Superclass defaults

[Bas van Dijk]

On 29 August 2011 11:11, Aleksey Khudyakov <alexey.skladnoy at gmail.com> wrote:
>> "Option 3 avoids that problem but risks perplexity: if I make use of
>> some cool package which introduces some Foo :: * -> *, I might notice
>> that Foo is a monad and add a Monad Foo instance in my own code,
>> expecting the Applicative Foo instance to be generated in concert; to
>> my horror, I find my code has subtle bugs because the package
>> introduced a different, non-monadic, Applicative Foo instance which
>> I'm accidentally using instead."
>>
>> talks about "subtle bugs". Could you give an example of such a bug?
>>
>> I would expect that the non-monadic Applicative Foo instance is always
>>  somehow "compatible" with the monadic one. However I don't have a
>> clear definition of "compatible" yet...
>>
> I think it's something like that. Module Foo defines list and make
> ZipList-like Applicative instance. Would you add standard list monad
> you have a bug.
>
> But if you add monad instance which is not compatible with existing
> applicative you have bug whether you use extension or not.
>
> module Foo where
> data [a] = a : [a] | []
>
> instance Functor [] where
>  fmap = map
> instamce Applicative [] where
>  pure = repeat
>  (<*>) = zipWith ($)
>
> module Main where
> instance Monad [] where
>  return x = [x]
>  (>>=) = concatMap
>

Indeed. So in other words your saying that if a programmer uses a
module which defines a stream-like list type like for example:

newtype StreamList a = SL { toList :: [a] }

instance Functor StreamList where
    fmap f (SL xs) = SL (map f xs)

instance Applicative StreamList where
    pure x = SL $ repeat x
    SL fs <*> SL xs = SL $ zipWith ($) fs xs

And she decides to add a monad instance like the regular list monad:

instance Monad StreamList where
    return x = SL [x]
    xs >>= f = SL $ concatMap (toList . f) $ toList xs

That would be a mistake on her part since 'ap' would not be equivalent to '<*>'.

The correct monad instance should be something like:

instance Monad StreamList where
    return = pure
    xs >>= f = SL $ join $ fmap (toList . f) $ toList xs
        where
          join :: [[a]] -> [a]
          join []           = []
          join ([]    :xss) =     join (map tail xss)
          join ((x:xs):xss) = x : join (map tail xss)

where 'ap' does equal '<*>' (not tested nor proofed yet though).

I think a good definition of "compatible" would be that forall mf mx.
ap mf mx = mf <*> mx.

So I would still like to see an example where a user defined,
non-monadic '<*>' causes bugs because it's not compatible to the
intrinsic one.

Regards,

Bas