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,
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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