In opposition of Functor as super-class of Monad

[S. Doaitse Swierstra]

There are very good reasons for not following this road; indeed everything which is a Monad can also be made an instance of Applicative. But more often than not we want to have a more specific implementation. Because Applicative is less general, there is in general more that you can do with it.

An analogue is the relation between regular grammars and context-free grammars; indeed, once we have the latter concept we might argue that we do not need the first one any more. But if we know that something is in the first category we can do all kins of nice things which we cannot do with conxet-free grammars, such as constructing a finite state machine for recognising sentences.

You proposal would introduce overlapping instances is such cases where we want to give a ``better'' implementation in case we know we are dealing with the more restricted case.

I have explained this phenomenon for the first time in:


@inproceedings{SwieDupo96,
	Author = {Swierstra, S. D. and Duponcheel, L.},
	Booktitle = {Advanced Functional Programming},
	Date-Added = {2009-01-04 17:21:54 +0100},
	Date-Modified = {2009-01-04 17:21:54 +0100},
	Editor = {Launchbury, John and Meijer, Erik and Sheard, Tim},
	Pages = {184-207},
	Publisher = {Springer-Verlag},
	Series = {LNCS-Tutorial},
	Title = {Deterministic, Error-Correcting Combinator Parsers},
	Urlpdf = {http://www.cs.uu.nl/people/doaitse/Papers/1996/DetErrCorrComPars.pdf},
	Volume = {1129},
	Year = {1996}}

If you look at the uu-parsinglib library you will see that the Applicative instance of the parsers used there is definitely more involved that what you can do with the monadic interface. Your proposal would ruin this library.

Unless we have things like e.g. named instances, the possibility to choose between overlapping instances, etc. I think we should leave things the way they are; the only reason I see for having superclasses is to be able to use functions from those classes in the default implementations of functions in the new class, and to group functionality coming from several classes.

 Doaitse












On Oct 24, 2012, at 10:01 , Petr P <petr.mvd at gmail.com>
 wrote:

>  Hi,
> 
> I was thinking lately about the well known problem that Monad is
> neither Functor nor Applicative. As I understand, it is caused by some
> historical issues. What I like about Haskell is that it allows to
> describe very nicely what different objects actually are - something
> that I find very important for programming. And this issue violates
> this principle.
> 
> This has been discussed here more than year ago in
> http://www.haskell.org/pipermail/haskell-prime/2011-January/003312.html
> :
> 
> On 1/4/11 11:24, oleg at okmij.org wrote:
>> I'd like to argue in opposition of making Functor a super-class of
>> Monad. I would argue that superclass constraints are not the right
>> tool for expressing mathematical relationship such that all monads are
>> functors and applicatives.
>> 
>> Then argument is practical. It seems that making Functor a superclass
>> of Monad makes defining new monad instances more of a chore, leading
>> to code duplication. To me, code duplication is a sign that an
>> abstraction is missing or misused.
>> ...
> 
> The main objections were that it would break existing code and that it
> would lead to code duplication. The former is serious, the second can
> be easily solved by standard Haskell, since one can define
> 
> instance Applicative ... where
>    pure   = return
>    (<*>)  = ap
> instance Functor ... where
>    fmap   = liftM
> 
> To address the first objection:
> AFAIK nobody mentioned the "Default superclass instances" proposal:
> http://hackage.haskell.org/trac/ghc/wiki/DefaultSuperclassInstances
> To give an example how it would work:
> 
>    class Applicative f => Monad f where
>      (>>=) :: f a -> (a -> f b) -> f b
>      ...
>      instance Applicative f where
>        ff <*> fs = ff >>= \ f -> fs >>= \ s -> return (f s)
>        ...
> 
> This says that if somebody defines an instance of Monad it
> automatically becomes an instance of Applicative as defined in the
> nested "instance" block. So there is no need to define
> Applicative/Functor explicitly, making existing code work.
> 
> Implementing this proposal would allow making Monad to extend Functor
> and Applicative without breaking existing code. Moreover, this would
> simplify other things, for example it would be possible to define an
> instance of Traversable and the instances for Functor and Foldable
> would be defined implicitly using fmapDefault and foldMapDefault. I'm
> sure there are many other cases where splitting type classes into a
> more fine-grained hierarchy would be beneficial, and the main reason
> against it is simply not to break compatibility with existing code.
> 
> IMHO this would be worthwhile to consider for some future revision of Haskell.
> 
>  Best regards,
>  Petr Pudlak
> 
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