refactor: Add Optional to type annotations

19 files changed, 81 insertions, 77 deletions

diff --git a/sphinx/application.py b/sphinx/application.py
index 4735beffd..afbb0f981 100644
--- a/sphinx/application.py
+++ b/sphinx/application.py
@@ -141,9 +141,9 @@ class Sphinx:
         self.phase = BuildPhase.INITIALIZATION
         self.verbosity = verbosity
         self.extensions: Dict[str, Extension] = {}
-        self.builder: Builder = None
-        self.env: BuildEnvironment = None
-        self.project: Project = None
+        self.builder: Optional[Builder] = None
+        self.env: Optional[BuildEnvironment] = None
+        self.project: Optional[Project] = None
         self.registry = SphinxComponentRegistry()
         self.html_themes: Dict[str, str] = {}
 
@@ -174,7 +174,7 @@ class Sphinx:
 
         if status is None:
             self._status: IO = StringIO()
-            self.quiet = True
+            self.quiet: bool = True
         else:
             self._status = status
             self.quiet = False
diff --git a/sphinx/builders/__init__.py b/sphinx/builders/__init__.py
index bedc65b61..722f9a280 100644
--- a/sphinx/builders/__init__.py
+++ b/sphinx/builders/__init__.py
@@ -11,7 +11,8 @@
 import pickle
 import time
 from os import path
-from typing import TYPE_CHECKING, Any, Dict, Iterable, List, Sequence, Set, Tuple, Type, Union
+from typing import (TYPE_CHECKING, Any, Dict, Iterable, List, Optional, Sequence, Set, Tuple,
+                    Type, Union)
 
 from docutils import nodes
 from docutils.nodes import Node
@@ -88,7 +89,7 @@ class Builder:
         ensuredir(self.doctreedir)
 
         self.app: Sphinx = app
-        self.env: BuildEnvironment = None
+        self.env: Optional[BuildEnvironment] = None
         self.events: EventManager = app.events
         self.config: Config = app.config
         self.tags: Tags = app.tags
@@ -225,7 +226,7 @@ class Builder:
         self.compile_catalogs(set(repo.catalogs), message)
 
     def compile_specific_catalogs(self, specified_files: List[str]) -> None:
-        def to_domain(fpath: str) -> str:
+        def to_domain(fpath: str) -> Optional[str]:
             docname = self.env.path2doc(path.abspath(fpath))
             if docname:
                 return docname_to_domain(docname, self.config.gettext_compact)
diff --git a/sphinx/domains/__init__.py b/sphinx/domains/__init__.py
index 8f3e6a955..dbfad258c 100644
--- a/sphinx/domains/__init__.py
+++ b/sphinx/domains/__init__.py
@@ -11,8 +11,8 @@
 
 import copy
 from abc import ABC, abstractmethod
-from typing import (TYPE_CHECKING, Any, Callable, Dict, Iterable, List, NamedTuple, Tuple,
-                    Type, Union, cast)
+from typing import (TYPE_CHECKING, Any, Callable, Dict, Iterable, List, NamedTuple, Optional,
+                    Tuple, Type, Union, cast)
 
 from docutils import nodes
 from docutils.nodes import Element, Node, system_message
@@ -196,7 +196,7 @@ class Domain:
     #: data value for a fresh environment
     initial_data: Dict = {}
     #: data value
-    data: Dict = None
+    data: Dict
     #: data version, bump this when the format of `self.data` changes
     data_version = 0
 
@@ -251,7 +251,7 @@ class Domain:
         for role in objtype.roles:
             self._role2type.setdefault(role, []).append(name)
 
-    def role(self, name: str) -> RoleFunction:
+    def role(self, name: str) -> Optional[RoleFunction]:
         """Return a role adapter function that always gives the registered
         role its full name ('domain:name') as the first argument.
         """
@@ -269,7 +269,7 @@ class Domain:
         self._role_cache[name] = role_adapter
         return role_adapter
 
-    def directive(self, name: str) -> Callable:
+    def directive(self, name: str) -> Optional[Callable]:
         """Return a directive adapter class that always gives the registered
         directive its full name ('domain:name') as ``self.name``.
         """
@@ -318,7 +318,7 @@ class Domain:
 
     def resolve_xref(self, env: "BuildEnvironment", fromdocname: str, builder: "Builder",
                      typ: str, target: str, node: pending_xref, contnode: Element
-                     ) -> Element:
+                     ) -> Optional[Element]:
         """Resolve the pending_xref *node* with the given *typ* and *target*.
 
         This method should return a new node, to replace the xref node,
@@ -393,11 +393,11 @@ class Domain:
             return type.lname
         return _('%s %s') % (self.label, type.lname)
 
-    def get_enumerable_node_type(self, node: Node) -> str:
+    def get_enumerable_node_type(self, node: Node) -> Optional[str]:
         """Get type of enumerable nodes (experimental)."""
         enum_node_type, _ = self.enumerable_nodes.get(node.__class__, (None, None))
         return enum_node_type
 
-    def get_full_qualified_name(self, node: Element) -> str:
+    def get_full_qualified_name(self, node: Element) -> Optional[str]:
         """Return full qualified name for given node."""
         return None
diff --git a/sphinx/domains/c.py b/sphinx/domains/c.py
index b0711f68e..ed908c875 100644
--- a/sphinx/domains/c.py
+++ b/sphinx/domains/c.py
@@ -9,7 +9,8 @@
 """
 
 import re
-from typing import Any, Callable, Dict, Generator, Iterator, List, Tuple, TypeVar, Union, cast
+from typing import (Any, Callable, Dict, Generator, Iterator, List, Optional, Tuple, TypeVar,
+                    Union, cast)
 
 from docutils import nodes
 from docutils.nodes import Element, Node, TextElement, system_message
@@ -3807,7 +3808,7 @@ class CDomain(Domain):
 
     def _resolve_xref_inner(self, env: BuildEnvironment, fromdocname: str, builder: Builder,
                             typ: str, target: str, node: pending_xref,
-                            contnode: Element) -> Tuple[Element, str]:
+                            contnode: Element) -> Tuple[Optional[Element], Optional[str]]:
         parser = DefinitionParser(target, location=node, config=env.config)
         try:
             name = parser.parse_xref_object()
@@ -3844,7 +3845,7 @@ class CDomain(Domain):
 
     def resolve_xref(self, env: BuildEnvironment, fromdocname: str, builder: Builder,
                      typ: str, target: str, node: pending_xref,
-                     contnode: Element) -> Element:
+                     contnode: Element) -> Optional[Element]:
         return self._resolve_xref_inner(env, fromdocname, builder, typ,
                                         target, node, contnode)[0]
 
diff --git a/sphinx/domains/citation.py b/sphinx/domains/citation.py
index 772d486af..0e859acb4 100644
--- a/sphinx/domains/citation.py
+++ b/sphinx/domains/citation.py
@@ -8,7 +8,7 @@
     :license: BSD, see LICENSE for details.
 """
 
-from typing import TYPE_CHECKING, Any, Dict, List, Set, Tuple, cast
+from typing import TYPE_CHECKING, Any, Dict, List, Optional, Set, Tuple, cast
 
 from docutils import nodes
 from docutils.nodes import Element
@@ -88,7 +88,7 @@ class CitationDomain(Domain):
 
     def resolve_xref(self, env: "BuildEnvironment", fromdocname: str, builder: "Builder",
                      typ: str, target: str, node: pending_xref, contnode: Element
-                     ) -> Element:
+                     ) -> Optional[Element]:
         docname, labelid, lineno = self.citations.get(target, ('', '', 0))
         if not docname:
             return None
diff --git a/sphinx/domains/cpp.py b/sphinx/domains/cpp.py
index 7bb1e49aa..6c551b4a7 100644
--- a/sphinx/domains/cpp.py
+++ b/sphinx/domains/cpp.py
@@ -7594,7 +7594,7 @@ class CPPDomain(Domain):
 
     def _resolve_xref_inner(self, env: BuildEnvironment, fromdocname: str, builder: Builder,
                             typ: str, target: str, node: pending_xref,
-                            contnode: Element) -> Tuple[Element, str]:
+                            contnode: Element) -> Tuple[Optional[Element], Optional[str]]:
         # add parens again for those that could be functions
         if typ == 'any' or typ == 'func':
             target += '()'
@@ -7743,7 +7743,7 @@ class CPPDomain(Domain):
 
     def resolve_xref(self, env: BuildEnvironment, fromdocname: str, builder: Builder,
                      typ: str, target: str, node: pending_xref, contnode: Element
-                     ) -> Element:
+                     ) -> Optional[Element]:
         return self._resolve_xref_inner(env, fromdocname, builder, typ,
                                         target, node, contnode)[0]
 
diff --git a/sphinx/domains/javascript.py b/sphinx/domains/javascript.py
index 92d0e1d61..8511a1d6a 100644
--- a/sphinx/domains/javascript.py
+++ b/sphinx/domains/javascript.py
@@ -8,7 +8,7 @@
     :license: BSD, see LICENSE for details.
 """
 
-from typing import Any, Dict, Iterator, List, Tuple, cast
+from typing import Any, Dict, Iterator, List, Optional, Tuple, cast
 
 from docutils import nodes
 from docutils.nodes import Element, Node
@@ -413,7 +413,7 @@ class JavaScriptDomain(Domain):
 
     def resolve_xref(self, env: BuildEnvironment, fromdocname: str, builder: Builder,
                      typ: str, target: str, node: pending_xref, contnode: Element
-                     ) -> Element:
+                     ) -> Optional[Element]:
         mod_name = node.get('js:module')
         prefix = node.get('js:object')
         searchorder = 1 if node.hasattr('refspecific') else 0
diff --git a/sphinx/domains/math.py b/sphinx/domains/math.py
index 88db1ad0e..aa6f9422d 100644
--- a/sphinx/domains/math.py
+++ b/sphinx/domains/math.py
@@ -8,7 +8,7 @@
     :license: BSD, see LICENSE for details.
 """
 
-from typing import TYPE_CHECKING, Any, Dict, Iterable, List, Tuple
+from typing import TYPE_CHECKING, Any, Dict, Iterable, List, Optional, Tuple
 
 from docutils import nodes
 from docutils.nodes import Element, Node, make_id, system_message
@@ -97,7 +97,7 @@ class MathDomain(Domain):
 
     def resolve_xref(self, env: BuildEnvironment, fromdocname: str, builder: "Builder",
                      typ: str, target: str, node: pending_xref, contnode: Element
-                     ) -> Element:
+                     ) -> Optional[Element]:
         assert typ in ('eq', 'numref')
         docname, number = self.equations.get(target, (None, None))
         if docname:
diff --git a/sphinx/domains/python.py b/sphinx/domains/python.py
index 4464895ef..dbe2c87ca 100644
--- a/sphinx/domains/python.py
+++ b/sphinx/domains/python.py
@@ -15,7 +15,7 @@ import sys
 import typing
 import warnings
 from inspect import Parameter
-from typing import Any, Dict, Iterable, Iterator, List, NamedTuple, Tuple, Type, cast
+from typing import Any, Dict, Iterable, Iterator, List, NamedTuple, Optional, Tuple, Type, cast
 
 from docutils import nodes
 from docutils.nodes import Element, Node
@@ -1246,7 +1246,7 @@ class PythonDomain(Domain):
 
     def resolve_xref(self, env: BuildEnvironment, fromdocname: str, builder: Builder,
                      type: str, target: str, node: pending_xref, contnode: Element
-                     ) -> Element:
+                     ) -> Optional[Element]:
         modname = node.get('py:module')
         clsname = node.get('py:class')
         searchmode = 1 if node.hasattr('refspecific') else 0
@@ -1340,7 +1340,7 @@ class PythonDomain(Domain):
                 else:
                     yield (refname, refname, obj.objtype, obj.docname, obj.node_id, 1)
 
-    def get_full_qualified_name(self, node: Element) -> str:
+    def get_full_qualified_name(self, node: Element) -> Optional[str]:
         modname = node.get('py:module')
         clsname = node.get('py:class')
         target = node.get('reftarget')
diff --git a/sphinx/domains/rst.py b/sphinx/domains/rst.py
index d048c2dfb..539a610bb 100644
--- a/sphinx/domains/rst.py
+++ b/sphinx/domains/rst.py
@@ -9,7 +9,7 @@
 """
 
 import re
-from typing import Any, Dict, Iterator, List, Tuple, cast
+from typing import Any, Dict, Iterator, List, Optional, Tuple, cast
 
 from docutils.nodes import Element
 from docutils.parsers.rst import directives
@@ -247,7 +247,7 @@ class ReSTDomain(Domain):
 
     def resolve_xref(self, env: BuildEnvironment, fromdocname: str, builder: Builder,
                      typ: str, target: str, node: pending_xref, contnode: Element
-                     ) -> Element:
+                     ) -> Optional[Element]:
         objtypes = self.objtypes_for_role(typ)
         for objtype in objtypes:
             todocname, node_id = self.objects.get((objtype, target), (None, None))
diff --git a/sphinx/domains/std.py b/sphinx/domains/std.py
index 5e10646f0..7660f84c9 100644
--- a/sphinx/domains/std.py
+++ b/sphinx/domains/std.py
@@ -285,7 +285,7 @@ class OptionXRefRole(XRefRole):
 
 def split_term_classifiers(line: str) -> List[Optional[str]]:
     # split line into a term and classifiers. if no classifier, None is used..
-    parts = re.split(' +: +', line) + [None]
+    parts: List[Optional[str]] = re.split(' +: +', line) + [None]
     return parts
 
 
@@ -621,7 +621,7 @@ class StandardDomain(Domain):
     }
 
     # node_class -> (figtype, title_getter)
-    enumerable_nodes: Dict[Type[Node], Tuple[str, Callable]] = {
+    enumerable_nodes: Dict[Type[Node], Tuple[str, Optional[Callable]]] = {
         nodes.figure: ('figure', None),
         nodes.table: ('table', None),
         nodes.container: ('code-block', None),
@@ -812,7 +812,8 @@ class StandardDomain(Domain):
         return newnode
 
     def resolve_xref(self, env: "BuildEnvironment", fromdocname: str, builder: "Builder",
-                     typ: str, target: str, node: pending_xref, contnode: Element) -> Element:
+                     typ: str, target: str, node: pending_xref, contnode: Element
+                     ) -> Optional[Element]:
         if typ == 'ref':
             resolver = self._resolve_ref_xref
         elif typ == 'numref':
@@ -832,7 +833,7 @@ class StandardDomain(Domain):
 
     def _resolve_ref_xref(self, env: "BuildEnvironment", fromdocname: str,
                           builder: "Builder", typ: str, target: str, node: pending_xref,
-                          contnode: Element) -> Element:
+                          contnode: Element) -> Optional[Element]:
         if node['refexplicit']:
             # reference to anonymous label; the reference uses
             # the supplied link caption
@@ -850,7 +851,7 @@ class StandardDomain(Domain):
 
     def _resolve_numref_xref(self, env: "BuildEnvironment", fromdocname: str,
                              builder: "Builder", typ: str, target: str,
-                             node: pending_xref, contnode: Element) -> Element:
+                             node: pending_xref, contnode: Element) -> Optional[Element]:
         if target in self.labels:
             docname, labelid, figname = self.labels.get(target, ('', '', ''))
         else:
@@ -913,7 +914,7 @@ class StandardDomain(Domain):
 
     def _resolve_keyword_xref(self, env: "BuildEnvironment", fromdocname: str,
                               builder: "Builder", typ: str, target: str,
-                              node: pending_xref, contnode: Element) -> Element:
+                              node: pending_xref, contnode: Element) -> Optional[Element]:
         # keywords are oddballs: they are referenced by named labels
         docname, labelid, _ = self.labels.get(target, ('', '', ''))
         if not docname:
@@ -923,7 +924,7 @@ class StandardDomain(Domain):
 
     def _resolve_doc_xref(self, env: "BuildEnvironment", fromdocname: str,
                           builder: "Builder", typ: str, target: str,
-                          node: pending_xref, contnode: Element) -> Element:
+                          node: pending_xref, contnode: Element) -> Optional[Element]:
         # directly reference to document by source name; can be absolute or relative
         refdoc = node.get('refdoc', fromdocname)
         docname = docname_join(refdoc, node['reftarget'])
@@ -940,7 +941,7 @@ class StandardDomain(Domain):
 
     def _resolve_option_xref(self, env: "BuildEnvironment", fromdocname: str,
                              builder: "Builder", typ: str, target: str,
-                             node: pending_xref, contnode: Element) -> Element:
+                             node: pending_xref, contnode: Element) -> Optional[Element]:
         progname = node.get('std:program')
         target = target.strip()
         docname, labelid = self.progoptions.get((progname, target), ('', ''))
@@ -977,7 +978,7 @@ class StandardDomain(Domain):
 
     def _resolve_obj_xref(self, env: "BuildEnvironment", fromdocname: str,
                           builder: "Builder", typ: str, target: str,
-                          node: pending_xref, contnode: Element) -> Element:
+                          node: pending_xref, contnode: Element) -> Optional[Element]:
         objtypes = self.objtypes_for_role(typ) or []
         for objtype in objtypes:
             if (objtype, target) in self.objects:
@@ -1041,7 +1042,7 @@ class StandardDomain(Domain):
     def is_enumerable_node(self, node: Node) -> bool:
         return node.__class__ in self.enumerable_nodes
 
-    def get_numfig_title(self, node: Node) -> str:
+    def get_numfig_title(self, node: Node) -> Optional[str]:
         """Get the title of enumerable nodes to refer them using its title"""
         if self.is_enumerable_node(node):
             elem = cast(Element, node)
@@ -1055,7 +1056,7 @@ class StandardDomain(Domain):
 
         return None
 
-    def get_enumerable_node_type(self, node: Node) -> str:
+    def get_enumerable_node_type(self, node: Node) -> Optional[str]:
         """Get type of enumerable nodes."""
         def has_child(node: Element, cls: Type) -> bool:
             return any(isinstance(child, cls) for child in node)
@@ -1094,7 +1095,7 @@ class StandardDomain(Domain):
                 # Maybe it is defined in orphaned document.
                 raise ValueError from exc
 
-    def get_full_qualified_name(self, node: Element) -> str:
+    def get_full_qualified_name(self, node: Element) -> Optional[str]:
         if node.get('reftype') == 'option':
             progname = node.get('std:program')
             command = ws_re.split(node.get('reftarget'))
@@ -1109,7 +1110,8 @@ class StandardDomain(Domain):
             return None
 
 
-def warn_missing_reference(app: "Sphinx", domain: Domain, node: pending_xref) -> bool:
+def warn_missing_reference(app: "Sphinx", domain: Domain, node: pending_xref
+                           ) -> Optional[bool]:
     if (domain and domain.name != 'std') or node['reftype'] != 'ref':
         return None
     else:
diff --git a/sphinx/environment/__init__.py b/sphinx/environment/__init__.py
index 0483dcdf9..2914a78af 100644
--- a/sphinx/environment/__init__.py
+++ b/sphinx/environment/__init__.py
@@ -14,8 +14,8 @@ from collections import defaultdict
 from copy import copy
 from datetime import datetime
 from os import path
-from typing import (TYPE_CHECKING, Any, Callable, Dict, Generator, Iterator, List, Set, Tuple,
-                    Union)
+from typing import (TYPE_CHECKING, Any, Callable, Dict, Generator, Iterator, List, Optional,
+                    Set, Tuple, Union)
 
 from docutils import nodes
 from docutils.nodes import Node
@@ -87,7 +87,7 @@ class BuildEnvironment:
     transformations to resolve links to them.
     """
 
-    domains: Dict[str, Domain] = None
+    domains: Dict[str, Domain]
 
     # --------- ENVIRONMENT INITIALIZATION -------------------------------------
 
@@ -266,7 +266,7 @@ class BuildEnvironment:
         raise an exception if the user tries to use an environment with an
         incompatible versioning method.
         """
-        condition: Union[bool, Callable] = None
+        condition: Union[bool, Callable]
         if callable(method):
             condition = method
         else:
@@ -309,7 +309,7 @@ class BuildEnvironment:
             domain.merge_domaindata(docnames, other.domaindata[domainname])
         self.events.emit('env-merge-info', self, docnames, other)
 
-    def path2doc(self, filename: str) -> str:
+    def path2doc(self, filename: str) -> Optional[str]:
         """Return the docname for the filename if the file is document.
 
         *filename* should be absolute or relative to the source directory.
@@ -577,7 +577,7 @@ class BuildEnvironment:
         # allow custom references to be resolved
         self.events.emit('doctree-resolved', doctree, docname)
 
-    def collect_relations(self) -> Dict[str, List[str]]:
+    def collect_relations(self) -> Dict[str, List[Optional[str]]]:
         traversed = set()
 
         def traverse_toctree(parent: str, docname: str) -> Iterator[Tuple[str, str]]:
diff --git a/sphinx/environment/adapters/toctree.py b/sphinx/environment/adapters/toctree.py
index 6822c42c9..a62e951d7 100644
--- a/sphinx/environment/adapters/toctree.py
+++ b/sphinx/environment/adapters/toctree.py
@@ -313,7 +313,7 @@ class TocTree:
         return toc
 
     def get_toctree_for(self, docname: str, builder: "Builder", collapse: bool,
-                        **kwargs: Any) -> Element:
+                        **kwargs: Any) -> Optional[Element]:
         """Return the global TOC nodetree."""
         doctree = self.env.get_doctree(self.env.config.root_doc)
         toctrees: List[Element] = []
diff --git a/sphinx/environment/collectors/__init__.py b/sphinx/environment/collectors/__init__.py
index e27091018..f4020431f 100644
--- a/sphinx/environment/collectors/__init__.py
+++ b/sphinx/environment/collectors/__init__.py
@@ -8,7 +8,7 @@
     :license: BSD, see LICENSE for details.
 """
 
-from typing import TYPE_CHECKING, Dict, List, Set
+from typing import TYPE_CHECKING, Dict, List, Optional, Set
 
 from docutils import nodes
 
@@ -27,7 +27,7 @@ class EnvironmentCollector:
     entries and toctrees, etc.
     """
 
-    listener_ids: Dict[str, int] = None
+    listener_ids: Optional[Dict[str, int]] = None
 
     def enable(self, app: "Sphinx") -> None:
         assert self.listener_ids is None
diff --git a/sphinx/pycode/__init__.py b/sphinx/pycode/__init__.py
index c55a4fe4a..8e79385e2 100644
--- a/sphinx/pycode/__init__.py
+++ b/sphinx/pycode/__init__.py
@@ -25,6 +25,13 @@ from sphinx.pycode.parser import Parser
 
 
 class ModuleAnalyzer:
+    annotations: Dict[Tuple[str, str], str]
+    attr_docs: Dict[Tuple[str, str], List[str]]
+    finals: List[str]
+    overloads: Dict[str, List[Signature]]
+    tagorder: Dict[str, int]
+    tags: Dict[str, Tuple[str, int, int]]
+
     # cache for analyzer objects -- caches both by module and file name
     cache: Dict[Tuple[str, str], Any] = {}
 
@@ -134,13 +141,6 @@ class ModuleAnalyzer:
         # cache the source code as well
         self.code = source.read()
 
-        # will be filled by analyze()
-        self.annotations: Dict[Tuple[str, str], str] = None
-        self.attr_docs: Dict[Tuple[str, str], List[str]] = None
-        self.finals: List[str] = None
-        self.overloads: Dict[str, List[Signature]] = None
-        self.tagorder: Dict[str, int] = None
-        self.tags: Dict[str, Tuple[str, int, int]] = None
         self._analyzed = False
 
     def parse(self) -> None:
diff --git a/sphinx/pycode/parser.py b/sphinx/pycode/parser.py
index fa249d8c5..a00b481ce 100644
--- a/sphinx/pycode/parser.py
+++ b/sphinx/pycode/parser.py
@@ -129,8 +129,8 @@ class TokenProcessor:
         lines = iter(buffers)
         self.buffers = buffers
         self.tokens = tokenize.generate_tokens(lambda: next(lines))
-        self.current: Token = None
-        self.previous: Token = None
+        self.current: Optional[Token] = None
+        self.previous: Optional[Token] = None
 
     def get_line(self, lineno: int) -> str:
         """Returns specified line."""
@@ -178,7 +178,7 @@ class AfterCommentParser(TokenProcessor):
 
     def __init__(self, lines: List[str]) -> None:
         super().__init__(lines)
-        self.comment: str = None
+        self.comment: Optional[str] = None
 
     def fetch_rvalue(self) -> List[Token]:
         """Fetch right-hand value of assignment."""
@@ -223,16 +223,16 @@ class VariableCommentPicker(ast.NodeVisitor):
         self.encoding = encoding
         self.context: List[str] = []
         self.current_classes: List[str] = []
-        self.current_function: ast.FunctionDef = None
+        self.current_function: Optional[ast.FunctionDef] = None
         self.comments: Dict[Tuple[str, str], str] = OrderedDict()
         self.annotations: Dict[Tuple[str, str], str] = {}
-        self.previous: ast.AST = None
+        self.previous: Optional[ast.AST] = None
         self.deforders: Dict[str, int] = {}
         self.finals: List[str] = []
         self.overloads: Dict[str, List[Signature]] = {}
-        self.typing: str = None
-        self.typing_final: str = None
-        self.typing_overload: str = None
+        self.typing: Optional[str] = None
+        self.typing_final: Optional[str] = None
+        self.typing_overload: Optional[str] = None
         super().__init__()
 
     def get_qualname_for(self, name: str) -> Optional[List[str]]:
@@ -308,7 +308,7 @@ class VariableCommentPicker(ast.NodeVisitor):
 
         return False
 
-    def get_self(self) -> ast.arg:
+    def get_self(self) -> Optional[ast.arg]:
         """Returns the name of first argument if in function."""
         if self.current_function and self.current_function.args.args:
             return self.current_function.args.args[0]
@@ -466,7 +466,7 @@ class DefinitionFinder(TokenProcessor):
 
     def __init__(self, lines: List[str]) -> None:
         super().__init__(lines)
-        self.decorator: Token = None
+        self.decorator: Optional[Token] = None
         self.context: List[str] = []
         self.indents: List = []
         self.definitions: Dict[str, Tuple[str, int, int]] = {}
diff --git a/sphinx/search/__init__.py b/sphinx/search/__init__.py
index 2a3420244..4b0567969 100644
--- a/sphinx/search/__init__.py
+++ b/sphinx/search/__init__.py
@@ -12,7 +12,7 @@ import pickle
 import re
 from importlib import import_module
 from os import path
-from typing import IO, Any, Dict, Iterable, List, Set, Tuple, Type
+from typing import IO, Any, Dict, Iterable, List, Optional, Set, Tuple, Type
 
 from docutils import nodes
 from docutils.nodes import Node
@@ -440,7 +440,7 @@ class IndexBuilder:
         else:
             return []
 
-    def get_js_stemmer_rawcode(self) -> str:
+    def get_js_stemmer_rawcode(self) -> Optional[str]:
         return None
 
     def get_js_stemmer_code(self) -> str:
diff --git a/sphinx/transforms/i18n.py b/sphinx/transforms/i18n.py
index 8f6d37d8d..2a5d6f121 100644
--- a/sphinx/transforms/i18n.py
+++ b/sphinx/transforms/i18n.py
@@ -10,7 +10,7 @@
 
 from os import path
 from textwrap import indent
-from typing import TYPE_CHECKING, Any, Dict, List, Tuple, Type, TypeVar
+from typing import TYPE_CHECKING, Any, Dict, List, Optional, Tuple, Type, TypeVar
 
 from docutils import nodes
 from docutils.io import StringInput
@@ -416,7 +416,7 @@ class Locale(SphinxTransform):
                                .format(old_xref_rawsources, new_xref_rawsources),
                                location=node)
 
-            def get_ref_key(node: addnodes.pending_xref) -> Tuple[str, str, str]:
+            def get_ref_key(node: addnodes.pending_xref) -> Optional[Tuple[str, str, str]]:
                 case = node["refdomain"], node["reftype"]
                 if case == ('std', 'term'):
                     return None
diff --git a/sphinx/util/__init__.py b/sphinx/util/__init__.py
index d420f4f77..f1a6f1af6 100644
--- a/sphinx/util/__init__.py
+++ b/sphinx/util/__init__.py
@@ -22,8 +22,8 @@ from datetime import datetime
 from importlib import import_module
 from os import path
 from time import mktime, strptime
-from typing import (IO, TYPE_CHECKING, Any, Callable, Dict, Iterable, Iterator, List, Pattern,
-                    Set, Tuple, Type)
+from typing import (IO, TYPE_CHECKING, Any, Callable, Dict, Iterable, Iterator, List, Optional,
+                    Pattern, Set, Tuple, Type)
 from urllib.parse import parse_qsl, quote_plus, urlencode, urlsplit, urlunsplit
 
 from sphinx.deprecation import RemovedInSphinx50Warning
@@ -408,7 +408,7 @@ def import_object(objname: str, source: str = None) -> Any:
             raise ExtensionError('Could not import %s' % objname, exc) from exc
 
 
-def split_full_qualified_name(name: str) -> Tuple[str, str]:
+def split_full_qualified_name(name: str) -> Tuple[Optional[str], str]:
     """Split full qualified name to a pair of modname and qualname.
 
     A qualname is an abbreviation for "Qualified name" introduced at PEP-3155