diff --git a/builtins/2.7/_ast.pyi b/builtins/2.7/_ast.pyi
index a82350bfd..961c2e64d 100644
--- a/builtins/2.7/_ast.pyi
+++ b/builtins/2.7/_ast.pyi
@@ -1,10 +1,11 @@
-from typing import Any, Tuple
+from typing import Any
+from typing import Tuple as TypingTuple
 
 PyCF_ONLY_AST = ...  # type: int
 
 class AST(object):
-    _attributes = ...  # type: Tuple[str]
-    _fields = ...  # type: Tuple[str]
+    _attributes = ...  # type: TypingTuple[str]
+    _fields = ...  # type: TypingTuple[str]
     def __init__(self, *args, **kwargs) -> None: pass
 
 class alias(AST):
diff --git a/builtins/2.7/_collections.pyi b/builtins/2.7/_collections.pyi
index 35d668ae9..5855277dc 100644
--- a/builtins/2.7/_collections.pyi
+++ b/builtins/2.7/_collections.pyi
@@ -1,6 +1,6 @@
 """Stub file for the '_collections' module."""
 
-from typing import Any, Generic, Iterator, TypeVar
+from typing import Any, Generic, Iterator, TypeVar, Optional, Union
 
 class defaultdict(dict):
     default_factory = ...  # type: None
@@ -10,8 +10,8 @@ class defaultdict(dict):
     def __copy__(self) -> "defaultdict": ...
     def copy(self) -> "defaultdict": ...
 
-_T = TypeVar('T')
-_T2 = TypeVar('T2')
+_T = TypeVar('_T')
+_T2 = TypeVar('_T2')
 
 class deque(Generic[_T]):
     maxlen = ...  # type: Optional[int]
diff --git a/builtins/2.7/_functools.pyi b/builtins/2.7/_functools.pyi
index ceb3870d0..ef59af088 100644
--- a/builtins/2.7/_functools.pyi
+++ b/builtins/2.7/_functools.pyi
@@ -1,8 +1,8 @@
 """Stub file for the '_functools' module."""
 
-from typing import Any, Callable, Iterator, Optional, TypeVar
+from typing import Any, Callable, Iterator, Optional, TypeVar, Tuple
 
-_T = TypeVar("T")
+_T = TypeVar("_T")
 def reduce(function: Callable[[_T, _T], _T],
            sequence: Iterator[_T], initial=Optional[_T]) -> _T: ...
 
diff --git a/builtins/2.7/_io.pyi b/builtins/2.7/_io.pyi
index f776cf1fc..a8119a877 100644
--- a/builtins/2.7/_io.pyi
+++ b/builtins/2.7/_io.pyi
@@ -1,4 +1,4 @@
-from typing import Any, Iterable, Tuple, List, Union
+from typing import Any, Optional, Iterable, Tuple, List, Union
 
 DEFAULT_BUFFER_SIZE = ...  # type: int
 
@@ -10,7 +10,7 @@ class UnsupportedOperation(ValueError, IOError): ...
 
 
 class _IOBase(object):
-    closed = ...  # type: getset_descriptor
+    closed = ...  # type: bool
     def __enter__(self) -> "_IOBase": ...
     def __exit__(self, type, value, traceback) -> bool: ...
     def __iter__(self) -> "_IOBase": ...
@@ -76,16 +76,16 @@ class FileIO(_RawIOBase):
     def write(self, pbuf: str) -> int: ...
 
 class IncrementalNewlineDecoder(object):
-    newlines = ...  # type: AnyStr
+    newlines = ...  # type: Union[str, unicode]
     def decode(self, input, final) -> Any: ...
     def getstate(self) -> Tuple[Any, int]: ...
     def setstate(self, state: Tuple[Any, int]) -> None: ...
     def reset(self) -> None: ...
 
 class _TextIOBase(_IOBase):
-    errors = ...  # type: Optional[]
-    newlines = ...  # type: AnyStr
-    encoding = ...  # type: Optional[]
+    errors = ...  # type: Optional[str]
+    newlines = ...  # type: Union[str, unicode]
+    encoding = ...  # type: Optional[str]
     def read(self, n: int = ...) -> str: ...
     def write(self): ...
     def detach(self): ...
diff --git a/builtins/2.7/_random.pyi b/builtins/2.7/_random.pyi
index 7b5cba32e..b8cef226e 100644
--- a/builtins/2.7/_random.pyi
+++ b/builtins/2.7/_random.pyi
@@ -1,7 +1,7 @@
-from typing import Optional, Any
+from typing import Optional, Union, Any
 
 class Random(object):
-    def __init__(self, seed: x, object = None) -> None: ...
+    def __init__(self, seed: Optional[Union[int, Any]] = ..., object = ...) -> None: ...
     def getstate(self) -> tuple: ...
     def setstate(self, state: tuple) -> None: ...
     def random(self) -> float: ...
diff --git a/builtins/2.7/_sha256.pyi b/builtins/2.7/_sha256.pyi
index a429ec7e0..4cf40c1f3 100644
--- a/builtins/2.7/_sha256.pyi
+++ b/builtins/2.7/_sha256.pyi
@@ -1,3 +1,5 @@
+from typing import Optional
+
 class sha224(object):
     name = ...  # type: str
     block_size = ...  # type: int
diff --git a/builtins/2.7/_sha512.pyi b/builtins/2.7/_sha512.pyi
index 5da79aabb..f9e4928af 100644
--- a/builtins/2.7/_sha512.pyi
+++ b/builtins/2.7/_sha512.pyi
@@ -1,3 +1,5 @@
+from typing import Optional
+
 class sha384(object):
     name = ...  # type: str
     block_size = ...  # type: int
diff --git a/builtins/2.7/_socket.pyi b/builtins/2.7/_socket.pyi
index cb87cce1f..6f72ba9df 100644
--- a/builtins/2.7/_socket.pyi
+++ b/builtins/2.7/_socket.pyi
@@ -1,4 +1,4 @@
-from typing import Tuple, Union, IO, Any, overload
+from typing import Tuple, Union, IO, Any, Optional, overload
 
 AF_APPLETALK = ...  # type: int
 AF_ASH = ...  # type: int
@@ -42,7 +42,6 @@ BTPROTO_HCI = ...  # type: int
 BTPROTO_L2CAP = ...  # type: int
 BTPROTO_RFCOMM = ...  # type: int
 BTPROTO_SCO = ...  # type: int
-CAPI = ...  # type: PyCapsule
 EAI_ADDRFAMILY = ...  # type: int
 EAI_AGAIN = ...  # type: int
 EAI_BADFLAGS = ...  # type: int
@@ -238,9 +237,14 @@ TIPC_WAIT_FOREVER = ...  # type: int
 TIPC_WITHDRAWN = ...  # type: int
 TIPC_ZONE_SCOPE = ...  # type: int
 
+# PyCapsule
+CAPI = ...  # type: Any
+
 has_ipv6 = ...  # type: bool
 
 class error(IOError): ...
+class gaierror(error): ...
+class timeout(error): ...
 
 class SocketType(object):
     family = ...  # type: int
diff --git a/builtins/2.7/_sre.pyi b/builtins/2.7/_sre.pyi
index 01561576c..2f1500f66 100644
--- a/builtins/2.7/_sre.pyi
+++ b/builtins/2.7/_sre.pyi
@@ -1,6 +1,6 @@
 """Stub file for the '_sre' module."""
 
-from typing import Any, Optional, Mapping, Sequence, Dict, List, Tuple, overload
+from typing import Any, Union, Iterable, Optional, Mapping, Sequence, Dict, List, Tuple, overload
 
 CODESIZE = ...  # type: int
 MAGIC = ...  # type: int
diff --git a/builtins/2.7/_struct.pyi b/builtins/2.7/_struct.pyi
index a0700f203..a9048b7f5 100644
--- a/builtins/2.7/_struct.pyi
+++ b/builtins/2.7/_struct.pyi
@@ -1,5 +1,7 @@
 """Stub file for the '_struct' module."""
 
+from typing import Any, AnyStr, Tuple
+
 class error(Exception): ...
 
 class Struct(object):
diff --git a/builtins/2.7/_symtable.pyi b/builtins/2.7/_symtable.pyi
index bd2a677de..b2c92902b 100644
--- a/builtins/2.7/_symtable.pyi
+++ b/builtins/2.7/_symtable.pyi
@@ -22,6 +22,9 @@ TYPE_FUNCTION = ...  # type: int
 TYPE_MODULE = ...  # type: int
 USE = ...  # type: int
 
+class _symtable_entry(object):
+    ...
+
 class symtable(object):
     children = ...  # type: List[_symtable_entry]
     id = ...  # type: int
diff --git a/builtins/2.7/array.pyi b/builtins/2.7/array.pyi
index e0ea9a83a..baaa50e13 100644
--- a/builtins/2.7/array.pyi
+++ b/builtins/2.7/array.pyi
@@ -1,6 +1,7 @@
 """Stub file for the 'array' module."""
 
-from typing import Any, Generic, IO, Iterable, Sequence, TypeVar, Union, overload
+from typing import (Any, Generic, IO, Iterable, Sequence, TypeVar,
+                    Union, overload, Iterator, Tuple, BinaryIO)
 
 T = TypeVar('T')
 
@@ -42,7 +43,7 @@ class array(Generic[T]):
     def index(self, x: T) -> int: ...
     def insert(self, i: int, x: T) -> None: ...
     def pop(self, i: int = ...) -> T: ...
-    def read(self, f: file, n: int) -> None:
+    def read(self, f: IO[str], n: int) -> None:
         raise DeprecationWarning()
     def remove(self, x: T) -> None: ...
     def reverse(self) -> None: ...
@@ -51,5 +52,5 @@ class array(Generic[T]):
     def tolist(self) -> List[T]: ...
     def tostring(self) -> str: ...
     def tounicode(self) -> unicode: ...
-    def write(self, f: file) -> None:
+    def write(self, f: IO[str]) -> None:
         raise DeprecationWarning()
diff --git a/builtins/2.7/cStringIO.pyi b/builtins/2.7/cStringIO.pyi
index bb49c9bd4..418b3fd2e 100644
--- a/builtins/2.7/cStringIO.pyi
+++ b/builtins/2.7/cStringIO.pyi
@@ -24,10 +24,11 @@ class StringIO(IO[str]):
     def truncate(self, size: int = None) -> int:
         raise IOError()
     def writable(self) -> bool: ...
-    def next(self) -> str: ...
-    def __iter__(self) -> "InputType": ...
+    def __next__(self) -> str: ...
     def __enter__(self) -> Any: ...
     def __exit__(self, exc_type: type, exc_val: Any, exc_tb: Any) -> Any: ...
+    # The C extension actually returns an "InputType".
+    def __iter__(self) -> Iterator[str]: ...
     # only StringO:
     def reset(self) -> None: ...
     def write(self, b: Union[str, unicode]) -> None: ...
diff --git a/builtins/2.7/exceptions.pyi b/builtins/2.7/exceptions.pyi
index 27021b791..1f29e909a 100644
--- a/builtins/2.7/exceptions.pyi
+++ b/builtins/2.7/exceptions.pyi
@@ -1,4 +1,4 @@
-from typing import Any, List
+from typing import Any, List, Optional
 
 class StandardError(Exception): ...
 class ArithmeticError(StandardError): ...
diff --git a/builtins/2.7/operator.pyi b/builtins/2.7/operator.pyi
index f06724345..4f12ab197 100644
--- a/builtins/2.7/operator.pyi
+++ b/builtins/2.7/operator.pyi
@@ -115,10 +115,10 @@ def truth(x: Any) -> bool: ...
 def xor(a: Any, b: Any) -> Any: ...
 
 class attrgetter(object):
-    def __init__(self, name: Any): ...
+    def __init__(self, name: Any) -> None: ...
 
 class itemgetter(object):
-    def __init__(self, key: Any): ...
+    def __init__(self, key: Any) -> None: ...
 
 class methodcaller(object):
-    def __init__(self, method_name: str, *args, **kwargs): ...
+    def __init__(self, method_name: str, *args, **kwargs) -> None: ...
diff --git a/builtins/2.7/posix.pyi b/builtins/2.7/posix.pyi
index 3847880cb..2257c8c84 100644
--- a/builtins/2.7/posix.pyi
+++ b/builtins/2.7/posix.pyi
@@ -1,4 +1,4 @@
-from typing import List, Mapping, Tuple, Union, Sequence, IO, Any, Optional
+from typing import List, Mapping, Tuple, Union, Sequence, IO, Optional, TypeVar
 
 error = OSError
 
@@ -110,7 +110,7 @@ def fchdir(fd: int) -> None: ...
 def fchmod(fd: int, mode: int) -> None: ...
 def fchown(fd: int, uid: int, gid: int) -> None: ...
 def fdatasync(fd: int) -> None: ...
-def fdopen(fd: int, mode: str = ..., bufsize: int = ...) -> file: ...
+def fdopen(fd: int, mode: str = ..., bufsize: int = ...) -> IO[str]: ...
 def fork() -> int:
     raise OSError()
 def forkpty() -> Tuple[int, int]:
@@ -143,8 +143,8 @@ def kill(pid: int, sig: int) -> None: ...
 def killpg(pgid: int, sig: int) -> None: ...
 def lchown(path: unicode, uid: int, gid: int) -> None: ...
 def link(source: unicode, link_name: str) -> None: ...
-_t = TypeVar
-def listdir(path: _t) -> List[_t]: ...
+_T = TypeVar("_T")
+def listdir(path: _T) -> List[_T]: ...
 def lseek(fd: int, pos: int, how: int) -> None: ...
 def lstat(path: unicode) -> stat_result: ...
 def major(device: int) -> int: ...
@@ -158,10 +158,10 @@ def open(file: unicode, flags: int, mode: int = ...) -> int: ...
 def openpty() -> Tuple[int, int]: ...
 def pathconf(path: unicode, name: str) -> str: ...
 def pipe() -> Tuple[int, int]: ...
-def popen(command: str, mode: str = ..., bufsize: int = ...) -> file: ...
+def popen(command: str, mode: str = ..., bufsize: int = ...) -> IO[str]: ...
 def putenv(varname: str, value: str) -> None: ...
 def read(fd: int, n: int) -> str: ...
-def readlink(path: _t) -> _t: ...
+def readlink(path: _T) -> _T: ...
 def remove(path: unicode) -> None: ...
 def rename(src: unicode, dst: unicode) -> None: ...
 def rmdir(path: unicode) -> None: ...
@@ -179,7 +179,7 @@ def setsid() -> None: ...
 def setuid(pid: int) -> None: ...
 def stat(path: unicode) -> stat_result: ...
 def statvfs(path: unicode) -> statvfs_result: ...
-def stat_float_times(fd: int) -> NoneType: ...
+def stat_float_times(fd: int) -> None: ...
 def strerror(code: int) -> str: ...
 def symlink(source: unicode, link_name: unicode) -> None: ...
 def sysconf(name: Union[str, int]) -> int: ...
@@ -187,7 +187,7 @@ def system(command: unicode) -> int: ...
 def tcgetpgrp(fd: int) -> int: ...
 def tcsetpgrp(fd: int, pg: int) -> None: ...
 def times() -> Tuple[float, float, float, float, float]: ...
-def tmpfile() -> file: ...
+def tmpfile() -> IO[str]: ...
 def ttyname(fd: int) -> str: ...
 def umask(mask: int) -> int: ...
 def uname() -> Tuple[str, str, str, str, str]: ...
diff --git a/builtins/2.7/pwd.pyi b/builtins/2.7/pwd.pyi
index 71013c51d..facd9dbea 100644
--- a/builtins/2.7/pwd.pyi
+++ b/builtins/2.7/pwd.pyi
@@ -1,8 +1,6 @@
-def getpwall() -> list<struct_passwd>
-def getpwnam(name:str) -> struct_passwd
-def getpwuid(uid:int) -> struct_passwd
+from typing import List
 
-class struct_passwd(tuple): ...
+class struct_passwd(tuple):
     n_fields = ...  # type: int
     n_sequence_fields = ...  # type: int
     n_unnamed_fields = ...  # type: int
@@ -13,3 +11,8 @@ class struct_passwd(tuple): ...
     pw_gecos = ...  # type: str
     pw_gid = ...  # type: int
     pw_uid = ...  # type: int
+
+def getpwall() -> List[struct_passwd]: ...
+def getpwnam(name:str) -> struct_passwd: ...
+def getpwuid(uid:int) -> struct_passwd: ...
+
diff --git a/builtins/2.7/select.pyi b/builtins/2.7/select.pyi
index 872564d82..ba6e9afbb 100644
--- a/builtins/2.7/select.pyi
+++ b/builtins/2.7/select.pyi
@@ -1,6 +1,6 @@
 """Stubs for the 'select' module."""
 
-from typing import Any, Optional
+from typing import Any, Optional, Tuple, Iterable
 
 EPOLLERR = ...  # type: int
 EPOLLET = ...  # type: int
diff --git a/builtins/2.7/sys.pyi b/builtins/2.7/sys.pyi
index 52fffa7e5..1e955a80a 100644
--- a/builtins/2.7/sys.pyi
+++ b/builtins/2.7/sys.pyi
@@ -1,7 +1,7 @@
 """Stubs for the 'sys' module."""
 
 from typing import (
-    List, Sequence, Any, Dict, Tuple, BinaryIO, overload
+    IO, Union, List, Sequence, Any, Dict, Tuple, BinaryIO, overload
 )
 
 class _flags:
@@ -63,12 +63,11 @@ path = ...  # type: List[str]
 platform = ...  # type: str
 prefix = ...  # type: str
 py3kwarning = ...  # type: bool
-stderr = ...  # type: file
-stdin = ...  # type: file
-stdout = ...  # type: file
+stderr = ...  # type: IO[str]
+stdin = ...  # type: IO[str]
+stdout = ...  # type: IO[str]
 subversion = ...  # type: tuple
 version = ...  # type: str
-version_info = ...  # type: Tuple[int]
 warnoptions = ...  # type: object
 float_info = ...  # type: _float_info
 version_info = ...  # type: _version_info
diff --git a/builtins/2.7/unicodedata.pyi b/builtins/2.7/unicodedata.pyi
index 9e3be51be..ab233af39 100644
--- a/builtins/2.7/unicodedata.pyi
+++ b/builtins/2.7/unicodedata.pyi
@@ -1,12 +1,13 @@
 """Stubs for the 'unicodedata' module."""
 
-from typing import Any, TypeVar
+from typing import Any, TypeVar, Union, Optional
 
 ucd_3_2_0 = ... # type: UCD
-ucnhash_CAPI = ... # type: Any (PyCapsule)
 unidata_version = ... # type: str
+# PyCapsule
+ucnhash_CAPI = ... # type: Any
 
-_default = TypeVar("default")
+_default = TypeVar("_default")
 
 def bidirectional(unichr: unicode) -> str: ...
 def category(unichr: unicode) -> str: ...
@@ -19,7 +20,7 @@ def lookup(name: str): unicode
 def mirrored(unichr: unicode): int
 def name(chr: unicode, default=_default) -> Union[str, _default]: ...
 def normalize(form: str, unistr: unicode) -> unicode: ...
-def numeric(chr, default=_default): Union[float, _default]: ...
+def numeric(chr, default=_default) -> Union[float, _default]: ...
 
 class UCD(object):
     unidata_version = ... # type: str
@@ -36,4 +37,4 @@ class UCD(object):
     def mirrored(unichr: unicode): int
     def name(chr: unicode, default=_default) -> Union[str, _default]: ...
     def normalize(form: str, unistr: unicode) -> unicode: ...
-    def numeric(chr, default=_default): Union[float, _default]: ...
+    def numeric(chr, default=_default) -> Union[float, _default]: ...
diff --git a/builtins/2.7/zipimport.pyi b/builtins/2.7/zipimport.pyi
index b794f7d7b..e13bc10cc 100644
--- a/builtins/2.7/zipimport.pyi
+++ b/builtins/2.7/zipimport.pyi
@@ -1,6 +1,6 @@
 """Stub file for the 'zipimport' module."""
 
-from typing import Dict
+from typing import Dict, Optional
 
 class ZipImportError(ImportError):
     pass
diff --git a/builtins/2.7/zlib.pyi b/builtins/2.7/zlib.pyi
index 74eeed33e..72bfc88c1 100644
--- a/builtins/2.7/zlib.pyi
+++ b/builtins/2.7/zlib.pyi
@@ -24,13 +24,13 @@ def decompress(data: str, wbits: int = ..., bufsize: int = ...) -> str: ...
 
 class compressobj:
     def __init__(level: int = ..., method: int = ..., wbits: int = ..., memlevel: int = ...,
-                 strategy: int = ...): ...
+                 strategy: int = ...) -> None: ...
+    def copy(self) -> "compressobj": ...
     def compress(self, data: str) -> str: ...
-    def copy(self) -> _Compress: ...
-    def flush(self) -> NoneType: ...
+    def flush(self) -> None: ...
 
 class decompressobj:
-    def __init__(wbits: int = ...): ...
-    def copy(self) -> _Compress: ...
+    def __init__(wbits: int = ...) -> None: ...
+    def copy(self) -> "decompressobj": ...
     def decompress(self, data: str) -> str: ...
-    def flush(self) -> NoneType: ...
+    def flush(self) -> None: ...