Improve static typing strictness (#10569)

49 files changed, 223 insertions, 170 deletions

diff --git a/sphinx/application.py b/sphinx/application.py
index c11b48916..e0e77a3f5 100644
--- a/sphinx/application.py
+++ b/sphinx/application.py
@@ -943,7 +943,7 @@ class Sphinx:
         """
         self.registry.add_post_transform(transform)
 
-    def add_js_file(self, filename: str, priority: int = 500,
+    def add_js_file(self, filename: Optional[str], priority: int = 500,
                     loading_method: Optional[str] = None, **kwargs: Any) -> None:
         """Register a JavaScript file to include in the HTML output.
 
diff --git a/sphinx/builders/__init__.py b/sphinx/builders/__init__.py
index 9705ba894..62a369a91 100644
--- a/sphinx/builders/__init__.py
+++ b/sphinx/builders/__init__.py
@@ -301,7 +301,9 @@ class Builder:
                        summary=__('targets for %d source files that are out of date') %
                        len(to_build))
 
-    def build(self, docnames: Iterable[str], summary: str = None, method: str = 'update') -> None:  # NOQA
+    def build(
+        self, docnames: Iterable[str], summary: Optional[str] = None, method: str = 'update'
+    ) -> None:
         """Main build method.
 
         First updates the environment, and then calls :meth:`write`.
diff --git a/sphinx/builders/_epub_base.py b/sphinx/builders/_epub_base.py
index 78d3d89a0..99035dc42 100644
--- a/sphinx/builders/_epub_base.py
+++ b/sphinx/builders/_epub_base.py
@@ -4,7 +4,7 @@ import html
 import os
 import re
 from os import path
-from typing import Any, Dict, List, NamedTuple, Set, Tuple
+from typing import Any, Dict, List, NamedTuple, Optional, Set, Tuple
 from zipfile import ZIP_DEFLATED, ZIP_STORED, ZipFile
 
 from docutils import nodes
@@ -446,7 +446,7 @@ class EpubBuilder(StandaloneHTMLBuilder):
         pass
 
     def handle_page(self, pagename: str, addctx: Dict, templatename: str = 'page.html',
-                    outfilename: str = None, event_arg: Any = None) -> None:
+                    outfilename: Optional[str] = None, event_arg: Any = None) -> None:
         """Create a rendered page.
 
         This method is overwritten for genindex pages in order to fix href link
diff --git a/sphinx/builders/changes.py b/sphinx/builders/changes.py
index 3a1f5bd65..618be0b3e 100644
--- a/sphinx/builders/changes.py
+++ b/sphinx/builders/changes.py
@@ -127,7 +127,7 @@ class ChangesBuilder(Builder):
             with open(targetfn, 'w', encoding='utf-8') as f:
                 text = ''.join(hl(i + 1, line) for (i, line) in enumerate(lines))
                 ctx = {
-                    'filename': self.env.doc2path(docname, None),
+                    'filename': self.env.doc2path(docname, False),
                     'text': text
                 }
                 f.write(self.templates.render('changes/rstsource.html', ctx))
diff --git a/sphinx/builders/dirhtml.py b/sphinx/builders/dirhtml.py
index bf8af15bb..e3191775c 100644
--- a/sphinx/builders/dirhtml.py
+++ b/sphinx/builders/dirhtml.py
@@ -1,7 +1,7 @@
 """Directory HTML builders."""
 
 from os import path
-from typing import Any, Dict
+from typing import Any, Dict, Optional
 
 from sphinx.application import Sphinx
 from sphinx.builders.html import StandaloneHTMLBuilder
@@ -19,7 +19,7 @@ class DirectoryHTMLBuilder(StandaloneHTMLBuilder):
     """
     name = 'dirhtml'
 
-    def get_target_uri(self, docname: str, typ: str = None) -> str:
+    def get_target_uri(self, docname: str, typ: Optional[str] = None) -> str:
         if docname == 'index':
             return ''
         if docname.endswith(SEP + 'index'):
diff --git a/sphinx/builders/dummy.py b/sphinx/builders/dummy.py
index f4f1356f6..5cb9cae10 100644
--- a/sphinx/builders/dummy.py
+++ b/sphinx/builders/dummy.py
@@ -1,6 +1,6 @@
 """Do syntax checks, but no writing."""
 
-from typing import Any, Dict, Set
+from typing import Any, Dict, Optional, Set
 
 from docutils.nodes import Node
 
@@ -21,7 +21,7 @@ class DummyBuilder(Builder):
     def get_outdated_docs(self) -> Set[str]:
         return self.env.found_docs
 
-    def get_target_uri(self, docname: str, typ: str = None) -> str:
+    def get_target_uri(self, docname: str, typ: Optional[str] = None) -> str:
         return ''
 
     def prepare_writing(self, docnames: Set[str]) -> None:
diff --git a/sphinx/builders/epub3.py b/sphinx/builders/epub3.py
index 46c636c7d..76776554e 100644
--- a/sphinx/builders/epub3.py
+++ b/sphinx/builders/epub3.py
@@ -77,7 +77,7 @@ class Epub3Builder(_epub_base.EpubBuilder):
         self.build_toc()
         self.build_epub()
 
-    def content_metadata(self) -> Dict:
+    def content_metadata(self) -> Dict[str, Any]:
         """Create a dictionary with all metadata for the content.opf
         file properly escaped.
         """
@@ -144,11 +144,11 @@ class Epub3Builder(_epub_base.EpubBuilder):
 
         return navstack[0].children
 
-    def navigation_doc_metadata(self, navlist: List[NavPoint]) -> Dict:
+    def navigation_doc_metadata(self, navlist: List[NavPoint]) -> Dict[str, Any]:
         """Create a dictionary with all metadata for the nav.xhtml file
         properly escaped.
         """
-        metadata: Dict = {}
+        metadata = {}
         metadata['lang'] = html.escape(self.config.epub_language)
         metadata['toc_locale'] = html.escape(self.guide_titles['toc'])
         metadata['navlist'] = navlist
@@ -217,7 +217,7 @@ def validate_config_values(app: Sphinx) -> None:
 
 def convert_epub_css_files(app: Sphinx, config: Config) -> None:
     """This converts string styled epub_css_files to tuple styled one."""
-    epub_css_files: List[Tuple[str, Dict]] = []
+    epub_css_files: List[Tuple[str, Dict[str, Any]]] = []
     for entry in config.epub_css_files:
         if isinstance(entry, str):
             epub_css_files.append((entry, {}))
@@ -236,7 +236,7 @@ def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_builder(Epub3Builder)
 
     # config values
-    app.add_config_value('epub_basename', lambda self: make_filename(self.project), None)
+    app.add_config_value('epub_basename', lambda self: make_filename(self.project), False)
     app.add_config_value('epub_version', 3.0, 'epub')  # experimental
     app.add_config_value('epub_theme', 'epub', 'epub')
     app.add_config_value('epub_theme_options', {}, 'epub')
diff --git a/sphinx/builders/gettext.py b/sphinx/builders/gettext.py
index cfc89146b..acdd9d137 100644
--- a/sphinx/builders/gettext.py
+++ b/sphinx/builders/gettext.py
@@ -5,7 +5,8 @@ from collections import OrderedDict, defaultdict
 from datetime import datetime, timedelta, tzinfo
 from os import getenv, path, walk
 from time import time
-from typing import Any, DefaultDict, Dict, Generator, Iterable, List, Set, Tuple, Union
+from typing import (Any, DefaultDict, Dict, Generator, Iterable, List, Optional, Set, Tuple,
+                    Union)
 from uuid import uuid4
 
 from docutils import nodes
@@ -78,7 +79,9 @@ class MsgOrigin:
 
 
 class GettextRenderer(SphinxRenderer):
-    def __init__(self, template_path: str = None, outdir: str = None) -> None:
+    def __init__(
+        self, template_path: Optional[str] = None, outdir: Optional[str] = None
+    ) -> None:
         self.outdir = outdir
         if template_path is None:
             template_path = path.join(package_dir, 'templates', 'gettext')
@@ -93,7 +96,7 @@ class GettextRenderer(SphinxRenderer):
         self.env.filters['e'] = escape
         self.env.filters['escape'] = escape
 
-    def render(self, filename: str, context: Dict) -> str:
+    def render(self, filename: str, context: Dict[str, Any]) -> str:
         def _relpath(s: str) -> str:
             return canon_path(relpath(s, self.outdir))
 
@@ -127,7 +130,7 @@ class I18nBuilder(Builder):
         self.tags = I18nTags()
         self.catalogs: DefaultDict[str, Catalog] = defaultdict(Catalog)
 
-    def get_target_uri(self, docname: str, typ: str = None) -> str:
+    def get_target_uri(self, docname: str, typ: Optional[str] = None) -> str:
         return ''
 
     def get_outdated_docs(self) -> Set[str]:
@@ -179,10 +182,10 @@ class LocalTimeZone(tzinfo):
         super().__init__(*args, **kwargs)
         self.tzdelta = tzdelta
 
-    def utcoffset(self, dt: datetime) -> timedelta:
+    def utcoffset(self, dt: Optional[datetime]) -> timedelta:
         return self.tzdelta
 
-    def dst(self, dt: datetime) -> timedelta:
+    def dst(self, dt: Optional[datetime]) -> timedelta:
         return timedelta(0)
 
 
@@ -249,7 +252,9 @@ class MessageCatalogBuilder(I18nBuilder):
             except Exception as exc:
                 raise ThemeError('%s: %r' % (template, exc)) from exc
 
-    def build(self, docnames: Iterable[str], summary: str = None, method: str = 'update') -> None:  # NOQA
+    def build(
+        self, docnames: Iterable[str], summary: Optional[str] = None, method: str = 'update'
+    ) -> None:
         self._extract_from_template()
         super().build(docnames, summary, method)
 
diff --git a/sphinx/builders/html/__init__.py b/sphinx/builders/html/__init__.py
index cfd4b5c96..e65ef18fa 100644
--- a/sphinx/builders/html/__init__.py
+++ b/sphinx/builders/html/__init__.py
@@ -823,7 +823,7 @@ class StandaloneHTMLBuilder(Builder):
                 if jsfile:
                     copyfile(jsfile, path.join(self.outdir, '_static', '_stemmer.js'))
 
-    def copy_theme_static_files(self, context: Dict) -> None:
+    def copy_theme_static_files(self, context: Dict[str, Any]) -> None:
         def onerror(filename: str, error: Exception) -> None:
             logger.warning(__('Failed to copy a file in html_static_file: %s: %r'),
                            filename, error)
diff --git a/sphinx/builders/linkcheck.py b/sphinx/builders/linkcheck.py
index 4dff0d4a6..3a964db02 100644
--- a/sphinx/builders/linkcheck.py
+++ b/sphinx/builders/linkcheck.py
@@ -4,6 +4,7 @@ import json
 import re
 import socket
 import time
+from copy import deepcopy
 from datetime import datetime, timezone
 from email.utils import parsedate_to_datetime
 from html.parser import HTMLParser
@@ -117,7 +118,7 @@ class CheckExternalLinksBuilder(DummyBuilder):
         socket.setdefaulttimeout(5.0)
 
     def process_result(self, result: CheckResult) -> None:
-        filename = self.env.doc2path(result.docname, None)
+        filename = self.env.doc2path(result.docname, False)
 
         linkstat = {"filename": filename, "lineno": result.lineno,
                     "status": result.status, "code": result.code, "uri": result.uri,
@@ -202,7 +203,7 @@ class HyperlinkAvailabilityChecker:
         self.rate_limits: Dict[str, RateLimit] = {}
         self.rqueue: Queue = Queue()
         self.workers: List[Thread] = []
-        self.wqueue: PriorityQueue = PriorityQueue()
+        self.wqueue: PriorityQueue[CheckRequest] = PriorityQueue()
 
         self.to_ignore = [re.compile(x) for x in self.config.linkcheck_ignore]
 
@@ -267,7 +268,7 @@ class HyperlinkAvailabilityCheckWorker(Thread):
         if self.config.linkcheck_timeout:
             kwargs['timeout'] = self.config.linkcheck_timeout
 
-        def get_request_headers() -> Dict:
+        def get_request_headers() -> Dict[str, str]:
             url = urlparse(uri)
             candidates = ["%s://%s" % (url.scheme, url.netloc),
                           "%s://%s/" % (url.scheme, url.netloc),
@@ -276,7 +277,7 @@ class HyperlinkAvailabilityCheckWorker(Thread):
 
             for u in candidates:
                 if u in self.config.linkcheck_request_headers:
-                    headers = dict(DEFAULT_REQUEST_HEADERS)
+                    headers = deepcopy(DEFAULT_REQUEST_HEADERS)
                     headers.update(self.config.linkcheck_request_headers[u])
                     return headers
 
@@ -561,19 +562,19 @@ def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_builder(CheckExternalLinksBuilder)
     app.add_post_transform(HyperlinkCollector)
 
-    app.add_config_value('linkcheck_ignore', [], None)
-    app.add_config_value('linkcheck_exclude_documents', [], None)
-    app.add_config_value('linkcheck_allowed_redirects', {}, None)
-    app.add_config_value('linkcheck_auth', [], None)
-    app.add_config_value('linkcheck_request_headers', {}, None)
-    app.add_config_value('linkcheck_retries', 1, None)
-    app.add_config_value('linkcheck_timeout', None, None, [int])
-    app.add_config_value('linkcheck_workers', 5, None)
-    app.add_config_value('linkcheck_anchors', True, None)
+    app.add_config_value('linkcheck_ignore', [], False)
+    app.add_config_value('linkcheck_exclude_documents', [], False)
+    app.add_config_value('linkcheck_allowed_redirects', {}, False)
+    app.add_config_value('linkcheck_auth', [], False)
+    app.add_config_value('linkcheck_request_headers', {}, False)
+    app.add_config_value('linkcheck_retries', 1, False)
+    app.add_config_value('linkcheck_timeout', None, False, [int])
+    app.add_config_value('linkcheck_workers', 5, False)
+    app.add_config_value('linkcheck_anchors', True, False)
     # Anchors starting with ! are ignored since they are
     # commonly used for dynamic pages
-    app.add_config_value('linkcheck_anchors_ignore', ["^!"], None)
-    app.add_config_value('linkcheck_rate_limit_timeout', 300.0, None)
+    app.add_config_value('linkcheck_anchors_ignore', ["^!"], False)
+    app.add_config_value('linkcheck_rate_limit_timeout', 300.0, False)
 
     app.add_event('linkcheck-process-uri')
 
diff --git a/sphinx/builders/manpage.py b/sphinx/builders/manpage.py
index ad1138c2c..b10fef48b 100644
--- a/sphinx/builders/manpage.py
+++ b/sphinx/builders/manpage.py
@@ -2,7 +2,7 @@
 
 import warnings
 from os import path
-from typing import Any, Dict, List, Set, Tuple, Union
+from typing import Any, Dict, List, Optional, Set, Tuple, Union
 
 from docutils.frontend import OptionParser
 from docutils.io import FileOutput
@@ -40,7 +40,7 @@ class ManualPageBuilder(Builder):
     def get_outdated_docs(self) -> Union[str, List[str]]:
         return 'all manpages'  # for now
 
-    def get_target_uri(self, docname: str, typ: str = None) -> str:
+    def get_target_uri(self, docname: str, typ: Optional[str] = None) -> str:
         return ''
 
     @progress_message(__('writing'))
@@ -111,9 +111,9 @@ def default_man_pages(config: Config) -> List[Tuple[str, str, str, List[str], in
 def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_builder(ManualPageBuilder)
 
-    app.add_config_value('man_pages', default_man_pages, None)
-    app.add_config_value('man_show_urls', False, None)
-    app.add_config_value('man_make_section_directory', False, None)
+    app.add_config_value('man_pages', default_man_pages, False)
+    app.add_config_value('man_show_urls', False, False)
+    app.add_config_value('man_make_section_directory', False, False)
 
     return {
         'version': 'builtin',
diff --git a/sphinx/builders/singlehtml.py b/sphinx/builders/singlehtml.py
index d177474a6..9930e150e 100644
--- a/sphinx/builders/singlehtml.py
+++ b/sphinx/builders/singlehtml.py
@@ -1,7 +1,7 @@
 """Single HTML builders."""
 
 from os import path
-from typing import Any, Dict, List, Tuple, Union
+from typing import Any, Dict, List, Optional, Tuple, Union
 
 from docutils import nodes
 from docutils.nodes import Node
@@ -27,10 +27,10 @@ class SingleFileHTMLBuilder(StandaloneHTMLBuilder):
 
     copysource = False
 
-    def get_outdated_docs(self) -> Union[str, List[str]]:  # type: ignore
+    def get_outdated_docs(self) -> Union[str, List[str]]:  # type: ignore[override]
         return 'all documents'
 
-    def get_target_uri(self, docname: str, typ: str = None) -> str:
+    def get_target_uri(self, docname: str, typ: Optional[str] = None) -> str:
         if docname in self.env.all_docs:
             # all references are on the same page...
             return self.config.root_doc + self.out_suffix + \
@@ -39,7 +39,7 @@ class SingleFileHTMLBuilder(StandaloneHTMLBuilder):
             # chances are this is a html_additional_page
             return docname + self.out_suffix
 
-    def get_relative_uri(self, from_: str, to: str, typ: str = None) -> str:
+    def get_relative_uri(self, from_: str, to: str, typ: Optional[str] = None) -> str:
         # ignore source
         return self.get_target_uri(to, typ)
 
@@ -113,7 +113,7 @@ class SingleFileHTMLBuilder(StandaloneHTMLBuilder):
 
         return {self.config.root_doc: new_fignumbers}
 
-    def get_doc_context(self, docname: str, body: str, metatags: str) -> Dict:
+    def get_doc_context(self, docname: str, body: str, metatags: str) -> Dict[str, Any]:
         # no relation links...
         toctree = TocTree(self.env).get_toctree_for(self.config.root_doc, self, False)
         # if there is no toctree, toc is None
diff --git a/sphinx/builders/texinfo.py b/sphinx/builders/texinfo.py
index 33b866e56..ee869dc7d 100644
--- a/sphinx/builders/texinfo.py
+++ b/sphinx/builders/texinfo.py
@@ -3,7 +3,7 @@
 import os
 import warnings
 from os import path
-from typing import Any, Dict, Iterable, List, Tuple, Union
+from typing import Any, Dict, Iterable, List, Optional, Tuple, Union
 
 from docutils import nodes
 from docutils.frontend import OptionParser
@@ -52,13 +52,13 @@ class TexinfoBuilder(Builder):
     def get_outdated_docs(self) -> Union[str, List[str]]:
         return 'all documents'  # for now
 
-    def get_target_uri(self, docname: str, typ: str = None) -> str:
+    def get_target_uri(self, docname: str, typ: Optional[str] = None) -> str:
         if docname not in self.docnames:
             raise NoUri(docname, typ)
         else:
             return '%' + docname
 
-    def get_relative_uri(self, from_: str, to: str, typ: str = None) -> str:
+    def get_relative_uri(self, from_: str, to: str, typ: Optional[str] = None) -> str:
         # ignore source path
         return self.get_target_uri(to, typ)
 
@@ -202,13 +202,13 @@ def default_texinfo_documents(config: Config) -> List[Tuple[str, str, str, str,
 def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_builder(TexinfoBuilder)
 
-    app.add_config_value('texinfo_documents', default_texinfo_documents, None)
-    app.add_config_value('texinfo_appendices', [], None)
-    app.add_config_value('texinfo_elements', {}, None)
-    app.add_config_value('texinfo_domain_indices', True, None, [list])
-    app.add_config_value('texinfo_show_urls', 'footnote', None)
-    app.add_config_value('texinfo_no_detailmenu', False, None)
-    app.add_config_value('texinfo_cross_references', True, None)
+    app.add_config_value('texinfo_documents', default_texinfo_documents, False)
+    app.add_config_value('texinfo_appendices', [], False)
+    app.add_config_value('texinfo_elements', {}, False)
+    app.add_config_value('texinfo_domain_indices', True, False, [list])
+    app.add_config_value('texinfo_show_urls', 'footnote', False)
+    app.add_config_value('texinfo_no_detailmenu', False, False)
+    app.add_config_value('texinfo_cross_references', True, False)
 
     return {
         'version': 'builtin',
diff --git a/sphinx/builders/text.py b/sphinx/builders/text.py
index bcd479864..4e125a0c0 100644
--- a/sphinx/builders/text.py
+++ b/sphinx/builders/text.py
@@ -1,7 +1,7 @@
 """Plain-text Sphinx builder."""
 
 from os import path
-from typing import Any, Dict, Iterator, Set, Tuple
+from typing import Any, Dict, Iterator, Optional, Set, Tuple
 
 from docutils.io import StringOutput
 from docutils.nodes import Node
@@ -25,7 +25,7 @@ class TextBuilder(Builder):
     allow_parallel = True
     default_translator_class = TextTranslator
 
-    current_docname: str = None
+    current_docname: Optional[str] = None
 
     def init(self) -> None:
         # section numbers for headings in the currently visited document
@@ -49,7 +49,7 @@ class TextBuilder(Builder):
                 # source doesn't exist anymore
                 pass
 
-    def get_target_uri(self, docname: str, typ: str = None) -> str:
+    def get_target_uri(self, docname: str, typ: Optional[str] = None) -> str:
         return ''
 
     def prepare_writing(self, docnames: Set[str]) -> None:
diff --git a/sphinx/builders/xml.py b/sphinx/builders/xml.py
index 0f45b912c..e86c7684c 100644
--- a/sphinx/builders/xml.py
+++ b/sphinx/builders/xml.py
@@ -1,7 +1,7 @@
 """Docutils-native XML and pseudo-XML builders."""
 
 from os import path
-from typing import Any, Dict, Iterator, Set, Type, Union
+from typing import Any, Dict, Iterator, Optional, Set, Type, Union
 
 from docutils import nodes
 from docutils.io import StringOutput
@@ -53,7 +53,7 @@ class XMLBuilder(Builder):
                 # source doesn't exist anymore
                 pass
 
-    def get_target_uri(self, docname: str, typ: str = None) -> str:
+    def get_target_uri(self, docname: str, typ: Optional[str] = None) -> str:
         return docname
 
     def prepare_writing(self, docnames: Set[str]) -> None:
diff --git a/sphinx/cmd/quickstart.py b/sphinx/cmd/quickstart.py
index 1509ee7fd..44a188b27 100644
--- a/sphinx/cmd/quickstart.py
+++ b/sphinx/cmd/quickstart.py
@@ -183,7 +183,7 @@ class QuickstartRenderer(SphinxRenderer):
             return super().render(template_name, context)
 
 
-def ask_user(d: Dict) -> None:
+def ask_user(d: Dict[str, Any]) -> None:
     """Ask the user for quickstart values missing from *d*.
 
     Values are:
diff --git a/sphinx/config.py b/sphinx/config.py
index 2fb41f066..92395dd27 100644
--- a/sphinx/config.py
+++ b/sphinx/config.py
@@ -158,7 +158,9 @@ class Config:
         self.extensions: List[str] = config.get('extensions', [])
 
     @classmethod
-    def read(cls, confdir: str, overrides: Dict = None, tags: Tags = None) -> "Config":
+    def read(
+        cls, confdir: str, overrides: Optional[Dict] = None, tags: Optional[Tags] = None
+    ) -> "Config":
         """Create a Config object from configuration file."""
         filename = path.join(confdir, CONFIG_FILENAME)
         if not path.isfile(filename):
diff --git a/sphinx/directives/code.py b/sphinx/directives/code.py
index 9437fe9a5..0ea492e12 100644
--- a/sphinx/directives/code.py
+++ b/sphinx/directives/code.py
@@ -1,7 +1,7 @@
 import sys
 import textwrap
 from difflib import unified_diff
-from typing import TYPE_CHECKING, Any, Dict, List, Tuple
+from typing import TYPE_CHECKING, Any, Dict, List, Optional, Tuple
 
 from docutils import nodes
 from docutils.nodes import Element, Node
@@ -48,7 +48,9 @@ class Highlight(SphinxDirective):
                                        linenothreshold=linenothreshold)]
 
 
-def dedent_lines(lines: List[str], dedent: int, location: Tuple[str, int] = None) -> List[str]:
+def dedent_lines(
+    lines: List[str], dedent: Optional[int], location: Optional[Tuple[str, int]] = None
+) -> List[str]:
     if dedent is None:
         return textwrap.dedent(''.join(lines)).splitlines(True)
 
@@ -186,7 +188,7 @@ class LiteralIncludeReader:
         ('diff', 'end-at'),
     ]
 
-    def __init__(self, filename: str, options: Dict, config: Config) -> None:
+    def __init__(self, filename: str, options: Dict[str, Any], config: Config) -> None:
         self.filename = filename
         self.options = options
         self.encoding = options.get('encoding', config.source_encoding)
@@ -200,7 +202,9 @@ class LiteralIncludeReader:
                 raise ValueError(__('Cannot use both "%s" and "%s" options') %
                                  (option1, option2))
 
-    def read_file(self, filename: str, location: Tuple[str, int] = None) -> List[str]:
+    def read_file(
+        self, filename: str, location: Optional[Tuple[str, int]] = None
+    ) -> List[str]:
         try:
             with open(filename, encoding=self.encoding, errors='strict') as f:
                 text = f.read()
@@ -216,7 +220,7 @@ class LiteralIncludeReader:
                                   'be wrong, try giving an :encoding: option') %
                                (self.encoding, filename)) from exc
 
-    def read(self, location: Tuple[str, int] = None) -> Tuple[str, int]:
+    def read(self, location: Optional[Tuple[str, int]] = None) -> Tuple[str, int]:
         if 'diff' in self.options:
             lines = self.show_diff()
         else:
@@ -233,14 +237,16 @@ class LiteralIncludeReader:
 
         return ''.join(lines), len(lines)
 
-    def show_diff(self, location: Tuple[str, int] = None) -> List[str]:
+    def show_diff(self, location: Optional[Tuple[str, int]] = None) -> List[str]:
         new_lines = self.read_file(self.filename)
         old_filename = self.options.get('diff')
         old_lines = self.read_file(old_filename)
         diff = unified_diff(old_lines, new_lines, old_filename, self.filename)
         return list(diff)
 
-    def pyobject_filter(self, lines: List[str], location: Tuple[str, int] = None) -> List[str]:
+    def pyobject_filter(
+        self, lines: List[str], location: Optional[Tuple[str, int]] = None
+    ) -> List[str]:
         pyobject = self.options.get('pyobject')
         if pyobject:
             from sphinx.pycode import ModuleAnalyzer
@@ -258,7 +264,9 @@ class LiteralIncludeReader:
 
         return lines
 
-    def lines_filter(self, lines: List[str], location: Tuple[str, int] = None) -> List[str]:
+    def lines_filter(
+        self, lines: List[str], location: Optional[Tuple[str, int]] = None
+    ) -> List[str]:
         linespec = self.options.get('lines')
         if linespec:
             linelist = parselinenos(linespec, len(lines))
@@ -282,7 +290,9 @@ class LiteralIncludeReader:
 
         return lines
 
-    def start_filter(self, lines: List[str], location: Tuple[str, int] = None) -> List[str]:
+    def start_filter(
+        self, lines: List[str], location: Optional[Tuple[str, int]] = None
+    ) -> List[str]:
         if 'start-at' in self.options:
             start = self.options.get('start-at')
             inclusive = False
@@ -313,7 +323,9 @@ class LiteralIncludeReader:
 
         return lines
 
-    def end_filter(self, lines: List[str], location: Tuple[str, int] = None) -> List[str]:
+    def end_filter(
+        self, lines: List[str], location: Optional[Tuple[str, int]] = None
+    ) -> List[str]:
         if 'end-at' in self.options:
             end = self.options.get('end-at')
             inclusive = True
@@ -340,21 +352,27 @@ class LiteralIncludeReader:
 
         return lines
 
-    def prepend_filter(self, lines: List[str], location: Tuple[str, int] = None) -> List[str]:
+    def prepend_filter(
+        self, lines: List[str], location: Optional[Tuple[str, int]] = None
+    ) -> List[str]:
         prepend = self.options.get('prepend')
         if prepend:
             lines.insert(0, prepend + '\n')
 
         return lines
 
-    def append_filter(self, lines: List[str], location: Tuple[str, int] = None) -> List[str]:
+    def append_filter(
+        self, lines: List[str], location: Optional[Tuple[str, int]] = None
+    ) -> List[str]:
         append = self.options.get('append')
         if append:
             lines.append(append + '\n')
 
         return lines
 
-    def dedent_filter(self, lines: List[str], location: Tuple[str, int] = None) -> List[str]:
+    def dedent_filter(
+        self, lines: List[str], location: Optional[Tuple[str, int]] = None
+    ) -> List[str]:
         if 'dedent' in self.options:
             return dedent_lines(lines, self.options.get('dedent'), location=location)
         else:
diff --git a/sphinx/directives/other.py b/sphinx/directives/other.py
index 38a332674..de2427d46 100644
--- a/sphinx/directives/other.py
+++ b/sphinx/directives/other.py
@@ -119,7 +119,7 @@ class TocTree(SphinxDirective):
                 if url_re.match(ref) or ref == 'self':
                     toctree['entries'].append((title, ref))
                 elif docname not in self.env.found_docs:
-                    if excluded(self.env.doc2path(docname, None)):
+                    if excluded(self.env.doc2path(docname, False)):
                         message = __('toctree contains reference to excluded document %r')
                         subtype = 'excluded'
                     else:
diff --git a/sphinx/domains/python.py b/sphinx/domains/python.py
index 370244a43..99901d2b2 100644
--- a/sphinx/domains/python.py
+++ b/sphinx/domains/python.py
@@ -99,8 +99,8 @@ def parse_reftarget(reftarget: str, suppress_prefix: bool = False
     return reftype, reftarget, title, refspecific
 
 
-def type_to_xref(target: str, env: BuildEnvironment = None, suppress_prefix: bool = False
-                 ) -> addnodes.pending_xref:
+def type_to_xref(target: str, env: Optional[BuildEnvironment] = None,
+                 suppress_prefix: bool = False) -> addnodes.pending_xref:
     """Convert a type string to a cross reference node."""
     if env:
         kwargs = {'py:module': env.ref_context.get('py:module'),
@@ -239,7 +239,9 @@ def _parse_annotation(annotation: str, env: BuildEnvironment) -> List[Node]:
         return [type_to_xref(annotation, env)]
 
 
-def _parse_arglist(arglist: str, env: BuildEnvironment = None) -> addnodes.desc_parameterlist:
+def _parse_arglist(
+    arglist: str, env: Optional[BuildEnvironment] = None
+) -> addnodes.desc_parameterlist:
     """Parse a list of arguments using AST parser"""
     params = addnodes.desc_parameterlist(arglist)
     sig = signature_from_str('(%s)' % arglist)
diff --git a/sphinx/environment/adapters/indexentries.py b/sphinx/environment/adapters/indexentries.py
index 49881b76d..364331286 100644
--- a/sphinx/environment/adapters/indexentries.py
+++ b/sphinx/environment/adapters/indexentries.py
@@ -3,7 +3,7 @@
 import re
 import unicodedata
 from itertools import groupby
-from typing import Any, Dict, List, Pattern, Tuple, cast
+from typing import Any, Dict, List, Optional, Pattern, Tuple, cast
 
 from sphinx.builders import Builder
 from sphinx.domains.index import IndexDomain
@@ -26,7 +26,7 @@ class IndexEntries:
         new: Dict[str, List] = {}
 
         def add_entry(word: str, subword: str, main: str, link: bool = True,
-                      dic: Dict = new, key: str = None) -> None:
+                      dic: Dict[str, List] = new, key: Optional[str] = None) -> None:
             # Force the word to be unicode if it's a ASCII bytestring.
             # This will solve problems with unicode normalization later.
             # For instance the RFC role will add bytestrings at the moment
@@ -118,7 +118,7 @@ class IndexEntries:
             #     (in module foo)
             #     (in module bar)
             oldkey = ''
-            oldsubitems: Dict[str, List] = None
+            oldsubitems: Optional[Dict[str, List]] = None
             i = 0
             while i < len(newlist):
                 key, (targets, subitems, _key) = newlist[i]
diff --git a/sphinx/environment/adapters/toctree.py b/sphinx/environment/adapters/toctree.py
index a04c4da8f..6db274000 100644
--- a/sphinx/environment/adapters/toctree.py
+++ b/sphinx/environment/adapters/toctree.py
@@ -164,7 +164,7 @@ class TocTree:
                                        ref, location=toctreenode)
                 except KeyError:
                     # this is raised if the included file does not exist
-                    if excluded(self.env.doc2path(ref, None)):
+                    if excluded(self.env.doc2path(ref, False)):
                         message = __('toctree contains reference to excluded document %r')
                     else:
                         message = __('toctree contains reference to nonexisting document %r')
diff --git a/sphinx/errors.py b/sphinx/errors.py
index a0263c613..8521010ff 100644
--- a/sphinx/errors.py
+++ b/sphinx/errors.py
@@ -1,6 +1,6 @@
 """Contains SphinxError and a few subclasses."""
 
-from typing import Any
+from typing import Any, Optional
 
 
 class SphinxError(Exception):
@@ -39,7 +39,9 @@ class ApplicationError(SphinxError):
 class ExtensionError(SphinxError):
     """Extension error."""
 
-    def __init__(self, message: str, orig_exc: Exception = None, modname: str = None) -> None:
+    def __init__(
+        self, message: str, orig_exc: Optional[Exception] = None, modname: Optional[str] = None
+    ) -> None:
         super().__init__(message)
         self.message = message
         self.orig_exc = orig_exc
diff --git a/sphinx/ext/apidoc.py b/sphinx/ext/apidoc.py
index ebea66a6c..9bfd69051 100644
--- a/sphinx/ext/apidoc.py
+++ b/sphinx/ext/apidoc.py
@@ -18,7 +18,7 @@ from copy import copy
 from fnmatch import fnmatch
 from importlib.machinery import EXTENSION_SUFFIXES
 from os import path
-from typing import Any, Generator, List, Tuple
+from typing import Any, Generator, List, Optional, Tuple
 
 import sphinx.locale
 from sphinx import __display_version__, package_dir
@@ -58,7 +58,7 @@ def module_join(*modnames: str) -> str:
     return '.'.join(filter(None, modnames))
 
 
-def is_packagedir(dirname: str = None, files: List[str] = None) -> bool:
+def is_packagedir(dirname: Optional[str] = None, files: Optional[List[str]] = None) -> bool:
     """Check given *files* contains __init__ file."""
     if files is None and dirname is None:
         return False
@@ -88,7 +88,7 @@ def write_file(name: str, text: str, opts: Any) -> None:
 
 
 def create_module_file(package: str, basename: str, opts: Any,
-                       user_template_dir: str = None) -> None:
+                       user_template_dir: Optional[str] = None) -> None:
     """Build the text of the file and write the file."""
     options = copy(OPTIONS)
     if opts.includeprivate and 'private-members' not in options:
@@ -107,7 +107,8 @@ def create_module_file(package: str, basename: str, opts: Any,
 
 def create_package_file(root: str, master_package: str, subroot: str, py_files: List[str],
                         opts: Any, subs: List[str], is_namespace: bool,
-                        excludes: List[str] = [], user_template_dir: str = None) -> None:
+                        excludes: List[str] = [], user_template_dir: Optional[str] = None
+                        ) -> None:
     """Build the text of the file and write the file."""
     # build a list of sub packages (directories containing an __init__ file)
     subpackages = [module_join(master_package, subroot, pkgname)
@@ -145,7 +146,7 @@ def create_package_file(root: str, master_package: str, subroot: str, py_files:
 
 
 def create_modules_toc_file(modules: List[str], opts: Any, name: str = 'modules',
-                            user_template_dir: str = None) -> None:
+                            user_template_dir: Optional[str] = None) -> None:
     """Create the module's index."""
     modules.sort()
     prev_module = ''
@@ -231,7 +232,7 @@ def has_child_module(rootpath: str, excludes: List[str], opts: Any) -> bool:
 
 
 def recurse_tree(rootpath: str, excludes: List[str], opts: Any,
-                 user_template_dir: str = None) -> List[str]:
+                 user_template_dir: Optional[str] = None) -> List[str]:
     """
     Look for every file in the directory tree and create the corresponding
     ReST files.
diff --git a/sphinx/ext/autodoc/__init__.py b/sphinx/ext/autodoc/__init__.py
index 78623a92f..2a6bf1880 100644
--- a/sphinx/ext/autodoc/__init__.py
+++ b/sphinx/ext/autodoc/__init__.py
@@ -34,7 +34,6 @@ from sphinx.util.typing import stringify as stringify_typehint
 if TYPE_CHECKING:
     from sphinx.ext.autodoc.directive import DocumenterBridge
 
-
 logger = logging.getLogger(__name__)
 
 
@@ -623,7 +622,7 @@ class Documenter:
                 return False, []  # type: ignore
             # specific members given
             selected = []
-            for name in self.options.members:  # type: str
+            for name in self.options.members:
                 if name in members:
                     selected.append((name, members[name].value))
                 else:
@@ -1677,7 +1676,7 @@ class ClassDocumenter(DocstringSignatureMixin, ModuleLevelDocumenter):  # type:
                 return False, []  # type: ignore
             # specific members given
             selected = []
-            for name in self.options.members:  # type: str
+            for name in self.options.members:
                 if name in members:
                     selected.append(members[name])
                 else:
diff --git a/sphinx/ext/autosummary/__init__.py b/sphinx/ext/autosummary/__init__.py
index eb5498e16..c8601c1f8 100644
--- a/sphinx/ext/autosummary/__init__.py
+++ b/sphinx/ext/autosummary/__init__.py
@@ -74,6 +74,7 @@ from sphinx.ext.autodoc import INSTANCEATTR, Documenter
 from sphinx.ext.autodoc.directive import DocumenterBridge, Options
 from sphinx.ext.autodoc.importer import import_module
 from sphinx.ext.autodoc.mock import mock
+from sphinx.extension import Extension
 from sphinx.locale import __
 from sphinx.project import Project
 from sphinx.pycode import ModuleAnalyzer, PycodeError
@@ -145,10 +146,10 @@ deprecated_alias('sphinx.ext.autosummary',
 
 
 class FakeApplication:
-    def __init__(self):
+    def __init__(self) -> None:
         self.doctreedir = None
         self.events = None
-        self.extensions = {}
+        self.extensions: Dict[str, Extension] = {}
         self.srcdir = None
         self.config = Config()
         self.project = Project(None, None)
@@ -243,7 +244,7 @@ class Autosummary(SphinxDirective):
                 docname = posixpath.join(tree_prefix, real_name)
                 docname = posixpath.normpath(posixpath.join(dirname, docname))
                 if docname not in self.env.found_docs:
-                    if excluded(self.env.doc2path(docname, None)):
+                    if excluded(self.env.doc2path(docname, False)):
                         msg = __('autosummary references excluded document %r. Ignored.')
                     else:
                         msg = __('autosummary: stub file not found %r. '
diff --git a/sphinx/ext/coverage.py b/sphinx/ext/coverage.py
index 1be815861..79e460435 100644
--- a/sphinx/ext/coverage.py
+++ b/sphinx/ext/coverage.py
@@ -24,12 +24,12 @@ logger = logging.getLogger(__name__)
 
 
 # utility
-def write_header(f: IO, text: str, char: str = '-') -> None:
+def write_header(f: IO[str], text: str, char: str = '-') -> None:
     f.write(text + '\n')
     f.write(char * len(text) + '\n')
 
 
-def compile_regex_list(name: str, exps: str) -> List[Pattern]:
+def compile_regex_list(name: str, exps: str) -> List[Pattern[str]]:
     lst = []
     for exp in exps:
         try:
@@ -53,14 +53,14 @@ class CoverageBuilder(Builder):
             pattern = path.join(self.srcdir, pattern)
             self.c_sourcefiles.extend(glob.glob(pattern))
 
-        self.c_regexes: List[Tuple[str, Pattern]] = []
+        self.c_regexes: List[Tuple[str, Pattern[str]]] = []
         for (name, exp) in self.config.coverage_c_regexes.items():
             try:
                 self.c_regexes.append((name, re.compile(exp)))
             except Exception:
                 logger.warning(__('invalid regex %r in coverage_c_regexes'), exp)
 
-        self.c_ignorexps: Dict[str, List[Pattern]] = {}
+        self.c_ignorexps: Dict[str, List[Pattern[str]]] = {}
         for (name, exps) in self.config.coverage_ignore_c_items.items():
             self.c_ignorexps[name] = compile_regex_list('coverage_ignore_c_items',
                                                         exps)
diff --git a/sphinx/ext/doctest.py b/sphinx/ext/doctest.py
index 0d414697c..4168e998a 100644
--- a/sphinx/ext/doctest.py
+++ b/sphinx/ext/doctest.py
@@ -9,8 +9,8 @@ import sys
 import time
 from io import StringIO
 from os import path
-from typing import (TYPE_CHECKING, Any, Callable, Dict, Iterable, List, Sequence, Set, Tuple,
-                    Type)
+from typing import (TYPE_CHECKING, Any, Callable, Dict, Iterable, List, Optional, Sequence,
+                    Set, Tuple, Type)
 
 from docutils import nodes
 from docutils.nodes import Element, Node, TextElement
@@ -225,7 +225,7 @@ class TestGroup:
 
 class TestCode:
     def __init__(self, code: str, type: str, filename: str,
-                 lineno: int, options: Dict = None) -> None:
+                 lineno: int, options: Optional[Dict] = None) -> None:
         self.code = code
         self.type = type
         self.filename = filename
@@ -317,7 +317,7 @@ class DocTestBuilder(Builder):
             logger.info(text, nonl=True)
         self.outfile.write(text)
 
-    def get_target_uri(self, docname: str, typ: str = None) -> str:
+    def get_target_uri(self, docname: str, typ: Optional[str] = None) -> str:
         return ''
 
     def get_outdated_docs(self) -> Set[str]:
@@ -362,11 +362,11 @@ Doctest summary
             filename = relpath(node.source, self.env.srcdir)\
                 .rsplit(':docstring of ', maxsplit=1)[0]
         except Exception:
-            filename = self.env.doc2path(docname, base=None)
+            filename = self.env.doc2path(docname, False)
         return filename
 
     @staticmethod
-    def get_line_number(node: Node) -> int:
+    def get_line_number(node: Node) -> Optional[int]:
         """Get the real line number or admit we don't know."""
         # TODO:  Work out how to store or calculate real (file-relative)
         #       line numbers for doctest blocks in docstrings.
diff --git a/sphinx/ext/graphviz.py b/sphinx/ext/graphviz.py
index b4a69a0f2..0459c4a96 100644
--- a/sphinx/ext/graphviz.py
+++ b/sphinx/ext/graphviz.py
@@ -6,7 +6,7 @@ import re
 import subprocess
 from os import path
 from subprocess import PIPE, CalledProcessError
-from typing import Any, Dict, List, Tuple
+from typing import Any, Dict, List, Optional, Tuple
 
 from docutils import nodes
 from docutils.nodes import Node
@@ -210,7 +210,7 @@ class GraphvizSimple(SphinxDirective):
 
 
 def render_dot(self: SphinxTranslator, code: str, options: Dict, format: str,
-               prefix: str = 'graphviz', filename: str = None) -> Tuple[str, str]:
+               prefix: str = 'graphviz', filename: Optional[str] = None) -> Tuple[str, str]:
     """Render graphviz code into a PNG or PDF output file."""
     graphviz_dot = options.get('graphviz_dot', self.builder.config.graphviz_dot)
     hashkey = (code + str(options) + str(graphviz_dot) +
diff --git a/sphinx/ext/imgmath.py b/sphinx/ext/imgmath.py
index e32a18851..6bc503d65 100644
--- a/sphinx/ext/imgmath.py
+++ b/sphinx/ext/imgmath.py
@@ -7,7 +7,7 @@ import subprocess
 import tempfile
 from os import path
 from subprocess import PIPE, CalledProcessError
-from typing import Any, Dict, List, Tuple
+from typing import Any, Dict, List, Optional, Tuple
 
 from docutils import nodes
 from docutils.nodes import Element
@@ -34,7 +34,9 @@ templates_path = path.join(package_dir, 'templates', 'imgmath')
 class MathExtError(SphinxError):
     category = 'Math extension error'
 
-    def __init__(self, msg: str, stderr: str = None, stdout: str = None) -> None:
+    def __init__(
+        self, msg: str, stderr: Optional[str] = None, stdout: Optional[str] = None
+    ) -> None:
         if stderr:
             msg += '\n[stderr]\n' + stderr
         if stdout:
@@ -53,7 +55,7 @@ depthsvg_re = re.compile(r'.*, depth=(.*)pt')
 depthsvgcomment_re = re.compile(r'<!-- DEPTH=(-?\d+) -->')
 
 
-def read_svg_depth(filename: str) -> int:
+def read_svg_depth(filename: str) -> Optional[int]:
     """Read the depth from comment at last line of SVG file
     """
     with open(filename, encoding="utf-8") as f:
diff --git a/sphinx/ext/inheritance_diagram.py b/sphinx/ext/inheritance_diagram.py
index c8a3dc763..5a1321328 100644
--- a/sphinx/ext/inheritance_diagram.py
+++ b/sphinx/ext/inheritance_diagram.py
@@ -32,7 +32,7 @@ import builtins
 import inspect
 import re
 from importlib import import_module
-from typing import Any, Dict, Iterable, List, Tuple, cast
+from typing import Any, Dict, Iterable, List, Optional, Tuple, cast
 
 from docutils import nodes
 from docutils.nodes import Node
@@ -131,8 +131,9 @@ class InheritanceGraph:
     graphviz dot graph from them.
     """
     def __init__(self, class_names: List[str], currmodule: str, show_builtins: bool = False,
-                 private_bases: bool = False, parts: int = 0, aliases: Dict[str, str] = None,
-                 top_classes: List[Any] = []) -> None:
+                 private_bases: bool = False, parts: int = 0,
+                 aliases: Optional[Dict[str, str]] = None, top_classes: List[Any] = []
+                 ) -> None:
         """*class_names* is a list of child classes to show bases from.
 
         If *show_builtins* is True, then Python builtins will be shown
@@ -212,7 +213,9 @@ class InheritanceGraph:
 
         return list(all_classes.values())
 
-    def class_name(self, cls: Any, parts: int = 0, aliases: Dict[str, str] = None) -> str:
+    def class_name(
+        self, cls: Any, parts: int = 0, aliases: Optional[Dict[str, str]] = None
+    ) -> str:
         """Given a class object, return a fully-qualified name.
 
         This works for things I've tested in matplotlib so far, but may not be
@@ -256,13 +259,14 @@ class InheritanceGraph:
         'style': '"setlinewidth(0.5)"',
     }
 
-    def _format_node_attrs(self, attrs: Dict) -> str:
+    def _format_node_attrs(self, attrs: Dict[str, Any]) -> str:
         return ','.join(['%s=%s' % x for x in sorted(attrs.items())])
 
-    def _format_graph_attrs(self, attrs: Dict) -> str:
+    def _format_graph_attrs(self, attrs: Dict[str, Any]) -> str:
         return ''.join(['%s=%s;\n' % x for x in sorted(attrs.items())])
 
-    def generate_dot(self, name: str, urls: Dict = {}, env: BuildEnvironment = None,
+    def generate_dot(self, name: str, urls: Dict[str, str] = {},
+                     env: Optional[BuildEnvironment] = None,
                      graph_attrs: Dict = {}, node_attrs: Dict = {}, edge_attrs: Dict = {}
                      ) -> str:
         """Generate a graphviz dot graph from the classes that were passed in
diff --git a/sphinx/ext/intersphinx.py b/sphinx/ext/intersphinx.py
index b493a0f02..1fc350386 100644
--- a/sphinx/ext/intersphinx.py
+++ b/sphinx/ext/intersphinx.py
@@ -98,7 +98,7 @@ def _strip_basic_auth(url: str) -> str:
     return urlunsplit(frags)
 
 
-def _read_from_url(url: str, config: Config = None) -> IO:
+def _read_from_url(url: str, config: Optional[Config] = None) -> IO:
     """Reads data from *url* with an HTTP *GET*.
 
     This function supports fetching from resources which use basic HTTP auth as
@@ -652,7 +652,7 @@ def inspect_main(argv: List[str]) -> None:
         sys.exit(1)
 
     class MockConfig:
-        intersphinx_timeout: int = None
+        intersphinx_timeout: Optional[int] = None
         tls_verify = False
         user_agent = None
 
diff --git a/sphinx/ext/mathjax.py b/sphinx/ext/mathjax.py
index d0d360e2e..a9e4deba3 100644
--- a/sphinx/ext/mathjax.py
+++ b/sphinx/ext/mathjax.py
@@ -65,7 +65,7 @@ def html_visit_displaymath(self: HTMLTranslator, node: nodes.math_block) -> None
     raise nodes.SkipNode
 
 
-def install_mathjax(app: Sphinx, pagename: str, templatename: str, context: Dict,
+def install_mathjax(app: Sphinx, pagename: str, templatename: str, context: Dict[str, Any],
                     event_arg: Any) -> None:
     if app.builder.format != 'html' or app.builder.math_renderer_name != 'mathjax':  # type: ignore  # NOQA
         return
diff --git a/sphinx/highlighting.py b/sphinx/highlighting.py
index 62f10f7a1..bb020850f 100644
--- a/sphinx/highlighting.py
+++ b/sphinx/highlighting.py
@@ -2,7 +2,7 @@
 
 from functools import partial
 from importlib import import_module
-from typing import Any, Dict
+from typing import Any, Dict, Optional
 
 from packaging import version
 from pygments import __version__ as pygmentsversion
@@ -99,7 +99,7 @@ class PygmentsBridge:
     latex_formatter = LatexFormatter
 
     def __init__(self, dest: str = 'html', stylename: str = 'sphinx',
-                 latex_engine: str = None) -> None:
+                 latex_engine: Optional[str] = None) -> None:
         self.dest = dest
         self.latex_engine = latex_engine
 
@@ -126,7 +126,7 @@ class PygmentsBridge:
         kwargs.update(self.formatter_args)
         return self.formatter(**kwargs)
 
-    def get_lexer(self, source: str, lang: str, opts: Dict = None,
+    def get_lexer(self, source: str, lang: str, opts: Optional[Dict] = None,
                   force: bool = False, location: Any = None) -> Lexer:
         if not opts:
             opts = {}
@@ -165,7 +165,7 @@ class PygmentsBridge:
 
         return lexer
 
-    def highlight_block(self, source: str, lang: str, opts: Dict = None,
+    def highlight_block(self, source: str, lang: str, opts: Optional[Dict] = None,
                         force: bool = False, location: Any = None, **kwargs: Any) -> str:
         if not isinstance(source, str):
             source = source.decode()
diff --git a/sphinx/locale/__init__.py b/sphinx/locale/__init__.py
index ae320054a..54a4570e3 100644
--- a/sphinx/locale/__init__.py
+++ b/sphinx/locale/__init__.py
@@ -167,7 +167,7 @@ def init_console(locale_dir: str, catalog: str) -> Tuple[NullTranslations, bool]
     """
     try:
         # encoding is ignored
-        language, _ = locale.getlocale(locale.LC_MESSAGES)  # type: Tuple[Optional[str], Any]
+        language, _ = locale.getlocale(locale.LC_MESSAGES)
     except AttributeError:
         # LC_MESSAGES is not always defined. Fallback to the default language
         # in case it is not.
@@ -191,7 +191,7 @@ def _lazy_translate(catalog: str, namespace: str, message: str) -> str:
     return translator.gettext(message)
 
 
-def get_translation(catalog: str, namespace: str = 'general') -> Callable:
+def get_translation(catalog: str, namespace: str = 'general') -> Callable[[str], str]:
     """Get a translation function based on the *catalog* and *namespace*.
 
     The extension can use this API to translate the messages on the
diff --git a/sphinx/roles.py b/sphinx/roles.py
index 7cc5fd14b..83dd60ea7 100644
--- a/sphinx/roles.py
+++ b/sphinx/roles.py
@@ -1,7 +1,7 @@
 """Handlers for additional ReST roles."""
 
 import re
-from typing import TYPE_CHECKING, Any, Dict, List, Tuple, Type
+from typing import TYPE_CHECKING, Any, Dict, List, Optional, Tuple, Type
 
 import docutils.parsers.rst.directives
 import docutils.parsers.rst.roles
@@ -64,7 +64,8 @@ class XRefRole(ReferenceRole):
     innernodeclass: Type[TextElement] = nodes.literal
 
     def __init__(self, fix_parens: bool = False, lowercase: bool = False,
-                 nodeclass: Type[Element] = None, innernodeclass: Type[TextElement] = None,
+                 nodeclass: Optional[Type[Element]] = None,
+                 innernodeclass: Optional[Type[TextElement]] = None,
                  warn_dangling: bool = False) -> None:
         self.fix_parens = fix_parens
         self.lowercase = lowercase
diff --git a/sphinx/setup_command.py b/sphinx/setup_command.py
index 5e63df3a7..bbeaa2281 100644
--- a/sphinx/setup_command.py
+++ b/sphinx/setup_command.py
@@ -7,7 +7,7 @@ import os
 import sys
 import warnings
 from io import StringIO
-from typing import Any, Dict
+from typing import Any, Dict, Optional
 
 from sphinx.application import Sphinx
 from sphinx.cmd.build import handle_exception
@@ -90,15 +90,15 @@ class BuildDoc(Command):
     def initialize_options(self) -> None:
         self.fresh_env = self.all_files = False
         self.pdb = False
-        self.source_dir: str = None
-        self.build_dir: str = None
+        self.source_dir: Optional[str] = None
+        self.build_dir: Optional[str] = None
         self.builder = 'html'
         self.warning_is_error = False
         self.project = ''
         self.version = ''
         self.release = ''
         self.today = ''
-        self.config_dir: str = None
+        self.config_dir: Optional[str] = None
         self.link_index = False
         self.copyright = ''
         # Link verbosity to distutils' (which uses 1 by default).
diff --git a/sphinx/util/math.py b/sphinx/util/math.py
index 7caf662dc..0c42a00ed 100644
--- a/sphinx/util/math.py
+++ b/sphinx/util/math.py
@@ -1,5 +1,7 @@
 """Utility functions for math."""
 
+from typing import Optional
+
 from docutils import nodes
 
 from sphinx.builders.html import HTMLTranslator
@@ -20,7 +22,7 @@ def get_node_equation_number(writer: HTMLTranslator, node: nodes.math_block) ->
         return node['number']
 
 
-def wrap_displaymath(text: str, label: str, numbering: bool) -> str:
+def wrap_displaymath(text: str, label: Optional[str], numbering: bool) -> str:
     def is_equation(part: str) -> str:
         return part.strip()
 
diff --git a/sphinx/util/nodes.py b/sphinx/util/nodes.py
index 1a861a060..0646b44e6 100644
--- a/sphinx/util/nodes.py
+++ b/sphinx/util/nodes.py
@@ -513,7 +513,7 @@ _non_id_translate_digraphs = {
 
 
 def make_id(env: "BuildEnvironment", document: nodes.document,
-            prefix: str = '', term: str = None) -> str:
+            prefix: str = '', term: Optional[str] = None) -> str:
     """Generate an appropriate node_id for given *prefix* and *term*."""
     node_id = None
     if prefix:
@@ -550,7 +550,8 @@ def find_pending_xref_condition(node: addnodes.pending_xref, condition: str
 
 
 def make_refnode(builder: "Builder", fromdocname: str, todocname: str, targetid: str,
-                 child: Union[Node, List[Node]], title: str = None) -> nodes.reference:
+                 child: Union[Node, List[Node]], title: Optional[str] = None
+                 ) -> nodes.reference:
     """Shortcut to create a reference node."""
     node = nodes.reference('', '', internal=True)
     if fromdocname == todocname and targetid:
diff --git a/sphinx/util/osutil.py b/sphinx/util/osutil.py
index d0ed42c8c..bfc80adcf 100644
--- a/sphinx/util/osutil.py
+++ b/sphinx/util/osutil.py
@@ -112,7 +112,7 @@ def make_filename_from_project(project: str) -> str:
     return make_filename(project_suffix_re.sub('', project)).lower()
 
 
-def relpath(path: str, start: str = os.curdir) -> str:
+def relpath(path: str, start: Optional[str] = os.curdir) -> str:
     """Return a relative filepath to *path* either from the current directory or
     from an optional *start* directory.
 
diff --git a/sphinx/util/parallel.py b/sphinx/util/parallel.py
index 193d2a80d..e89418ad3 100644
--- a/sphinx/util/parallel.py
+++ b/sphinx/util/parallel.py
@@ -81,7 +81,9 @@ class ParallelTasks:
         logging.convert_serializable(collector.logs)
         pipe.send((failed, collector.logs, ret))
 
-    def add_task(self, task_func: Callable, arg: Any = None, result_func: Callable = None) -> None:  # NOQA
+    def add_task(
+        self, task_func: Callable, arg: Any = None, result_func: Optional[Callable] = None
+    ) -> None:
         tid = self._taskid
         self._taskid += 1
         self._result_funcs[tid] = result_func or (lambda arg, result: None)
diff --git a/sphinx/util/stemmer/__init__.py b/sphinx/util/stemmer/__init__.py
index 6d27592d8..9f91ce59e 100644
--- a/sphinx/util/stemmer/__init__.py
+++ b/sphinx/util/stemmer/__init__.py
@@ -8,7 +8,7 @@ from sphinx.deprecation import RemovedInSphinx70Warning
 
 
 class PorterStemmer:
-    def __init__(self):
+    def __init__(self) -> None:
         warnings.warn(f"{self.__class__.__name__} is deprecated, use "
                       "snowballstemmer.stemmer('porter') instead.",
                       RemovedInSphinx70Warning, stacklevel=2)
@@ -22,7 +22,7 @@ class PorterStemmer:
 
 
 class BaseStemmer:
-    def __init__(self):
+    def __init__(self) -> None:
         warnings.warn(f"{self.__class__.__name__} is deprecated, use "
                       "snowballstemmer.stemmer('porter') instead.",
                       RemovedInSphinx70Warning, stacklevel=3)
@@ -32,7 +32,7 @@ class BaseStemmer:
 
 
 class PyStemmer(BaseStemmer):
-    def __init__(self):  # NoQA
+    def __init__(self) -> None:
         super().__init__()
         self.stemmer = snowballstemmer.stemmer('porter')
 
@@ -44,7 +44,7 @@ class PyStemmer(BaseStemmer):
 
 
 class StandardStemmer(BaseStemmer):
-    def __init__(self):  # NoQA
+    def __init__(self) -> None:
         super().__init__()
         self.stemmer = snowballstemmer.stemmer('porter')
 
diff --git a/sphinx/util/tags.py b/sphinx/util/tags.py
index 89276732d..ac69ae852 100644
--- a/sphinx/util/tags.py
+++ b/sphinx/util/tags.py
@@ -1,4 +1,4 @@
-from typing import Iterator, List
+from typing import Iterator, List, Optional
 
 from jinja2 import nodes
 from jinja2.environment import Environment
@@ -35,7 +35,7 @@ class BooleanParser(Parser):
 
 
 class Tags:
-    def __init__(self, tags: List[str] = None) -> None:
+    def __init__(self, tags: Optional[List[str]] = None) -> None:
         self.tags = dict.fromkeys(tags or [], True)
 
     def has(self, tag: str) -> bool:
diff --git a/sphinx/util/template.py b/sphinx/util/template.py
index 5a73515b3..23c68e36b 100644
--- a/sphinx/util/template.py
+++ b/sphinx/util/template.py
@@ -3,7 +3,7 @@
 import os
 from functools import partial
 from os import path
-from typing import Callable, Dict, List, Tuple, Union
+from typing import Any, Callable, Dict, List, Optional, Tuple, Union
 
 from jinja2 import TemplateNotFound
 from jinja2.environment import Environment
@@ -17,15 +17,15 @@ from sphinx.util import rst, texescape
 
 
 class BaseRenderer:
-    def __init__(self, loader: BaseLoader = None) -> None:
+    def __init__(self, loader: Optional[BaseLoader] = None) -> None:
         self.env = SandboxedEnvironment(loader=loader, extensions=['jinja2.ext.i18n'])
         self.env.filters['repr'] = repr
         self.env.install_gettext_translations(get_translator())
 
-    def render(self, template_name: str, context: Dict) -> str:
+    def render(self, template_name: str, context: Dict[str, Any]) -> str:
         return self.env.get_template(template_name).render(context)
 
-    def render_string(self, source: str, context: Dict) -> str:
+    def render_string(self, source: str, context: Dict[str, Any]) -> str:
         return self.env.from_string(source).render(context)
 
 
@@ -41,25 +41,27 @@ class FileRenderer(BaseRenderer):
         super().__init__(loader)
 
     @classmethod
-    def render_from_file(cls, filename: str, context: Dict) -> str:
+    def render_from_file(cls, filename: str, context: Dict[str, Any]) -> str:
         dirname = os.path.dirname(filename)
         basename = os.path.basename(filename)
         return cls(dirname).render(basename, context)
 
 
 class SphinxRenderer(FileRenderer):
-    def __init__(self, template_path: Union[str, List[str]] = None) -> None:
+    def __init__(self, template_path: Union[None, str, List[str]] = None) -> None:
         if template_path is None:
             template_path = os.path.join(package_dir, 'templates')
         super().__init__(template_path)
 
     @classmethod
-    def render_from_file(cls, filename: str, context: Dict) -> str:
+    def render_from_file(cls, filename: str, context: Dict[str, Any]) -> str:
         return FileRenderer.render_from_file(filename, context)
 
 
 class LaTeXRenderer(SphinxRenderer):
-    def __init__(self, template_path: str = None, latex_engine: str = None) -> None:
+    def __init__(
+        self, template_path: Optional[str] = None, latex_engine: Optional[str] = None
+    ) -> None:
         if template_path is None:
             template_path = os.path.join(package_dir, 'templates', 'latex')
         super().__init__(template_path)
@@ -81,7 +83,9 @@ class LaTeXRenderer(SphinxRenderer):
 
 
 class ReSTRenderer(SphinxRenderer):
-    def __init__(self, template_path: Union[str, List[str]] = None, language: str = None) -> None:  # NOQA
+    def __init__(
+        self, template_path: Union[None, str, List[str]] = None, language: Optional[str] = None
+    ) -> None:
         super().__init__(template_path)
 
         # add language to environment
diff --git a/sphinx/util/texescape.py b/sphinx/util/texescape.py
index 83c78bb38..ba885f695 100644
--- a/sphinx/util/texescape.py
+++ b/sphinx/util/texescape.py
@@ -1,7 +1,7 @@
 """TeX escaping helper."""
 
 import re
-from typing import Dict
+from typing import Dict, Optional
 
 tex_replacements = [
     # map TeX special chars
@@ -100,7 +100,7 @@ _tex_hlescape_map: Dict[int, str] = {}
 _tex_hlescape_map_without_unicode: Dict[int, str] = {}
 
 
-def escape(s: str, latex_engine: str = None) -> str:
+def escape(s: str, latex_engine: Optional[str] = None) -> str:
     """Escape text for LaTeX output."""
     if latex_engine in ('lualatex', 'xelatex'):
         # unicode based LaTeX engine
@@ -109,7 +109,7 @@ def escape(s: str, latex_engine: str = None) -> str:
         return s.translate(_tex_escape_map)
 
 
-def hlescape(s: str, latex_engine: str = None) -> str:
+def hlescape(s: str, latex_engine: Optional[str] = None) -> str:
     """Escape text for LaTeX highlighter."""
     if latex_engine in ('lualatex', 'xelatex'):
         # unicode based LaTeX engine
diff --git a/sphinx/util/typing.py b/sphinx/util/typing.py
index c070eb00c..eed7a7b95 100644
--- a/sphinx/util/typing.py
+++ b/sphinx/util/typing.py
@@ -69,7 +69,9 @@ InventoryItem = Tuple[str, str, str, str]
 Inventory = Dict[str, Dict[str, InventoryItem]]
 
 
-def get_type_hints(obj: Any, globalns: Dict = None, localns: Dict = None) -> Dict[str, Any]:
+def get_type_hints(
+    obj: Any, globalns: Optional[Dict[str, Any]] = None, localns: Optional[Dict] = None
+) -> Dict[str, Any]:
     """Return a dictionary containing type hints for a function, method, module or class object.
 
     This is a simple wrapper of `typing.get_type_hints()` that does not raise an error on
diff --git a/sphinx/writers/html5.py b/sphinx/writers/html5.py
index 9f33f5458..3ed72f882 100644
--- a/sphinx/writers/html5.py
+++ b/sphinx/writers/html5.py
@@ -837,13 +837,13 @@ class HTML5Translator(SphinxTranslator, BaseTranslator):
             node['ids'].remove(id)
 
     @property
-    def _fieldlist_row_index(self):
+    def _fieldlist_row_index(self) -> int:
         warnings.warn('_fieldlist_row_index is deprecated',
                       RemovedInSphinx60Warning, stacklevel=2)
         return self._fieldlist_row_indices[-1]
 
     @property
-    def _table_row_index(self):
+    def _table_row_index(self) -> int:
         warnings.warn('_table_row_index is deprecated',
                       RemovedInSphinx60Warning, stacklevel=2)
         return self._table_row_indices[-1]
diff --git a/sphinx/writers/latex.py b/sphinx/writers/latex.py
index 447943c86..5debd681f 100644
--- a/sphinx/writers/latex.py
+++ b/sphinx/writers/latex.py
@@ -8,7 +8,7 @@ import re
 import warnings
 from collections import defaultdict
 from os import path
-from typing import TYPE_CHECKING, Any, Dict, Iterable, List, Set, Tuple, cast
+from typing import TYPE_CHECKING, Any, Dict, Iterable, List, Optional, Set, Tuple, cast
 
 from docutils import nodes, writers
 from docutils.nodes import Element, Node, Text
@@ -172,7 +172,9 @@ class Table:
                 assert self.cells[(self.row + row, self.col + col)] == 0
                 self.cells[(self.row + row, self.col + col)] = self.cell_id
 
-    def cell(self, row: int = None, col: int = None) -> "TableCell":
+    def cell(
+        self, row: Optional[int] = None, col: Optional[int] = None
+    ) -> Optional["TableCell"]:
         """Returns a cell object (i.e. rectangular area) containing given position.
 
         If no option arguments: ``row`` or ``col`` are given, the current position;
@@ -496,7 +498,7 @@ class LaTeXTranslator(SphinxTranslator):
         return renderer.render(template_name, variables)
 
     @property
-    def table(self) -> Table:
+    def table(self) -> Optional[Table]:
         """Get current table."""
         if self.tables:
             return self.tables[-1]
diff --git a/sphinx/writers/texinfo.py b/sphinx/writers/texinfo.py
index cafc8341f..6b176bb3b 100644
--- a/sphinx/writers/texinfo.py
+++ b/sphinx/writers/texinfo.py
@@ -3,8 +3,8 @@
 import re
 import textwrap
 from os import path
-from typing import (TYPE_CHECKING, Any, Dict, Iterable, Iterator, List, Pattern, Set, Tuple,
-                    Union, cast)
+from typing import (TYPE_CHECKING, Any, Dict, Iterable, Iterator, List, Optional, Pattern, Set,
+                    Tuple, Union, cast)
 
 from docutils import nodes, writers
 from docutils.nodes import Element, Node, Text
@@ -91,7 +91,7 @@ def find_subsections(section: Element) -> List[nodes.section]:
     return result
 
 
-def smart_capwords(s: str, sep: str = None) -> str:
+def smart_capwords(s: str, sep: Optional[str] = None) -> str:
     """Like string.capwords() but does not capitalize words that already
     contain a capital letter."""
     words = s.split(sep)
@@ -173,7 +173,7 @@ class TexinfoTranslator(SphinxTranslator):
         self.body: List[str] = []
         self.context: List[str] = []
         self.descs: List[addnodes.desc] = []
-        self.previous_section: nodes.section = None
+        self.previous_section: Optional[nodes.section] = None
         self.section_level = 0
         self.seen_title = False
         self.next_section_ids: Set[str] = set()
@@ -184,7 +184,7 @@ class TexinfoTranslator(SphinxTranslator):
         self.in_footnote = 0
         self.in_samp = 0
         self.handled_abbrs: Set[str] = set()
-        self.colwidths: List[int] = None
+        self.colwidths: Optional[List[int]] = None
 
     def finish(self) -> None:
         if self.previous_section is None: