Determine whether a value is a function in Haskell

Question

Is it possible to write a function isFunc :: a -> Bool to determine whether an arbitrary value is a function (of any kind) such that

foo :: Int -> Int
bar :: Char -> Char -> Char    

> isFunc foo
True
> isFunc bar
True
> isFunc 3
False
> isFunc 'a'
False

I'm using Data.Dynamic so I can't determine the type in advance.

Answer 1

Parametricity says no. The only functions of type

a -> Bool

are constant functions.

However, with a bit of ad hoc polymorphism and a bit more chutzpah, you can do this:

{-# LANGUAGE OverlappingInstances, FlexibleInstances #-}

class Sick x where
  isFunc :: x -> Bool

instance Sick (a -> b) where
  isFunc _ = True

instance Sick x where
  isFunc _ = False

and then it looks like you have

*Sick> isFunc 3
False
*Sick> isFunc id
True

But it does seem like a peculiar thing to do. What use is the resulting Bool to you?