[Haskell-cafe] Re: Aren't type system extensions fun?

[Gleb Alexeyev]

Andrew Coppin wrote:

> What a perplexing example! :-}

For a bit less mind-boggling example, try meditating about the next two 
functions. It may be instructive to comment out type signatures and see 
what happens.

{-# OPTIONS -fglasgow-exts #-}

foo :: (forall a . a -> a) -> (Bool, String)
foo g = (g True, g "bzzt")

bar :: (forall a . Num a => a) -> (Integer, Float)
bar x = (x `div` 3, x / 3)


In a nutshell, rank-N typing is simple. Rank-1 polymorphism allows us to 
type functions like map, foldr etc we all know and love. Rank-1 
polymorphic types contain type variables that may be instantiated with 
any monomorphic type (e.g., Int, String, etc). Rank-2 polymorphic 
functions accept rank-1 polymorphic values as argument. Rank-N 
polymorphic functions accept rank-(N-1) polymorphic values as argument.

As a practical example of the need for higher-rank polymorphism you may 
want to read about ST monad.