transformers: remove instance MonadFix ExceptT and ErrorT

[Ross Paterson]

On Tue, Aug 12, 2014 at 08:02:13PM -0400, David Feuer wrote:
> On Aug 12, 2014 7:50 PM, "Bertram Felgenhauer" <
> bertram.felgenhauer at googlemail.com> wrote:
> > I tend to agree that those MonadFix instances are not immensely useful.
> 
> From my perspective as a generally ignorant person, I think these should be
> kept as long as
> 
> 1. They satisfy the required laws and
> 2. No more useful instances can be written.
> 
> That said, it might make sense to remove them if
> 
> 1*. You can formulate a new law that distinguishes the instances you consider
> sensible from the ones you consider insensible.

There is a law that discriminates against the instances on strict monads,
known as right shrinking or right tightening:

	mfix (\ (x,_) -> f x >>= rightM g)  =  mfix f >>= rightM g

where

	rightM :: Monad m => (a -> m b) -> a -> m (a, b)
	rightM f x = f x >>= \ y -> return (x, y)

A special case is

	mfix (const e) = e

In do-notation, these become

	do {rec {ss; x <- e}; ss'}  =  do {rec {ss}; x <- e; ss'}
		(x not free in ss or e)

	do {rec {x <- e}; ss}  =  do {x <- e; ss}
		(x not free in e)

This law is pretty handy, but it was deliberately omitted from the axioms
for the MonadFix class, to permit the axioms for Maybe, Either, [] and IO.
The transformers package is just following those.