On Tue, Apr 14, 2009 at 03:08:05PM -0700, Arthur Chan wrote:
You know, I was wondering... if Monads are a subset of Functors, and Applicative is a subset of Functors, and Monads are a subset of Applicative... shouldn't it be possible to tack on the definitions that automatically derive Functor and Applicative? Isn't it the case that there is really only one way to define Applicative for a Monad anyway? And isn't there only one way to define fmap for a Monad that makes sense?
Actually, it's already possible to do this, in a way. If you have a Monad, then fmap is liftM, pure is return, and (<*>) is ap. So you already have implementations of Functor and Applicative. In fact, I routinely do this: import Text.ParserCombinators.Parsec instance Applicative (GenParser tok st) where pure = return (<*>) = ap There are also various proposals which would help in automating this sort of process, like "class aliases". But in general, having a nicer class hierarchy as Bob suggests would be much better. -Brent