On Tue, Jun 1, 2010 at 12:40 PM, Cory Knapp <cory.m.kn...@gmail.com> wrote:
> Thanks! That was exactly the sort of response I was looking for. > > This explains why you need to double up for your current definitions. To >> choose between two booleans (which will in turn allow you to choose >> between >> 'a's), you need a CB (CB a). You can eliminate the asymmetric type, >> though, >> like so: >> >> cand :: CB a -> CB a -> CB a >> cand p q t f = p (q t f) f >> >> Right. When he was working on it, I thought of that, and seemed to have > completely forgotten when I reworked it. > > >> You can probably always do this, but it will become more tedious the more >> complex your functions get. >> >> > >type CB a = forall a . a -> a -> a >> >> Note: this is universal quantification, not existential. >> >> As I would assume. But I always see the "forall" keyword used when > discussing "existential quantification". I don't know if I've ever seen an > "exists" keyword. Is there one? How would it be used? > There is no exists keyword, in GHC at least. See for example this page: http://www.haskell.org/ghc/docs/6.12.2/html/users_guide/data-type-extensions.html When the forall appears in certain places it behaves differently. For example: * In a function signature it is universal, but where it appears matters. Putting it on the left side of function arrows increases the rank of the type. This leads to Rank N types. * In the case of data constructors it can behave as existential quantification when it introduces a type variable on the right-hand side of the equal sign in the data declaration. At least, that's my understanding. Also, haskell prime has a proposal for an exists keyword: http://hackage.haskell.org/trac/haskell-prime/wiki/ExistentialQuantification Jason
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