src/HOL/Tools/Nitpick/nitpick_model.ML

 (* nut NameTable.table -> KK.raw_bound list -> nut -> int list list *)
 fun tuple_list_for_name rel_table bounds name =
   the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]
 
 (* term -> term *)
-fun unarize_and_unbox_term (Const (@{const_name FunBox}, _) $ t1) =
-    unarize_and_unbox_term t1
-  | unarize_and_unbox_term (Const (@{const_name PairBox},
-                                   Type ("fun", [T1, Type ("fun", [T2, _])]))
-                            $ t1 $ t2) =
-    let val Ts = map unarize_unbox_and_uniterize_type [T1, T2] in
-      Const (@{const_name Pair}, Ts ---> Type ("*", Ts))
-      $ unarize_and_unbox_term t1 $ unarize_and_unbox_term t2
+fun unarize_unbox_etc_term (Const (@{const_name FinFun}, _) $ t1) =
+    unarize_unbox_etc_term t1
+  | unarize_unbox_etc_term (Const (@{const_name FunBox}, _) $ t1) =
+    unarize_unbox_etc_term t1
+  | unarize_unbox_etc_term
+        (Const (@{const_name PairBox},
+                Type (@{type_name fun}, [T1, Type (@{type_name fun}, [T2, _])]))
+         $ t1 $ t2) =
+    let val Ts = map uniterize_unarize_unbox_etc_type [T1, T2] in
+      Const (@{const_name Pair}, Ts ---> Type (@{type_name "*"}, Ts))
+      $ unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
     end
-  | unarize_and_unbox_term (Const (s, T)) =
-    Const (s, unarize_unbox_and_uniterize_type T)
-  | unarize_and_unbox_term (t1 $ t2) =
-    unarize_and_unbox_term t1 $ unarize_and_unbox_term t2
-  | unarize_and_unbox_term (Free (s, T)) =
-    Free (s, unarize_unbox_and_uniterize_type T)
-  | unarize_and_unbox_term (Var (x, T)) =
-    Var (x, unarize_unbox_and_uniterize_type T)
-  | unarize_and_unbox_term (Bound j) = Bound j
-  | unarize_and_unbox_term (Abs (s, T, t')) =
-    Abs (s, unarize_unbox_and_uniterize_type T, unarize_and_unbox_term t')
+  | unarize_unbox_etc_term (Const (s, T)) =
+    Const (s, uniterize_unarize_unbox_etc_type T)
+  | unarize_unbox_etc_term (t1 $ t2) =
+    unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
+  | unarize_unbox_etc_term (Free (s, T)) =
+    Free (s, uniterize_unarize_unbox_etc_type T)
+  | unarize_unbox_etc_term (Var (x, T)) =
+    Var (x, uniterize_unarize_unbox_etc_type T)
+  | unarize_unbox_etc_term (Bound j) = Bound j
+  | unarize_unbox_etc_term (Abs (s, T, t')) =
+    Abs (s, uniterize_unarize_unbox_etc_type T, unarize_unbox_etc_term t')
 
 (* typ -> typ -> (typ * typ) * (typ * typ) *)
-fun factor_out_types (T1 as Type ("*", [T11, T12]))
-                     (T2 as Type ("*", [T21, T22])) =
+fun factor_out_types (T1 as Type (@{type_name "*"}, [T11, T12]))
+                     (T2 as Type (@{type_name "*"}, [T21, T22])) =
     let val (n1, n2) = pairself num_factors_in_type (T11, T21) in
       if n1 = n2 then
         let
           val ((T11', opt_T12'), (T21', opt_T22')) = factor_out_types T12 T22
         in
-          ((Type ("*", [T11, T11']), opt_T12'),
-           (Type ("*", [T21, T21']), opt_T22'))
+          ((Type (@{type_name "*"}, [T11, T11']), opt_T12'),
+           (Type (@{type_name "*"}, [T21, T21']), opt_T22'))
         end
       else if n1 < n2 then
         case factor_out_types T1 T21 of
           (p1, (T21', NONE)) => (p1, (T21', SOME T22))
         | (p1, (T21', SOME T22')) =>
-          (p1, (T21', SOME (Type ("*", [T22', T22]))))
+          (p1, (T21', SOME (Type (@{type_name "*"}, [T22', T22]))))
       else
         swap (factor_out_types T2 T1)
     end
-  | factor_out_types (Type ("*", [T11, T12])) T2 = ((T11, SOME T12), (T2, NONE))
-  | factor_out_types T1 (Type ("*", [T21, T22])) = ((T1, NONE), (T21, SOME T22))
+  | factor_out_types (Type (@{type_name "*"}, [T11, T12])) T2 =
+    ((T11, SOME T12), (T2, NONE))
+  | factor_out_types T1 (Type (@{type_name "*"}, [T21, T22])) =
+    ((T1, NONE), (T21, SOME T22))
   | factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))
 
 (* bool -> typ -> typ -> (term * term) list -> term *)
 fun make_plain_fun maybe_opt T1 T2 =
   let

     val cut = length (HOLogic.strip_tupleT T1)
     val (ps1, ps2) = pairself HOLogic.flat_tupleT_paths (T1, T2)
     val (ts1, ts2) = t |> HOLogic.strip_ptuple ps |> chop cut
   in (HOLogic.mk_ptuple ps1 T1 ts1, HOLogic.mk_ptuple ps2 T2 ts2) end
 (* typ -> term -> term -> term *)
-fun pair_up (Type ("*", [T1', T2']))
+fun pair_up (Type (@{type_name "*"}, [T1', T2']))
             (t1 as Const (@{const_name Pair},
-                          Type ("fun", [_, Type ("fun", [_, T1])])) $ t11 $ t12)
-            t2 =
+                          Type (@{type_name fun},
+                                [_, Type (@{type_name fun}, [_, T1])]))
+             $ t11 $ t12) t2 =
     if T1 = T1' then HOLogic.mk_prod (t1, t2)
     else HOLogic.mk_prod (t11, pair_up T2' t12 t2)
   | pair_up _ t1 t2 = HOLogic.mk_prod (t1, t2)
 (* typ -> term -> term list * term list -> (term * term) list*)
 fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3
 
 (* typ -> typ -> typ -> term -> term *)
-fun typecast_fun (Type ("fun", [T1', T2'])) T1 T2 t =
+fun typecast_fun (Type (@{type_name fun}, [T1', T2'])) T1 T2 t =
     let
       (* typ -> typ -> typ -> typ -> term -> term *)
       fun do_curry T1 T1a T1b T2 t =
         let
           val (maybe_opt, ps) = dest_plain_fun t

           t |> do_curry T1 T1a T1b T2 |> do_arrow T1' T2' T1a (T1b --> T2)
         | ((T1a', SOME T1b'), (_, NONE)) =>
           t |> do_arrow T1a' (T1b' --> T2') T1 T2 |> do_uncurry T1' T2'
         | _ => raise TYPE ("Nitpick_Model.typecast_fun.do_fun", [T1, T1'], [])
       (* typ -> typ -> term -> term *)
-      and do_term (Type ("fun", [T1', T2'])) (Type ("fun", [T1, T2])) t =
+      and do_term (Type (@{type_name fun}, [T1', T2']))
+                  (Type (@{type_name fun}, [T1, T2])) t =
           do_fun T1' T2' T1 T2 t
-        | do_term (T' as Type ("*", Ts' as [T1', T2'])) (Type ("*", [T1, T2]))
+        | do_term (T' as Type (@{type_name "*"}, Ts' as [T1', T2']))
+                  (Type (@{type_name "*"}, [T1, T2]))
                   (Const (@{const_name Pair}, _) $ t1 $ t2) =
           Const (@{const_name Pair}, Ts' ---> T')
           $ do_term T1' T1 t1 $ do_term T2' T2 t2
         | do_term T' T t =
           if T = T' then t

 fun truth_const_sort_key @{const True} = "0"
   | truth_const_sort_key @{const False} = "2"
   | truth_const_sort_key _ = "1"
 
 (* typ -> term list -> term *)
-fun mk_tuple (Type ("*", [T1, T2])) ts =
+fun mk_tuple (Type (@{type_name "*"}, [T1, T2])) ts =
     HOLogic.mk_prod (mk_tuple T1 ts,
         mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))
   | mk_tuple _ (t :: _) = t
   | mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])
 

                   tps then
           Const (unknown, T1 --> T2)
         else
           aux tps
       end
-    (* typ -> typ -> typ -> (term * term) list -> term *)
-    fun make_map T1 T2 T2' =
+    (* bool -> typ -> typ -> typ -> (term * term) list -> term *)
+    fun make_map maybe_opt T1 T2 T2' =
       let
         val update_const = Const (@{const_name fun_upd},
                                   (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
         (* (term * term) list -> term *)
         fun aux' [] = Const (@{const_abbrev Map.empty}, T1 --> T2)
           | aux' ((t1, t2) :: ps) =
             (case t2 of
                Const (@{const_name None}, _) => aux' ps
              | _ => update_const $ aux' ps $ t1 $ t2)
         fun aux ps =
-          if not (is_complete_type datatypes false T1) then
+          if maybe_opt andalso not (is_complete_type datatypes false T1) then
             update_const $ aux' ps $ Const (unrep, T1)
             $ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))
           else
             aux' ps
       in aux end
     (* typ list -> term -> term *)
     fun polish_funs Ts t =
       (case fastype_of1 (Ts, t) of
-         Type ("fun", [T1, T2]) =>
+         Type (@{type_name fun}, [T1, T2]) =>
          if is_plain_fun t then
            case T2 of
              @{typ bool} =>
              let
                val (maybe_opt, ts_pair) =

                make_set maybe_opt T1 T2
                         (sort_wrt (truth_const_sort_key o snd) (op ~~ ts_pair))
              end
            | Type (@{type_name option}, [T2']) =>
              let
-               val ts_pair = snd (dest_plain_fun t)
-                             |> pairself (map (polish_funs Ts))
-             in make_map T1 T2 T2' (rev (op ~~ ts_pair)) end
+               val (maybe_opt, ts_pair) =
+                 dest_plain_fun t ||> pairself (map (polish_funs Ts))
+             in make_map maybe_opt T1 T2 T2' (rev (op ~~ ts_pair)) end
            | _ => raise SAME ()
          else
            raise SAME ()
        | _ => raise SAME ())
       handle SAME () =>

                $ (t2 as Const (s, _)) =>
                if s = unknown then polish_funs Ts t11
                else polish_funs Ts t1 $ polish_funs Ts t2
              | t1 $ t2 => polish_funs Ts t1 $ polish_funs Ts t2
              | Abs (s, T, t') => Abs (s, T, polish_funs (T :: Ts) t')
-             | Const (s, Type ("fun", [T1, T2])) =>
+             | Const (s, Type (@{type_name fun}, [T1, T2])) =>
                if s = opt_flag orelse s = non_opt_flag then
                  Abs ("x", T1, Const (unknown, T2))
                else
                  t
              | t => t
     (* bool -> typ -> typ -> typ -> term list -> term list -> term *)
     fun make_fun maybe_opt T1 T2 T' ts1 ts2 =
       ts1 ~~ ts2 |> sort (nice_term_ord o pairself fst)
                  |> make_plain_fun maybe_opt T1 T2
-                 |> unarize_and_unbox_term
-                 |> typecast_fun (unarize_unbox_and_uniterize_type T')
-                                 (unarize_unbox_and_uniterize_type T1)
-                                 (unarize_unbox_and_uniterize_type T2)
+                 |> unarize_unbox_etc_term
+                 |> typecast_fun (uniterize_unarize_unbox_etc_type T')
+                                 (uniterize_unarize_unbox_etc_type T1)
+                                 (uniterize_unarize_unbox_etc_type T2)
     (* (typ * int) list -> typ -> typ -> int -> term *)
-    fun term_for_atom seen (T as Type ("fun", [T1, T2])) T' j _ =
+    fun term_for_atom seen (T as Type (@{type_name fun}, [T1, T2])) T' j _ =
         let
           val k1 = card_of_type card_assigns T1
           val k2 = card_of_type card_assigns T2
         in
-          term_for_rep seen T T' (Vect (k1, Atom (k2, 0)))
+          term_for_rep true seen T T' (Vect (k1, Atom (k2, 0)))
                        [nth_combination (replicate k1 (k2, 0)) j]
           handle General.Subscript =>
                  raise ARG ("Nitpick_Model.reconstruct_term.term_for_atom",
                             signed_string_of_int j ^ " for " ^
                             string_for_rep (Vect (k1, Atom (k2, 0))))
         end
-      | term_for_atom seen (Type ("*", [T1, T2])) _ j k =
+      | term_for_atom seen (Type (@{type_name "*"}, [T1, T2])) _ j k =
         let
           val k1 = card_of_type card_assigns T1
           val k2 = k div k1
         in
           list_comb (HOLogic.pair_const T1 T2,

                 val seen = seen |> maybe_cyclic ? cons (T, j)
                 val ts =
                   if length arg_Ts = 0 then
                     []
                   else
-                    map3 (fn Ts => term_for_rep seen Ts Ts) arg_Ts arg_Rs
-                         arg_jsss
+                    map3 (fn Ts =>
+                             term_for_rep (constr_s <> @{const_name FinFun})
+                                          seen Ts Ts) arg_Ts arg_Rs arg_jsss
                     |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)
                     |> dest_n_tuple (length uncur_arg_Ts)
                 val t =
                   if constr_s = @{const_name Abs_Frac} then
                     let

     (* (typ * int) list -> int -> rep -> typ -> typ -> typ -> int list
        -> term *)
     and term_for_vect seen k R T1 T2 T' js =
       make_fun true T1 T2 T'
                (map (fn j => term_for_atom seen T1 T1 j k) (index_seq 0 k))
-               (map (term_for_rep seen T2 T2 R o single)
+               (map (term_for_rep true seen T2 T2 R o single)
                     (batch_list (arity_of_rep R) js))
-    (* (typ * int) list -> typ -> typ -> rep -> int list list -> term *)
-    and term_for_rep seen T T' Unit [[]] = term_for_atom seen T T' 0 1
-      | term_for_rep seen T T' (R as Atom (k, j0)) [[j]] =
+    (* bool -> (typ * int) list -> typ -> typ -> rep -> int list list -> term *)
+    and term_for_rep _ seen T T' Unit [[]] = term_for_atom seen T T' 0 1
+      | term_for_rep _ seen T T' (R as Atom (k, j0)) [[j]] =
         if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0) k
         else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])
-      | term_for_rep seen (Type ("*", [T1, T2])) _ (Struct [R1, R2]) [js] =
+      | term_for_rep _ seen (Type (@{type_name "*"}, [T1, T2])) _
+                     (Struct [R1, R2]) [js] =
         let
           val arity1 = arity_of_rep R1
           val (js1, js2) = chop arity1 js
         in
           list_comb (HOLogic.pair_const T1 T2,
-                     map3 (fn T => term_for_rep seen T T) [T1, T2] [R1, R2]
+                     map3 (fn T => term_for_rep true seen T T) [T1, T2] [R1, R2]
                           [[js1], [js2]])
         end
-      | term_for_rep seen (Type ("fun", [T1, T2])) T' (Vect (k, R')) [js] =
+      | term_for_rep _ seen (Type (@{type_name fun}, [T1, T2])) T'
+                     (Vect (k, R')) [js] =
         term_for_vect seen k R' T1 T2 T' js
-      | term_for_rep seen (Type ("fun", [T1, T2])) T' (Func (R1, Formula Neut))
-                     jss =
+      | term_for_rep _ seen (Type (@{type_name fun}, [T1, T2])) T'
+                     (Func (R1, Formula Neut)) jss =
         let
           val jss1 = all_combinations_for_rep R1
-          val ts1 = map (term_for_rep seen T1 T1 R1 o single) jss1
+          val ts1 = map (term_for_rep true seen T1 T1 R1 o single) jss1
           val ts2 =
-            map (fn js => term_for_rep seen T2 T2 (Atom (2, 0))
+            map (fn js => term_for_rep true seen T2 T2 (Atom (2, 0))
                                        [[int_from_bool (member (op =) jss js)]])
                 jss1
         in make_fun false T1 T2 T' ts1 ts2 end
-      | term_for_rep seen (Type ("fun", [T1, T2])) T' (Func (R1, R2)) jss =
+      | term_for_rep maybe_opt seen (Type (@{type_name fun}, [T1, T2])) T'
+                     (Func (R1, R2)) jss =
         let
           val arity1 = arity_of_rep R1
           val jss1 = all_combinations_for_rep R1
-          val ts1 = map (term_for_rep seen T1 T1 R1 o single) jss1
+          val ts1 = map (term_for_rep false seen T1 T1 R1 o single) jss1
           val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)
-          val ts2 = map (term_for_rep seen T2 T2 R2 o the_default []
+          val ts2 = map (term_for_rep false seen T2 T2 R2 o the_default []
                          o AList.lookup (op =) grouped_jss2) jss1
-        in make_fun true T1 T2 T' ts1 ts2 end
-      | term_for_rep seen T T' (Opt R) jss =
-        if null jss then Const (unknown, T) else term_for_rep seen T T' R jss
-      | term_for_rep _ T _ R jss =
+        in make_fun maybe_opt T1 T2 T' ts1 ts2 end
+      | term_for_rep _ seen T T' (Opt R) jss =
+        if null jss then Const (unknown, T)
+        else term_for_rep true seen T T' R jss
+      | term_for_rep _ _ T _ R jss =
         raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",
                    Refute.string_of_typ T ^ " " ^ string_for_rep R ^ " " ^
                    string_of_int (length jss))
-  in polish_funs [] o unarize_and_unbox_term oooo term_for_rep [] end
+  in polish_funs [] o unarize_unbox_etc_term oooo term_for_rep true [] end
 
 (* atom_pool -> scope -> nut list -> nut NameTable.table -> KK.raw_bound list
    -> nut -> term *)
 fun term_for_name pool scope sel_names rel_table bounds name =
   let val T = type_of name in

     fun pretty_for_assign name =
       let
         val (oper, (t1, T'), T) =
           case name of
             FreeName (s, T, _) =>
-            let val t = Free (s, unarize_unbox_and_uniterize_type T) in
+            let val t = Free (s, uniterize_unarize_unbox_etc_type T) in
               ("=", (t, format_term_type thy def_table formats t), T)
             end
           | ConstName (s, T, _) =>
             (assign_operator_for_const (s, T),
              user_friendly_const hol_ctxt base_step_names formats (s, T), T)

              Pretty.str oper, Syntax.pretty_term ctxt t2])
       end
     (* dtype_spec -> Pretty.T *)
     fun pretty_for_datatype ({typ, card, complete, ...} : dtype_spec) =
       Pretty.block (Pretty.breaks
-          [Syntax.pretty_typ ctxt (unarize_unbox_and_uniterize_type typ),
-           Pretty.str "=",
-           Pretty.enum "," "{" "}"
-               (map (Syntax.pretty_term ctxt) (all_values_of_type card typ) @
-                (if fun_from_pair complete false then []
-                 else [Pretty.str unrep]))])
+          (Syntax.pretty_typ ctxt (uniterize_unarize_unbox_etc_type typ) ::
+           (case typ of
+              Type (@{type_name fin_fun}, _) => [Pretty.str "[finite]"]
+            | Type (@{type_name fun_box}, _) => [Pretty.str "[boxed]"]
+            | Type (@{type_name pair_box}, _) => [Pretty.str "[boxed]"]
+            | _ => []) @
+           [Pretty.str "=",
+            Pretty.enum "," "{" "}"
+                (map (Syntax.pretty_term ctxt) (all_values_of_type card typ) @
+                 (if fun_from_pair complete false then []
+                  else [Pretty.str unrep]))]))
     (* typ -> dtype_spec list *)
     fun integer_datatype T =
       [{typ = T, card = card_of_type card_assigns T, co = false,
         standard = true, complete = (false, false), concrete = (true, true),
         deep = true, constrs = []}]

     val (skolem_names, nonskolem_nonsel_names) =
       List.partition is_skolem_name nonsel_names
     val (eval_names, noneval_nonskolem_nonsel_names) =
       List.partition (String.isPrefix eval_prefix o nickname_of)
                      nonskolem_nonsel_names
-      ||> filter_out (curry (op =) @{const_name bisim_iterator_max}
+      ||> filter_out (member (op =) [@{const_name bisim},
+                                     @{const_name bisim_iterator_max}]
                       o nickname_of)
     val free_names =
       map (fn x as (s, T) =>
               case filter (curry (op =) x
                        o pairf nickname_of
-                               (unarize_unbox_and_uniterize_type o type_of))
+                               (uniterize_unarize_unbox_etc_type o type_of))
                        free_names of
                 [name] => name
               | [] => FreeName (s, T, Any)
               | _ => raise TERM ("Nitpick_Model.reconstruct_hol_model",
                                  [Const x])) all_frees