PyPy is written in RPython, which is Python with type annotations strict enough to allow hard precompilation to C. The type syntax is completely different from this new thing.[1] Only the built-in types are fully defined. There's "anytype", "sequence", and "object" to cover more general types without giving full details. This allows hard compilation of the stuff that compiles down to machine code, while dealing with user-defined object types more dynamically. That's one approach to typing Python.

Von Rossum on PyPy (2016): "Otherwise, there are specialized versions of Python like PyPy that are still around."

[1] https://bitbucket.org/pypy/pypy/src/default/rpython/translat...