Ackermann very inefficient with Haskell/GHC

Question

I try computing Ackermann(4,1) and there\'s a big difference in performance between different languages/compilers. Below are results on my

Answer 1

Writing the algorithm in Haskell in a way that looks similar to the way you wrote it in C is not the same algorithm, because the semantics of recursion are quite different.

Here is a version using the same mathematical algorithm, but where we represent calls to the Ackermann function symbolically using a data type. That way, we can control the semantics of the recursion more precisely.

When compiled with optimization, this version runs in constant memory, but it is slow - about 4.5 minutes in an environment similar to yours. But I'm sure it could be modified to be much faster. This is just to give the idea.

data Ack = Ack !Int

ack :: Int -> Int -> Int
ack m n = length . ackR $ Ack m : replicate n (Ack 0)
  where
    ackR n@(Ack 0 : _) = n
    ackR n             = ackR $ ack' n

    ack' [] = []
    ack' (Ack 0 : n) = Ack 0 : ack' n
    ack' [Ack m]     = [Ack (m-1), Ack 0]
    ack' (Ack m : n) = Ack (m-1) : ack' (Ack m : decr n)

    decr (Ack 0 : n) = n
    decr n           = decr $ ack' n