Hello, A professor of mine was recently playing around during a lecture with Church booleans (I.e., true = \x y -> x; false = \x y -> y) in Scala and OCaml. I missed what he did, so I reworked it in Haskell and got this:
type CB a = a -> a -> a
ct :: CB aC ct x y = x
cf :: CB a cf x y = y
cand :: CB (CB a) -> CB a -> CB a cand p q = p q cf
cor :: CB (CB a) -> CB a -> CB a cor p q = p ct q
I found the lack of type symmetry (the fact that the predicate arguments don't have the same time) somewhat disturbing, so I tried to find a way to fix it. I remembered reading about existential types being used for similar type-hackery, so I added quantification to the CB type and got
type CB a = forall a . a -> a -> a
ctrue :: CB a ctrue x y = x
cfalse :: CB a cfalse x y = y
cand :: CB a -> CB a -> CB a cand p q = p q cfalse
cor :: CB a -> CB a -> CB a cor p q = p ctrue q
which works. But I haven't the faintest idea why that "forall" in the type makes things work... I just don't fully understand existential type quantification. Could anyone explain to me what's going on that makes the second code work? Thanks, Cory