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Who uses the second meaning?

In my experience, "purely functional" always means "you can express pure functions on the type level" (thus guaranteeing that it is referentially transparent and has no side effects) -- see https://en.wikipedia.org/wiki/Pure_function

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I'm working with Python and I'm sympathetic to the problem so I'd be curious if you have examples of what Python issues are fixed with OCaml.
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A few ways in which Python is not really functional:

The scoping rules of Python are not lexical

Lambdas in Python are not multiline

Recursion is not a practical way to write code due to stack overflows

Monkey patching

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Pure functional doesn't mean no side effects but controlled side effects.
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