)
blanchet@33192
   549
                                   $ Abs (s, T, Const (@{const_name "op ="}, _)
blanchet@33192
   550
                                                $ Bound 0 $ t')) =
blanchet@33192
   551
    betapply (Abs (s, T, t'), t) |> unfold_outer_the_binders
blanchet@33192
   552
  | unfold_outer_the_binders t = t
blanchet@33192
   553
(* typ list -> int -> term * term -> bool *)
blanchet@33192
   554
fun bisimilar_values _ 0 _ = true
blanchet@33192
   555
  | bisimilar_values coTs max_depth (t1, t2) =
blanchet@33192
   556
    let val T = fastype_of t1 in
blanchet@33192
   557
      if exists_subtype (member (op =) coTs) T then
blanchet@33192
   558
        let
blanchet@33192
   559
          val ((head1, args1), (head2, args2)) =
blanchet@33192
   560
            pairself (strip_comb o unfold_outer_the_binders) (t1, t2)
blanchet@34121
   561
          val max_depth = max_depth - (if member (op =) coTs T then 1 else 0)
blanchet@33192
   562
        in
blanchet@33192
   563
          head1 = head2
blanchet@33192
   564
          andalso forall (bisimilar_values coTs max_depth) (args1 ~~ args2)
blanchet@33192
   565
        end
blanchet@33192
   566
      else
blanchet@33192
   567
        t1 = t2
blanchet@33192
   568
    end
blanchet@33192
   569
blanchet@33192
   570
(* params -> scope -> (term option * int list) list -> styp list -> nut list
blanchet@34126
   571
  -> nut list -> nut list -> nut NameTable.table -> KK.raw_bound list
blanchet@33192
   572
  -> Pretty.T * bool *)
blanchet@33192
   573
fun reconstruct_hol_model {show_skolems, show_datatypes, show_consts}
blanchet@34124
   574
        ({ext_ctxt as {thy, ctxt, max_bisim_depth, boxes, wfs, user_axioms,
blanchet@34124
   575
                       debug, binary_ints, destroy_constrs, specialize,
blanchet@34124
   576
                       skolemize, star_linear_preds, uncurry, fast_descrs,
blanchet@34124
   577
                       tac_timeout, evals, case_names, def_table, nondef_table,
blanchet@34124
   578
                       user_nondefs, simp_table, psimp_table, intro_table,
blanchet@34124
   579
                       ground_thm_table, ersatz_table, skolems, special_funs,
blanchet@34124
   580
                       unrolled_preds, wf_cache, constr_cache},
blanchet@34124
   581
         card_assigns, bits, bisim_depth, datatypes, ofs} : scope)
blanchet@34124
   582
        formats all_frees free_names sel_names nonsel_names rel_table bounds =
blanchet@33192
   583
  let
blanchet@33192
   584
    val (wacky_names as (_, base_name, step_name, _), ctxt) =
blanchet@33192
   585
      add_wacky_syntax ctxt
blanchet@33192
   586
    val ext_ctxt =
blanchet@33192
   587
      {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
blanchet@33192
   588
       wfs = wfs, user_axioms = user_axioms, debug = debug,
blanchet@34124
   589
       binary_ints = binary_ints, destroy_constrs = destroy_constrs,
blanchet@34124
   590
       specialize = specialize, skolemize = skolemize,
blanchet@34124
   591
       star_linear_preds = star_linear_preds, uncurry = uncurry,
blanchet@34124
   592
       fast_descrs = fast_descrs, tac_timeout = tac_timeout, evals = evals,
blanchet@34124
   593
       case_names = case_names, def_table = def_table,
blanchet@33192
   594
       nondef_table = nondef_table, user_nondefs = user_nondefs,
blanchet@33192
   595
       simp_table = simp_table, psimp_table = psimp_table,
blanchet@33192
   596
       intro_table = intro_table, ground_thm_table = ground_thm_table,
blanchet@33192
   597
       ersatz_table = ersatz_table, skolems = skolems,
blanchet@33192
   598
       special_funs = special_funs, unrolled_preds = unrolled_preds,
blanchet@33580
   599
       wf_cache = wf_cache, constr_cache = constr_cache}
blanchet@33192
   600
    val scope = {ext_ctxt = ext_ctxt, card_assigns = card_assigns,
blanchet@34124
   601
                 bits = bits, bisim_depth = bisim_depth, datatypes = datatypes,
blanchet@34124
   602
                 ofs = ofs}
blanchet@33192
   603
    (* typ -> typ -> rep -> int list list -> term *)
blanchet@33192
   604
    val term_for_rep = reconstruct_term wacky_names scope sel_names rel_table
blanchet@33192
   605
                                        bounds
blanchet@34124
   606
    (* nat -> typ -> nat -> typ *)
blanchet@34124
   607
    fun nth_value_of_type card T n = term_for_rep T T (Atom (card, 0)) [[n]]
blanchet@34124
   608
    (* nat -> typ -> typ list *)
blanchet@34124
   609
    fun all_values_of_type card T =
blanchet@34124
   610
      index_seq 0 card |> map (nth_value_of_type card T) |> sort nice_term_ord
blanchet@33192
   611
    (* dtype_spec list -> dtype_spec -> bool *)
blanchet@33192
   612
    fun is_codatatype_wellformed (cos : dtype_spec list)
blanchet@33192
   613
                                 ({typ, card, ...} : dtype_spec) =
blanchet@33192
   614
      let
blanchet@34124
   615
        val ts = all_values_of_type card typ
blanchet@33192
   616
        val max_depth = Integer.sum (map #card cos)
blanchet@33192
   617
      in
blanchet@33192
   618
        forall (not o bisimilar_values (map #typ cos) max_depth)
blanchet@33192
   619
               (all_distinct_unordered_pairs_of ts)
blanchet@33192
   620
      end
blanchet@33192
   621
    (* string -> Pretty.T *)
blanchet@33192
   622
    fun pretty_for_assign name =
blanchet@33192
   623
      let
blanchet@33192
   624
        val (oper, (t1, T'), T) =
blanchet@33192
   625
          case name of
blanchet@33192
   626
            FreeName (s, T, _) =>
blanchet@34124
   627
            let val t = Free (s, unbit_and_unbox_type T) in
blanchet@33192
   628
              ("=", (t, format_term_type thy def_table formats t), T)
blanchet@33192
   629
            end
blanchet@33192
   630
          | ConstName (s, T, _) =>
blanchet@33192
   631
            (assign_operator_for_const (s, T),
blanchet@33192
   632
             user_friendly_const ext_ctxt (base_name, step_name) formats (s, T),
blanchet@33192
   633
             T)
blanchet@33232
   634
          | _ => raise NUT ("Nitpick_Model.reconstruct_hol_model.\
blanchet@33192
   635
                            \pretty_for_assign", [name])
blanchet@33192
   636
        val t2 = if rep_of name = Any then
blanchet@33192
   637
                   Const (@{const_name undefined}, T')
blanchet@33192
   638
                 else
blanchet@33192
   639
                   tuple_list_for_name rel_table bounds name
blanchet@33192
   640
                   |> term_for_rep T T' (rep_of name)
blanchet@33192
   641
      in
blanchet@33192
   642
        Pretty.block (Pretty.breaks
blanchet@33571
   643
            [setmp_show_all_types (Syntax.pretty_term ctxt) t1,
blanchet@33192
   644
             Pretty.str oper, Syntax.pretty_term ctxt t2])
blanchet@33192
   645
      end
blanchet@33192
   646
    (* dtype_spec -> Pretty.T *)
blanchet@34123
   647
    fun pretty_for_datatype ({typ, card, complete, ...} : dtype_spec) =
blanchet@33192
   648
      Pretty.block (Pretty.breaks
blanchet@34124
   649
          [Syntax.pretty_typ ctxt (unbit_and_unbox_type typ), Pretty.str "=",
blanchet@33192
   650
           Pretty.enum "," "{" "}"
blanchet@34124
   651
               (map (Syntax.pretty_term ctxt) (all_values_of_type card typ)
blanchet@34124
   652
                @ (if complete then [] else [Pretty.str unrep]))])
blanchet@33192
   653
    (* typ -> dtype_spec list *)
blanchet@33192
   654
    fun integer_datatype T =
blanchet@33192
   655
      [{typ = T, card = card_of_type card_assigns T, co = false,
blanchet@34123
   656
        complete = false, concrete = true, shallow = false, constrs = []}]
blanchet@33232
   657
      handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []
blanchet@33192
   658
    val (codatatypes, datatypes) =
blanchet@33558
   659
      datatypes |> filter_out #shallow
blanchet@33558
   660
                |> List.partition #co
blanchet@33558
   661
                ||> append (integer_datatype nat_T @ integer_datatype int_T)
blanchet@33192
   662
    val block_of_datatypes =
blanchet@33192
   663
      if show_datatypes andalso not (null datatypes) then
blanchet@33192
   664
        [Pretty.big_list ("Datatype" ^ plural_s_for_list datatypes ^ ":")
blanchet@33192
   665
                         (map pretty_for_datatype datatypes)]
blanchet@33192
   666
      else
blanchet@33192
   667
        []
blanchet@33192
   668
    val block_of_codatatypes =
blanchet@33192
   669
      if show_datatypes andalso not (null codatatypes) then
blanchet@33192
   670
        [Pretty.big_list ("Codatatype" ^ plural_s_for_list codatatypes ^ ":")
blanchet@33192
   671
                         (map pretty_for_datatype codatatypes)]
blanchet@33192
   672
      else
blanchet@33192
   673
        []
blanchet@33192
   674
    (* bool -> string -> nut list -> Pretty.T list *)
blanchet@33192
   675
    fun block_of_names show title names =
blanchet@33192
   676
      if show andalso not (null names) then
blanchet@33192
   677
        Pretty.str (title ^ plural_s_for_list names ^ ":")
blanchet@33192
   678
        :: map (Pretty.indent indent_size o pretty_for_assign)
blanchet@33192
   679
               (sort_wrt (original_name o nickname_of) names)
blanchet@33192
   680
      else
blanchet@33192
   681
        []
blanchet@33192
   682
    val (skolem_names, nonskolem_nonsel_names) =
blanchet@33192
   683
      List.partition is_skolem_name nonsel_names
blanchet@33192
   684
    val (eval_names, noneval_nonskolem_nonsel_names) =
blanchet@33192
   685
      List.partition (String.isPrefix eval_prefix o nickname_of)
blanchet@33192
   686
                     nonskolem_nonsel_names
blanchet@34121
   687
      ||> filter_out (curry (op =) @{const_name bisim_iterator_max}
blanchet@34121
   688
                      o nickname_of)
blanchet@33192
   689
    val free_names =
blanchet@33192
   690
      map (fn x as (s, T) =>
blanchet@34121
   691
              case filter (curry (op =) x
blanchet@34124
   692
                           o pairf nickname_of (unbit_and_unbox_type o type_of))
blanchet@33192
   693
                          free_names of
blanchet@33192
   694
                [name] => name
blanchet@33192
   695
              | [] => FreeName (s, T, Any)
blanchet@33232
   696
              | _ => raise TERM ("Nitpick_Model.reconstruct_hol_model",
blanchet@33192
   697
                                 [Const x])) all_frees
blanchet@33192
   698
    val chunks = block_of_names true "Free variable" free_names @
blanchet@33192
   699
                 block_of_names show_skolems "Skolem constant" skolem_names @
blanchet@33192
   700
                 block_of_names true "Evaluated term" eval_names @
blanchet@33192
   701
                 block_of_datatypes @ block_of_codatatypes @
blanchet@33192
   702
                 block_of_names show_consts "Constant"
blanchet@33192
   703
                                noneval_nonskolem_nonsel_names
blanchet@33192
   704
  in
blanchet@33192
   705
    (Pretty.chunks (if null chunks then [Pretty.str "Empty assignment"]
blanchet@33192
   706
                    else chunks),
blanchet@33192
   707
     bisim_depth >= 0
blanchet@33192
   708
     orelse forall (is_codatatype_wellformed codatatypes) codatatypes)
blanchet@33192
   709
  end
blanchet@33192
   710
blanchet@33192
   711
(* scope -> Time.time option -> nut list -> nut list -> nut NameTable.table
blanchet@34126
   712
   -> KK.raw_bound list -> term -> bool option *)
blanchet@33192
   713
fun prove_hol_model (scope as {ext_ctxt as {thy, ctxt, ...}, card_assigns, ...})
blanchet@33192
   714
                    auto_timeout free_names sel_names rel_table bounds prop =
blanchet@33192
   715
  let
blanchet@33192
   716
    (* typ * int -> term *)
blanchet@33192
   717
    fun free_type_assm (T, k) =
blanchet@33192
   718
      let
blanchet@33192
   719
        (* int -> term *)
blanchet@33192
   720
        val atom = atom true T
blanchet@33192
   721
        fun equation_for_atom j = HOLogic.eq_const T $ Bound 0 $ atom j
blanchet@33192
   722
        val eqs = map equation_for_atom (index_seq 0 k)
blanchet@33192
   723
        val compreh_assm =
blanchet@33192
   724
          Const (@{const_name All}, (T --> bool_T) --> bool_T)
blanchet@33192
   725
              $ Abs ("x", T, foldl1 HOLogic.mk_disj eqs)
blanchet@33192
   726
        val distinct_assm = distinctness_formula T (map atom (index_seq 0 k))
blanchet@33192
   727
      in HOLogic.mk_conj (compreh_assm, distinct_assm) end
blanchet@33192
   728
    (* nut -> term *)
blanchet@33192
   729
    fun free_name_assm name =
blanchet@33192
   730
      HOLogic.mk_eq (Free (nickname_of name, type_of name),
blanchet@33192
   731
                     term_for_name scope sel_names rel_table bounds name)
blanchet@33192
   732
    val freeT_assms = map free_type_assm (filter (is_TFree o fst) card_assigns)
blanchet@33192
   733
    val model_assms = map free_name_assm free_names
blanchet@33192
   734
    val assm = List.foldr HOLogic.mk_conj @{const True}
blanchet@33192
   735
                          (freeT_assms @ model_assms)
blanchet@33192
   736
    (* bool -> bool *)
blanchet@33192
   737
    fun try_out negate =
blanchet@33192
   738
      let
blanchet@33192
   739
        val concl = (negate ? curry (op $) @{const Not})
blanchet@33192
   740
                    (ObjectLogic.atomize_term thy prop)
blanchet@33192
   741
        val goal = HOLogic.mk_Trueprop (HOLogic.mk_imp (assm, concl))
blanchet@33192
   742
                   |> map_types (map_type_tfree
blanchet@33192
   743
                          (fn (s, []) => TFree (s, HOLogic.typeS)
blanchet@33192
   744
                            | x => TFree x))
blanchet@33192
   745
                   |> cterm_of thy |> Goal.init
blanchet@33192
   746
      in
blanchet@33192
   747
        (goal |> SINGLE (DETERM_TIMEOUT auto_timeout
blanchet@33192
   748
                                        (auto_tac (clasimpset_of ctxt)))
blanchet@33192
   749
              |> the |> Goal.finish ctxt; true)
blanchet@33192
   750
        handle THM _ => false
blanchet@33192
   751
             | TimeLimit.TimeOut => false
blanchet@33192
   752
      end
blanchet@33192
   753
  in
blanchet@33705
   754
    if try_out false then SOME true
blanchet@33705
   755
    else if try_out true then SOME false
blanchet@33192
   756
    else NONE
blanchet@33192
   757
  end
blanchet@33192
   758
blanchet@33192
   759
end;