Alternative instance for Const

[chessai .]

As far as I'm aware, distributivity is neither required nor adhered to by
many types in core libraries and beyond. Only left and right identity, and
associativity. This instance would also play well with the existing
Applicative instance.

On Sat, Mar 21, 2020, 3:54 PM Oleg Grenrus <oleg.grenrus at iki.fi> wrote:

> https://wiki.haskell.org/Typeclassopedia#Laws_6
>
> On 21.3.2020 23.46, Simon Jakobi via Libraries wrote:
> > Hi Zemyla,
> >
> > Could you clarify where the requirement for distributivity comes from?
> >
> > The haddocks for Alternative don't mention it:
> >
> http://downloads.haskell.org/~ghc/8.10.1-rc1/docs/html/libraries/base-4.14.0.0/Control-Applicative.html#t:Alternative
> >
> > Thanks,
> > Simon
> >
> > Am Sa., 21. März 2020 um 21:23 Uhr schrieb Zemyla <zemyla at gmail.com>:
> >> No, the Alternative instance should be based on semirings instead. The
> one you propose isn't distributive.
> >>
> >> Lacking general semirings, the best we can do at the moment is newtypes
> for each semiring we have. For instance:
> >>
> >> newtype NumConst a b = NumConst { getNumConst :: a }
> >>    deriving (Functor)
> >>
> >> instance Num a => Applicative (NumConst a) where
> >>    pure = const (NumConst 1)
> >>    (<*>) = (coerce :: (a -> a -> a) -> NumConst a (u -> v) -> NumConst
> a u -> NumConst a v) (*)
> >>
> >> instance Num a => Alternative (NumConst a) where
> >>    empty = NumConst 0
> >>    (<|>) = (coerce :: (a -> a -> a) -> NumConst a b -> NumConst a b ->
> NumConst a b) (+)
> >>
> >> On Sat, Mar 21, 2020, 13:44 chessai . <chessai1996 at gmail.com> wrote:
> >>> We already have
> >>>
> >>> instance Monoid m => Applicative (Const m)
> >>>
> >>> we could easily add
> >>>
> >>> instance Monoid m => Alternative (Const m) where
> >>>    empty = coerce mempty
> >>>    (<|>) = coerce (<>)
> >>>
> >>> which trivially satisfies left/right identity and associativity.
> >>>
> >>> I propose we add this instance to base.
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