diff --git a/.editorconfig b/.editorconfig
new file mode 100644
index 00000000..5374960a
--- /dev/null
+++ b/.editorconfig
@@ -0,0 +1,14 @@
+root = true
+
+[*]
+charset = utf-8
+end_of_line = lf
+indent_style = space
+insert_final_newline = true
+trim_trailing_whitespace = true
+
+[*.py]
+indent_size = 4
+
+[*.md]
+indent_size = 2
diff --git a/.gitignore b/.gitignore
index 1b4a42b9..bdb15c94 100644
--- a/.gitignore
+++ b/.gitignore
@@ -12,4 +12,5 @@ jedi.egg-info/
 record.json
 /.cache/
 /.pytest_cache
+/.mypy_cache
 /venv/
diff --git a/.readthedocs.yml b/.readthedocs.yml
new file mode 100644
index 00000000..1893a4fd
--- /dev/null
+++ b/.readthedocs.yml
@@ -0,0 +1,2 @@
+python:
+   pip_install: true
diff --git a/.travis.yml b/.travis.yml
index d7c418a4..e16e2689 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -8,6 +8,7 @@ python:
 
 env:
   - JEDI_TEST_ENVIRONMENT=38
+  - JEDI_TEST_ENVIRONMENT=39
   - JEDI_TEST_ENVIRONMENT=37
   - JEDI_TEST_ENVIRONMENT=36
   - JEDI_TEST_ENVIRONMENT=interpreter
@@ -15,7 +16,7 @@ env:
 matrix:
   include:
     - python: 3.8
-      script: 
+      script:
         - 'pip install coverage'
         - 'coverage run --source jedi -m pytest'
         - 'coverage report'
@@ -30,8 +31,8 @@ matrix:
       install:
         - 'pip install .[qa]'
       script:
-        # Ignore F401, which are unused imports. flake8 is a primitive tool and is sometimes wrong.
-        - 'flake8 --extend-ignore F401 {posargs:jedi}'
+        - 'flake8 jedi setup.py'
+        - 'mypy jedi sith.py'
 install:
     - sudo apt-get -y install python3-venv
     - pip install .[testing]
@@ -47,9 +48,15 @@ script:
           # Only required for JEDI_TEST_ENVIRONMENT=38, because it's not always
           # available.
           download_name=python-$test_env_version
-          wget https://s3.amazonaws.com/travis-python-archives/binaries/ubuntu/16.04/x86_64/$download_name.tar.bz2
-          sudo tar xjf $download_name.tar.bz2 --directory / opt/python
-          ln -s "/opt/python/${test_env_version}/bin/python" /home/travis/bin/$python_bin
+          if [ "$JEDI_TEST_ENVIRONMENT" == "39" ]; then
+            wget https://storage.googleapis.com/travis-ci-language-archives/python/binaries/ubuntu/16.04/x86_64/python-3.9-dev.tar.bz2
+            sudo tar xjf python-3.9-dev.tar.bz2 --directory / opt/python
+            ln -s "/opt/python/3.9-dev/bin/python" /home/travis/bin/python3.9
+          else
+            wget https://s3.amazonaws.com/travis-python-archives/binaries/ubuntu/16.04/x86_64/$download_name.tar.bz2
+            sudo tar xjf $download_name.tar.bz2 --directory / opt/python
+            ln -s "/opt/python/${test_env_version}/bin/python" /home/travis/bin/$python_bin
+          fi
         elif [ "${python_path#/opt/pyenv/shims}" != "$python_path" ]; then
           # Activate pyenv version (required with JEDI_TEST_ENVIRONMENT=36).
           pyenv_bin="$(pyenv whence --path "$python_bin" | head -n1)"
diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index a1b2d301..f288f8f4 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -16,6 +16,8 @@ Unreleased
 - Functions with ``@property`` now return ``property`` instead of ``function``
   in ``Name().type``
 - Started using annotations
+- Better support for the walrus operator
+- Project attributes are now read accessible
 
 This is likely going to be the last minor release before 1.0.
 
diff --git a/README.rst b/README.rst
index 80590f76..f63feb8d 100644
--- a/README.rst
+++ b/README.rst
@@ -52,9 +52,16 @@ Jedi can currently be used with the following editors/projects:
 - wdb_ - Web Debugger
 - `Eric IDE`_ (Available as a plugin)
 - `IPython 6.0.0+ <https://ipython.readthedocs.io/en/stable/whatsnew/version6.html>`_
+- `xonsh shell <https://xon.sh/contents.html>`_ has `jedi extension <https://xon.sh/xontribs.html#jedi>`_
 
 and many more!
 
+There are a few language servers that use Jedi:
+
+- `jedi-language-server <https://github.com/pappasam/jedi-language-server>`_
+- `python-language-server <https://github.com/palantir/python-language-server>`_
+- `anakin-language-server <https://github.com/muffinmad/anakin-language-server>`_
+
 Here are some pictures taken from jedi-vim_:
 
 .. image:: https://github.com/davidhalter/jedi/raw/master/docs/_screenshots/screenshot_complete.png
diff --git a/docs/docs/usage.rst b/docs/docs/usage.rst
index b148ad76..2ef8b848 100644
--- a/docs/docs/usage.rst
+++ b/docs/docs/usage.rst
@@ -3,11 +3,21 @@
 Using Jedi
 ==========
 
-|jedi| is can be used with a variety of plugins and software. It is also possible
-to use |jedi| in the :ref:`Python shell or with IPython <repl-completion>`.
+|jedi| is can be used with a variety of :ref:`plugins <editor-plugins>`,
+`language servers <language-servers>` and other software.
+It is also possible to use |jedi| in the :ref:`Python shell or with IPython
+<repl-completion>`.
 
 Below you can also find a list of :ref:`recipes for type hinting <recipes>`.
 
+.. _language-servers:
+
+Language Servers
+--------------
+
+- `jedi-language-server <https://github.com/pappasam/jedi-language-server>`_
+- `python-language-server <https://github.com/palantir/python-language-server>`_
+- `anakin-language-server <https://github.com/muffinmad/anakin-language-server>`_
 
 .. _editor-plugins:
 
@@ -83,6 +93,16 @@ Web Debugger
 
 - wdb_
 
+xonsh shell
+~~~~~~~~~~~
+
+Jedi is a preinstalled extension in `xonsh shell <https://xon.sh/contents.html>`_. 
+Run the following command to enable:
+
+::
+
+    xontrib load jedi
+
 and many more!
 
 .. _repl-completion:
diff --git a/jedi/api/__init__.py b/jedi/api/__init__.py
index 3a9d5a68..7942f6b4 100644
--- a/jedi/api/__init__.py
+++ b/jedi/api/__init__.py
@@ -49,7 +49,7 @@ from jedi.inference.utils import to_list
 sys.setrecursionlimit(3000)
 
 
-class Script(object):
+class Script:
     """
     A Script is the base for completions, goto or whatever you want to do with
     Jedi. The counter part of this class is :class:`Interpreter`, which works
@@ -122,7 +122,7 @@ class Script(object):
         self._module_node, code = self._inference_state.parse_and_get_code(
             code=code,
             path=self.path,
-            use_latest_grammar=path and path.suffix == 'pyi',
+            use_latest_grammar=path and path.suffix == '.pyi',
             cache=False,  # No disk cache, because the current script often changes.
             diff_cache=settings.fast_parser,
             cache_path=settings.cache_directory,
@@ -157,6 +157,7 @@ class Script(object):
             # We are in a stub file. Try to load the stub properly.
             stub_module = load_proper_stub_module(
                 self._inference_state,
+                self._inference_state.latest_grammar,
                 file_io,
                 names,
                 self._module_node
@@ -234,6 +235,11 @@ class Script(object):
             leaf = self._module_node.get_leaf_for_position(pos)
             if leaf is None or leaf.type == 'string':
                 return []
+            if leaf.end_pos == (line, column) and leaf.type == 'operator':
+                next_ = leaf.get_next_leaf()
+                if next_.start_pos == leaf.end_pos \
+                        and next_.type in ('number', 'string', 'keyword'):
+                    leaf = next_
 
         context = self._get_module_context().create_context(leaf)
 
diff --git a/jedi/api/classes.py b/jedi/api/classes.py
index cadff7b1..0cd3371d 100644
--- a/jedi/api/classes.py
+++ b/jedi/api/classes.py
@@ -14,18 +14,18 @@ These classes are the much biggest part of the API, because they contain
 the interesting information about all operations.
 """
 import re
+from pathlib import Path
 from typing import Optional
 
-from parso.python.tree import search_ancestor
+from parso.tree import search_ancestor
 
 from jedi import settings
 from jedi import debug
 from jedi.inference.utils import unite
 from jedi.cache import memoize_method
-from jedi.inference import imports
-from jedi.inference.imports import ImportName
 from jedi.inference.compiled.mixed import MixedName
-from jedi.inference.gradual.typeshed import StubModuleValue
+from jedi.inference.names import ImportName, SubModuleName
+from jedi.inference.gradual.stub_value import StubModuleValue
 from jedi.inference.gradual.conversion import convert_names, convert_values
 from jedi.inference.base_value import ValueSet
 from jedi.api.keywords import KeywordName
@@ -53,7 +53,7 @@ def _values_to_definitions(values):
     return [Name(c.inference_state, c.name) for c in values]
 
 
-class BaseName(object):
+class BaseName:
     """
     The base class for all definitions, completions and signatures.
     """
@@ -92,17 +92,15 @@ class BaseName(object):
         return self._name.get_root_context()
 
     @property
-    def module_path(self) -> Optional[str]:
+    def module_path(self) -> Optional[Path]:
         """
         Shows the file path of a module. e.g. ``/usr/lib/python3.9/os.py``
-
-        :rtype: str or None
         """
         module = self._get_module_context()
         if module.is_stub() or not module.is_compiled():
             # Compiled modules should not return a module path even if they
             # have one.
-            path = self._get_module_context().py__file__()
+            path: Optional[Path] = self._get_module_context().py__file__()
             if path is not None:
                 return path
 
@@ -185,7 +183,7 @@ class BaseName(object):
                     tree_name.is_definition():
                 resolve = True
 
-        if isinstance(self._name, imports.SubModuleName) or resolve:
+        if isinstance(self._name, SubModuleName) or resolve:
             for value in self._name.infer():
                 return value.api_type
         return self._name.api_type
@@ -720,6 +718,24 @@ class Completion(BaseName):
 
         return super().type
 
+    def get_completion_prefix_length(self):
+        """
+        Returns the length of the prefix being completed.
+        For example, completing ``isinstance``::
+
+            isinstan# <-- Cursor is here
+
+        would return 8, because len('isinstan') == 8.
+
+        Assuming the following function definition::
+
+            def foo(param=0):
+                pass
+
+        completing ``foo(par`` would return 3.
+        """
+        return self._like_name_length
+
     def __repr__(self):
         return '<%s: %s>' % (type(self).__name__, self._name.get_public_name())
 
diff --git a/jedi/api/completion_cache.py b/jedi/api/completion_cache.py
index 6dac6a4e..46e9bead 100644
--- a/jedi/api/completion_cache.py
+++ b/jedi/api/completion_cache.py
@@ -1,7 +1,13 @@
-_cache = {}
+from typing import Dict, Tuple, Callable
+
+CacheValues = Tuple[str, str, str]
+CacheValuesCallback = Callable[[], CacheValues]
 
 
-def save_entry(module_name, name, cache):
+_cache: Dict[str, Dict[str, CacheValues]] = {}
+
+
+def save_entry(module_name: str, name: str, cache: CacheValues) -> None:
     try:
         module_cache = _cache[module_name]
     except KeyError:
@@ -9,8 +15,8 @@ def save_entry(module_name, name, cache):
     module_cache[name] = cache
 
 
-def _create_get_from_cache(number):
-    def _get_from_cache(module_name, name, get_cache_values):
+def _create_get_from_cache(number: int) -> Callable[[str, str, CacheValuesCallback], str]:
+    def _get_from_cache(module_name: str, name: str, get_cache_values: CacheValuesCallback) -> str:
         try:
             return _cache[module_name][name][number]
         except KeyError:
diff --git a/jedi/api/environment.py b/jedi/api/environment.py
index cd353617..3f1f238f 100644
--- a/jedi/api/environment.py
+++ b/jedi/api/environment.py
@@ -30,7 +30,7 @@ class InvalidPythonEnvironment(Exception):
     """
 
 
-class _BaseEnvironment(object):
+class _BaseEnvironment:
     @memoize_method
     def get_grammar(self):
         version_string = '%s.%s' % (self.version_info.major, self.version_info.minor)
@@ -121,7 +121,7 @@ class Environment(_BaseEnvironment):
         return self._get_subprocess().get_sys_path()
 
 
-class _SameEnvironmentMixin(object):
+class _SameEnvironmentMixin:
     def __init__(self):
         self._start_executable = self.executable = sys.executable
         self.path = sys.prefix
@@ -384,7 +384,8 @@ def _get_executable_path(path, safe=True):
 
 
 def _get_executables_from_windows_registry(version):
-    import winreg
+    # https://github.com/python/typeshed/pull/3794 adds winreg
+    import winreg  # type: ignore[import]
 
     # TODO: support Python Anaconda.
     sub_keys = [
diff --git a/jedi/api/errors.py b/jedi/api/errors.py
index 6dc9ae2d..10cb62af 100644
--- a/jedi/api/errors.py
+++ b/jedi/api/errors.py
@@ -8,7 +8,7 @@ def parso_to_jedi_errors(grammar, module_node):
     return [SyntaxError(e) for e in grammar.iter_errors(module_node)]
 
 
-class SyntaxError(object):
+class SyntaxError:
     """
     Syntax errors are generated by :meth:`.Script.get_syntax_errors`.
     """
diff --git a/jedi/api/helpers.py b/jedi/api/helpers.py
index 97afb363..98685918 100644
--- a/jedi/api/helpers.py
+++ b/jedi/api/helpers.py
@@ -203,7 +203,7 @@ def filter_follow_imports(names, follow_builtin_imports=False):
             yield name
 
 
-class CallDetails(object):
+class CallDetails:
     def __init__(self, bracket_leaf, children, position):
         ['bracket_leaf', 'call_index', 'keyword_name_str']
         self.bracket_leaf = bracket_leaf
diff --git a/jedi/api/interpreter.py b/jedi/api/interpreter.py
index d7d573c7..befafe5a 100644
--- a/jedi/api/interpreter.py
+++ b/jedi/api/interpreter.py
@@ -17,7 +17,7 @@ def _create(inference_state, obj):
     )
 
 
-class NamespaceObject(object):
+class NamespaceObject:
     def __init__(self, dct):
         self.__dict__ = dct
 
diff --git a/jedi/api/keywords.py b/jedi/api/keywords.py
index c016dadf..95c49227 100644
--- a/jedi/api/keywords.py
+++ b/jedi/api/keywords.py
@@ -1,9 +1,16 @@
 import pydoc
 from contextlib import suppress
+from typing import Dict, Optional
 
 from jedi.inference.names import AbstractArbitraryName
 
-from pydoc_data import topics as pydoc_topics
+try:
+    # https://github.com/python/typeshed/pull/4351 adds pydoc_data
+    from pydoc_data import topics  # type: ignore[import]
+    pydoc_topics: Optional[Dict[str, str]] = topics.topics
+except ImportError:
+    # Python 3.6.8 embeddable does not have pydoc_data.
+    pydoc_topics = None
 
 
 class KeywordName(AbstractArbitraryName):
@@ -40,6 +47,6 @@ def imitate_pydoc(string):
         return ''
 
     try:
-        return pydoc_topics.topics[label].strip() if pydoc_topics else ''
+        return pydoc_topics[label].strip() if pydoc_topics else ''
     except KeyError:
         return ''
diff --git a/jedi/api/project.py b/jedi/api/project.py
index ae00c38b..8c438f26 100644
--- a/jedi/api/project.py
+++ b/jedi/api/project.py
@@ -56,7 +56,7 @@ def _remove_duplicates_from_path(path):
         yield p
 
 
-class Project(object):
+class Project:
     """
     Projects are a simple way to manage Python folders and define how Jedi does
     import resolution. It is mostly used as a parameter to :class:`.Script`.
@@ -152,6 +152,29 @@ class Project(object):
         """
         return self._path
 
+    @property
+    def sys_path(self):
+        """
+        The sys path provided to this project. This can be None and in that
+        case will be auto generated.
+        """
+        return self._sys_path
+
+    @property
+    def smart_sys_path(self):
+        """
+        If the sys path is going to be calculated in a smart way, where
+        additional paths are added.
+        """
+        return self._smart_sys_path
+
+    @property
+    def load_unsafe_extensions(self):
+        """
+        Wheter the project loads unsafe extensions.
+        """
+        return self._load_unsafe_extensions
+
     @inference_state_as_method_param_cache()
     def _get_base_sys_path(self, inference_state):
         # The sys path has not been set explicitly.
@@ -343,8 +366,11 @@ class Project(object):
 
 def _is_potential_project(path):
     for name in _CONTAINS_POTENTIAL_PROJECT:
-        if path.joinpath(name).exists():
-            return True
+        try:
+            if path.joinpath(name).exists():
+                return True
+        except OSError:
+            continue
     return False
 
 
diff --git a/jedi/api/refactoring/__init__.py b/jedi/api/refactoring/__init__.py
index 7f8394c9..14c4d910 100644
--- a/jedi/api/refactoring/__init__.py
+++ b/jedi/api/refactoring/__init__.py
@@ -12,7 +12,7 @@ EXPRESSION_PARTS = (
 ).split()
 
 
-class ChangedFile(object):
+class ChangedFile:
     def __init__(self, inference_state, from_path, to_path,
                  module_node, node_to_str_map):
         self._inference_state = inference_state
@@ -72,7 +72,7 @@ class ChangedFile(object):
         return '<%s: %s>' % (self.__class__.__name__, self._from_path)
 
 
-class Refactoring(object):
+class Refactoring:
     def __init__(self, inference_state, file_to_node_changes, renames=()):
         self._inference_state = inference_state
         self._renames = renames
diff --git a/jedi/cache.py b/jedi/cache.py
index 29ed979f..1ff45201 100644
--- a/jedi/cache.py
+++ b/jedi/cache.py
@@ -13,14 +13,15 @@ these variables are being cleaned after every API usage.
 """
 import time
 from functools import wraps
+from typing import Any, Dict, Tuple
 
 from jedi import settings
 from parso.cache import parser_cache
 
-_time_caches = {}
+_time_caches: Dict[str, Dict[Any, Tuple[float, Any]]] = {}
 
 
-def clear_time_caches(delete_all=False):
+def clear_time_caches(delete_all: bool = False) -> None:
     """ Jedi caches many things, that should be completed after each completion
     finishes.
 
diff --git a/jedi/debug.py b/jedi/debug.py
index 4066cff7..2b2bcfb8 100644
--- a/jedi/debug.py
+++ b/jedi/debug.py
@@ -1,6 +1,7 @@
 import os
 import time
 from contextlib import contextmanager
+from typing import Callable, Optional
 
 _inited = False
 
@@ -20,7 +21,7 @@ try:
         raise ImportError
     else:
         # Use colorama for nicer console output.
-        from colorama import Fore, init
+        from colorama import Fore, init  # type: ignore[import]
         from colorama import initialise
 
         def _lazy_colorama_init():  # noqa: F811
@@ -45,7 +46,7 @@ try:
             _inited = True
 
 except ImportError:
-    class Fore(object):
+    class Fore:  # type: ignore[no-redef]
         RED = ''
         GREEN = ''
         YELLOW = ''
@@ -62,7 +63,7 @@ enable_warning = False
 enable_notice = False
 
 # callback, interface: level, str
-debug_function = None
+debug_function: Optional[Callable[[str, str], None]] = None
 _debug_indent = 0
 _start_time = time.time()
 
diff --git a/jedi/file_io.py b/jedi/file_io.py
index c4518fdb..ead17335 100644
--- a/jedi/file_io.py
+++ b/jedi/file_io.py
@@ -3,7 +3,7 @@ import os
 from parso import file_io
 
 
-class AbstractFolderIO(object):
+class AbstractFolderIO:
     def __init__(self, path):
         self.path = path
 
@@ -57,7 +57,7 @@ class FolderIO(AbstractFolderIO):
                     del dirs[i]
 
 
-class FileIOFolderMixin(object):
+class FileIOFolderMixin:
     def get_parent_folder(self):
         return FolderIO(os.path.dirname(self.path))
 
diff --git a/jedi/inference/__init__.py b/jedi/inference/__init__.py
index 68217365..7409aa84 100644
--- a/jedi/inference/__init__.py
+++ b/jedi/inference/__init__.py
@@ -81,7 +81,7 @@ from jedi.inference.imports import follow_error_node_imports_if_possible
 from jedi.plugins import plugin_manager
 
 
-class InferenceState(object):
+class InferenceState:
     def __init__(self, project, environment=None, script_path=None):
         if environment is None:
             environment = project.get_environment()
@@ -120,14 +120,15 @@ class InferenceState(object):
         debug.dbg('execute result: %s in %s', value_set, value)
         return value_set
 
-    @property
+    # mypy doesn't suppport decorated propeties (https://github.com/python/mypy/issues/1362)
+    @property  # type: ignore[misc]
     @inference_state_function_cache()
     def builtins_module(self):
         module_name = 'builtins'
         builtins_module, = self.import_module((module_name,), sys_path=())
         return builtins_module
 
-    @property
+    @property  # type: ignore[misc]
     @inference_state_function_cache()
     def typing_module(self):
         typing_module, = self.import_module(('typing',))
@@ -169,6 +170,8 @@ class InferenceState(object):
                 return tree_name_to_values(self, context, name)
             elif type_ == 'param':
                 return context.py__getattribute__(name.value, position=name.end_pos)
+            elif type_ == 'namedexpr_test':
+                return context.infer_node(def_)
         else:
             result = follow_error_node_imports_if_possible(context, name)
             if result is not None:
diff --git a/jedi/inference/analysis.py b/jedi/inference/analysis.py
index 1e51db55..c272a9cb 100644
--- a/jedi/inference/analysis.py
+++ b/jedi/inference/analysis.py
@@ -26,7 +26,7 @@ CODES = {
 }
 
 
-class Error(object):
+class Error:
     def __init__(self, name, module_path, start_pos, message=None):
         self.path = module_path
         self._start_pos = start_pos
diff --git a/jedi/inference/arguments.py b/jedi/inference/arguments.py
index c22d70de..8602f494 100644
--- a/jedi/inference/arguments.py
+++ b/jedi/inference/arguments.py
@@ -124,7 +124,7 @@ def _parse_argument_clinic(string):
             allow_kwargs = True
 
 
-class _AbstractArgumentsMixin(object):
+class _AbstractArgumentsMixin:
     def unpack(self, funcdef=None):
         raise NotImplementedError
 
diff --git a/jedi/inference/base_value.py b/jedi/inference/base_value.py
index c0f960d4..e51e063c 100644
--- a/jedi/inference/base_value.py
+++ b/jedi/inference/base_value.py
@@ -22,7 +22,7 @@ from jedi.cache import memoize_method
 sentinel = object()
 
 
-class HelperValueMixin(object):
+class HelperValueMixin:
     def get_root_context(self):
         value = self
         if value.parent_context is None:
@@ -111,7 +111,7 @@ class HelperValueMixin(object):
                         .py__getattribute__('__anext__').execute_with_values()
                         .py__getattribute__('__await__').execute_with_values()
                         .py__stop_iteration_returns()
-                )  # noqa
+                )  # noqa: E124
             ])
         return self.py__iter__(contextualized_node)
 
@@ -363,7 +363,7 @@ class TreeValue(Value):
         return '<%s: %s>' % (self.__class__.__name__, self.tree_node)
 
 
-class ContextualizedNode(object):
+class ContextualizedNode:
     def __init__(self, context, node):
         self.context = context
         self.node = node
@@ -405,7 +405,7 @@ def _getitem(value, index_values, contextualized_node):
     return result
 
 
-class ValueSet(object):
+class ValueSet:
     def __init__(self, iterable):
         self._set = frozenset(iterable)
         for value in iterable:
diff --git a/jedi/inference/compiled/__init__.py b/jedi/inference/compiled/__init__.py
index faf5d373..09ac19f9 100644
--- a/jedi/inference/compiled/__init__.py
+++ b/jedi/inference/compiled/__init__.py
@@ -1,3 +1,6 @@
+# This file also re-exports symbols for wider use. We configure mypy and flake8
+# to be aware that this file does this.
+
 from jedi.inference.compiled.value import CompiledValue, CompiledName, \
     CompiledValueFilter, CompiledValueName, create_from_access_path
 from jedi.inference.base_value import LazyValueWrapper
diff --git a/jedi/inference/compiled/access.py b/jedi/inference/compiled/access.py
index 46dc8249..42fe7ebe 100644
--- a/jedi/inference/compiled/access.py
+++ b/jedi/inference/compiled/access.py
@@ -1,5 +1,6 @@
 import inspect
 import types
+import traceback
 import sys
 import operator as op
 from collections import namedtuple
@@ -117,13 +118,18 @@ def load_module(inference_state, dotted_name, sys_path):
         __import__(dotted_name)
     except ImportError:
         # If a module is "corrupt" or not really a Python module or whatever.
-        print('Module %s not importable in path %s.' % (dotted_name, sys_path), file=sys.stderr)
+        warnings.warn(
+            "Module %s not importable in path %s." % (dotted_name, sys_path),
+            UserWarning,
+            stacklevel=2,
+        )
         return None
     except Exception:
         # Since __import__ pretty much makes code execution possible, just
         # catch any error here and print it.
-        import traceback
-        print("Cannot import:\n%s" % traceback.format_exc(), file=sys.stderr)
+        warnings.warn(
+            "Cannot import:\n%s" % traceback.format_exc(), UserWarning, stacklevel=2
+        )
         return None
     finally:
         sys.path = temp
@@ -134,7 +140,7 @@ def load_module(inference_state, dotted_name, sys_path):
     return create_access_path(inference_state, module)
 
 
-class AccessPath(object):
+class AccessPath:
     def __init__(self, accesses):
         self.accesses = accesses
 
@@ -156,7 +162,7 @@ def get_api_type(obj):
     return 'instance'
 
 
-class DirectObjectAccess(object):
+class DirectObjectAccess:
     def __init__(self, inference_state, obj):
         self._inference_state = inference_state
         self._obj = obj
diff --git a/jedi/inference/compiled/mixed.py b/jedi/inference/compiled/mixed.py
index e96957ed..43e0ed6c 100644
--- a/jedi/inference/compiled/mixed.py
+++ b/jedi/inference/compiled/mixed.py
@@ -3,7 +3,7 @@ Used only for REPL Completion.
 """
 
 import inspect
-import os
+from pathlib import Path
 
 from jedi.parser_utils import get_cached_code_lines
 
@@ -190,8 +190,16 @@ def _find_syntax_node_name(inference_state, python_object):
     except TypeError:
         # The type might not be known (e.g. class_with_dict.__weakref__)
         return None
-    if path is None or not os.path.exists(path):
-        # The path might not exist or be e.g. <stdin>.
+    path = None if path is None else Path(path)
+    try:
+        if path is None or not path.exists():
+            # The path might not exist or be e.g. <stdin>.
+            return None
+    except OSError:
+        # Might raise an OSError on Windows:
+        #
+        #     [WinError 123] The filename, directory name, or volume label
+        #     syntax is incorrect: '<string>'
         return None
 
     file_io = FileIO(path)
diff --git a/jedi/inference/compiled/subprocess/__init__.py b/jedi/inference/compiled/subprocess/__init__.py
index 6f4097c3..0795de30 100644
--- a/jedi/inference/compiled/subprocess/__init__.py
+++ b/jedi/inference/compiled/subprocess/__init__.py
@@ -29,19 +29,19 @@ _MAIN_PATH = os.path.join(os.path.dirname(__file__), '__main__.py')
 PICKLE_PROTOCOL = 4
 
 
-class _GeneralizedPopen(subprocess.Popen):
-    def __init__(self, *args, **kwargs):
-        if os.name == 'nt':
-            try:
-                # Was introduced in Python 3.7.
-                CREATE_NO_WINDOW = subprocess.CREATE_NO_WINDOW
-            except AttributeError:
-                CREATE_NO_WINDOW = 0x08000000
-            kwargs['creationflags'] = CREATE_NO_WINDOW
-        # The child process doesn't need file descriptors except 0, 1, 2.
-        # This is unix only.
-        kwargs['close_fds'] = 'posix' in sys.builtin_module_names
-        super().__init__(*args, **kwargs)
+def _GeneralizedPopen(*args, **kwargs):
+    if os.name == 'nt':
+        try:
+            # Was introduced in Python 3.7.
+            CREATE_NO_WINDOW = subprocess.CREATE_NO_WINDOW
+        except AttributeError:
+            CREATE_NO_WINDOW = 0x08000000
+        kwargs['creationflags'] = CREATE_NO_WINDOW
+    # The child process doesn't need file descriptors except 0, 1, 2.
+    # This is unix only.
+    kwargs['close_fds'] = 'posix' in sys.builtin_module_names
+
+    return subprocess.Popen(*args, **kwargs)
 
 
 def _enqueue_output(out, queue_):
@@ -81,7 +81,7 @@ def _cleanup_process(process, thread):
             pass
 
 
-class _InferenceStateProcess(object):
+class _InferenceStateProcess:
     def __init__(self, inference_state):
         self._inference_state_weakref = weakref.ref(inference_state)
         self._inference_state_id = id(inference_state)
@@ -162,7 +162,7 @@ class InferenceStateSubprocess(_InferenceStateProcess):
             self._compiled_subprocess.delete_inference_state(self._inference_state_id)
 
 
-class CompiledSubprocess(object):
+class CompiledSubprocess:
     is_crashed = False
 
     def __init__(self, executable, env_vars=None):
@@ -280,7 +280,7 @@ class CompiledSubprocess(object):
         self._inference_state_deletion_queue.append(inference_state_id)
 
 
-class Listener(object):
+class Listener:
     def __init__(self):
         self._inference_states = {}
         # TODO refactor so we don't need to process anymore just handle
@@ -346,7 +346,7 @@ class Listener(object):
             pickle_dump(result, stdout, PICKLE_PROTOCOL)
 
 
-class AccessHandle(object):
+class AccessHandle:
     def __init__(self, subprocess, access, id_):
         self.access = access
         self._subprocess = subprocess
diff --git a/jedi/inference/compiled/subprocess/__main__.py b/jedi/inference/compiled/subprocess/__main__.py
index a9845a38..e1554334 100644
--- a/jedi/inference/compiled/subprocess/__main__.py
+++ b/jedi/inference/compiled/subprocess/__main__.py
@@ -1,5 +1,6 @@
 import os
 import sys
+from importlib.abc import MetaPathFinder
 from importlib.machinery import PathFinder
 
 # Remove the first entry, because it's simply a directory entry that equals
@@ -16,7 +17,7 @@ def _get_paths():
     return {'jedi': _jedi_path, 'parso': _parso_path}
 
 
-class _ExactImporter(object):
+class _ExactImporter(MetaPathFinder):
     def __init__(self, path_dct):
         self._path_dct = path_dct
 
diff --git a/jedi/inference/compiled/subprocess/functions.py b/jedi/inference/compiled/subprocess/functions.py
index 2d3ab607..601fe6c2 100644
--- a/jedi/inference/compiled/subprocess/functions.py
+++ b/jedi/inference/compiled/subprocess/functions.py
@@ -3,6 +3,7 @@ import os
 import inspect
 import importlib
 import warnings
+from pathlib import Path
 from zipimport import zipimporter
 from importlib.machinery import all_suffixes
 
@@ -211,7 +212,7 @@ def _from_loader(loader, string):
     if code is None:
         return None, is_package
     if isinstance(loader, zipimporter):
-        return ZipFileIO(module_path, code, cast_path(loader.archive)), is_package
+        return ZipFileIO(module_path, code, Path(cast_path(loader.archive))), is_package
 
     return KnownContentFileIO(module_path, code), is_package
 
@@ -229,7 +230,7 @@ def _get_source(loader, fullname):
                           name=fullname)
 
 
-class ImplicitNSInfo(object):
+class ImplicitNSInfo:
     """Stores information returned from an implicit namespace spec"""
     def __init__(self, name, paths):
         self.name = name
diff --git a/jedi/inference/compiled/value.py b/jedi/inference/compiled/value.py
index 6802e43d..88732f01 100644
--- a/jedi/inference/compiled/value.py
+++ b/jedi/inference/compiled/value.py
@@ -22,7 +22,7 @@ from jedi.inference.signature import BuiltinSignature
 from jedi.inference.context import CompiledContext, CompiledModuleContext
 
 
-class CheckAttribute(object):
+class CheckAttribute:
     """Raises :exc:`AttributeError` if the attribute X is not available."""
     def __init__(self, check_name=None):
         # Remove the py in front of e.g. py__call__.
@@ -324,8 +324,7 @@ class CompiledName(AbstractNameDefinition):
         self.string_name = name
 
     def py__doc__(self):
-        value, = self.infer()
-        return value.py__doc__()
+        return self.infer_compiled_value().py__doc__()
 
     def _get_qualified_names(self):
         parent_qualified_names = self.parent_context.get_qualified_names()
@@ -349,16 +348,12 @@ class CompiledName(AbstractNameDefinition):
 
     @property
     def api_type(self):
-        api = self.infer()
-        # If we can't find the type, assume it is an instance variable
-        if not api:
-            return "instance"
-        return next(iter(api)).api_type
+        return self.infer_compiled_value().api_type
 
-    @memoize_method
     def infer(self):
         return ValueSet([self.infer_compiled_value()])
 
+    @memoize_method
     def infer_compiled_value(self):
         return create_from_name(self._inference_state, self._parent_value, self.string_name)
 
diff --git a/jedi/inference/context.py b/jedi/inference/context.py
index 951f3bf6..cbbce0c7 100644
--- a/jedi/inference/context.py
+++ b/jedi/inference/context.py
@@ -13,7 +13,7 @@ from jedi import debug
 from jedi import parser_utils
 
 
-class AbstractContext(object):
+class AbstractContext:
     # Must be defined: inference_state and tree_node and parent_context as an attribute/property
 
     def __init__(self, inference_state):
@@ -216,7 +216,7 @@ class ValueContext(AbstractContext):
         return '%s(%s)' % (self.__class__.__name__, self._value)
 
 
-class TreeContextMixin(object):
+class TreeContextMixin:
     def infer_node(self, node):
         from jedi.inference.syntax_tree import infer_node
         return infer_node(self, node)
diff --git a/jedi/inference/docstrings.py b/jedi/inference/docstrings.py
index e9c94cdc..80afbecf 100644
--- a/jedi/inference/docstrings.py
+++ b/jedi/inference/docstrings.py
@@ -50,7 +50,7 @@ def _get_numpy_doc_string_cls():
     global _numpy_doc_string_cache
     if isinstance(_numpy_doc_string_cache, (ImportError, SyntaxError)):
         raise _numpy_doc_string_cache
-    from numpydoc.docscrape import NumpyDocString
+    from numpydoc.docscrape import NumpyDocString  # type: ignore[import]
     _numpy_doc_string_cache = NumpyDocString
     return _numpy_doc_string_cache
 
@@ -113,7 +113,7 @@ def _expand_typestr(type_str):
     elif type_str.startswith('{'):
         node = parse(type_str, version='3.7').children[0]
         if node.type == 'atom':
-            for leaf in node.children[1].children:
+            for leaf in getattr(node.children[1], "children", []):
                 if leaf.type == 'number':
                     if '.' in leaf.value:
                         yield 'float'
diff --git a/jedi/inference/filters.py b/jedi/inference/filters.py
index 6551cebc..2451f468 100644
--- a/jedi/inference/filters.py
+++ b/jedi/inference/filters.py
@@ -3,9 +3,11 @@ Filters are objects that you can use to filter names in different scopes. They
 are needed for name resolution.
 """
 from abc import abstractmethod
+from typing import List, MutableMapping, Type
 import weakref
 
 from parso.tree import search_ancestor
+from parso.python.tree import Name, UsedNamesMapping
 
 from jedi.inference import flow_analysis
 from jedi.inference.base_value import ValueSet, ValueWrapper, \
@@ -13,12 +15,13 @@ from jedi.inference.base_value import ValueSet, ValueWrapper, \
 from jedi.parser_utils import get_cached_parent_scope
 from jedi.inference.utils import to_list
 from jedi.inference.names import TreeNameDefinition, ParamName, \
-    AnonymousParamName, AbstractNameDefinition
+    AnonymousParamName, AbstractNameDefinition, NameWrapper
 
+_definition_name_cache: MutableMapping[UsedNamesMapping, List[Name]]
 _definition_name_cache = weakref.WeakKeyDictionary()
 
 
-class AbstractFilter(object):
+class AbstractFilter:
     _until_position = None
 
     def _filter(self, names):
@@ -35,8 +38,8 @@ class AbstractFilter(object):
         raise NotImplementedError
 
 
-class FilterWrapper(object):
-    name_wrapper_class = None
+class FilterWrapper:
+    name_wrapper_class: Type[NameWrapper]
 
     def __init__(self, wrapped_filter):
         self._wrapped_filter = wrapped_filter
@@ -229,7 +232,7 @@ class DictFilter(AbstractFilter):
         return '<%s: for {%s}>' % (self.__class__.__name__, keys)
 
 
-class MergedFilter(object):
+class MergedFilter:
     def __init__(self, *filters):
         self._filters = filters
 
@@ -320,7 +323,7 @@ class _OverwriteMeta(type):
         cls.overwritten_methods = base_dct
 
 
-class _AttributeOverwriteMixin(object):
+class _AttributeOverwriteMixin:
     def get_filters(self, *args, **kwargs):
         yield SpecialMethodFilter(self, self.overwritten_methods, self._wrapped_value)
         yield from self._wrapped_value.get_filters(*args, **kwargs)
diff --git a/jedi/inference/flow_analysis.py b/jedi/inference/flow_analysis.py
index 184f367f..89bfe578 100644
--- a/jedi/inference/flow_analysis.py
+++ b/jedi/inference/flow_analysis.py
@@ -1,12 +1,14 @@
+from typing import Dict, Optional
+
 from jedi.parser_utils import get_flow_branch_keyword, is_scope, get_parent_scope
 from jedi.inference.recursion import execution_allowed
 from jedi.inference.helpers import is_big_annoying_library
 
 
-class Status(object):
-    lookup_table = {}
+class Status:
+    lookup_table: Dict[Optional[bool], 'Status'] = {}
 
-    def __init__(self, value, name):
+    def __init__(self, value: Optional[bool], name: str) -> None:
         self._value = value
         self._name = name
         Status.lookup_table[value] = self
diff --git a/jedi/inference/gradual/annotation.py b/jedi/inference/gradual/annotation.py
index fa3aa5ae..eadcfc2e 100644
--- a/jedi/inference/gradual/annotation.py
+++ b/jedi/inference/gradual/annotation.py
@@ -53,8 +53,10 @@ def _infer_annotation_string(context, string, index=None):
     value_set = context.infer_node(node)
     if index is not None:
         value_set = value_set.filter(
-            lambda value: value.array_type == 'tuple'  # noqa
-                            and len(list(value.py__iter__())) >= index
+            lambda value: (
+                value.array_type == 'tuple'
+                and len(list(value.py__iter__())) >= index
+            )
         ).py__simple_getitem__(index)
     return value_set
 
diff --git a/jedi/inference/gradual/base.py b/jedi/inference/gradual/base.py
index 22c204a2..fb4740d3 100644
--- a/jedi/inference/gradual/base.py
+++ b/jedi/inference/gradual/base.py
@@ -37,7 +37,7 @@ class _BoundTypeVarName(AbstractNameDefinition):
         return '<%s %s -> %s>' % (self.__class__.__name__, self.py__name__(), self._value_set)
 
 
-class _TypeVarFilter(object):
+class _TypeVarFilter:
     """
     A filter for all given variables in a class.
 
@@ -246,7 +246,7 @@ class GenericClass(DefineGenericBaseClass, ClassMixin):
         return type_var_dict
 
 
-class _LazyGenericBaseClass(object):
+class _LazyGenericBaseClass:
     def __init__(self, class_value, lazy_base_class, generics_manager):
         self._class_value = class_value
         self._lazy_base_class = lazy_base_class
diff --git a/jedi/inference/gradual/generics.py b/jedi/inference/gradual/generics.py
index 6bd6aa63..f4a5ae9c 100644
--- a/jedi/inference/gradual/generics.py
+++ b/jedi/inference/gradual/generics.py
@@ -23,7 +23,7 @@ def _resolve_forward_references(context, value_set):
             yield value
 
 
-class _AbstractGenericManager(object):
+class _AbstractGenericManager:
     def get_index_and_execute(self, index):
         try:
             return self[index].execute_annotation()
diff --git a/jedi/inference/gradual/typeshed.py b/jedi/inference/gradual/typeshed.py
index e186bfc3..a4b28786 100644
--- a/jedi/inference/gradual/typeshed.py
+++ b/jedi/inference/gradual/typeshed.py
@@ -2,6 +2,7 @@ import os
 import re
 from functools import wraps
 from collections import namedtuple
+from typing import Dict, Mapping, Tuple
 from pathlib import Path
 
 from jedi import settings
@@ -74,7 +75,7 @@ def _get_typeshed_directories(version_info):
             yield PathInfo(str(base_path.joinpath(check_version)), is_third_party)
 
 
-_version_cache = {}
+_version_cache: Dict[Tuple[int, int], Mapping[str, PathInfo]] = {}
 
 
 def _cache_stub_file_map(version_info):
@@ -278,8 +279,8 @@ def _try_to_load_stub_from_file(inference_state, python_value_set, file_io, impo
         return None
     else:
         return create_stub_module(
-            inference_state, python_value_set, stub_module_node, file_io,
-            import_names
+            inference_state, inference_state.latest_grammar, python_value_set,
+            stub_module_node, file_io, import_names
         )
 
 
@@ -293,7 +294,8 @@ def parse_stub_module(inference_state, file_io):
     )
 
 
-def create_stub_module(inference_state, python_value_set, stub_module_node, file_io, import_names):
+def create_stub_module(inference_state, grammar, python_value_set,
+                       stub_module_node, file_io, import_names):
     if import_names == ('typing',):
         module_cls = TypingModuleWrapper
     else:
@@ -305,7 +307,7 @@ def create_stub_module(inference_state, python_value_set, stub_module_node, file
         string_names=import_names,
         # The code was loaded with latest_grammar, so use
         # that.
-        code_lines=get_cached_code_lines(inference_state.latest_grammar, file_io.path),
+        code_lines=get_cached_code_lines(grammar, file_io.path),
         is_package=file_name == '__init__.pyi',
     )
     return stub_module_value
diff --git a/jedi/inference/gradual/utils.py b/jedi/inference/gradual/utils.py
index 83162625..af3703c7 100644
--- a/jedi/inference/gradual/utils.py
+++ b/jedi/inference/gradual/utils.py
@@ -1,10 +1,9 @@
-import os
 from pathlib import Path
 
 from jedi.inference.gradual.typeshed import TYPESHED_PATH, create_stub_module
 
 
-def load_proper_stub_module(inference_state, file_io, import_names, module_node):
+def load_proper_stub_module(inference_state, grammar, file_io, import_names, module_node):
     """
     This function is given a random .pyi file and should return the proper
     module.
@@ -28,7 +27,8 @@ def load_proper_stub_module(inference_state, file_io, import_names, module_node)
         actual_value_set = inference_state.import_module(import_names, prefer_stubs=False)
 
         stub = create_stub_module(
-            inference_state, actual_value_set, module_node, file_io, import_names
+            inference_state, grammar, actual_value_set,
+            module_node, file_io, import_names
         )
         inference_state.stub_module_cache[import_names] = stub
         return stub
diff --git a/jedi/inference/imports.py b/jedi/inference/imports.py
index 8de3fe84..f464b08b 100644
--- a/jedi/inference/imports.py
+++ b/jedi/inference/imports.py
@@ -32,7 +32,7 @@ from jedi.inference.compiled.subprocess.functions import ImplicitNSInfo
 from jedi.plugins import plugin_manager
 
 
-class ModuleCache(object):
+class ModuleCache:
     def __init__(self):
         self._name_cache = {}
 
@@ -150,7 +150,7 @@ def _level_to_base_import_path(project_path, directory, level):
             return None, directory
 
 
-class Importer(object):
+class Importer:
     def __init__(self, inference_state, import_path, module_context, level=0):
         """
         An implementation similar to ``__import__``. Use `follow`
@@ -498,8 +498,8 @@ def load_module_from_path(inference_state, file_io, import_names=None, is_packag
             values = NO_VALUES
 
         return create_stub_module(
-            inference_state, values, parse_stub_module(inference_state, file_io),
-            file_io, import_names
+            inference_state, inference_state.latest_grammar, values,
+            parse_stub_module(inference_state, file_io), file_io, import_names
         )
     else:
         module = _load_python_module(
diff --git a/jedi/inference/lazy_value.py b/jedi/inference/lazy_value.py
index 0ece8690..b149f21e 100644
--- a/jedi/inference/lazy_value.py
+++ b/jedi/inference/lazy_value.py
@@ -2,7 +2,7 @@ from jedi.inference.base_value import ValueSet, NO_VALUES
 from jedi.common import monkeypatch
 
 
-class AbstractLazyValue(object):
+class AbstractLazyValue:
     def __init__(self, data, min=1, max=1):
         self.data = data
         self.min = min
diff --git a/jedi/inference/names.py b/jedi/inference/names.py
index 81161359..2be1427c 100644
--- a/jedi/inference/names.py
+++ b/jedi/inference/names.py
@@ -1,11 +1,13 @@
 from abc import abstractmethod
 from inspect import Parameter
+from typing import Optional, Tuple
 
 from parso.tree import search_ancestor
 
 from jedi.parser_utils import find_statement_documentation, clean_scope_docstring
 from jedi.inference.utils import unite
 from jedi.inference.base_value import ValueSet, NO_VALUES
+from jedi.inference.cache import inference_state_method_cache
 from jedi.inference import docstrings
 from jedi.cache import memoize_method
 from jedi.inference.helpers import deep_ast_copy, infer_call_of_leaf
@@ -23,9 +25,9 @@ def _merge_name_docs(names):
     return doc
 
 
-class AbstractNameDefinition(object):
-    start_pos = None
-    string_name = None
+class AbstractNameDefinition:
+    start_pos: Optional[Tuple[int, int]] = None
+    string_name: str
     parent_context = None
     tree_name = None
     is_value_name = True
@@ -223,7 +225,7 @@ class AbstractTreeName(AbstractNameDefinition):
         return self.tree_name.start_pos
 
 
-class ValueNameMixin(object):
+class ValueNameMixin:
     def infer(self):
         return ValueSet([self._value])
 
@@ -330,6 +332,12 @@ class TreeNameDefinition(AbstractTreeName):
             node = node.parent
         return indexes
 
+    @property
+    def inference_state(self):
+        # Used by the cache function below
+        return self.parent_context.inference_state
+
+    @inference_state_method_cache(default='')
     def py__doc__(self):
         api_type = self.api_type
         if api_type in ('function', 'class'):
@@ -346,7 +354,7 @@ class TreeNameDefinition(AbstractTreeName):
         return ''
 
 
-class _ParamMixin(object):
+class _ParamMixin:
     def maybe_positional_argument(self, include_star=True):
         options = [Parameter.POSITIONAL_ONLY, Parameter.POSITIONAL_OR_KEYWORD]
         if include_star:
@@ -604,7 +612,7 @@ class SubModuleName(ImportName):
     _level = 1
 
 
-class NameWrapper(object):
+class NameWrapper:
     def __init__(self, wrapped_name):
         self._wrapped_name = wrapped_name
 
@@ -615,7 +623,7 @@ class NameWrapper(object):
         return '%s(%s)' % (self.__class__.__name__, self._wrapped_name)
 
 
-class StubNameMixin(object):
+class StubNameMixin:
     def py__doc__(self):
         from jedi.inference.gradual.conversion import convert_names
         # Stubs are not complicated and we can just follow simple statements
diff --git a/jedi/inference/recursion.py b/jedi/inference/recursion.py
index a0897fa8..a2f99c52 100644
--- a/jedi/inference/recursion.py
+++ b/jedi/inference/recursion.py
@@ -50,7 +50,7 @@ A function may not be executed more than this number of times recursively.
 """
 
 
-class RecursionDetector(object):
+class RecursionDetector:
     def __init__(self):
         self.pushed_nodes = []
 
@@ -92,7 +92,7 @@ def execution_recursion_decorator(default=NO_VALUES):
     return decorator
 
 
-class ExecutionRecursionDetector(object):
+class ExecutionRecursionDetector:
     """
     Catches recursions of executions.
     """
diff --git a/jedi/inference/references.py b/jedi/inference/references.py
index e1b97c41..7c77f6f8 100644
--- a/jedi/inference/references.py
+++ b/jedi/inference/references.py
@@ -5,7 +5,8 @@ from parso import python_bytes_to_unicode
 
 from jedi.debug import dbg
 from jedi.file_io import KnownContentFileIO
-from jedi.inference.imports import SubModuleName, load_module_from_path
+from jedi.inference.names import SubModuleName
+from jedi.inference.imports import load_module_from_path
 from jedi.inference.filters import ParserTreeFilter
 from jedi.inference.gradual.conversion import convert_names
 
@@ -203,11 +204,11 @@ def recurse_find_python_folders_and_files(folder_io, except_paths=()):
         # Delete folders that we don't want to iterate over.
         for file_io in file_ios:
             path = file_io.path
-            if path.endswith('.py') or path.endswith('.pyi'):
+            if path.suffix in ('.py', '.pyi'):
                 if path not in except_paths:
                     yield None, file_io
 
-            if path.endswith('.gitignore'):
+            if path.name == '.gitignore':
                 ignored_paths, ignored_names = \
                     gitignored_lines(root_folder_io, file_io)
                 except_paths |= ignored_paths
diff --git a/jedi/inference/signature.py b/jedi/inference/signature.py
index 5f203f79..565a269b 100644
--- a/jedi/inference/signature.py
+++ b/jedi/inference/signature.py
@@ -5,7 +5,7 @@ from jedi import debug
 from jedi import parser_utils
 
 
-class _SignatureMixin(object):
+class _SignatureMixin:
     def to_string(self):
         def param_strings():
             is_positional = False
diff --git a/jedi/inference/syntax_tree.py b/jedi/inference/syntax_tree.py
index fb7743cb..192328f3 100644
--- a/jedi/inference/syntax_tree.py
+++ b/jedi/inference/syntax_tree.py
@@ -287,10 +287,11 @@ def infer_atom(context, atom):
     state = context.inference_state
     if atom.type == 'name':
         # This is the first global lookup.
-        stmt = tree.search_ancestor(
-            atom, 'expr_stmt', 'lambdef'
-        ) or atom
-        if stmt.type == 'lambdef':
+        stmt = tree.search_ancestor(atom, 'expr_stmt', 'lambdef', 'if_stmt') or atom
+        if stmt.type == 'if_stmt':
+            if not any(n.start_pos <= atom.start_pos < n.end_pos for n in stmt.get_test_nodes()):
+                stmt = atom
+        elif stmt.type == 'lambdef':
             stmt = atom
         position = stmt.start_pos
         if _is_annotation_name(atom):
@@ -753,6 +754,8 @@ def tree_name_to_values(inference_state, context, tree_name):
         types = NO_VALUES
     elif typ == 'del_stmt':
         types = NO_VALUES
+    elif typ == 'namedexpr_test':
+        types = infer_node(context, node)
     else:
         raise ValueError("Should not happen. type: %s" % typ)
     return types
diff --git a/jedi/inference/sys_path.py b/jedi/inference/sys_path.py
index b7457e88..e701686f 100644
--- a/jedi/inference/sys_path.py
+++ b/jedi/inference/sys_path.py
@@ -14,8 +14,8 @@ from jedi import debug
 _BUILDOUT_PATH_INSERTION_LIMIT = 10
 
 
-def _abs_path(module_context, path: str):
-    path = Path(path)
+def _abs_path(module_context, str_path: str):
+    path = Path(str_path)
     if path.is_absolute():
         return path
 
@@ -164,15 +164,18 @@ def _get_paths_from_buildout_script(inference_state, buildout_script_path):
         inference_state, module_node,
         file_io=file_io,
         string_names=None,
-        code_lines=get_cached_code_lines(inference_state.grammar, str(buildout_script_path)),
+        code_lines=get_cached_code_lines(inference_state.grammar, buildout_script_path),
     ).as_context()
     yield from check_sys_path_modifications(module_context)
 
 
 def _get_parent_dir_with_file(path: Path, filename):
     for parent in path.parents:
-        if parent.joinpath(filename).is_file():
-            return parent
+        try:
+            if parent.joinpath(filename).is_file():
+                return parent
+        except OSError:
+            continue
     return None
 
 
diff --git a/jedi/inference/utils.py b/jedi/inference/utils.py
index e4c66537..ab10bcd9 100644
--- a/jedi/inference/utils.py
+++ b/jedi/inference/utils.py
@@ -70,7 +70,7 @@ def reraise_uncaught(func):
     return wrapper
 
 
-class PushBackIterator(object):
+class PushBackIterator:
     def __init__(self, iterator):
         self.pushes = []
         self.iterator = iterator
diff --git a/jedi/inference/value/__init__.py b/jedi/inference/value/__init__.py
index 2e17ba26..62164215 100644
--- a/jedi/inference/value/__init__.py
+++ b/jedi/inference/value/__init__.py
@@ -1,3 +1,6 @@
+# Re-export symbols for wider use. We configure mypy and flake8 to be aware that
+# this file does this.
+
 from jedi.inference.value.module import ModuleValue
 from jedi.inference.value.klass import ClassValue
 from jedi.inference.value.function import FunctionValue, \
diff --git a/jedi/inference/value/function.py b/jedi/inference/value/function.py
index 967ee6c0..2471a065 100644
--- a/jedi/inference/value/function.py
+++ b/jedi/inference/value/function.py
@@ -53,7 +53,7 @@ class FunctionAndClassBase(TreeValue):
             return None
 
 
-class FunctionMixin(object):
+class FunctionMixin:
     api_type = 'function'
 
     def get_filters(self, origin_scope=None):
diff --git a/jedi/inference/value/instance.py b/jedi/inference/value/instance.py
index 153ab4f4..c2c20359 100644
--- a/jedi/inference/value/instance.py
+++ b/jedi/inference/value/instance.py
@@ -1,6 +1,6 @@
 from abc import abstractproperty
 
-from parso.python.tree import search_ancestor
+from parso.tree import search_ancestor
 
 from jedi import debug
 from jedi import settings
@@ -401,21 +401,10 @@ class AnonymousInstance(_BaseTreeInstance):
     _arguments = None
 
 
-class CompiledInstanceName(compiled.CompiledName):
-    def __init__(self, inference_state, instance, klass, name):
-        parent_value = klass.parent_context.get_value()
-        assert parent_value is not None, "How? Please reproduce and report"
-        super().__init__(
-            inference_state,
-            parent_value,
-            name.string_name
-        )
-        self._instance = instance
-        self._class_member_name = name
-
+class CompiledInstanceName(NameWrapper):
     @iterator_to_value_set
     def infer(self):
-        for result_value in self._class_member_name.infer():
+        for result_value in self._wrapped_name.infer():
             if result_value.api_type == 'function':
                 yield CompiledBoundMethod(result_value)
             else:
@@ -434,11 +423,7 @@ class CompiledInstanceClassFilter(AbstractFilter):
         return self._convert(self._class_filter.values())
 
     def _convert(self, names):
-        klass = self._class_filter.compiled_value
-        return [
-            CompiledInstanceName(self._instance.inference_state, self._instance, klass, n)
-            for n in names
-        ]
+        return [CompiledInstanceName(n) for n in names]
 
 
 class BoundMethod(FunctionMixin, ValueWrapper):
@@ -516,6 +501,18 @@ class SelfName(TreeNameDefinition):
     def get_defining_qualified_value(self):
         return self._instance
 
+    def infer(self):
+        stmt = search_ancestor(self.tree_name, 'expr_stmt')
+        if stmt is not None:
+            if stmt.children[1].type == "annassign":
+                from jedi.inference.gradual.annotation import infer_annotation
+                values = infer_annotation(
+                    self.parent_context, stmt.children[1].children[1]
+                ).execute_annotation()
+                if values:
+                    return values
+        return super().infer()
+
 
 class LazyInstanceClassName(NameWrapper):
     def __init__(self, instance, class_member_name):
diff --git a/jedi/inference/value/iterable.py b/jedi/inference/value/iterable.py
index 18611a56..2f970fe8 100644
--- a/jedi/inference/value/iterable.py
+++ b/jedi/inference/value/iterable.py
@@ -19,7 +19,7 @@ from jedi.inference.context import CompForContext
 from jedi.inference.value.dynamic_arrays import check_array_additions
 
 
-class IterableMixin(object):
+class IterableMixin:
     def py__next__(self, contextualized_node=None):
         return self.py__iter__(contextualized_node)
 
@@ -127,7 +127,7 @@ def comprehension_from_atom(inference_state, value, atom):
     )
 
 
-class ComprehensionMixin(object):
+class ComprehensionMixin:
     @inference_state_method_cache()
     def _get_comp_for_context(self, parent_context, comp_for):
         return CompForContext(parent_context, comp_for)
@@ -175,7 +175,7 @@ class ComprehensionMixin(object):
         return "<%s of %s>" % (type(self).__name__, self._sync_comp_for_node)
 
 
-class _DictMixin(object):
+class _DictMixin:
     def _get_generics(self):
         return tuple(c_set.py__class__() for c_set in self.get_mapping_item_values())
 
@@ -247,7 +247,7 @@ class GeneratorComprehension(_BaseComprehension, GeneratorBase):
     pass
 
 
-class _DictKeyMixin(object):
+class _DictKeyMixin:
     # TODO merge with _DictMixin?
     def get_mapping_item_values(self):
         return self._dict_keys(), self._dict_values()
diff --git a/jedi/inference/value/klass.py b/jedi/inference/value/klass.py
index 79d070ba..0135624a 100644
--- a/jedi/inference/value/klass.py
+++ b/jedi/inference/value/klass.py
@@ -142,7 +142,7 @@ class ClassFilter(ParserTreeFilter):
         return [name for name in names if self._access_possible(name)]
 
 
-class ClassMixin(object):
+class ClassMixin:
     def is_class(self):
         return True
 
diff --git a/jedi/inference/value/module.py b/jedi/inference/value/module.py
index 4de1e621..a5073b0e 100644
--- a/jedi/inference/value/module.py
+++ b/jedi/inference/value/module.py
@@ -1,5 +1,6 @@
 import os
 from pathlib import Path
+from typing import Optional
 
 from jedi.inference.cache import inference_state_method_cache
 from jedi.inference.names import AbstractNameDefinition, ModuleName
@@ -33,7 +34,7 @@ class _ModuleAttributeName(AbstractNameDefinition):
         return compiled.get_string_value_set(self.parent_context.inference_state)
 
 
-class SubModuleDictMixin(object):
+class SubModuleDictMixin:
     @inference_state_method_cache()
     def sub_modules_dict(self):
         """
@@ -79,7 +80,7 @@ class ModuleMixin(SubModuleDictMixin):
     def is_stub(self):
         return False
 
-    @property
+    @property  # type: ignore[misc]
     @inference_state_method_cache()
     def name(self):
         return self._module_name_class(self, self.string_names[-1])
@@ -145,7 +146,7 @@ class ModuleValue(ModuleMixin, TreeValue):
         )
         self.file_io = file_io
         if file_io is None:
-            self._path = None
+            self._path: Optional[Path] = None
         else:
             self._path = Path(file_io.path)
         self.string_names = string_names  # Optional[Tuple[str, ...]]
@@ -165,7 +166,7 @@ class ModuleValue(ModuleMixin, TreeValue):
             return None
         return '.'.join(self.string_names)
 
-    def py__file__(self) -> Path:
+    def py__file__(self) -> Optional[Path]:
         """
         In contrast to Python's __file__ can be None.
         """
diff --git a/jedi/inference/value/namespace.py b/jedi/inference/value/namespace.py
index 0ea9ecf4..fe629a07 100644
--- a/jedi/inference/value/namespace.py
+++ b/jedi/inference/value/namespace.py
@@ -38,7 +38,7 @@ class ImplicitNamespaceValue(Value, SubModuleDictMixin):
     def get_qualified_names(self):
         return ()
 
-    @property
+    @property  # type: ignore[misc]
     @inference_state_method_cache()
     def name(self):
         string_name = self.py__package__()[-1]
diff --git a/jedi/parser_utils.py b/jedi/parser_utils.py
index 81c8391e..9c1290be 100644
--- a/jedi/parser_utils.py
+++ b/jedi/parser_utils.py
@@ -90,7 +90,7 @@ def get_flow_branch_keyword(flow_node, node):
         first_leaf = child.get_first_leaf()
         if first_leaf in _FLOW_KEYWORDS:
             keyword = first_leaf
-    return 0
+    return None
 
 
 def clean_scope_docstring(scope_node):
@@ -239,7 +239,7 @@ def get_parent_scope(node, include_flows=False):
         return None  # It's a module already.
 
     while True:
-        if is_scope(scope) or include_flows and isinstance(scope, tree.Flow):
+        if is_scope(scope):
             if scope.type in ('classdef', 'funcdef', 'lambdef'):
                 index = scope.children.index(':')
                 if scope.children[index].start_pos >= node.start_pos:
@@ -251,6 +251,14 @@ def get_parent_scope(node, include_flows=False):
                         scope = scope.parent
                         continue
             return scope
+        elif include_flows and isinstance(scope, tree.Flow):
+            # The cursor might be on `if foo`, so the parent scope will not be
+            # the if, but the parent of the if.
+            if not (scope.type == 'if_stmt'
+                    and any(n.start_pos <= node.start_pos < n.end_pos
+                            for n in scope.get_test_nodes())):
+                return scope
+
         scope = scope.parent
 
 
diff --git a/jedi/plugins/__init__.py b/jedi/plugins/__init__.py
index 23588bd4..8067676d 100644
--- a/jedi/plugins/__init__.py
+++ b/jedi/plugins/__init__.py
@@ -1,7 +1,7 @@
 from functools import wraps
 
 
-class _PluginManager(object):
+class _PluginManager:
     def __init__(self):
         self._registered_plugins = []
         self._cached_base_callbacks = {}
diff --git a/jedi/plugins/pytest.py b/jedi/plugins/pytest.py
index 432385e3..cec23733 100644
--- a/jedi/plugins/pytest.py
+++ b/jedi/plugins/pytest.py
@@ -1,6 +1,6 @@
 from pathlib import Path
 
-from parso.python.tree import search_ancestor
+from parso.tree import search_ancestor
 from jedi.inference.cache import inference_state_method_cache
 from jedi.inference.imports import load_module_from_path
 from jedi.inference.filters import ParserTreeFilter
diff --git a/jedi/plugins/stdlib.py b/jedi/plugins/stdlib.py
index d9733dff..17f1df3b 100644
--- a/jedi/plugins/stdlib.py
+++ b/jedi/plugins/stdlib.py
@@ -257,7 +257,7 @@ class ReversedObject(AttributeOverwrite):
         super().__init__(reversed_obj)
         self._iter_list = iter_list
 
-    def py__iter__(self, contextualized_node):
+    def py__iter__(self, contextualized_node=None):
         return self._iter_list
 
     @publish_method('__next__')
@@ -819,7 +819,8 @@ def get_metaclass_filters(func):
                     and metaclass.get_root_context().py__name__() == 'enum':
                 filter_ = ParserTreeFilter(parent_context=cls.as_context())
                 return [DictFilter({
-                    name.string_name: EnumInstance(cls, name).name for name in filter_.values()
+                    name.string_name: EnumInstance(cls, name).name
+                    for name in filter_.values()
                 })]
         return func(cls, metaclasses, is_instance)
     return wrapper
@@ -837,6 +838,14 @@ class EnumInstance(LazyValueWrapper):
         return ValueName(self, self._name.tree_name)
 
     def _get_wrapped_value(self):
+        n = self._name.string_name
+        if n.startswith('__') and n.endswith('__') or self._name.api_type == 'function':
+            inferred = self._name.infer()
+            if inferred:
+                return next(iter(inferred))
+            o, = self.inference_state.builtins_module.py__getattribute__('object')
+            return o
+
         value, = self._cls.execute_with_values()
         return value
 
diff --git a/jedi/settings.py b/jedi/settings.py
index 6764a3e5..c31a474a 100644
--- a/jedi/settings.py
+++ b/jedi/settings.py
@@ -69,8 +69,11 @@ Adds an opening bracket after a function for completions.
 # ----------------
 
 if platform.system().lower() == 'windows':
-    _cache_directory = os.path.join(os.getenv('LOCALAPPDATA') or 
-                                    os.path.expanduser('~'), 'Jedi', 'Jedi')
+    _cache_directory = os.path.join(
+        os.getenv('LOCALAPPDATA') or os.path.expanduser('~'),
+        'Jedi',
+        'Jedi',
+    )
 elif platform.system().lower() == 'darwin':
     _cache_directory = os.path.join('~', 'Library', 'Caches', 'Jedi')
 else:
@@ -98,7 +101,7 @@ parse the parts again that have changed, while reusing the rest of the syntax
 tree.
 """
 
-_cropped_file_size = 10e6  # 1 Megabyte
+_cropped_file_size = int(10e6)  # 1 Megabyte
 """
 Jedi gets extremely slow if the file size exceed a few thousand lines.
 To avoid getting stuck completely Jedi crops the file at some point.
diff --git a/jedi/utils.py b/jedi/utils.py
index 631cf473..b7e1c1a8 100644
--- a/jedi/utils.py
+++ b/jedi/utils.py
@@ -2,7 +2,7 @@
 Utilities for end-users.
 """
 
-import __main__
+import __main__  # type: ignore[import]
 from collections import namedtuple
 import logging
 import traceback
@@ -65,7 +65,7 @@ def setup_readline(namespace_module=__main__, fuzzy=False):
             level=logging.DEBUG
         )
 
-    class JediRL(object):
+    class JediRL:
         def complete(self, text, state):
             """
             This complete stuff is pretty weird, a generator would make
diff --git a/setup.cfg b/setup.cfg
index 39633dc1..98a775aa 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -13,7 +13,42 @@ ignore =
   E721,
   # Line break before binary operator
   W503,
+  # Single letter loop variables are often fine
+  E741,
+per-file-ignores =
+  # Ignore apparently unused imports in files where we're (implicitly)
+  # re-exporting them.
+  jedi/__init__.py:F401
+  jedi/inference/compiled/__init__.py:F401
+  jedi/inference/value/__init__.py:F401
 exclude = jedi/third_party/* .tox/*
 
 [pycodestyle]
 max-line-length = 100
+
+
+[mypy]
+# Ensure generics are explicit about what they are (e.g: `List[str]` rather than
+# just `List`)
+disallow_any_generics = True
+
+disallow_subclassing_any = True
+
+# Avoid creating future gotchas emerging from bad typing
+warn_redundant_casts = True
+warn_unused_ignores = True
+warn_return_any = True
+warn_unused_configs = True
+
+warn_unreachable = True
+
+# Require values to be explicitly re-exported; this makes things easier for
+# Flake8 too and avoids accidentally importing thing from the "wrong" place
+# (which helps avoid circular imports)
+implicit_reexport = False
+
+strict_equality = True
+
+[mypy-jedi,jedi.inference.compiled,jedi.inference.value,parso]
+# Various __init__.py files which contain re-exports we want to implicitly make.
+implicit_reexport = True
diff --git a/setup.py b/setup.py
index 33e24614..1f660a4d 100755
--- a/setup.py
+++ b/setup.py
@@ -32,7 +32,7 @@ setup(name='jedi',
       long_description=readme,
       packages=find_packages(exclude=['test', 'test.*']),
       python_requires='>=3.6',
-      install_requires=['parso>=0.7.0,<0.8.0'],
+      install_requires=['parso>=0.8.0,<0.9.0'],
       extras_require={
           'testing': [
               'pytest<6.0.0',
@@ -43,7 +43,8 @@ setup(name='jedi',
               'Django<3.1',  # For now pin this.
           ],
           'qa': [
-              'flake8==3.7.9',
+              'flake8==3.8.3',
+              'mypy==0.782',
           ],
       },
       package_data={'jedi': ['*.pyi', 'third_party/typeshed/LICENSE',
diff --git a/sith.py b/sith.py
index 3b286894..7736ab8a 100755
--- a/sith.py
+++ b/sith.py
@@ -44,7 +44,7 @@ Options:
   --pudb                Launch pudb when error is raised.
 """
 
-from docopt import docopt
+from docopt import docopt  # type: ignore[import]
 
 import json
 import os
diff --git a/test/completion/named_expression.py b/test/completion/named_expression.py
index 37c835a5..11293b68 100644
--- a/test/completion/named_expression.py
+++ b/test/completion/named_expression.py
@@ -1,3 +1,6 @@
+# For assignment expressions / named expressions / walrus operators / whatever
+# they are called.
+
 # python >= 3.8
 b = (a:=1, a)
 
@@ -11,3 +14,39 @@ b = ('':=1,)
 
 #? int()
 b[0]
+
+def test_assignments():
+    match = ''
+    #? str()
+    match
+    #? 8 int()
+    if match := 1:
+        #? int()
+        match
+    #? int()
+    match
+
+def test_assignments2():
+    class Foo:
+        match = ''
+    #? str()
+    Foo.match
+    #? 13 int()
+    if Foo.match := 1:
+        #? str()
+        Foo.match
+    #? str()
+    Foo.match
+
+    #?
+    y
+    #? 16 str()
+    if y := Foo.match:
+        #? str()
+        y
+    #? str()
+    y
+
+    #? 8 str()
+    if z := Foo.match:
+        pass
diff --git a/test/completion/pep0484_basic.py b/test/completion/pep0484_basic.py
index 54ec8770..e20fe440 100644
--- a/test/completion/pep0484_basic.py
+++ b/test/completion/pep0484_basic.py
@@ -179,3 +179,22 @@ def argskwargs(*args: int, **kwargs: float):
     next(iter(kwargs.keys()))
     #? float()
     kwargs['']
+
+
+class NotCalledClass:
+    def __init__(self, x):
+        self.x: int = x
+        self.y: int = ''
+        #? int()
+        self.x
+        #? int()
+        self.y
+        #? int()
+        self.y
+        self.z: int
+        self.z = ''
+        #? str() int()
+        self.z
+        self.w: float
+        #? float()
+        self.w
diff --git a/test/examples/import-recursion/cadquery_simple/__init__.py b/test/examples/import-recursion/cadquery_simple/__init__.py
new file mode 100644
index 00000000..e87c6632
--- /dev/null
+++ b/test/examples/import-recursion/cadquery_simple/__init__.py
@@ -0,0 +1 @@
+from .cq import selectors
diff --git a/test/examples/import-recursion/cadquery_simple/cq.py b/test/examples/import-recursion/cadquery_simple/cq.py
new file mode 100644
index 00000000..90bb9ac7
--- /dev/null
+++ b/test/examples/import-recursion/cadquery_simple/cq.py
@@ -0,0 +1 @@
+from . import selectors
diff --git a/test/examples/import-recursion/cq_example.py b/test/examples/import-recursion/cq_example.py
new file mode 100644
index 00000000..00a57176
--- /dev/null
+++ b/test/examples/import-recursion/cq_example.py
@@ -0,0 +1,3 @@
+import cadquery_simple as cq
+
+cq.
diff --git a/test/test_api/test_api.py b/test/test_api/test_api.py
index c86be78c..51c0da3b 100644
--- a/test/test_api/test_api.py
+++ b/test/test_api/test_api.py
@@ -15,7 +15,7 @@ from test.helpers import test_dir, get_example_dir
 
 
 def test_preload_modules():
-    def check_loaded(*modules):
+    def check_loaded(*module_names):
         for grammar_cache in cache.parser_cache.values():
             if None in grammar_cache:
                 break
@@ -25,9 +25,9 @@ def test_preload_modules():
             if path is not None and str(path).startswith(str(typeshed.TYPESHED_PATH))
         )
         # +1 for None module (currently used)
-        assert len(grammar_cache) - typeshed_cache_count == len(modules) + 1
-        for i in modules:
-            assert [i in k for k in grammar_cache.keys() if k is not None]
+        assert len(grammar_cache) - typeshed_cache_count == len(module_names) + 1
+        for i in module_names:
+            assert [i in str(k) for k in grammar_cache.keys() if k is not None]
 
     old_cache = cache.parser_cache.copy()
     cache.parser_cache.clear()
@@ -370,3 +370,35 @@ def test_multi_goto(Script):
     y, = script.goto(line=4)
     assert x.line == 1
     assert y.line == 2
+
+
+@pytest.mark.parametrize(
+    'code, column, expected', [
+        ('str() ', 3, 'str'),
+        ('str() ', 4, 'str'),
+        ('str() ', 5, 'str'),
+        ('str() ', 6, None),
+        ('str(    ) ', 6, None),
+        ('   1', 1, None),
+        ('str(1) ', 3, 'str'),
+        ('str(1) ', 4, 'int'),
+        ('str(1) ', 5, 'int'),
+        ('str(1) ', 6, 'str'),
+        ('str(1) ', 7, None),
+        ('str( 1) ', 4, 'str'),
+        ('str( 1) ', 5, 'int'),
+        ('str(+1) ', 4, 'str'),
+        ('str(+1) ', 5, 'int'),
+        ('str(1, 1.) ', 3, 'str'),
+        ('str(1, 1.) ', 4, 'int'),
+        ('str(1, 1.) ', 5, 'int'),
+        ('str(1, 1.) ', 6, None),
+        ('str(1, 1.) ', 7, 'float'),
+    ]
+)
+def test_infer_after_parentheses(Script, code, column, expected):
+    completions = Script(code).infer(column=column)
+    if expected is None:
+        assert completions == []
+    else:
+        assert [c.name for c in completions] == [expected]
diff --git a/test/test_api/test_call_signatures.py b/test/test_api/test_call_signatures.py
index 473edc9d..70631ebd 100644
--- a/test/test_api/test_call_signatures.py
+++ b/test/test_api/test_call_signatures.py
@@ -121,11 +121,8 @@ def test_multiple_signatures(Script):
 
 
 def test_get_signatures_whitespace(Script):
-    s = dedent("""\
-    abs( 
-    def x():
-        pass
-    """)  # noqa
+    # note: trailing space after 'abs'
+    s = 'abs( \ndef x():\n    pass\n'
     assert_signature(Script, s, 'abs', 0, line=1, column=5)
 
 
diff --git a/test/test_api/test_classes.py b/test/test_api/test_classes.py
index 6add83f6..4a6f7323 100644
--- a/test/test_api/test_classes.py
+++ b/test/test_api/test_classes.py
@@ -513,10 +513,14 @@ def test_added_equals_to_params(Script):
 
     assert run('foo(bar').name_with_symbols == 'bar='
     assert run('foo(bar').complete == '='
+    assert run('foo(bar').get_completion_prefix_length() == 3
     assert run('foo(bar, baz').complete == '='
+    assert run('foo(bar, baz').get_completion_prefix_length() == 3
     assert run('    bar').name_with_symbols == 'bar'
     assert run('    bar').complete == ''
+    assert run('    bar').get_completion_prefix_length() == 3
     x = run('foo(bar=isins').name_with_symbols
+    assert run('foo(bar=isins').get_completion_prefix_length() == 5
     assert x == 'isinstance'
 
 
diff --git a/test/test_api/test_interpreter.py b/test/test_api/test_interpreter.py
index 33d33816..4615764e 100644
--- a/test/test_api/test_interpreter.py
+++ b/test/test_api/test_interpreter.py
@@ -621,7 +621,8 @@ def bar():
 
         # typing is available via globals.
         ({'return': 'typing.Union[str, int]'}, ['int', 'str'], ''),
-        ({'return': 'typing.Union["str", int]'}, ['int'], ''),
+        ({'return': 'typing.Union["str", int]'},
+         ['int', 'str'] if sys.version_info >= (3, 9) else ['int'], ''),
         ({'return': 'typing.Union["str", 1]'}, [], ''),
         ({'return': 'typing.Optional[str]'}, ['NoneType', 'str'], ''),
         ({'return': 'typing.Optional[str, int]'}, [], ''),  # Takes only one arg
diff --git a/test/test_api/test_project.py b/test/test_api/test_project.py
index 7ec880ad..9ca4686c 100644
--- a/test/test_api/test_project.py
+++ b/test/test_api/test_project.py
@@ -6,6 +6,7 @@ import pytest
 from ..helpers import get_example_dir, set_cwd, root_dir, test_dir
 from jedi import Interpreter
 from jedi.api import Project, get_default_project
+from jedi.api.project import _is_potential_project, _CONTAINS_POTENTIAL_PROJECT
 
 
 def test_django_default_project(Script):
@@ -17,7 +18,12 @@ def test_django_default_project(Script):
     )
     c, = script.complete()
     assert c.name == "SomeModel"
-    assert script._inference_state.project._django is True
+
+    project = script._inference_state.project
+    assert project._django is True
+    assert project.sys_path is None
+    assert project.smart_sys_path is True
+    assert project.load_unsafe_extensions is False
 
 
 def test_django_default_project_of_file(Script):
@@ -155,3 +161,21 @@ def test_complete_search(Script, string, completions, all_scopes):
     project = Project(test_dir)
     defs = project.complete_search(string, all_scopes=all_scopes)
     assert [d.complete for d in defs] == completions
+
+
+@pytest.mark.parametrize(
+    'path,expected', [
+        (Path(__file__).parents[2], True), # The path of the project
+        (Path(__file__).parents[1], False), # The path of the tests, not a project
+        (Path.home(), None)
+    ]
+)
+def test_is_potential_project(path, expected):
+
+    if expected is None:
+        try:
+            expected = _CONTAINS_POTENTIAL_PROJECT in os.listdir(path)
+        except OSError:
+            expected = False
+
+    assert _is_potential_project(path) == expected
diff --git a/test/test_inference/test_docstring.py b/test/test_inference/test_docstring.py
index 3fc54eb1..62d36683 100644
--- a/test/test_inference/test_docstring.py
+++ b/test/test_inference/test_docstring.py
@@ -206,6 +206,24 @@ def test_numpydoc_parameters_set_of_values():
     assert 'capitalize' in names
     assert 'numerator' in names
 
+@pytest.mark.skipif(numpydoc_unavailable,
+                    reason='numpydoc module is unavailable')
+def test_numpydoc_parameters_set_single_value():
+    """
+    This is found in numpy  masked-array I'm not too sure what this means but should not crash
+    """
+    s = dedent('''
+    def foobar(x, y):
+        """
+        Parameters
+        ----------
+        x : {var}, optional
+        """
+        x.''')
+    names = [c.name for c in jedi.Script(s).complete()]
+    # just don't crash
+    assert names == []
+
 
 @pytest.mark.skipif(numpydoc_unavailable,
                     reason='numpydoc module is unavailable')
diff --git a/test/test_inference/test_gradual/test_conversion.py b/test/test_inference/test_gradual/test_conversion.py
index fd201aee..c77a06b0 100644
--- a/test/test_inference/test_gradual/test_conversion.py
+++ b/test/test_inference/test_gradual/test_conversion.py
@@ -1,4 +1,5 @@
 import os
+from parso.cache import parser_cache
 
 from test.helpers import root_dir
 from jedi.api.project import Project
@@ -64,6 +65,17 @@ def test_goto_import(Script):
     assert not d.is_stub()
 
 
+def test_stub_get_line_code(Script):
+    code = 'from abc import ABC; ABC'
+    script = Script(code)
+    d, = script.goto(only_stubs=True)
+    assert d.get_line_code() == 'class ABC(metaclass=ABCMeta): ...\n'
+    del parser_cache[script._inference_state.latest_grammar._hashed][d.module_path]
+    d, = Script(path=d.module_path).goto(d.line, d.column, only_stubs=True)
+    assert d.is_stub()
+    assert d.get_line_code() == 'class ABC(metaclass=ABCMeta): ...\n'
+
+
 def test_os_stat_result(Script):
     d, = Script('import os; os.stat_result').goto()
     assert d.is_stub()
diff --git a/test/test_inference/test_imports.py b/test/test_inference/test_imports.py
index 32acf093..8e49244f 100644
--- a/test/test_inference/test_imports.py
+++ b/test/test_inference/test_imports.py
@@ -29,13 +29,13 @@ def test_find_module_basic():
 
 def test_find_module_package():
     file_io, is_package = _find_module('json')
-    assert file_io.path.endswith(os.path.join('json', '__init__.py'))
+    assert file_io.path.parts[-2:] == ('json', '__init__.py')
     assert is_package is True
 
 
 def test_find_module_not_package():
     file_io, is_package = _find_module('io')
-    assert file_io.path.endswith('io.py')
+    assert file_io.path.name == 'io.py'
     assert is_package is False
 
 
@@ -55,8 +55,8 @@ def test_find_module_package_zipped(Script, inference_state, environment):
         full_name='pkg'
     )
     assert file_io is not None
-    assert file_io.path.endswith(os.path.join('pkg.zip', 'pkg', '__init__.py'))
-    assert file_io._zip_path.endswith('pkg.zip')
+    assert file_io.path.parts[-3:] == ('pkg.zip', 'pkg', '__init__.py')
+    assert file_io._zip_path.name == 'pkg.zip'
     assert is_package is True
 
 
@@ -108,7 +108,7 @@ def test_find_module_not_package_zipped(Script, inference_state, environment):
         string='not_pkg',
         full_name='not_pkg'
     )
-    assert file_io.path.endswith(os.path.join('not_pkg.zip', 'not_pkg.py'))
+    assert file_io.path.parts[-2:] == ('not_pkg.zip', 'not_pkg.py')
     assert is_package is False
 
 
@@ -468,3 +468,9 @@ def test_relative_import_star(Script):
     script = Script(source, path='export.py')
 
     assert script.complete(3, len("furl.c"))
+
+
+def test_import_recursion(Script):
+    path = get_example_dir('import-recursion', "cq_example.py")
+    for c in Script(path=path).complete(3, 3):
+        c.docstring()
diff --git a/test/test_inference/test_signature.py b/test/test_inference/test_signature.py
index 500759bc..02f119a8 100644
--- a/test/test_inference/test_signature.py
+++ b/test/test_inference/test_signature.py
@@ -340,3 +340,20 @@ def test_overload(Script, code):
     x1, x2 = Script(code, path=os.path.join(dir_, 'foo.py')).get_signatures()
     assert x1.to_string() == 'with_overload(x: int, y: int) -> float'
     assert x2.to_string() == 'with_overload(x: str, y: list) -> float'
+
+
+def test_enum(Script):
+    script = Script('''\
+        from enum import Enum
+
+        class Planet(Enum):
+            MERCURY = (3.303e+23, 2.4397e6)
+            VENUS = (4.869e+24, 6.0518e6)
+
+            def __init__(self, mass, radius):
+                self.mass = mass  # in kilograms
+                self.radius = radius  # in meters
+
+        Planet.MERCURY''')
+    completion, = script.complete()
+    assert not completion.get_signatures()