For example,
class BasicTransitionFunction(TransitionFunction[GrammarBasedState]):
...
where TransitionFunction is the base class of BasicTransitionFunction, and GrammarBasedState is also a class name. I only know that [] can be used to indexed arrays. What does it mean here?
This is the syntax for generic types. Like @Sraw said, it means that TransitionFunction is a generic type. For example, List is a generic type, so you can have List[Int].
This is the same idea as for C++ templates (e.g. std::vector<int>).
So here BasicTransitionFunction is a subclass of a TransitionFunction between GrammarBasedStates.
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