diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 69124678..50d1f6c8 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -8,7 +8,7 @@ repos:
   - id: trailing-whitespace
 
 - repo: https://github.com/pre-commit/mirrors-mypy
-  rev: v0.750
+  rev: v0.770
   hooks:
   - id: mypy
     exclude: '^(docs|tasks|tests)|setup\.py'
diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 2b6af82a..3ce556a3 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -5,6 +5,10 @@ Changelog
 ~~~~~~~~~~~~
 
 * Canonicalize version before comparing specifiers. (:issue:`282`)
+* Change type hint for ``canonicalize_name`` to return
+  ``packaging.utils.NormalizedName``.
+  This enables the use of static typing tools (like mypy) to detect mixing of
+  normalized and un-normalized names.
 
 20.3 - 2020-03-05
 ~~~~~~~~~~~~~~~~~
diff --git a/packaging/_compat.py b/packaging/_compat.py
index a145f7ee..e54bd4ed 100644
--- a/packaging/_compat.py
+++ b/packaging/_compat.py
@@ -5,9 +5,9 @@
 
 import sys
 
-from ._typing import MYPY_CHECK_RUNNING
+from ._typing import TYPE_CHECKING
 
-if MYPY_CHECK_RUNNING:  # pragma: no cover
+if TYPE_CHECKING:  # pragma: no cover
     from typing import Any, Dict, Tuple, Type
 
 
diff --git a/packaging/_typing.py b/packaging/_typing.py
index dc6dfce7..77a8b918 100644
--- a/packaging/_typing.py
+++ b/packaging/_typing.py
@@ -18,22 +18,31 @@
 
 In packaging, all static-typing related imports should be guarded as follows:
 
-    from packaging._typing import MYPY_CHECK_RUNNING
+    from packaging._typing import TYPE_CHECKING
 
-    if MYPY_CHECK_RUNNING:
+    if TYPE_CHECKING:
         from typing import ...
 
 Ref: https://github.com/python/mypy/issues/3216
 """
 
-MYPY_CHECK_RUNNING = False
+__all__ = ["TYPE_CHECKING", "cast"]
 
-if MYPY_CHECK_RUNNING:  # pragma: no cover
-    import typing
-
-    cast = typing.cast
+# The TYPE_CHECKING constant defined by the typing module is False at runtime
+# but True while type checking.
+if False:  # pragma: no cover
+    from typing import TYPE_CHECKING
+else:
+    TYPE_CHECKING = False
+
+# typing's cast syntax requires calling typing.cast at runtime, but we don't
+# want to import typing at runtime. Here, we inform the type checkers that
+# we're importing `typing.cast` as `cast` and re-implement typing.cast's
+# runtime behavior in a block that is ignored by type checkers.
+if TYPE_CHECKING:  # pragma: no cover
+    # not executed at runtime
+    from typing import cast
 else:
-    # typing's cast() is needed at runtime, but we don't want to import typing.
-    # Thus, we use a dummy no-op version, which we tell mypy to ignore.
-    def cast(type_, value):  # type: ignore
+    # executed at runtime
+    def cast(type_, value):  # noqa
         return value
diff --git a/packaging/markers.py b/packaging/markers.py
index f0174711..87cd3f95 100644
--- a/packaging/markers.py
+++ b/packaging/markers.py
@@ -13,10 +13,10 @@
 from pyparsing import Literal as L  # noqa
 
 from ._compat import string_types
-from ._typing import MYPY_CHECK_RUNNING
+from ._typing import TYPE_CHECKING
 from .specifiers import Specifier, InvalidSpecifier
 
-if MYPY_CHECK_RUNNING:  # pragma: no cover
+if TYPE_CHECKING:  # pragma: no cover
     from typing import Any, Callable, Dict, List, Optional, Tuple, Union
 
     Operator = Callable[[str, str], bool]
diff --git a/packaging/requirements.py b/packaging/requirements.py
index 1b547927..91f81ede 100644
--- a/packaging/requirements.py
+++ b/packaging/requirements.py
@@ -11,11 +11,11 @@
 from pyparsing import Literal as L  # noqa
 from six.moves.urllib import parse as urlparse
 
-from ._typing import MYPY_CHECK_RUNNING
+from ._typing import TYPE_CHECKING
 from .markers import MARKER_EXPR, Marker
 from .specifiers import LegacySpecifier, Specifier, SpecifierSet
 
-if MYPY_CHECK_RUNNING:  # pragma: no cover
+if TYPE_CHECKING:  # pragma: no cover
     from typing import List
 
 
diff --git a/packaging/specifiers.py b/packaging/specifiers.py
index 4eeef14f..9f7dd278 100644
--- a/packaging/specifiers.py
+++ b/packaging/specifiers.py
@@ -9,11 +9,11 @@
 import re
 
 from ._compat import string_types, with_metaclass
-from ._typing import MYPY_CHECK_RUNNING
+from ._typing import TYPE_CHECKING
 from .utils import canonicalize_version
 from .version import Version, LegacyVersion, parse
 
-if MYPY_CHECK_RUNNING:  # pragma: no cover
+if TYPE_CHECKING:  # pragma: no cover
     from typing import (
         List,
         Dict,
diff --git a/packaging/tags.py b/packaging/tags.py
index 25d8e008..9064910b 100644
--- a/packaging/tags.py
+++ b/packaging/tags.py
@@ -22,9 +22,9 @@
 import sysconfig
 import warnings
 
-from ._typing import MYPY_CHECK_RUNNING, cast
+from ._typing import TYPE_CHECKING, cast
 
-if MYPY_CHECK_RUNNING:  # pragma: no cover
+if TYPE_CHECKING:  # pragma: no cover
     from typing import (
         Dict,
         FrozenSet,
diff --git a/packaging/utils.py b/packaging/utils.py
index 44f1bf98..19579c1a 100644
--- a/packaging/utils.py
+++ b/packaging/utils.py
@@ -5,19 +5,22 @@
 
 import re
 
-from ._typing import MYPY_CHECK_RUNNING
+from ._typing import TYPE_CHECKING, cast
 from .version import InvalidVersion, Version
 
-if MYPY_CHECK_RUNNING:  # pragma: no cover
-    from typing import Union
+if TYPE_CHECKING:  # pragma: no cover
+    from typing import NewType, Union
+
+    NormalizedName = NewType("NormalizedName", str)
 
 _canonicalize_regex = re.compile(r"[-_.]+")
 
 
 def canonicalize_name(name):
-    # type: (str) -> str
+    # type: (str) -> NormalizedName
     # This is taken from PEP 503.
-    return _canonicalize_regex.sub("-", name).lower()
+    value = _canonicalize_regex.sub("-", name).lower()
+    return cast("NormalizedName", value)
 
 
 def canonicalize_version(_version):
diff --git a/packaging/version.py b/packaging/version.py
index f39a2a12..00371e86 100644
--- a/packaging/version.py
+++ b/packaging/version.py
@@ -8,9 +8,9 @@
 import re
 
 from ._structures import Infinity, NegativeInfinity
-from ._typing import MYPY_CHECK_RUNNING
+from ._typing import TYPE_CHECKING
 
-if MYPY_CHECK_RUNNING:  # pragma: no cover
+if TYPE_CHECKING:  # pragma: no cover
     from typing import Callable, Iterator, List, Optional, SupportsInt, Tuple, Union
 
     from ._structures import InfinityType, NegativeInfinityType