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