Generalize indexing function

[George Wilson]

Does this class have any laws? From what I can tell, this is useful only as
an overloading of some identifiers - I don't see what useful functions I
could write in terms of this as an abstraction.

Cheers,
George

On Sun, 11 Apr 2021, 08:49 Dannyu NDos, <ndospark320 at gmail.com> wrote:

> I noticed that the list indexing function, (!!), is generalizable. I'm
> showing some instances:
>
> {-# LANGUAGE MultiParamTypeClasses #-}
>
> import Data.Complex
> import Data.Functor.Compose
> import Data.Functor.Product
> import Data.Functor.Sum
> import Data.List.NonEmpty
> import Data.Maybe
>
> infix 9 !?
> infixl 9 !
>
> class Indexable i a where
>     (!?) :: i b -> a -> Maybe b
>
> (!) :: Indexable i a => i b -> a -> b
> x ! n = fromJust (x !? n)
>
> instance Indexable [] Int where
>     [] !? _ = Nothing
>     (x:_) !? 0 = Just x
>     (_:xs) !? n
>         | n < 0 = Nothing
>         | otherwise = xs !? (n-1)
>
> instance Indexable ((->) a) (Identity a) where
>     f !? Identity n = Just (f n)
>
> instance Indexable ((,) a) () where
>     (_,x) !? _ = Just x
>
> instance Indexable Complex Bool where
>     (x :+ _) !? False = Just x
>     (_ :+ y) !? True = Just y
>
> instance (Indexable f a, Indexable g b) => Indexable (Compose f g) (a,b)
> where
>     Compose z !? (m,n) = do
>         y <- z !? m
>         y !? n
>
> instance (Indexable f a, Indexable g b) => Indexable (Product f g) (Either
> a b) where
>     Pair x _ !? Left m = x !? m
>     Pair _ y !? Right n = y !? n
>
> instance (Indexable f a, Indexable g a) => Indexable (Sum f g) (Identity
> a) where
>     InL x !? Identity n = x !? n
>     InR y !? Identity n = y !? n
>
> instance Indexable NonEmpty Int where
>     (x :| xs) !? n = (x : xs) !? n
>
>
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