python
diff --git a/‎mypy/meet.py
Lines changed: 8 additions & 2 deletions b/‎mypy/meet.py
Lines changed: 8 additions & 2 deletions
diff --git a/‎mypy/test/testtypes.py
Lines changed: 14 additions & 5 deletions b/‎mypy/test/testtypes.py
Lines changed: 14 additions & 5 deletions
diff --git a/‎mypy/typefixture.py
Lines changed: 1 addition & 0 deletions b/‎mypy/typefixture.py
Lines changed: 1 addition & 0 deletions
@@ -185,6 +185,8 @@ def visit_instance(self, t: Instance) -> Type:
                     return self.s
                 else:
                     return NoneTyp()
+        elif isinstance(self.s, TypeType):
+            return meet_types(t, self.s)
         else:
             return self.default(self.s)
 
@@ -210,9 +212,13 @@ def visit_partial_type(self, t: PartialType) -> Type:
 
     def visit_type_type(self, t: TypeType) -> Type:
         if isinstance(self.s, TypeType):
-            return TypeType(self.meet(t.item, self.s.item), line=t.line)
+            typ = self.meet(t.item, self.s.item)
+            if not isinstance(typ, NoneTyp):
+                typ = TypeType(typ, line=t.line)
+            return typ
+        elif isinstance(self.s, Instance) and self.s.type.fullname() == 'builtins.type':
+            return t
         else:
-            # XXX Other cases, e.g. type <--> Type[]?
             return NoneTyp()
 
     def meet(self, s, t):
 
@@ -179,7 +179,7 @@ def test_erase_with_type_object(self):
 
     def test_erase_with_type_type(self):
         self.assert_erase(self.fx.type_a, self.fx.type_a)
-        self.assert_erase(self.fx.type_t, TypeType(self.fx.anyt))
+        self.assert_erase(self.fx.type_t, self.fx.type_any)
 
     def assert_erase(self, orig, result):
         assert_equal(str(erase_type(orig)), str(result))
@@ -497,11 +497,11 @@ def test_simple_type_objects(self):
 
     def test_type_type(self):
         self.assert_join(self.fx.type_a, self.fx.type_b, self.fx.type_a)
-        self.assert_join(self.fx.type_b, TypeType(self.fx.anyt), TypeType(self.fx.anyt))
+        self.assert_join(self.fx.type_b, self.fx.type_any, self.fx.type_any)
         self.assert_join(self.fx.type_b, self.fx.type_type, self.fx.type_type)
         self.assert_join(self.fx.type_b, self.fx.type_c, self.fx.type_a)
         self.assert_join(self.fx.type_c, self.fx.type_d, TypeType(self.fx.o))
-        self.assert_join(self.fx.type_type, TypeType(self.fx.anyt), self.fx.type_type)
+        self.assert_join(self.fx.type_type, self.fx.type_any, self.fx.type_type)
         self.assert_join(self.fx.type_b, self.fx.anyt, self.fx.anyt)
 
     # There are additional test cases in check-inference.test.
@@ -691,13 +691,13 @@ def test_meet_interface_types(self):
         self.assert_meet(self.fx.f, self.fx.f2, self.fx.nonet)
         self.assert_meet(self.fx.f, self.fx.f3, self.fx.f3)
 
-    def test_join_interface_and_class_types(self):
+    def test_meet_interface_and_class_types(self):
         self.assert_meet(self.fx.o, self.fx.f, self.fx.f)
         self.assert_meet(self.fx.a, self.fx.f, self.fx.nonet)
 
         self.assert_meet(self.fx.e, self.fx.f, self.fx.e)
 
-    def test_join_class_types_with_shared_interfaces(self):
+    def test_meet_class_types_with_shared_interfaces(self):
         # These have nothing special with respect to meets, unlike joins. These
         # are for completeness only.
         self.assert_meet(self.fx.e, self.fx.e2, self.fx.nonet)
@@ -712,6 +712,15 @@ def test_meet_with_generic_interfaces(self):
         self.assert_meet(fx.gfa, fx.gfa, fx.gfa)
         self.assert_meet(fx.gfb, fx.m1, fx.nonet)
 
+    def test_type_type(self):
+        self.assert_meet(self.fx.type_a, self.fx.type_b, self.fx.type_b)
+        self.assert_meet(self.fx.type_b, self.fx.type_any, self.fx.type_b)
+        self.assert_meet(self.fx.type_b, self.fx.type_type, self.fx.type_b)
+        self.assert_meet(self.fx.type_b, self.fx.type_c, self.fx.nonet)
+        self.assert_meet(self.fx.type_c, self.fx.type_d, self.fx.nonet)
+        self.assert_meet(self.fx.type_type, self.fx.type_any, self.fx.type_any)
+        self.assert_meet(self.fx.type_b, self.fx.anyt, self.fx.type_b)
+
     # FIX generic interfaces + ranges
 
     def assert_meet(self, s, t, meet):
 
@@ -146,6 +146,7 @@ def __init__(self, variance: int=COVARIANT) -> None:
         self.type_c = TypeType(self.c)
         self.type_d = TypeType(self.d)
         self.type_t = TypeType(self.t)
+        self.type_any = TypeType(self.anyt)
 
     # Helper methods