From: SKRdJ@nowhere.net   
      
   On Sat, 23 Jun 2018 18:23:02 -0700, Richard Fateman wrote:   
      
   > On Saturday, June 23, 2018 at 5:34:27 PM UTC-7, S.K.R. de Jong wrote:   
   >> Are there any symbolic systems that can deal with Ackermann functions   
   >> computations?   
   >   
   > Can you be more specific on what you mean by "deal"?   
   >   
   > It is not especially symbolic. The obvious definition usually causes   
   > problems with stack space because it is a heavily-recursive function.   
   >   
   > Symbolic systems also use stack space, so they suffer the same fate.   
   >   
   >   
   >  Here's a definition in lisp.   
   >   
   > (defun ackermann (x y)   
   >   (cond ((= y 0) 0)   
   >         ((= x 0) (* 2 y))   
   >         ((= y 1) 2)   
   >         (t (ackermann (- x 1) (ackermann x (- y 1))))))   
      
   	That's what I am asking about. Implementing it in Lisp (or I   
   guess any other language that allows one to do recursion) is fairly   
   straighforward. The problem is, like you point out, that the fact that it   
   is heavily recursive makes this function choke for even small arguments.   
   However, by hand, and using uparrow notation, one can do significantly   
   better. For example, let's define a variant of what you defined above:   
      
   	A(x, y) = A(x - 1, A(x, y - 1)), where A(x, 1) = x, A(1, y) = 2y,   
   with y > 1, and x, y positive integers   
      
   With uparrow notation, it is not difficult to return an explicit result   
   for A(4, 4). However, a straightforward Lisp implementation, similar to   
   the one above, would choke trying to compute A(4, 4). Hence my question.   
      
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