Am Montag, 16. Februar 2009 19:22 schrieb Wolfgang Jeltsch:
Am Montag, 16. Februar 2009 19:04 schrieb Kim-Ee Yeoh:
Despite its rank-2 type, runST really doesn't have anything to do with existential quantification.
First, I thought so too but I changed my mind. To my knowledge a type (forall a. T[a]) -> T' is equivalent to the type exists a. (T[a] -> T'). It’s the same as in predicate logic – Curry-Howard in action.
Oops, this is probably not true. The statement holds for classical predicate logic with only non-empty domains. But in constructivist logic only the first of the above statements follows from the second, not the other way round. So arguing with the Curry-Howard isomorphism fails and indeed, the two types are not equivalent. There is just a function from the second to the first (it’s the function application function ($) actually). Best wishes, Wolfgang