Question

isAlphaNum :: Char -> Bool
isAlphaNum = (||) <$> isAlpha <*> isNum 

I can see that it works, but I don’t understand where the instances of Applicative (or Functor) come from.

Answer 1

This is the Applicative instance for ((->) r), functions from a common type. It combines functions with the same first argument type into a single function by duplicating a single argument to use for all of them. (<$>) is function composition, pure is const, and here’s what (<*>) translates to:

s :: (r -> a -> b) -> (r -> a) -> r -> b
s f g x = f x (g x)

This function is perhaps better known as the S combinator.

The ((->) r) functor is also the Reader monad, where the shared argument is the “environment” value, e.g.:

newtype Reader r a = Reader (r -> a)

I wouldn’t say it’s common to do this for the sake of making functions point-free, but in some cases it can actually improve clarity once you’re used to the idiom. The example you gave, for instance, I can read very easily as meaning “is a character a letter or number”.