ExceptT vs. EitherT

[Henning Thielemann]

Am 13.08.2013 23:09, schrieb David Luposchainsky:
> On 2013-08-13 22:57, Gabriel Gonzalez wrote:
>> I don't really see the value in `Except` either, but it's there to
>> satisfy Ross who wants an `Identity`-specialized version of the monad
>> transformer.
>
> I think at this rate, we're running out of terms for "crashing" pretty
> soon. Exception vs. error is bad enough, and now some want to add Except
> to that list.
>
> On the other hand, EitherT already exists in a current and used library,
> it is very clear what that transformer does, and it goes hand in hand
> with MaybeT.
>
> Furthermore I think Hennings objections are not very convincing:

In all cases I listed you can define an instance that is mathematically 
sound, that is, it fulfills some nice laws. But from the view of a 
programmer, I want additionally safety. I want that programs are 
rejected that are "obviously" wrong.

Returning to "Either": You can define a monad instance on it that 
fulfills all monad laws, i.e. it is mathematically sound. This instance 
already exist. But for me Either is just a plain set sum, a union type. 
I may use it for lists that may contain two types of elements. I may use 
it for constructing larger sum types without the need to define a new 
'data'. This is for example useful in GHCi. But then - why should this 
type also be a monad, where the Left and Right are handled very 
differently? When I want to have the exception semantics I prefer to 
make that explicit using the Except type. (Currently I use my own 
Exceptional type for that purpose.)

My general concern is that the discussion is focussed on whether an 
instance fulfills mathematical laws, but not on software engineering 
aspects. Although some types are structurally equivalent (Either and 
Except, pair and Writer, function and Reader monad), they have very 
different uses. If I want to combine two types in one, I want to express 
this by Either. If I want exception handling, I want to express this by 
Except. Either should not have a monad instance, and Except should not 
have a function like partitionEithers.

A strength of Haskell's type system is safety. Safety means that certain 
things are forbidden. In contrast to that, a discussion focussed on 
fulfilling mathematical laws tends to allow as much as possible. On the 
one hand we encourage people to artificially make types distinct by 
newtype wrapping. E.g. we define newtype Id = Id Int, in order to forbid 
arithmetic operations that are useless for Id's. On the other hand we 
throw together many applications to a single type by defining more and 
more instances for base types and base classes. In the long run we end 
up with MATLAB semantics: They put so much applications into one type 
(complex valued tensors used for bools, reals, complex numbers, 
polynomials, matrices, graphs etc.) that you better not touch a working 
program, if you want to keep it running.

That said, instance Monad Either and instance Monad (->) already exist. 
We cannot remove them easily, because may people rely on them. However, 
we can discourage their use and propose the clean way via types from the 
transformers package. Then the exception handling monad in 
'transformers' should not have a name that resembles "Either", because 
its use is very different from a plain union type. For me "Exept" is a 
good choice, because the intended application is exception handling.


> - Monad for pairs duplicates Writer, which is existing functionality but
> without the newtype wrapper safety. There is no equivalent for this with
> Either.

In transformer the Writer monad could also have been defined as

   data Writer w a = Writer a w

and vice versa the Except monad could be defined by

   newtype Except e a = Except (Either e a)

I don't think there is a substantial difference. I order to be 
consistent with the current style of type definitions in 'transformers', 
I think the definition will be:

   newtype ExceptT e m a = ExceptT (m (Either e a))
   type Except = ExceptT e Identity a


> - Num for functions - I have yet to see an example where that is
> beneficial beyond "funny how that works".

I guess that people liked to write sin+cos or 2*exp. If not, there must 
be enough other reasons to publish
   http://hackage.haskell.org/package/NumInstances