Question

Is it possible to write a function arity :: a -> Integer to determine the arity of arbitrary functions, such that

> arity map
2
> arity foldr
3
> arity id
1
> arity "hello"
0

?

Answer 1

It’s easy with OverlappingInstances:

{-# LANGUAGE FlexibleInstances, OverlappingInstances #-}

class Arity f where
  arity :: f -> Int

instance Arity x where
  arity _ = 0

instance Arity f => Arity ((->) a f) where
  arity f = 1 + arity (f undefined) 

Upd Found problem. You need to specify non-polymorphic type for polymorphic functions:

arity (foldr :: (a -> Int -> Int) -> Int -> [a] -> Int)

Don’t know how to solve this yet.

Upd2 as Sjoerd Visscher commented below “you have to specify a non-polymorphic type, as the answer depends on which type you choose”.