All Monads are Functors

[Jon Fairbairn]

On 2006-08-25 at 19:09PDT Ashley Yakeley wrote:
> Jon Fairbairn wrote:
> 
>  > There has been discussion in the past about whether Monad
>  > should be defined as
>  >
>  >> class Functor m => Monad m where ...
> 
> It's more complicated now that we have Ross Patterson's "Applicative".
> 
> http://haskell.org/ghc/dist/current/docs/libraries/base/Control-Applicative.html

FSVO "complicated"... it looks like a Good Thing to me,
although I don't like the names much. [It would be nice if
there were a bit more commentary in the Haddock -- referring
to a paper is fine, but in day to day programming a scan
through several modules to find what one wants is hampered
by having to step out to read the papers.]

> The correct decl I think is this:
> 
>    class Applicative m => Monad m where
>      -- remove "return"
>      ...
> 
> and changing the names of the Applicative functions:
> 
>    class Functor f => Applicative f where
>      return :: a -> f a
>      ap :: f (a -> b) -> f a -> f b

Better, I think, and though I can see a case for using
“unit” instead of return (as it's more neutral; “return (+1)
<*> [1..10]” looks a bit odd) using “return” would be less
of a shock to the system.

> This would mean moving Applicative into the Prelude.

Good, though I'm still very much in favour of moving as much
out of the Prelude as possible.

> I think "joining up the classes" is a good idea,

Definitely -- as is slicing them into finer layers (of which
this is also an example).
-- 
Jón Fairbairn                              Jon.Fairbairn at cl.cam.ac.uk