src/HOL/Tools/ATP/atp_util.ML

   val varify_and_instantiate_type : Proof.context -> typ -> typ -> typ -> typ
   val typ_of_dtyp :
     Datatype_Aux.descr -> (Datatype_Aux.dtyp * typ) list -> Datatype_Aux.dtyp
     -> typ
   val is_type_surely_finite : Proof.context -> typ -> bool
-  val is_type_surely_infinite : Proof.context -> typ list -> typ -> bool
+  val is_type_surely_infinite : Proof.context -> typ -> bool
   val monomorphic_term : Type.tyenv -> term -> term
   val eta_expand : typ list -> term -> int -> term
   val transform_elim_prop : term -> term
   val specialize_type : theory -> (string * typ) -> term -> term
   val strip_subgoal :

 
 (* Similar to "Nitpick_HOL.bounded_exact_card_of_type".
    0 means infinite type, 1 means singleton type (e.g., "unit"), and 2 means
    cardinality 2 or more. The specified default cardinality is returned if the
    cardinality of the type can't be determined. *)
-fun tiny_card_of_type ctxt default_card assigns T =
+fun tiny_card_of_type ctxt default_card T =
   let
     val thy = Proof_Context.theory_of ctxt
     val max = 2 (* 1 would be too small for the "fun" case *)
     fun aux slack avoid T =
       if member (op =) avoid T then
         0
-      else case AList.lookup (Sign.typ_instance thy o swap) assigns T of
-        SOME k => k
-      | NONE =>
-        case T of
-          Type (@{type_name fun}, [T1, T2]) =>
-          (case (aux slack avoid T1, aux slack avoid T2) of
-             (k, 1) => if slack andalso k = 0 then 0 else 1
-           | (0, _) => 0
-           | (_, 0) => 0
-           | (k1, k2) =>
-             if k1 >= max orelse k2 >= max then max
-             else Int.min (max, Integer.pow k2 k1))
-        | @{typ prop} => 2
-        | @{typ bool} => 2 (* optimization *)
-        | @{typ nat} => 0 (* optimization *)
-        | Type ("Int.int", []) => 0 (* optimization *)
-        | Type (s, _) =>
-          (case datatype_constrs thy T of
-             constrs as _ :: _ =>
-             let
-               val constr_cards =
-                 map (Integer.prod o map (aux slack (T :: avoid)) o binder_types
-                      o snd) constrs
-             in
-               if exists (curry (op =) 0) constr_cards then 0
-               else Int.min (max, Integer.sum constr_cards)
-             end
-           | [] =>
-             case Typedef.get_info ctxt s of
-               ({abs_type, rep_type, ...}, _) :: _ =>
-               (* We cheat here by assuming that typedef types are infinite if
-                  their underlying type is infinite. This is unsound in general
-                  but it's hard to think of a realistic example where this would
-                  not be the case. We are also slack with representation types:
-                  If a representation type has the form "sigma => tau", we
-                  consider it enough to check "sigma" for infiniteness. (Look
-                  for "slack" in this function.) *)
-               (case varify_and_instantiate_type ctxt
-                         (Logic.varifyT_global abs_type) T
-                         (Logic.varifyT_global rep_type)
-                     |> aux true avoid of
-                  0 => 0
-                | 1 => 1
-                | _ => default_card)
-             | [] => default_card)
-          (* Very slightly unsound: Type variables are assumed not to be
-             constrained to cardinality 1. (In practice, the user would most
-             likely have used "unit" directly anyway.) *)
-        | TFree _ => if default_card = 1 then 2 else default_card
-          (* Schematic type variables that contain only unproblematic sorts
-             (with no finiteness axiom) can safely be considered infinite. *)
-        | TVar _ => default_card
+      else case T of
+        Type (@{type_name fun}, [T1, T2]) =>
+        (case (aux slack avoid T1, aux slack avoid T2) of
+           (k, 1) => if slack andalso k = 0 then 0 else 1
+         | (0, _) => 0
+         | (_, 0) => 0
+         | (k1, k2) =>
+           if k1 >= max orelse k2 >= max then max
+           else Int.min (max, Integer.pow k2 k1))
+      | @{typ prop} => 2
+      | @{typ bool} => 2 (* optimization *)
+      | @{typ nat} => 0 (* optimization *)
+      | Type ("Int.int", []) => 0 (* optimization *)
+      | Type (s, _) =>
+        (case datatype_constrs thy T of
+           constrs as _ :: _ =>
+           let
+             val constr_cards =
+               map (Integer.prod o map (aux slack (T :: avoid)) o binder_types
+                    o snd) constrs
+           in
+             if exists (curry (op =) 0) constr_cards then 0
+             else Int.min (max, Integer.sum constr_cards)
+           end
+         | [] =>
+           case Typedef.get_info ctxt s of
+             ({abs_type, rep_type, ...}, _) :: _ =>
+             (* We cheat here by assuming that typedef types are infinite if
+                their underlying type is infinite. This is unsound in general
+                but it's hard to think of a realistic example where this would
+                not be the case. We are also slack with representation types:
+                If a representation type has the form "sigma => tau", we
+                consider it enough to check "sigma" for infiniteness. (Look
+                for "slack" in this function.) *)
+             (case varify_and_instantiate_type ctxt
+                       (Logic.varifyT_global abs_type) T
+                       (Logic.varifyT_global rep_type)
+                   |> aux true avoid of
+                0 => 0
+              | 1 => 1
+              | _ => default_card)
+           | [] => default_card)
+        (* Very slightly unsound: Type variables are assumed not to be
+           constrained to cardinality 1. (In practice, the user would most
+           likely have used "unit" directly anyway.) *)
+      | TFree _ => if default_card = 1 then 2 else default_card
+      | TVar _ => default_card
   in Int.min (max, aux false [] T) end
 
-fun is_type_surely_finite ctxt T = tiny_card_of_type ctxt 0 [] T <> 0
-fun is_type_surely_infinite ctxt infinite_Ts T =
-  tiny_card_of_type ctxt 1 (map (rpair 0) infinite_Ts) T = 0
+fun is_type_surely_finite ctxt T = tiny_card_of_type ctxt 0 T <> 0
+fun is_type_surely_infinite ctxt T = tiny_card_of_type ctxt 1 T = 0
 
 fun monomorphic_term subst =
   map_types (map_type_tvar (fn v =>
       case Type.lookup subst v of
         SOME typ => typ