option nolet
print "**********************************************"
print "* recursion: Ackermann function,version 1.0  *"
print "* peter.vlasschaert@gmail.com,13/02/2020     *"
print "**********************************************"
!https://rosettacode.org/wiki/Ackermann_function
print
print "********************************************"
print "*  ack(m,n) =>   algo                      *"
print "* n+1                   if m=0             *"
print "* ack(m-1,1)            if m>0 and  n=0    *"
print "* ack(m-1,ack(m,n-1))   if m>0 and  n>0    *"
print "********************************************"
print
DECLARE FUNCTION ack 
print " example :    "
print " ack(4,0)= ";ack(4,0)
print
dim ackm(0:3,0:7)
mat ackm = 0
print " input matrix : ackm(0:3,0:7) "
mat print ackm
for i = 0 to 3
  for j = 0 to 7
  ackm(i,j) = ack(i,j)
  next j
next i
print " output matrix : "
mat print ackm
print
print "**************************************"
print "problem : ack(4,1) => out of memory   "
print "**************************************"
print "ack(0,k) =k+1                         "
print "ack(1,k) =k+2                         "
print "ack(3,k) =2^(k+3)-3                   "
print "ack(4,k) =2^(ack(4,k-1)+3) -3 if k>0 "
print "ack(4,0) =13  ,see output : matrix    "
print "**************************************"
end

function ack(m,n)
if  m=0 then 
ack = n+1
else if (n=0) then
ack=10*(ack(m-1,1))/10! notation correction
else
 ack = ack(m - 1, ack(m, n - 1))
end if
end function