[Haskell-beginners] several questions: multi-param typeclasses, etc.

[Brent Yorgey]

Hi Michael,

On Sun, Nov 01, 2009 at 07:15:17AM -0800, Michael Mossey wrote:
> I'm trying to understand multi-param typeclasses; a particular one
> (MonadError); and functional dependencies.
> 
> For example, throwError in in the MonadError class definition:
> 
> class Monad m => MonadError e m | m -> e where
>     throwError :: e -> m a
>
> In a sense, there is no single type that is an instance of MonadError.
> 
> Is this the right way to put it?

I think a better way to put it is that an instance of MonadError is a
PAIR of types, instead of a single type.

>    Error e => MonadError e (Either e)
> 
> The code doesn't give the definition, but I suppose it would be:
> 
>              throwError e = Left e ???

Right. (No pun intended ;)

> Now I'm interested in understanding this functional dependency between
> m and e. For the compiler to decide that a particular instance's
> definition of throwError is available, it  must decide that
> 
>    e is of class Error (it is given by class constraint)
>    m is a Monad (Either e is such)
>    and then this m -> e thing: I don't know how to put this into words

The m -> e thing isn't a constraint that needs to be satisfied; it
gives some extra information to help the compiler with inferring which
instance to use.  In particular, "m -> e" says "the type chosen for m
DETERMINES the type chosen for e"; put another way, "there cannot be
two instances with the same type for m but different types for e".  So
in this case you could not also make an instance

  MonadError String (Either e).

-Brent