ApplicativeZip

[Oleg Grenrus]

After thinking for a while (and looking onto MonadZip [] instance), I realised that:
`MonadZip []` is the same as `Applicative ZIpList`, not `Applicative []`

I guess that answers my question.

Also Information preservation law:
    liftM (const ()) ma = liftM (const ()) mb
excludes the default implementation of munzip for non-deterministic computations, as the information is “multiplied".

The naturality law follows from Applicative laws.

—

After some thinking (and re-reading the "Monadic zipping (used for monad comprehensions)” comment in the documentation), this is obvious. But I’ll try to make a documentation improvement patch, so no-one have to wonder this that much again.

- Oleg

> On 06 Mar 2015, at 10:30, David Feuer <david.feuer at gmail.com> wrote:
> 
> It was already discussed, I think,  but I don't remember the conclusion!
> 
> On Mar 6, 2015 3:27 AM, "Oleg Grenrus" <oleg.grenrus at iki.fi> wrote:
> After Edward Kmett mentioned that we should add MonadZip to Data.Monoid instances, that got me thinking about:
> 
> Why we don’t have ApplicativeZip?
> 
> class Applicative f => ApplicativeZip f where
>         {-# MINIMAL azip | azipWith #-}
>     azip :: m a -> m b -> m (a,b)
>     azip = azipWith (,)
> 
>     -- This is `liftA2` but can be done more efficiently for some instances (is it true?)
>     azipWith :: (a -> b -> c) -> m a -> m b -> m c
>     azipWith f = azip (uncurry f)
> 
>     aunzip :: m (a,b) -> (m a, m b)
>     aunzip mab = (fst <$> mab, liftM <$> mab)
> 
> and
> 
> class (Monad m, ApplicativeZip m) => MonadZip m where
>     mzip :: m a -> m b -> m (a,b)
>     mzip = azip
> 
>     mzipWith :: (a -> b -> c) -> m a -> m b -> m c
>     mzipWith = azipWith
> 
>     munzip :: m (a,b) -> (m a, m b)
>     munzip = aunzip
> 
> IMHO that should been done during AMP-reform, sorry if this topic is already discussed.
> 
> - Oleg
> 
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