Python Type Hints are Turing Complete.
Grigore showed that Java generics are Turing complete by describing a
reduction from Turing machines to Java subtyping. We apply Grigore’s algorithm
to Python type hints and deduce that they are Turing complete. In addition, we
present an alternative reduction in which the Turing machines are simulated in
real time, resulting in significantly lower compilation times. Our work is
accompanied by a Python implementation of both reductions that compiles Turing
machines into Python subtyping machines.
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