[Haskell-cafe] Existential quantification of environments.
k.schupke at imperial.ac.uk
Tue Nov 22 11:19:27 EST 2005
Wolfgang Jeltsch wrote:
>>This seems to suggest:
>> Add a == exists (add :: a -> a -> a)
>Doesn't "exists" normally quantify over types and not over values?
It is quantifying over types, it is saying there exists a type "a -> a
-> a" that has
at least one value we will call "add"...
I think the important point is that the existential is a pair of (proof,
which through curry-howard-isomorphism is (value in set, set). Here we
are saying that
there is a set of "functions" with the type "a -> a -> a" ... for the
existential to be satisfied
there must be one called "add". Consider this as an assumption placed on
by the function.
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