diff --git a/funsor/factory.py b/funsor/factory.py
index f75cc41d8..ac33e44ac 100644
--- a/funsor/factory.py
+++ b/funsor/factory.py
@@ -60,6 +60,26 @@ class Bound:
     pass
 
 
+class ValueMeta(type):
+    def __getitem__(cls, value_type):
+        return Value(value_type)
+
+
+class Value(metaclass=ValueMeta):
+    def __init__(self, value_type):
+        if issubclass(value_type, Funsor):
+            raise TypeError("Types cannot depend on Funsor values")
+        self.value_type = value_type
+
+
+def _get_dependent_args(fields, hints, args):
+    return {
+        name: arg if isinstance(hint, Value) else arg.output
+        for name, arg, hint in zip(fields, args, hints)
+        if hint in (Funsor, Bound) or isinstance(hint, Value)
+    }
+
+
 def make_funsor(fn):
     """
     Decorator to dynamically create a subclass of
@@ -73,6 +93,8 @@ def make_funsor(fn):
     - Bound variable inputs (names) are typed :class:`Bound`.
     - Fresh variable inputs (names) are typed :class:`Fresh` together with
       lambda to compute the dependent domain.
+    - Ground value inputs (e.g. Python ints) are typed :class:`Value` together with
+      their actual data type, e.g. ``Value[int]``.
     - The return value is typed :class:`Fresh` together with a lambda to
       compute the dependent return domain.
 
@@ -94,7 +116,7 @@ def Unflatten(
     """
     input_types = typing.get_type_hints(fn)
     for name, hint in input_types.items():
-        if not (hint in (Funsor, Bound) or isinstance(hint, Fresh)):
+        if not (hint in (Funsor, Bound) or isinstance(hint, (Fresh, Value))):
             raise TypeError(f"Invalid type hint {name}: {hint}")
     output_type = input_types.pop("return")
     hints = tuple(input_types.values())
@@ -117,13 +139,15 @@ def __call__(cls, *args):
                     if not isinstance(arg, Variable):
                         raise ValueError(f"Cannot infer domain of {name}={arg}")
                     args[i] = arg
+                elif isinstance(hint, Value):
+                    if not isinstance(arg, hint.value_type):
+                        raise TypeError(
+                            f"invalid dependent value type: {arg}: {hint.value_type}"
+                        )
+                    args[i] = arg
 
             # Compute domains of fresh variables.
-            dependent_args = {
-                name: arg.output
-                for name, arg, hint in zip(cls._ast_fields, args, hints)
-                if hint in (Funsor, Bound)
-            }
+            dependent_args = _get_dependent_args(cls._ast_fields, hints, args)
             for i, (hint, arg) in enumerate(zip(hints, args)):
                 if isinstance(hint, Fresh):
                     domain = hint(**dependent_args)
@@ -135,11 +159,7 @@ def __call__(cls, *args):
     )
     def __init__(self, **kwargs):
         args = tuple(kwargs[k] for k in self._ast_fields)
-        dependent_args = {
-            name: arg.output
-            for name, arg, hint in zip(self._ast_fields, args, hints)
-            if hint in (Funsor, Bound)
-        }
+        dependent_args = _get_dependent_args(self._ast_fields, hints, args)
         output = output_type(**dependent_args)
         inputs = OrderedDict()
         fresh = set()
diff --git a/test/test_factory.py b/test/test_factory.py
index ea977b92a..a9fe8b78c 100644
--- a/test/test_factory.py
+++ b/test/test_factory.py
@@ -8,10 +8,12 @@
 
 import funsor.ops as ops
 from funsor.domains import Array, Bint, Real, Reals
-from funsor.factory import Bound, Fresh, make_funsor, to_funsor
+from funsor.factory import Bound, Fresh, Value, make_funsor, to_funsor
+from funsor.interpretations import reflect
+from funsor.interpreter import reinterpret
 from funsor.tensor import Tensor
 from funsor.terms import Cat, Funsor, Lambda, Number, eager
-from funsor.testing import check_funsor, random_tensor
+from funsor.testing import assert_close, check_funsor, random_tensor
 
 
 def test_lambda_lambda():
@@ -175,3 +177,49 @@ def Scatter1(
     value = Number(4, 9)
     x = Scatter1(destin, "a", "a", value, source)
     check_funsor(x, {"a": Bint[9], "b": Bint[3]}, Real)
+
+
+def test_value_dependence():
+    @make_funsor
+    def Sum(
+        x: Funsor,
+        dim: Value[int],
+    ) -> Fresh[lambda x, dim: Array[x.dtype, x.shape[:dim] + x.shape[dim + 1 :]]]:
+        return None
+
+    @eager.register(Sum, Tensor, int)
+    def eager_sum(x, dim):
+        data = x.data.sum(len(x.data.shape) - len(x.shape) + dim)
+        return Tensor(data, x.inputs, x.dtype)
+
+    x = random_tensor(OrderedDict(a=Bint[3]), Reals[2, 4, 5])
+
+    with reflect:
+        y0 = Sum(x, 0)
+        check_funsor(y0, x.inputs, Reals[4, 5])
+        y1 = Sum(x, 1)
+        check_funsor(y1, x.inputs, Reals[2, 5])
+        y2 = Sum(x, 2)
+        check_funsor(y2, x.inputs, Reals[2, 4])
+
+    z0 = reinterpret(y0)
+    check_funsor(z0, x.inputs, Reals[4, 5])
+    assert_close(z0.data, x.data.sum(1 + 0))
+    z1 = reinterpret(y1)
+    check_funsor(z1, x.inputs, Reals[2, 5])
+    assert_close(z1.data, x.data.sum(1 + 1))
+    z2 = reinterpret(y2)
+    check_funsor(z2, x.inputs, Reals[2, 4])
+    assert_close(z2.data, x.data.sum(1 + 2))
+
+    with pytest.raises(TypeError):
+        with reflect:
+            Sum(x, 1.5)
+
+    with pytest.raises(TypeError):
+
+        @make_funsor
+        def Sum(
+            x: Funsor, dim: Value[Number]
+        ) -> Fresh[lambda x, dim: Array[x.dtype, x.shape[:dim] + x.shape[dim + 1 :]]]:
+            return None