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In 1992 in the paper Imperative Functional Programming, Simon Peyton Jones and Philip Wadler write:

So monads are more powerful than continuations, but only because of the types! It is not clear whether this is only an artifact of the Hindley-Milner type system, or whether the types are revealing a difference of fundamental importance (our own intuition it's the latter -- but it's only an intuition.)

There seems to be a lack of evidence for the Hindley-Milner side of the question. (Perhaps there is an interesting paper in this as well).

My question is: Are the types that show monads are more powerful than continuations revealing something of fundamental importance? (ie are there some papers that have addressed this since 1992).

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