All Monads are Functors

[Jon Fairbairn]

On 2006-08-14 at 12:03+0400 Bulat Ziganshin wrote:
> Hello Taral,
> 
> Monday, August 14, 2006, 9:02:58 AM, you wrote:
> 
> > In my opinion, an instance definition of a subclass should allow the
> > superclass's methods to be defined as if they were part of the
> > subclass, e.g.:
> 
> > instance Monad [] where
> >     fmap = map
> >     return x = [x]
> >     join = concat
> 
> i support this idea. [...]

I'm not sure it's quite right. Surely it only makes sense if
it defines all the (necessary) superclass methods -- in
other words, what you are doing is defining an instance,
just omitting the "instance Functor []" line, which doesn't
seem like a great advantage. If we are going to play around
with this stuff, here's another suggestion that solves my
original problem more neatly:

In a class declaration, a superclass context is a
requirement that instances of the class have instances of
the superclass; this is similar to the type declarations of
the methods. We could have had

class Monad m where
      instance Functor m
      (>>=):: ...

instead of

class Functor m => Monad m where
      (>>=):: ...

of course, there's no reason to do that, but what I'm
proposing is that we allow default instance declarations in
class declarations in much the same way as default methods:

> class Functor m => Monad m where
>	(>>=):: ...
>       return:: ...
>	join:: ...
>	instance Functor m where
>		 fmap f =  (>>= return . f)

This shouldn't be hard to implement: all the compiler has to
do when reading an instance declaration for Monad is to
generate an instance declaration for Functor, substituting
the espression for m that comes from the instance
declaration for Monad.

I don't know whether there's anything to be gained by adding
the option of overriding the default inside an instance
declaration:

> instance Monad [] where
>     return x = [x]
>     join = concat
>     instance Functor [] where
>	       fmap = map


but clearly a top-level instance declaration would override
the default anyway.



-- 
Jón Fairbairn                              Jon.Fairbairn at cl.cam.ac.uk