diff --git a/CHANGELOG b/CHANGELOG
index d0af7297f..adb184bc3 100644
--- a/CHANGELOG
+++ b/CHANGELOG
@@ -1,3 +1,9 @@
+Version 2020.07.24
+* pyi parser: allow aliases inside a class to values outside the class.
+* Copy annotations instead of modifying them when adding a scope.
+* Make self.__class__ return Any in __init__.
+* Check object visibility before setting attributes.
+
 Version 2020.07.20
 * pyi parser: support importing TypedDict from typing_extensions.
 
diff --git a/pytype/__version__.py b/pytype/__version__.py
index 4c8803d96..43466e32b 100644
--- a/pytype/__version__.py
+++ b/pytype/__version__.py
@@ -1,2 +1,2 @@
 # pylint: skip-file
-__version__ = '2020.07.20'
+__version__ = '2020.07.24'
diff --git a/pytype/annotations_util.py b/pytype/annotations_util.py
index 35d8e2380..3124f5d37 100644
--- a/pytype/annotations_util.py
+++ b/pytype/annotations_util.py
@@ -79,13 +79,15 @@ def add_scope(self, annot, types, module):
         return new_annot
       return annot
     elif isinstance(annot, abstract.TupleClass):
-      annot.formal_type_parameters[abstract_utils.T] = self.add_scope(
+      params = dict(annot.formal_type_parameters)
+      params[abstract_utils.T] = self.add_scope(
           annot.formal_type_parameters[abstract_utils.T], types, module)
-      return annot
+      return abstract.TupleClass(
+          annot.base_cls, params, self.vm, annot.template)
     elif isinstance(annot, mixin.NestedAnnotation):
-      for key, typ in annot.get_inner_types():
-        annot.update_inner_type(key, self.add_scope(typ, types, module))
-      return annot
+      inner_types = [(key, self.add_scope(typ, types, module))
+                     for key, typ in annot.get_inner_types()]
+      return annot.replace(inner_types)
     return annot
 
   def get_type_parameters(self, annot, seen=None):
diff --git a/pytype/pyi/parser.py b/pytype/pyi/parser.py
index 1411756c3..f5ece562b 100644
--- a/pytype/pyi/parser.py
+++ b/pytype/pyi/parser.py
@@ -1169,15 +1169,26 @@ def new_class(self, decorators, class_name, parent_args, defs):
                    for val in constants + aliases + methods + classes}
       for val in aliases:
         name = val.name
+        seen_names = set()
         while isinstance(val, pytd.Alias):
           if isinstance(val.type, pytd.NamedType):
             _, _, base_name = val.type.name.rpartition(".")
+            if base_name in seen_names:
+              # This happens in cases like:
+              # class X:
+              #   Y = something.Y
+              # Since we try to resolve aliases immediately, we don't know what
+              # type to fill in when the alias value comes from outside the
+              # class. The best we can do is Any.
+              val = pytd.Constant(name, pytd.AnythingType())
+              continue
+            seen_names.add(base_name)
             if base_name in vals_dict:
               val = vals_dict[base_name]
               continue
-          raise ParseError(
-              "Illegal value for alias %r. Value must be an attribute "
-              "on the same class." % val.name)
+          # The alias value comes from outside the class. The best we can do is
+          # to fill in Any.
+          val = pytd.Constant(name, pytd.AnythingType())
         if isinstance(val, _NameAndSig):
           methods.append(val._replace(name=name))
         else:
diff --git a/pytype/pyi/parser_test.py b/pytype/pyi/parser_test.py
index b457645d7..0c041d032 100644
--- a/pytype/pyi/parser_test.py
+++ b/pytype/pyi/parser_test.py
@@ -374,6 +374,33 @@ def test_alias_lookup(self):
 
       x: somewhere.Foo""")
 
+  def test_external_alias(self):
+    self.check("""
+      from somewhere import Foo
+
+      class Bar:
+          Baz = Foo
+    """, """
+      from typing import Any
+
+      from somewhere import Foo
+
+      class Bar:
+          Baz: Any
+    """)
+
+  def test_same_named_alias(self):
+    self.check("""
+      import somewhere
+      class Bar:
+          Foo = somewhere.Foo
+    """, """
+      from typing import Any
+
+      class Bar:
+          Foo: Any
+    """)
+
   def test_type_params(self):
     ast = self.check("""
       from typing import TypeVar
@@ -1650,13 +1677,6 @@ class Foo:
           import foo
     """, 3, "syntax error")
 
-  def test_bad_alias(self):
-    self.check_error("""
-      class Foo:
-        if sys.version_info > (3, 4, 0):
-          a = b
-    """, 1, "Illegal value for alias 'a'")
-
   def test_no_class(self):
     self.check("""
       class Foo:
diff --git a/pytype/pytd/pytd_utils.py b/pytype/pytd/pytd_utils.py
index 2f4f962e5..a43bc43bc 100644
--- a/pytype/pytd/pytd_utils.py
+++ b/pytype/pytd/pytd_utils.py
@@ -565,7 +565,7 @@ def MergeBaseClass(cls, base):
   classes = cls.classes + tuple(c for c in base.classes
                                 if c.name not in class_names)
   if cls.slots:
-    slots = cls.clots + tuple(s for s in base.slots or () if s not in cls.slots)
+    slots = cls.slots + tuple(s for s in base.slots or () if s not in cls.slots)
   else:
     slots = base.slots
   return pytd.Class(name=cls.name,
diff --git a/pytype/tests/py3/test_generic.py b/pytype/tests/py3/test_generic.py
index c20747f86..06d633fb0 100644
--- a/pytype/tests/py3/test_generic.py
+++ b/pytype/tests/py3/test_generic.py
@@ -579,6 +579,21 @@ class Foo(List["Foo"]):
         pass
     """)
 
+  def test_type_parameter_count(self):
+    self.Check("""
+      from typing import Generic, List, TypeVar
+
+      T = TypeVar('T')
+      SomeAlias = List[T]
+
+      class Foo(Generic[T]):
+        def __init__(self, x: T, y: SomeAlias):
+          pass
+
+      def f(x: T) -> SomeAlias:
+        return [x]
+    """)
+
 
 class GenericFeatureTest(test_base.TargetPython3FeatureTest):
   """Tests for User-defined Generic Type."""
diff --git a/pytype/tests/test_attributes.py b/pytype/tests/test_attributes.py
index 59584b9fc..ef48ef651 100644
--- a/pytype/tests/test_attributes.py
+++ b/pytype/tests/test_attributes.py
@@ -503,24 +503,6 @@ def __getattribute__(self, name) -> bool
       def f(x) -> Any
     """)
 
-  @test_base.skip("TODO(b/63407497): implement strict checking for __setitem__")
-  def test_union_set_attribute(self):
-    ty, _ = self.InferWithErrors("""
-      class A(object):
-        x = "Hello world"
-      def f(i):
-        t = A()
-        l = [t]
-        l[i].x = 1  # not-writable
-        return l[i].x
-    """)
-    self.assertTypesMatchPytd(ty, """
-      from typing import Any
-      class A(object):
-        x = ...  # type: str
-      def f(i) -> Any
-    """)
-
   def test_set_class(self):
     ty = self.Infer("""
       def f(x):
@@ -846,5 +828,25 @@ def oops(self) -> None: ...
     """)
     self.assertErrorRegexes(errors, {"e": r"Annotation: int.*Assignment: str"})
 
+  def test_split(self):
+    ty = self.Infer("""
+      from typing import Union
+      class Foo:
+        pass
+      class Bar:
+        pass
+      def f(x):
+        # type: (Union[Foo, Bar]) -> None
+        if isinstance(x, Foo):
+          x.foo = 42
+    """)
+    self.assertTypesMatchPytd(ty, """
+      from typing import Union
+      class Foo:
+        foo: int
+      class Bar: ...
+      def f(x: Union[Foo, Bar]) -> None: ...
+    """)
+
 
 test_base.main(globals(), __name__ == "__main__")
diff --git a/pytype/tests/test_classes.py b/pytype/tests/test_classes.py
index 963eda595..57bc16054 100644
--- a/pytype/tests/test_classes.py
+++ b/pytype/tests/test_classes.py
@@ -1411,5 +1411,19 @@ class Foo(Any):
       list(Foo())
     """)
 
+  def test_instantiate_class(self):
+    self.Check("""
+      import abc
+      import six
+      @six.add_metaclass(abc.ABCMeta)
+      class Foo(object):
+        def __init__(self, x):
+          if x > 0:
+            print(self.__class__(x-1))
+        @abc.abstractmethod
+        def f(self):
+          pass
+    """)
+
 
 test_base.main(globals(), __name__ == "__main__")
diff --git a/pytype/tests/test_slots.py b/pytype/tests/test_slots.py
index 073b9b91c..698b18476 100644
--- a/pytype/tests/test_slots.py
+++ b/pytype/tests/test_slots.py
@@ -225,5 +225,18 @@ def __init__(self):
     """)
     self.assertErrorRegexes(errors, {"e": r"__baz"})
 
+  def test_union(self):
+    self.Check("""
+      from typing import Union
+      class Foo(object):
+        pass
+      class Bar(object):
+        __slots__ = ()
+      def f(x):
+        # type: (Union[Foo, Bar]) -> None
+        if isinstance(x, Foo):
+          x.foo = 42
+    """)
+
 
 test_base.main(globals(), __name__ == "__main__")
diff --git a/pytype/tools/annotate_ast/annotate_ast.py b/pytype/tools/annotate_ast/annotate_ast.py
index b569ed1ec..99f09b304 100644
--- a/pytype/tools/annotate_ast/annotate_ast.py
+++ b/pytype/tools/annotate_ast/annotate_ast.py
@@ -59,6 +59,9 @@ def visit_Name(self, node):
   def visit_Attribute(self, node):
     self._maybe_annotate(node)
 
+  def visit_FunctionDef(self, node):
+    self._maybe_annotate(node)
+
   def _maybe_annotate(self, node):
     """Annotates a node."""
     try:
diff --git a/pytype/tools/annotate_ast/annotate_ast_test.py b/pytype/tools/annotate_ast/annotate_ast_test.py
index a188d18ff..e921439e1 100644
--- a/pytype/tools/annotate_ast/annotate_ast_test.py
+++ b/pytype/tools/annotate_ast/annotate_ast_test.py
@@ -1,11 +1,9 @@
 import ast
-import itertools
 import textwrap
 
 from pytype import config
 from pytype.tests import test_base
 from pytype.tools.annotate_ast import annotate_ast
-import six
 
 
 class AnnotaterTest(test_base.TargetIndependentTest):
@@ -18,28 +16,10 @@ def annotate(self, source):
     module = annotate_ast.annotate_source(source, ast_factory, pytype_options)
     return module
 
-  def assert_annotations_equal(self, expected, module):
-    nodes = [
-        node for node in ast.walk(module)
-        if getattr(node, 'resolved_type', None)
-    ]
-    actual = {}
-    for node in nodes:
-      key = self._get_node_key(node)
-      actual[key] = '{} :: {!r}'.format(node.resolved_annotation,
-                                        node.resolved_type)
-
-    for key in sorted(set(itertools.chain(expected, actual))):
-      expected_pattern = expected.get(key)
-      if not expected_pattern:
-        self.fail('Unexpected annotation: {} -> {}'.format(key, actual[key]))
-      actual_text = actual.get(key)
-      if not actual_text:
-        self.fail(
-            'Expected to find node {} annotated, but it was not.'.format(key))
-      msg = ('Resolved annotation value does not match {!r}: Node {} annotated '
-             'with {}').format(expected_pattern, key, actual_text)
-      six.assertRegex(self, actual_text, expected_pattern, msg=msg)
+  def get_annotations_dict(self, module):
+    return {self._get_node_key(node): node.resolved_annotation
+            for node in ast.walk(module)
+            if hasattr(node, 'resolved_type')}
 
   def _get_node_key(self, node):
     base = (node.lineno, node.__class__.__name__)
@@ -48,25 +28,27 @@ def _get_node_key(self, node):
       return base + (node.id,)
     elif isinstance(node, ast.Attribute):
       return base + (node.attr,)
+    elif isinstance(node, ast.FunctionDef):
+      return base + (node.name,)
     else:
       return base
 
   def test_annotating_name(self):
     source = """
     a = 1
-    b = {}
-    c = []
+    b = {1: 'foo'}
+    c = [1, 2, 3]
     d = 3, 4
     """
     module = self.annotate(source)
 
     expected = {
         (1, 'Name', 'a'): 'int',
-        (2, 'Name', 'b'): 'dict',
-        (3, 'Name', 'c'): 'list',
-        (4, 'Name', 'd'): 'tuple',
+        (2, 'Name', 'b'): 'Dict[int, str]',
+        (3, 'Name', 'c'): 'List[int]',
+        (4, 'Name', 'd'): 'Tuple[int, int]',
     }
-    self.assert_annotations_equal(expected, module)
+    self.assertEqual(expected, self.get_annotations_dict(module))
 
   def test_annotating_attribute(self):
     source = """
@@ -84,6 +66,47 @@ def test_annotating_attribute(self):
         (2, 'Attribute', 'Bar'): 'Any',
         (2, 'Attribute', 'bar'): 'Any',
     }
-    self.assert_annotations_equal(expected, module)
+    self.assertEqual(expected, self.get_annotations_dict(module))
+
+  def test_annotating_for(self):
+    source = """
+    for i in 1, 2, 3:
+      pass
+    """
+
+    module = self.annotate(source)
+
+    expected = {
+        (1, 'Name', 'i'): 'int',
+    }
+    self.assertEqual(expected, self.get_annotations_dict(module))
+
+  def test_annotating_with(self):
+    source = """
+    with foo() as f:
+      pass
+    """
+
+    module = self.annotate(source)
+
+    expected = {
+        (1, 'Name', 'foo'): 'Any',
+        (1, 'Name', 'f'): 'Any',
+    }
+    self.assertEqual(expected, self.get_annotations_dict(module))
+
+  def test_annotating_def(self):
+    source = """
+    def foo(a, b):
+      # type: (str, int) -> str
+      pass
+    """
+
+    module = self.annotate(source)
+
+    expected = {
+        (1, 'FunctionDef', 'foo'): 'Callable[[str, int], str]',
+    }
+    self.assertEqual(expected, self.get_annotations_dict(module))
 
 test_base.main(globals(), __name__ == '__main__')
diff --git a/pytype/tools/traces/traces.py b/pytype/tools/traces/traces.py
index 7018e1af0..8c4efcd99 100644
--- a/pytype/tools/traces/traces.py
+++ b/pytype/tools/traces/traces.py
@@ -131,7 +131,7 @@ def __init__(self, matches):
   def match(self, symbol):
     for match in self._matches:
       if isinstance(match, self._PATTERN_TYPE):
-        if match.match(symbol):
+        if match.match(str(symbol)):
           return True
       elif match == symbol:
         return True
@@ -216,14 +216,21 @@ def match_Call(self, node):
             for tr in self._get_traces(
                 node.lineno, _CALL_OPS, name, maxmatch=1, num_lines=5)]
 
-  def match_Ellipsis(self, node):
-    return self._match_constant(node, Ellipsis)
-
   def match_Constant(self, node):
     # As of Python 3.8, bools, numbers, bytes, strings, ellipsis etc are
     # all constants instead of individual ast nodes.
     return self._match_constant(node, node.s)
 
+  def match_Ellipsis(self, node):
+    return self._match_constant(node, Ellipsis)
+
+  def match_FunctionDef(self, node):
+    symbol = _SymbolMatcher.from_regex(r"(%s|None)" % node.name)
+    return [
+        (self._get_match_location(node, tr.symbol), tr)
+        for tr in self._get_traces(node.lineno, ["MAKE_FUNCTION"], symbol, 1)
+    ]
+
   def match_Import(self, node):
     return list(self._match_import(node, is_from=False))
 
diff --git a/pytype/vm.py b/pytype/vm.py
index ed4ec47f9..692a28939 100644
--- a/pytype/vm.py
+++ b/pytype/vm.py
@@ -1391,6 +1391,9 @@ def _del_name(self, op, state, name, local):
   def _retrieve_attr(self, node, obj, attr):
     """Load an attribute from an object."""
     assert isinstance(obj, cfg.Variable), obj
+    if (attr == "__class__" and self.callself_stack and
+        obj.data == self.callself_stack[-1].data):
+      return node, self.new_unsolvable(node), []
     # Resolve the value independently for each value of obj
     result = self.program.NewVariable()
     log.debug("getting attr %s from %r", attr, obj)
@@ -1508,12 +1511,12 @@ def store_attr(self, state, obj, attr, value):
       log.info("Ignoring setattr on %r", obj)
       return state
     nodes = []
-    for val in obj.bindings:
+    for val in obj.Filter(state.node):
       # TODO(b/159038991): Check whether val.data is a descriptor (i.e. has
       # "__set__")
       nodes.append(self.attribute_handler.set_attribute(
           state.node, val.data, attr, value))
-    return state.change_cfg_node(self.join_cfg_nodes(nodes))
+    return state.change_cfg_node(self.join_cfg_nodes(nodes)) if nodes else state
 
   def del_attr(self, state, obj, attr):
     """Delete an attribute."""