[Haskell-beginners] Re: Thinking about monads (Brent Yorgey)

[Brent Yorgey]

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