Re: [Haskell-cafe] Data structure containing elements which are instances of the same type class

On Aug 15, 2012 3:21 AM, "wren ng thornton" wrote:

It's even easier than that.

(forall a. P(a)) -> Q <=> exists a. (P(a) -> Q)

Where P and Q are metatheoretic/schematic variables. This is just the usual thing about antecedents being in a "negative" position, and thus flipping as you move into/out of that position.

Most of this conversation is going over my head. I can certainly see how exists a. (P(a)->Q) implies that (forall a. P(a))->Q. The opposite certainly doesn't hold in classical logic. What sort of logic are you folks working in?