Generalize indexing function

[Keith]

Might be more convenient to use an associated type family. And in practice, using types like '()' and 'Bool' as indexes is not super useful when you've already committed to using 'Int' as the (partial) index type of '[]'.

- Keith

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On April 10, 2021 10:48:42 PM UTC, 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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