Add rudimentary mypy type checking

Add a very lax mypy configuration, add it to tox -e linting, and
fix/ignore the few errors that come up. The idea is to get it running
before diving in too much.

This enables:

- Progressively adding type annotations and enabling more strict
  options, which will improve the codebase (IMO).

- Annotating the public API in-line, and eventually exposing it to
  library users who use type checkers (with a py.typed file).

Though, none of this is done yet.

Refs https://github.com/pytest-dev/pytest/issues/3342.

.pre-commit-config.yaml

@@ -28,6 +28,7 @@ repos:
     hooks:
     -   id: flake8
         language_version: python3
+        additional_dependencies: [flake8-typing-imports]
 -   repo: https://github.com/asottile/reorder_python_imports
     rev: v1.4.0
     hooks:
@@ -42,6 +43,17 @@ repos:
     rev: v1.4.0
     hooks:
     -   id: rst-backticks
+-   repo: https://github.com/pre-commit/mirrors-mypy
+    rev: v0.711
+    hooks:
+    -   id: mypy
+        name: mypy (src)
+        files: ^src/
+        args: []
+    -   id: mypy
+        name: mypy (testing)
+        files: ^testing/
+        args: []
 -   repo: local
     hooks:
     -   id: rst