In analysis, functions are usually taken to be an algebra over the
reals (or C). This tempted me to define the following:
module FunctionAlgebra where
instance Num b => Num (a -> b) where
f + g = \x -> (f x) + (g x)
f - g = \x -> (f x) - (g x)
f * g = \x -> (f x) * (g x)
negate f = negate . f
abs f = abs . f
signum f = signum . f
fromInt i = \x -> fromInt i
fromInteger i = \x -> fromInteger i
Of course, this fails as class Num requires its members to be of
observable type (instances of Eq, Show). I think it's something
interesting which Haskell's type system is apparently capable of
expressing, even though the prelude types conflict with it. Maybe
someone will find it interesting enough to include support for it
in the Prelude. Of course, Open Source means if you think something
should happen, you can make it happen for yourself. =)
Bill
P.S.: How does one contribute binaries to the binary distribution
archive?
