diff --git a/sphinx/environment/__init__.py b/sphinx/environment/__init__.py
index 2ee34cc90..8e2db2b4e 100644
--- a/sphinx/environment/__init__.py
+++ b/sphinx/environment/__init__.py
@@ -14,12 +14,20 @@ import warnings
 from collections import defaultdict
 from copy import copy
 from os import path
+from typing import Any, Callable, Dict, Generator, Iterator, List, Set, Tuple, Union
+
+from docutils import nodes
+from docutils.nodes import Node
 
 from sphinx import addnodes
+from sphinx.config import Config
 from sphinx.deprecation import RemovedInSphinx40Warning
+from sphinx.domains import Domain
 from sphinx.environment.adapters.toctree import TocTree
 from sphinx.errors import SphinxError, BuildEnvironmentError, DocumentError, ExtensionError
+from sphinx.events import EventManager
 from sphinx.locale import __
+from sphinx.project import Project
 from sphinx.transforms import SphinxTransformer
 from sphinx.util import DownloadFiles, FilenameUniqDict
 from sphinx.util import logging
@@ -29,14 +37,9 @@ from sphinx.util.nodes import is_translatable
 
 if False:
     # For type annotation
-    from typing import Any, Callable, Dict, IO, Iterator, List, Optional, Set, Tuple, Union  # NOQA
-    from docutils import nodes  # NOQA
-    from sphinx.application import Sphinx  # NOQA
-    from sphinx.builders import Builder  # NOQA
-    from sphinx.config import Config  # NOQA
-    from sphinx.event import EventManager  # NOQA
-    from sphinx.domains import Domain  # NOQA
-    from sphinx.project import Project  # NOQA
+    from sphinx.application import Sphinx
+    from sphinx.builders import Builder
+
 
 logger = logging.getLogger(__name__)
 
@@ -89,8 +92,7 @@ class BuildEnvironment:
 
     # --------- ENVIRONMENT INITIALIZATION -------------------------------------
 
-    def __init__(self, app=None):
-        # type: (Sphinx) -> None
+    def __init__(self, app: "Sphinx" = None):
         self.app = None             # type: Sphinx
         self.doctreedir = None      # type: str
         self.srcdir = None          # type: str
@@ -188,19 +190,16 @@ class BuildEnvironment:
         if app:
             self.setup(app)
 
-    def __getstate__(self):
-        # type: () -> Dict
+    def __getstate__(self) -> Dict:
         """Obtains serializable data for pickling."""
         __dict__ = self.__dict__.copy()
         __dict__.update(app=None, domains={}, events=None)  # clear unpickable attributes
         return __dict__
 
-    def __setstate__(self, state):
-        # type: (Dict) -> None
+    def __setstate__(self, state: Dict) -> None:
         self.__dict__.update(state)
 
-    def setup(self, app):
-        # type: (Sphinx) -> None
+    def setup(self, app: "Sphinx") -> None:
         """Set up BuildEnvironment object."""
         if self.version and self.version != app.registry.get_envversion(app):
             raise BuildEnvironmentError(__('build environment version not current'))
@@ -228,8 +227,7 @@ class BuildEnvironment:
         # initialie settings
         self._update_settings(app.config)
 
-    def _update_config(self, config):
-        # type: (Config) -> None
+    def _update_config(self, config: Config) -> None:
         """Update configurations by new one."""
         self.config_status = CONFIG_OK
         if self.config is None:
@@ -246,8 +244,7 @@ class BuildEnvironment:
 
         self.config = config
 
-    def _update_settings(self, config):
-        # type: (Config) -> None
+    def _update_settings(self, config: Config) -> None:
         """Update settings by new config."""
         self.settings['input_encoding'] = config.source_encoding
         self.settings['trim_footnote_reference_space'] = config.trim_footnote_reference_space
@@ -256,8 +253,7 @@ class BuildEnvironment:
         # Allow to disable by 3rd party extension (workaround)
         self.settings.setdefault('smart_quotes', True)
 
-    def set_versioning_method(self, method, compare):
-        # type: (Union[str, Callable], bool) -> None
+    def set_versioning_method(self, method: Union[str, Callable], compare: bool) -> None:
         """This sets the doctree versioning method for this environment.
 
         Versioning methods are a builder property; only builders with the same
@@ -280,8 +276,7 @@ class BuildEnvironment:
         self.versioning_condition = condition
         self.versioning_compare = compare
 
-    def clear_doc(self, docname):
-        # type: (str) -> None
+    def clear_doc(self, docname: str) -> None:
         """Remove all traces of a source file in the inventory."""
         if docname in self.all_docs:
             self.all_docs.pop(docname, None)
@@ -291,8 +286,8 @@ class BuildEnvironment:
         for domain in self.domains.values():
             domain.clear_doc(docname)
 
-    def merge_info_from(self, docnames, other, app):
-        # type: (List[str], BuildEnvironment, Sphinx) -> None
+    def merge_info_from(self, docnames: List[str], other: "BuildEnvironment",
+                        app: "Sphinx") -> None:
         """Merge global information gathered about *docnames* while reading them
         from the *other* environment.
 
@@ -309,16 +304,14 @@ class BuildEnvironment:
             domain.merge_domaindata(docnames, other.domaindata[domainname])
         self.events.emit('env-merge-info', self, docnames, other)
 
-    def path2doc(self, filename):
-        # type: (str) -> Optional[str]
+    def path2doc(self, filename: str) -> str:
         """Return the docname for the filename if the file is document.
 
         *filename* should be absolute or relative to the source directory.
         """
         return self.project.path2doc(filename)
 
-    def doc2path(self, docname, base=True, suffix=None):
-        # type: (str, Union[bool, str], str) -> str
+    def doc2path(self, docname: str, base: Union[bool, str] = True, suffix: str = None) -> str:
         """Return the filename for the document name.
 
         If *base* is True, return absolute path under self.srcdir.
@@ -341,8 +334,7 @@ class BuildEnvironment:
             pathname = path.join(base, pathname)  # type: ignore
         return pathname
 
-    def relfn2path(self, filename, docname=None):
-        # type: (str, str) -> Tuple[str, str]
+    def relfn2path(self, filename: str, docname: str = None) -> Tuple[str, str]:
         """Return paths to a file referenced from a document, relative to
         documentation root and absolute.
 
@@ -361,13 +353,11 @@ class BuildEnvironment:
         return rel_fn, path.abspath(path.join(self.srcdir, rel_fn))
 
     @property
-    def found_docs(self):
-        # type: () -> Set[str]
+    def found_docs(self) -> Set[str]:
         """contains all existing docnames."""
         return self.project.docnames
 
-    def find_files(self, config, builder):
-        # type: (Config, Builder) -> None
+    def find_files(self, config: Config, builder: "Builder") -> None:
         """Find all source files in the source dir and put them in
         self.found_docs.
         """
@@ -395,8 +385,7 @@ class BuildEnvironment:
         except OSError as exc:
             raise DocumentError(__('Failed to scan documents in %s: %r') % (self.srcdir, exc))
 
-    def get_outdated_files(self, config_changed):
-        # type: (bool) -> Tuple[Set[str], Set[str], Set[str]]
+    def get_outdated_files(self, config_changed: bool) -> Tuple[Set[str], Set[str], Set[str]]:
         """Return (added, changed, removed) sets."""
         # clear all files no longer present
         removed = set(self.all_docs) - self.found_docs
@@ -446,8 +435,7 @@ class BuildEnvironment:
 
         return added, changed, removed
 
-    def check_dependents(self, app, already):
-        # type: (Sphinx, Set[str]) -> Iterator[str]
+    def check_dependents(self, app: "Sphinx", already: Set[str]) -> Generator[str, None, None]:
         to_rewrite = []  # type: List[str]
         for docnames in self.events.emit('env-get-updated', self):
             to_rewrite.extend(docnames)
@@ -457,8 +445,7 @@ class BuildEnvironment:
 
     # --------- SINGLE FILE READING --------------------------------------------
 
-    def prepare_settings(self, docname):
-        # type: (str) -> None
+    def prepare_settings(self, docname: str) -> None:
         """Prepare to set up environment for reading."""
         self.temp_data['docname'] = docname
         # defaults to the global default, but can be re-set in a document
@@ -469,13 +456,11 @@ class BuildEnvironment:
     # utilities to use while reading a document
 
     @property
-    def docname(self):
-        # type: () -> str
+    def docname(self) -> str:
         """Returns the docname of the document currently being parsed."""
         return self.temp_data['docname']
 
-    def new_serialno(self, category=''):
-        # type: (str) -> int
+    def new_serialno(self, category: str = '') -> int:
         """Return a serial number, e.g. for index entry targets.
 
         The number is guaranteed to be unique in the current document.
@@ -485,8 +470,7 @@ class BuildEnvironment:
         self.temp_data[key] = cur + 1
         return cur
 
-    def note_dependency(self, filename):
-        # type: (str) -> None
+    def note_dependency(self, filename: str) -> None:
         """Add *filename* as a dependency of the current document.
 
         This means that the document will be rebuilt if this file changes.
@@ -495,8 +479,7 @@ class BuildEnvironment:
         """
         self.dependencies[self.docname].add(filename)
 
-    def note_included(self, filename):
-        # type: (str) -> None
+    def note_included(self, filename: str) -> None:
         """Add *filename* as a included from other document.
 
         This means the document is not orphaned.
@@ -505,15 +488,13 @@ class BuildEnvironment:
         """
         self.included[self.docname].add(self.path2doc(filename))
 
-    def note_reread(self):
-        # type: () -> None
+    def note_reread(self) -> None:
         """Add the current document to the list of documents that will
         automatically be re-read at the next build.
         """
         self.reread_always.add(self.docname)
 
-    def get_domain(self, domainname):
-        # type: (str) -> Domain
+    def get_domain(self, domainname: str) -> Domain:
         """Return the domain instance with the specified name.
 
         Raises an ExtensionError if the domain is not registered.
@@ -525,8 +506,7 @@ class BuildEnvironment:
 
     # --------- RESOLVING REFERENCES AND TOCTREES ------------------------------
 
-    def get_doctree(self, docname):
-        # type: (str) -> nodes.document
+    def get_doctree(self, docname: str) -> nodes.document:
         """Read the doctree for a file from the pickle and return it."""
         filename = path.join(self.doctreedir, docname + '.doctree')
         with open(filename, 'rb') as f:
@@ -535,9 +515,9 @@ class BuildEnvironment:
         doctree.reporter = LoggingReporter(self.doc2path(docname))
         return doctree
 
-    def get_and_resolve_doctree(self, docname, builder, doctree=None,
-                                prune_toctrees=True, includehidden=False):
-        # type: (str, Builder, nodes.document, bool, bool) -> nodes.document
+    def get_and_resolve_doctree(self, docname: str, builder: "Builder",
+                                doctree: nodes.document = None, prune_toctrees: bool = True,
+                                includehidden: bool = False) -> nodes.document:
         """Read the doctree from the pickle, resolve cross-references and
         toctrees and return it.
         """
@@ -559,9 +539,9 @@ class BuildEnvironment:
 
         return doctree
 
-    def resolve_toctree(self, docname, builder, toctree, prune=True, maxdepth=0,
-                        titles_only=False, collapse=False, includehidden=False):
-        # type: (str, Builder, addnodes.toctree, bool, int, bool, bool, bool) -> nodes.Node
+    def resolve_toctree(self, docname: str, builder: "Builder", toctree: addnodes.toctree,
+                        prune: bool = True, maxdepth: int = 0, titles_only: bool = False,
+                        collapse: bool = False, includehidden: bool = False) -> Node:
         """Resolve a *toctree* node into individual bullet lists with titles
         as items, returning None (if no containing titles are found) or
         a new node.
@@ -577,12 +557,11 @@ class BuildEnvironment:
                                      maxdepth, titles_only, collapse,
                                      includehidden)
 
-    def resolve_references(self, doctree, fromdocname, builder):
-        # type: (nodes.document, str, Builder) -> None
+    def resolve_references(self, doctree: nodes.document, fromdocname: str,
+                           builder: "Builder") -> None:
         self.apply_post_transforms(doctree, fromdocname)
 
-    def apply_post_transforms(self, doctree, docname):
-        # type: (nodes.document, str) -> None
+    def apply_post_transforms(self, doctree: nodes.document, docname: str) -> None:
         """Apply all post-transforms."""
         try:
             # set env.docname during applying post-transforms
@@ -599,12 +578,10 @@ class BuildEnvironment:
         # allow custom references to be resolved
         self.events.emit('doctree-resolved', doctree, docname)
 
-    def collect_relations(self):
-        # type: () -> Dict[str, List[str]]
+    def collect_relations(self) -> Dict[str, List[str]]:
         traversed = set()
 
-        def traverse_toctree(parent, docname):
-            # type: (str, str) -> Iterator[Tuple[str, str]]
+        def traverse_toctree(parent: str, docname: str) -> Iterator[Tuple[str, str]]:
             if parent == docname:
                 logger.warning(__('self referenced toctree found. Ignored.'), location=docname)
                 return
@@ -633,8 +610,7 @@ class BuildEnvironment:
 
         return relations
 
-    def check_consistency(self):
-        # type: () -> None
+    def check_consistency(self) -> None:
         """Do consistency checks."""
         included = set().union(*self.included.values())  # type: ignore
         for docname in sorted(self.all_docs):
diff --git a/sphinx/environment/adapters/asset.py b/sphinx/environment/adapters/asset.py
index b57943967..bc282de0c 100644
--- a/sphinx/environment/adapters/asset.py
+++ b/sphinx/environment/adapters/asset.py
@@ -8,18 +8,14 @@
     :license: BSD, see LICENSE for details.
 """
 
-if False:
-    # For type annotation
-    from sphinx.environment import BuildEnvironment  # NOQA
+from sphinx.environment import BuildEnvironment
 
 
 class ImageAdapter:
-    def __init__(self, env):
-        # type: (BuildEnvironment) -> None
+    def __init__(self, env: BuildEnvironment) -> None:
         self.env = env
 
-    def get_original_image_uri(self, name):
-        # type: (str) -> str
+    def get_original_image_uri(self, name: str) -> str:
         """Get the original image URI."""
         while name in self.env.original_image_uri:
             name = self.env.original_image_uri[name]
diff --git a/sphinx/environment/adapters/indexentries.py b/sphinx/environment/adapters/indexentries.py
index 38d28f0b0..430c3dce2 100644
--- a/sphinx/environment/adapters/indexentries.py
+++ b/sphinx/environment/adapters/indexentries.py
@@ -11,33 +11,30 @@ import bisect
 import re
 import unicodedata
 from itertools import groupby
+from typing import Any, Dict, Pattern, List, Tuple
 
+from sphinx.builders import Builder
+from sphinx.environment import BuildEnvironment
 from sphinx.errors import NoUri
 from sphinx.locale import _, __
 from sphinx.util import split_into, logging
 
-if False:
-    # For type annotation
-    from typing import Any, Dict, Pattern, List, Tuple  # NOQA
-    from sphinx.builders import Builder  # NOQA
-    from sphinx.environment import BuildEnvironment  # NOQA
 
 logger = logging.getLogger(__name__)
 
 
 class IndexEntries:
-    def __init__(self, env):
-        # type: (BuildEnvironment) -> None
+    def __init__(self, env: BuildEnvironment) -> None:
         self.env = env
 
-    def create_index(self, builder, group_entries=True,
-                     _fixre=re.compile(r'(.*) ([(][^()]*[)])')):
-        # type: (Builder, bool, Pattern) -> List[Tuple[str, List[Tuple[str, Any]]]]
+    def create_index(self, builder: Builder, group_entries: bool = True,
+                     _fixre: Pattern = re.compile(r'(.*) ([(][^()]*[)])')
+                     ) -> List[Tuple[str, List[Tuple[str, Any]]]]:
         """Create the real index from the collected index entries."""
         new = {}  # type: Dict[str, List]
 
-        def add_entry(word, subword, main, link=True, dic=new, key=None):
-            # type: (str, str, str, bool, Dict, str) -> None
+        def add_entry(word: str, subword: str, main: str, link: bool = True,
+                      dic: Dict = new, key: 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
@@ -91,8 +88,7 @@ class IndexEntries:
 
         # sort the index entries; put all symbols at the front, even those
         # following the letters in ASCII, this is where the chr(127) comes from
-        def keyfunc(entry):
-            # type: (Tuple[str, List]) -> Tuple[str, str]
+        def keyfunc(entry: Tuple[str, List]) -> Tuple[str, str]:
             key, (void, void, category_key) = entry
             if category_key:
                 # using specified category key to sort
@@ -138,8 +134,7 @@ class IndexEntries:
                 i += 1
 
         # group the entries by letter
-        def keyfunc2(item):
-            # type: (Tuple[str, List]) -> str
+        def keyfunc2(item: Tuple[str, List]) -> str:
             # hack: mutating the subitems dicts to a list in the keyfunc
             k, v = item
             v[1] = sorted((si, se) for (si, (se, void, void)) in v[1].items())
diff --git a/sphinx/environment/adapters/toctree.py b/sphinx/environment/adapters/toctree.py
index fe7bd3d0d..d5f827dde 100644
--- a/sphinx/environment/adapters/toctree.py
+++ b/sphinx/environment/adapters/toctree.py
@@ -8,9 +8,11 @@
     :license: BSD, see LICENSE for details.
 """
 
-from typing import Iterable, cast
+from typing import cast
+from typing import Iterable, List
 
 from docutils import nodes
+from docutils.nodes import Element, Node
 
 from sphinx import addnodes
 from sphinx.locale import __
@@ -20,20 +22,18 @@ from sphinx.util.nodes import clean_astext, process_only_nodes
 
 if False:
     # For type annotation
-    from typing import Any, Dict, List  # NOQA
-    from sphinx.builders import Builder  # NOQA
-    from sphinx.environment import BuildEnvironment  # NOQA
+    from sphinx.builders import Builder
+    from sphinx.environment import BuildEnvironment
+
 
 logger = logging.getLogger(__name__)
 
 
 class TocTree:
-    def __init__(self, env):
-        # type: (BuildEnvironment) -> None
+    def __init__(self, env: "BuildEnvironment") -> None:
         self.env = env
 
-    def note(self, docname, toctreenode):
-        # type: (str, addnodes.toctree) -> None
+    def note(self, docname: str, toctreenode: addnodes.toctree) -> None:
         """Note a TOC tree directive in a document and gather information about
         file relations from it.
         """
@@ -48,9 +48,9 @@ class TocTree:
             self.env.files_to_rebuild.setdefault(includefile, set()).add(docname)
         self.env.toctree_includes.setdefault(docname, []).extend(includefiles)
 
-    def resolve(self, docname, builder, toctree, prune=True, maxdepth=0,
-                titles_only=False, collapse=False, includehidden=False):
-        # type: (str, Builder, addnodes.toctree, bool, int, bool, bool, bool) -> nodes.Element
+    def resolve(self, docname: str, builder: "Builder", toctree: addnodes.toctree,
+                prune: bool = True, maxdepth: int = 0, titles_only: bool = False,
+                collapse: bool = False, includehidden: bool = False) -> Element:
         """Resolve a *toctree* node into individual bullet lists with titles
         as items, returning None (if no containing titles are found) or
         a new node.
@@ -86,8 +86,7 @@ class TocTree:
         toctree_ancestors = self.get_toctree_ancestors(docname)
         excluded = Matcher(self.env.config.exclude_patterns)
 
-        def _toctree_add_classes(node, depth):
-            # type: (nodes.Element, int) -> None
+        def _toctree_add_classes(node: Element, depth: int) -> None:
             """Add 'toctree-l%d' and 'current' classes to the toctree."""
             for subnode in node.children:
                 if isinstance(subnode, (addnodes.compact_paragraph,
@@ -105,7 +104,7 @@ class TocTree:
                         if not subnode['anchorname']:
                             # give the whole branch a 'current' class
                             # (useful for styling it differently)
-                            branchnode = subnode  # type: nodes.Element
+                            branchnode = subnode  # type: Element
                             while branchnode:
                                 branchnode['classes'].append('current')
                                 branchnode = branchnode.parent
@@ -117,11 +116,12 @@ class TocTree:
                             subnode['iscurrent'] = True
                             subnode = subnode.parent
 
-        def _entries_from_toctree(toctreenode, parents, separate=False, subtree=False):
-            # type: (addnodes.toctree, List[str], bool, bool) -> List[nodes.Element]
+        def _entries_from_toctree(toctreenode: addnodes.toctree, parents: List[str],
+                                  separate: bool = False, subtree: bool = False
+                                  ) -> List[Element]:
             """Return TOC entries for a toctree node."""
             refs = [(e[0], e[1]) for e in toctreenode['entries']]
-            entries = []  # type: List[nodes.Element]
+            entries = []  # type: List[Element]
             for (title, ref) in refs:
                 try:
                     refdoc = None
@@ -265,8 +265,7 @@ class TocTree:
                     docname, refnode['refuri']) + refnode['anchorname']
         return newnode
 
-    def get_toctree_ancestors(self, docname):
-        # type: (str) -> List[str]
+    def get_toctree_ancestors(self, docname: str) -> List[str]:
         parent = {}
         for p, children in self.env.toctree_includes.items():
             for child in children:
@@ -278,8 +277,8 @@ class TocTree:
             d = parent[d]
         return ancestors
 
-    def _toctree_prune(self, node, depth, maxdepth, collapse=False):
-        # type: (nodes.Element, int, int, bool) -> None
+    def _toctree_prune(self, node: Element, depth: int, maxdepth: int, collapse: bool = False
+                       ) -> None:
         """Utility: Cut a TOC at a specified depth."""
         for subnode in node.children[:]:
             if isinstance(subnode, (addnodes.compact_paragraph,
@@ -300,8 +299,7 @@ class TocTree:
                         # recurse on visible children
                         self._toctree_prune(subnode, depth + 1, maxdepth,  collapse)
 
-    def get_toc_for(self, docname, builder):
-        # type: (str, Builder) -> nodes.Node
+    def get_toc_for(self, docname: str, builder: "Builder") -> Node:
         """Return a TOC nodetree -- for use on the same page only!"""
         tocdepth = self.env.metadata[docname].get('tocdepth', 0)
         try:
@@ -316,11 +314,11 @@ class TocTree:
             node['refuri'] = node['anchorname'] or '#'
         return toc
 
-    def get_toctree_for(self, docname, builder, collapse, **kwds):
-        # type: (str, Builder, bool, Any) -> nodes.Element
+    def get_toctree_for(self, docname: str, builder: "Builder", collapse: bool, **kwds
+                        ) -> Element:
         """Return the global TOC nodetree."""
         doctree = self.env.get_doctree(self.env.config.master_doc)
-        toctrees = []  # type: List[nodes.Element]
+        toctrees = []  # type: List[Element]
         if 'includehidden' not in kwds:
             kwds['includehidden'] = True
         if 'maxdepth' not in kwds:
diff --git a/sphinx/environment/collectors/__init__.py b/sphinx/environment/collectors/__init__.py
index 3f7b9344b..eb16a9f25 100644
--- a/sphinx/environment/collectors/__init__.py
+++ b/sphinx/environment/collectors/__init__.py
@@ -8,12 +8,12 @@
     :license: BSD, see LICENSE for details.
 """
 
-if False:
-    # For type annotation
-    from typing import Dict, List, Set  # NOQA
-    from docutils import nodes  # NOQA
-    from sphinx.sphinx import Sphinx  # NOQA
-    from sphinx.environment import BuildEnvironment  # NOQA
+from typing import Dict, List, Set
+
+from docutils import nodes
+
+from sphinx.application import Sphinx
+from sphinx.environment import BuildEnvironment
 
 
 class EnvironmentCollector:
@@ -27,8 +27,7 @@ class EnvironmentCollector:
 
     listener_ids = None  # type: Dict[str, int]
 
-    def enable(self, app):
-        # type: (Sphinx) -> None
+    def enable(self, app: Sphinx) -> None:
         assert self.listener_ids is None
         self.listener_ids = {
             'doctree-read':     app.connect('doctree-read', self.process_doc),
@@ -38,43 +37,39 @@ class EnvironmentCollector:
             'env-get-outdated': app.connect('env-get-outdated', self.get_outdated_docs),
         }
 
-    def disable(self, app):
-        # type: (Sphinx) -> None
+    def disable(self, app: Sphinx) -> None:
         assert self.listener_ids is not None
         for listener_id in self.listener_ids.values():
             app.disconnect(listener_id)
         self.listener_ids = None
 
-    def clear_doc(self, app, env, docname):
-        # type: (Sphinx, BuildEnvironment, str) -> None
+    def clear_doc(self, app: Sphinx, env: BuildEnvironment, docname: str) -> None:
         """Remove specified data of a document.
 
         This method is called on the removal of the document."""
         raise NotImplementedError
 
-    def merge_other(self, app, env, docnames, other):
-        # type: (Sphinx, BuildEnvironment, Set[str], BuildEnvironment) -> None
+    def merge_other(self, app: Sphinx, env: BuildEnvironment,
+                    docnames: Set[str], other: BuildEnvironment) -> None:
         """Merge in specified data regarding docnames from a different `BuildEnvironment`
         object which coming from a subprocess in parallel builds."""
         raise NotImplementedError
 
-    def process_doc(self, app, doctree):
-        # type: (Sphinx, nodes.document) -> None
+    def process_doc(self, app: Sphinx, doctree: nodes.document) -> None:
         """Process a document and gather specific data from it.
 
         This method is called after the document is read."""
         raise NotImplementedError
 
-    def get_updated_docs(self, app, env):
-        # type: (Sphinx, BuildEnvironment) -> List[str]
+    def get_updated_docs(self, app: Sphinx, env: BuildEnvironment) -> List[str]:
         """Return a list of docnames to re-read.
 
         This methods is called after reading the whole of documents (experimental).
         """
         return []
 
-    def get_outdated_docs(self, app, env, added, changed, removed):
-        # type: (Sphinx, BuildEnvironment, str, Set[str], Set[str], Set[str]) -> List[str]
+    def get_outdated_docs(self, app: Sphinx, env: BuildEnvironment,
+                          added: Set[str], changed: Set[str], removed: Set[str]) -> List[str]:
         """Return a list of docnames to re-read.
 
         This methods is called before reading the documents.
diff --git a/sphinx/environment/collectors/asset.py b/sphinx/environment/collectors/asset.py
index fed8280c1..e1d3abef1 100644
--- a/sphinx/environment/collectors/asset.py
+++ b/sphinx/environment/collectors/asset.py
@@ -11,22 +11,21 @@
 import os
 from glob import glob
 from os import path
+from typing import Any, Dict, List, Set
 
 from docutils import nodes
+from docutils.nodes import Node
 from docutils.utils import relative_path
 
 from sphinx import addnodes
+from sphinx.application import Sphinx
+from sphinx.environment import BuildEnvironment
 from sphinx.environment.collectors import EnvironmentCollector
 from sphinx.locale import __
 from sphinx.util import logging
 from sphinx.util.i18n import get_image_filename_for_language, search_image_for_language
 from sphinx.util.images import guess_mimetype
 
-if False:
-    # For type annotation
-    from typing import Dict, List, Set  # NOQA
-    from sphinx.sphinx import Sphinx  # NOQA
-    from sphinx.environment import BuildEnvironment  # NOQA
 
 logger = logging.getLogger(__name__)
 
@@ -34,16 +33,14 @@ logger = logging.getLogger(__name__)
 class ImageCollector(EnvironmentCollector):
     """Image files collector for sphinx.environment."""
 
-    def clear_doc(self, app, env, docname):
-        # type: (Sphinx, BuildEnvironment, str) -> None
+    def clear_doc(self, app: Sphinx, env: BuildEnvironment, docname: str) -> None:
         env.images.purge_doc(docname)
 
-    def merge_other(self, app, env, docnames, other):
-        # type: (Sphinx, BuildEnvironment, Set[str], BuildEnvironment) -> None
+    def merge_other(self, app: Sphinx, env: BuildEnvironment,
+                    docnames: Set[str], other: BuildEnvironment) -> None:
         env.images.merge_other(docnames, other.images)
 
-    def process_doc(self, app, doctree):
-        # type: (Sphinx, nodes.document) -> None
+    def process_doc(self, app: Sphinx, doctree: nodes.document) -> None:
         """Process and rewrite image URIs."""
         docname = app.env.docname
 
@@ -92,8 +89,8 @@ class ImageCollector(EnvironmentCollector):
                     continue
                 app.env.images.add_file(docname, imgpath)
 
-    def collect_candidates(self, env, imgpath, candidates, node):
-        # type: (BuildEnvironment, str, Dict[str, str], nodes.Node) -> None
+    def collect_candidates(self, env: BuildEnvironment, imgpath: str,
+                           candidates: Dict[str, str], node: Node) -> None:
         globbed = {}  # type: Dict[str, List[str]]
         for filename in glob(imgpath):
             new_imgpath = relative_path(path.join(env.srcdir, 'dummy'),
@@ -115,16 +112,14 @@ class ImageCollector(EnvironmentCollector):
 class DownloadFileCollector(EnvironmentCollector):
     """Download files collector for sphinx.environment."""
 
-    def clear_doc(self, app, env, docname):
-        # type: (Sphinx, BuildEnvironment, str) -> None
+    def clear_doc(self, app: Sphinx, env: BuildEnvironment, docname: str) -> None:
         env.dlfiles.purge_doc(docname)
 
-    def merge_other(self, app, env, docnames, other):
-        # type: (Sphinx, BuildEnvironment, Set[str], BuildEnvironment) -> None
+    def merge_other(self, app: Sphinx, env: BuildEnvironment,
+                    docnames: Set[str], other: BuildEnvironment) -> None:
         env.dlfiles.merge_other(docnames, other.dlfiles)
 
-    def process_doc(self, app, doctree):
-        # type: (Sphinx, nodes.document) -> None
+    def process_doc(self, app: Sphinx, doctree: nodes.document) -> None:
         """Process downloadable file paths. """
         for node in doctree.traverse(addnodes.download_reference):
             targetname = node['reftarget']
@@ -140,8 +135,7 @@ class DownloadFileCollector(EnvironmentCollector):
                 node['filename'] = app.env.dlfiles.add_file(app.env.docname, rel_filename)
 
 
-def setup(app):
-    # type: (Sphinx) -> Dict
+def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_env_collector(ImageCollector)
     app.add_env_collector(DownloadFileCollector)
 
diff --git a/sphinx/environment/collectors/dependencies.py b/sphinx/environment/collectors/dependencies.py
index b091b371d..63ae63e84 100644
--- a/sphinx/environment/collectors/dependencies.py
+++ b/sphinx/environment/collectors/dependencies.py
@@ -10,35 +10,30 @@
 
 import os
 from os import path
+from typing import Any, Dict, Set
 
+from docutils import nodes
 from docutils.utils import relative_path
 
+from sphinx.application import Sphinx
+from sphinx.environment import BuildEnvironment
 from sphinx.environment.collectors import EnvironmentCollector
 from sphinx.util.osutil import fs_encoding
 
-if False:
-    # For type annotation
-    from typing import Dict, Set  # NOQA
-    from docutils import nodes  # NOQA
-    from sphinx.sphinx import Sphinx  # NOQA
-    from sphinx.environment import BuildEnvironment  # NOQA
-
 
 class DependenciesCollector(EnvironmentCollector):
     """dependencies collector for sphinx.environment."""
 
-    def clear_doc(self, app, env, docname):
-        # type: (Sphinx, BuildEnvironment, str) -> None
+    def clear_doc(self, app: Sphinx, env: BuildEnvironment, docname: str) -> None:
         env.dependencies.pop(docname, None)
 
-    def merge_other(self, app, env, docnames, other):
-        # type: (Sphinx, BuildEnvironment, Set[str], BuildEnvironment) -> None
+    def merge_other(self, app: Sphinx, env: BuildEnvironment,
+                    docnames: Set[str], other: BuildEnvironment) -> None:
         for docname in docnames:
             if docname in other.dependencies:
                 env.dependencies[docname] = other.dependencies[docname]
 
-    def process_doc(self, app, doctree):
-        # type: (Sphinx, nodes.document) -> None
+    def process_doc(self, app: Sphinx, doctree: nodes.document) -> None:
         """Process docutils-generated dependency info."""
         cwd = os.getcwd()
         frompath = path.join(path.normpath(app.srcdir), 'dummy')
@@ -55,8 +50,7 @@ class DependenciesCollector(EnvironmentCollector):
             app.env.dependencies[app.env.docname].add(relpath)
 
 
-def setup(app):
-    # type: (Sphinx) -> Dict
+def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_env_collector(DependenciesCollector)
 
     return {
diff --git a/sphinx/environment/collectors/indexentries.py b/sphinx/environment/collectors/indexentries.py
index 2d8af7887..9c86779fc 100644
--- a/sphinx/environment/collectors/indexentries.py
+++ b/sphinx/environment/collectors/indexentries.py
@@ -8,34 +8,31 @@
     :license: BSD, see LICENSE for details.
 """
 
+from typing import Any, Dict, Set
+
+from docutils import nodes
+
 from sphinx import addnodes
+from sphinx.application import Sphinx
+from sphinx.environment import BuildEnvironment
 from sphinx.environment.collectors import EnvironmentCollector
 from sphinx.util import split_index_msg, logging
 
-if False:
-    # For type annotation
-    from typing import Dict, Set  # NOQA
-    from docutils import nodes  # NOQA
-    from sphinx.applicatin import Sphinx  # NOQA
-    from sphinx.environment import BuildEnvironment  # NOQA
-
 logger = logging.getLogger(__name__)
 
 
 class IndexEntriesCollector(EnvironmentCollector):
     name = 'indices'
 
-    def clear_doc(self, app, env, docname):
-        # type: (Sphinx, BuildEnvironment, str) -> None
+    def clear_doc(self, app: Sphinx, env: BuildEnvironment, docname: str) -> None:
         env.indexentries.pop(docname, None)
 
-    def merge_other(self, app, env, docnames, other):
-        # type: (Sphinx, BuildEnvironment, Set[str], BuildEnvironment) -> None
+    def merge_other(self, app: Sphinx, env: BuildEnvironment,
+                    docnames: Set[str], other: BuildEnvironment) -> None:
         for docname in docnames:
             env.indexentries[docname] = other.indexentries[docname]
 
-    def process_doc(self, app, doctree):
-        # type: (Sphinx, nodes.document) -> None
+    def process_doc(self, app: Sphinx, doctree: nodes.document) -> None:
         docname = app.env.docname
         entries = app.env.indexentries[docname] = []
         for node in doctree.traverse(addnodes.index):
@@ -50,8 +47,7 @@ class IndexEntriesCollector(EnvironmentCollector):
                     entries.append(entry)
 
 
-def setup(app):
-    # type: (Sphinx) -> Dict
+def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_env_collector(IndexEntriesCollector)
 
     return {
diff --git a/sphinx/environment/collectors/metadata.py b/sphinx/environment/collectors/metadata.py
index 9168e7840..a547d2551 100644
--- a/sphinx/environment/collectors/metadata.py
+++ b/sphinx/environment/collectors/metadata.py
@@ -8,33 +8,28 @@
     :license: BSD, see LICENSE for details.
 """
 
-from typing import List, cast
+from typing import Any, Dict, List, Set
+from typing import cast
 
 from docutils import nodes
 
+from sphinx.application import Sphinx
+from sphinx.environment import BuildEnvironment
 from sphinx.environment.collectors import EnvironmentCollector
 
-if False:
-    # For type annotation
-    from typing import Dict, Set  # NOQA
-    from sphinx.sphinx import Sphinx  # NOQA
-    from sphinx.environment import BuildEnvironment  # NOQA
-
 
 class MetadataCollector(EnvironmentCollector):
     """metadata collector for sphinx.environment."""
 
-    def clear_doc(self, app, env, docname):
-        # type: (Sphinx, BuildEnvironment, str) -> None
+    def clear_doc(self, app: Sphinx, env: BuildEnvironment, docname: str) -> None:
         env.metadata.pop(docname, None)
 
-    def merge_other(self, app, env, docnames, other):
-        # type: (Sphinx, BuildEnvironment, Set[str], BuildEnvironment) -> None
+    def merge_other(self, app: Sphinx, env: BuildEnvironment,
+                    docnames: Set[str], other: BuildEnvironment) -> None:
         for docname in docnames:
             env.metadata[docname] = other.metadata[docname]
 
-    def process_doc(self, app, doctree):
-        # type: (Sphinx, nodes.document) -> None
+    def process_doc(self, app: Sphinx, doctree: nodes.document) -> None:
         """Process the docinfo part of the doctree as metadata.
 
         Keep processing minimal -- just return what docutils says.
@@ -67,8 +62,7 @@ class MetadataCollector(EnvironmentCollector):
             doctree.pop(0)
 
 
-def setup(app):
-    # type: (Sphinx) -> Dict
+def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_env_collector(MetadataCollector)
 
     return {
diff --git a/sphinx/environment/collectors/title.py b/sphinx/environment/collectors/title.py
index 0f43eb0af..7d464f874 100644
--- a/sphinx/environment/collectors/title.py
+++ b/sphinx/environment/collectors/title.py
@@ -8,34 +8,30 @@
     :license: BSD, see LICENSE for details.
 """
 
+from typing import Any, Dict, Set
+
 from docutils import nodes
 
+from sphinx.application import Sphinx
+from sphinx.environment import BuildEnvironment
 from sphinx.environment.collectors import EnvironmentCollector
 from sphinx.transforms import SphinxContentsFilter
 
-if False:
-    # For type annotation
-    from typing import Dict, Set  # NOQA
-    from sphinx.sphinx import Sphinx  # NOQA
-    from sphinx.environment import BuildEnvironment  # NOQA
-
 
 class TitleCollector(EnvironmentCollector):
     """title collector for sphinx.environment."""
 
-    def clear_doc(self, app, env, docname):
-        # type: (Sphinx, BuildEnvironment, str) -> None
+    def clear_doc(self, app: Sphinx, env: BuildEnvironment, docname: str) -> None:
         env.titles.pop(docname, None)
         env.longtitles.pop(docname, None)
 
-    def merge_other(self, app, env, docnames, other):
-        # type: (Sphinx, BuildEnvironment, Set[str], BuildEnvironment) -> None
+    def merge_other(self, app: Sphinx, env: BuildEnvironment,
+                    docnames: Set[str], other: BuildEnvironment) -> None:
         for docname in docnames:
             env.titles[docname] = other.titles[docname]
             env.longtitles[docname] = other.longtitles[docname]
 
-    def process_doc(self, app, doctree):
-        # type: (Sphinx, nodes.document) -> None
+    def process_doc(self, app: Sphinx, doctree: nodes.document) -> None:
         """Add a title node to the document (just copy the first section title),
         and store that title in the environment.
         """
@@ -59,8 +55,7 @@ class TitleCollector(EnvironmentCollector):
         app.env.longtitles[app.env.docname] = longtitlenode
 
 
-def setup(app):
-    # type: (Sphinx) -> Dict
+def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_env_collector(TitleCollector)
 
     return {
diff --git a/sphinx/environment/collectors/toctree.py b/sphinx/environment/collectors/toctree.py
index 53009c753..d1e211d2c 100644
--- a/sphinx/environment/collectors/toctree.py
+++ b/sphinx/environment/collectors/toctree.py
@@ -8,31 +8,29 @@
     :license: BSD, see LICENSE for details.
 """
 
+from typing import Any, Dict, List, Set, Tuple, Type, TypeVar
 from typing import cast
 
 from docutils import nodes
+from docutils.nodes import Element, Node
 
 from sphinx import addnodes
+from sphinx.application import Sphinx
+from sphinx.environment import BuildEnvironment
 from sphinx.environment.adapters.toctree import TocTree
 from sphinx.environment.collectors import EnvironmentCollector
 from sphinx.locale import __
 from sphinx.transforms import SphinxContentsFilter
 from sphinx.util import url_re, logging
 
-if False:
-    # For type annotation
-    from typing import Dict, List, Set, Tuple, Type, TypeVar  # NOQA
-    from sphinx.application import Sphinx  # NOQA
-    from sphinx.environment import BuildEnvironment  # NOQA
 
-    N = TypeVar('N')
+N = TypeVar('N')
 
 logger = logging.getLogger(__name__)
 
 
 class TocTreeCollector(EnvironmentCollector):
-    def clear_doc(self, app, env, docname):
-        # type: (Sphinx, BuildEnvironment, str) -> None
+    def clear_doc(self, app: Sphinx, env: BuildEnvironment, docname: str) -> None:
         env.tocs.pop(docname, None)
         env.toc_secnumbers.pop(docname, None)
         env.toc_fignumbers.pop(docname, None)
@@ -46,8 +44,8 @@ class TocTreeCollector(EnvironmentCollector):
             if not fnset:
                 del env.files_to_rebuild[subfn]
 
-    def merge_other(self, app, env, docnames, other):
-        # type: (Sphinx, BuildEnvironment, Set[str], BuildEnvironment) -> None
+    def merge_other(self, app: Sphinx, env: BuildEnvironment, docnames: Set[str],
+                    other: BuildEnvironment) -> None:
         for docname in docnames:
             env.tocs[docname] = other.tocs[docname]
             env.toc_num_entries[docname] = other.toc_num_entries[docname]
@@ -61,14 +59,12 @@ class TocTreeCollector(EnvironmentCollector):
         for subfn, fnset in other.files_to_rebuild.items():
             env.files_to_rebuild.setdefault(subfn, set()).update(fnset & set(docnames))
 
-    def process_doc(self, app, doctree):
-        # type: (Sphinx, nodes.document) -> None
+    def process_doc(self, app: Sphinx, doctree: nodes.document) -> None:
         """Build a TOC from the doctree and store it in the inventory."""
         docname = app.env.docname
         numentries = [0]  # nonlocal again...
 
-        def traverse_in_section(node, cls):
-            # type: (nodes.Element, Type[N]) -> List[N]
+        def traverse_in_section(node: Element, cls: Type[N]) -> List[N]:
             """Like traverse(), but stay within the same section."""
             result = []  # type: List[N]
             if isinstance(node, cls):
@@ -80,9 +76,8 @@ class TocTreeCollector(EnvironmentCollector):
                     result.extend(traverse_in_section(child, cls))
             return result
 
-        def build_toc(node, depth=1):
-            # type: (nodes.Element, int) -> nodes.bullet_list
-            entries = []  # type: List[nodes.Element]
+        def build_toc(node: Element, depth: int = 1) -> nodes.bullet_list:
+            entries = []  # type: List[Element]
             for sectionnode in node:
                 # find all toctree nodes in this section and add them
                 # to the toc (just copying the toctree node which is then
@@ -107,7 +102,7 @@ class TocTreeCollector(EnvironmentCollector):
                         '', '', internal=True, refuri=docname,
                         anchorname=anchorname, *nodetext)
                     para = addnodes.compact_paragraph('', '', reference)
-                    item = nodes.list_item('', para)  # type: nodes.Element
+                    item = nodes.list_item('', para)  # type: Element
                     sub_item = build_toc(sectionnode, depth + 1)
                     if sub_item:
                         item += sub_item
@@ -135,12 +130,10 @@ class TocTreeCollector(EnvironmentCollector):
             app.env.tocs[docname] = nodes.bullet_list('')
         app.env.toc_num_entries[docname] = numentries[0]
 
-    def get_updated_docs(self, app, env):
-        # type: (Sphinx, BuildEnvironment) -> List[str]
+    def get_updated_docs(self, app: Sphinx, env: BuildEnvironment) -> List[str]:
         return self.assign_section_numbers(env) + self.assign_figure_numbers(env)
 
-    def assign_section_numbers(self, env):
-        # type: (BuildEnvironment) -> List[str]
+    def assign_section_numbers(self, env: BuildEnvironment) -> List[str]:
         """Assign a section number to each heading under a numbered toctree."""
         # a list of all docnames whose section numbers changed
         rewrite_needed = []
@@ -149,8 +142,7 @@ class TocTreeCollector(EnvironmentCollector):
         old_secnumbers = env.toc_secnumbers
         env.toc_secnumbers = {}
 
-        def _walk_toc(node, secnums, depth, titlenode=None):
-            # type: (nodes.Element, Dict, int, nodes.title) -> None
+        def _walk_toc(node: Element, secnums: Dict, depth: int, titlenode: nodes.title = None) -> None:  # NOQA
             # titlenode is the title of the document, it will get assigned a
             # secnumber too, so that it shows up in next/prev/parent rellinks
             for subnode in node.children:
@@ -184,8 +176,7 @@ class TocTreeCollector(EnvironmentCollector):
                 elif isinstance(subnode, addnodes.toctree):
                     _walk_toctree(subnode, depth)
 
-        def _walk_toctree(toctreenode, depth):
-            # type: (addnodes.toctree, int) -> None
+        def _walk_toctree(toctreenode: addnodes.toctree, depth: int) -> None:
             if depth == 0:
                 return
             for (title, ref) in toctreenode['entries']:
@@ -216,8 +207,7 @@ class TocTreeCollector(EnvironmentCollector):
 
         return rewrite_needed
 
-    def assign_figure_numbers(self, env):
-        # type: (BuildEnvironment) -> List[str]
+    def assign_figure_numbers(self, env: BuildEnvironment) -> List[str]:
         """Assign a figure number to each figure under a numbered toctree."""
 
         rewrite_needed = []
@@ -227,8 +217,7 @@ class TocTreeCollector(EnvironmentCollector):
         env.toc_fignumbers = {}
         fignum_counter = {}  # type: Dict[str, Dict[Tuple[int, ...], int]]
 
-        def get_figtype(node):
-            # type: (nodes.Node) -> str
+        def get_figtype(node: Node) -> str:
             for domain in env.domains.values():
                 figtype = domain.get_enumerable_node_type(node)
                 if figtype:
@@ -236,8 +225,7 @@ class TocTreeCollector(EnvironmentCollector):
 
             return None
 
-        def get_section_number(docname, section):
-            # type: (str, nodes.section) -> Tuple[int, ...]
+        def get_section_number(docname: str, section: nodes.section) -> Tuple[int, ...]:
             anchorname = '#' + section['ids'][0]
             secnumbers = env.toc_secnumbers.get(docname, {})
             if anchorname in secnumbers:
@@ -247,24 +235,22 @@ class TocTreeCollector(EnvironmentCollector):
 
             return secnum or tuple()
 
-        def get_next_fignumber(figtype, secnum):
-            # type: (str, Tuple[int, ...]) -> Tuple[int, ...]
+        def get_next_fignumber(figtype: str, secnum: Tuple[int, ...]) -> Tuple[int, ...]:
             counter = fignum_counter.setdefault(figtype, {})
 
             secnum = secnum[:env.config.numfig_secnum_depth]
             counter[secnum] = counter.get(secnum, 0) + 1
             return secnum + (counter[secnum],)
 
-        def register_fignumber(docname, secnum, figtype, fignode):
-            # type: (str, Tuple[int, ...], str, nodes.Element) -> None
+        def register_fignumber(docname: str, secnum: Tuple[int, ...],
+                               figtype: str, fignode: Element) -> None:
             env.toc_fignumbers.setdefault(docname, {})
             fignumbers = env.toc_fignumbers[docname].setdefault(figtype, {})
             figure_id = fignode['ids'][0]
 
             fignumbers[figure_id] = get_next_fignumber(figtype, secnum)
 
-        def _walk_doctree(docname, doctree, secnum):
-            # type: (str, nodes.Element, Tuple[int, ...]) -> None
+        def _walk_doctree(docname: str, doctree: Element, secnum: Tuple[int, ...]) -> None:
             for subnode in doctree.children:
                 if isinstance(subnode, nodes.section):
                     next_secnum = get_section_number(docname, subnode)
@@ -286,8 +272,7 @@ class TocTreeCollector(EnvironmentCollector):
 
                     _walk_doctree(docname, subnode, secnum)
 
-        def _walk_doc(docname, secnum):
-            # type: (str, Tuple[int, ...]) -> None
+        def _walk_doc(docname: str, secnum: Tuple[int, ...]) -> None:
             if docname not in assigned:
                 assigned.add(docname)
                 doctree = env.get_doctree(docname)
@@ -302,8 +287,7 @@ class TocTreeCollector(EnvironmentCollector):
         return rewrite_needed
 
 
-def setup(app):
-    # type: (Sphinx) -> Dict
+def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_env_collector(TocTreeCollector)
 
     return {
diff --git a/sphinx/util/__init__.py b/sphinx/util/__init__.py
index d7dd6d95f..7bfb3ad3e 100644
--- a/sphinx/util/__init__.py
+++ b/sphinx/util/__init__.py
@@ -166,7 +166,7 @@ class DownloadFiles(dict):
                    Hence don't hack this directly.
     """
 
-    def add_file(self, docname: str, filename: str) -> None:
+    def add_file(self, docname: str, filename: str) -> str:
         if filename not in self:
             digest = md5(filename.encode()).hexdigest()
             dest = '%s/%s' % (digest, os.path.basename(filename))