Many functions can be generalised

[David Menendez]

On Sat, Dec 3, 2016 at 12:50 AM, David Feuer <david.feuer at gmail.com> wrote:

> On Dec 2, 2016 6:14 PM, "David Menendez" <dave at zednenem.com> wrote:
>
> A while back, I found myself deriving this class:
>
>     class Functor f => Siftable f where
>         siftWith :: (a -> Maybe b) -> f a -> f b
>         sift :: (a -> Bool) -> f a -> f a
>         sift f = siftWith (\a -> if f a then Just a else Nothing)
>
>
> I would expect several classes, corresponding to different methods of
> Witherable:
>
> class Siftable a m | m -> a where
>   sift :: (a -> Bool) -> m -> m
>   default sift :: SiftWithable f => (a -> Bool) -> f a -> f a
>   sift p = siftWith (\x -> x <$ guard (p x))
>
> class Functor f => SiftWithable f where
>   siftWith :: (a -> Maybe b) -> f a -> f b
>
> class Siftable a m => SiftableA a m where
>   siftA :: Applicative g => (a -> g Bool) -> m -> g m
>   default siftA :: (SiftWithAAble f, Applicative g) => (a -> g Bool) -> f
> a -> g (f a)
>   siftA p = siftWithA (\x -> (x <$) . guard <$> p x)
>
> class (Traversable f, SiftWithAble f) => SiftWithAAble f where
>   siftWithA :: Applicative g => (a -> g (Maybe b)) -> f a -> g (f a)
>

Yes, sift is more general than siftWith (which I should have called
siftMap, in hindsight). But, so far as I know, the only things you can
define sift for but not siftWith are sets and set-like things.

At the time, I had also rejected sift by itself because I couldn’t think of
any laws, but now that I look at it again, I guess they would be:

    sift (const True) = id
    sift (\x -> p x && q x) = sift q . sift p

I think those would make sift a monoid homomorphism.

These still allow some weird instances, like sift _ = id, or something like
this:

    newtype Weird a = Map a Bool

    instance Ord a => Siftable a (Weird a) where
        sift p (Weird m) = Weird (Map.union (Map.updateMin (const False)
yes) no)
            where
            (yes, no) = Map.partitionWithKey (const . p) m

I imagine it isn’t worth making the laws tighter to forbid this.

-- 
Dave Menendez <dave at zednenem.com>
<http://www.eyrie.org/~zednenem/>
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