Problem Statement

The Ackermann function is a classic example of a recursive function, notable especially because it is not a primitive recursive function. It grows very quickly in value, as does the size of its call tree.

The Ackermann function is usually defined as follows:

Its arguments are never negative and it always terminates.

Write a function which returns the value of

A ( m , n )

{\displaystyle A(m,n)}

. Arbitrary precision is preferred (since the function grows so quickly), but not required.

Let's start with the solution:

                           forward is ackermann ( m n --> r )
  [ over 0 = iff
      [ nip 1 + ] done
    dup 0 = iff
      [ drop 1 - 1
        ackermann ] done
     over 1 - unrot 1 -
     ackermann ackermann ]   resolves ackermann ( m n --> r )

  3 10 ackermann echo