Man Or Boy

September 16, 2016

During the development of Algol 60, Donald Knuth devised a nasty test of recursion:

There are quite a few ALGOL60 translators in existence which have been designed to handle recursion and non-local references properly, and I thought perhaps a little test-program may be of value. Hence I have written the following simple routine, which may separate the man-compilers from the boy-compilers:

begin 
 real procedure A(k, x1, x2, x3, x4, x5);
 value k; integer k;
 begin
  real procedure B;
  begin 
   k := k - 1; 
   B := A := A(k, B, x1, x2, x3, x4)
  end;
  if k ≤ then A : = x4 + x5 else B
 end
 outreal(A(10, 1, -1, -1, 1, 0))
end

This uses nothing known to be tricky or ambiguous. My question is: What should the answer be? Unfortunately, I don’t have to a man-compiler myself, and so I was forced to try hand calculations. My conjecture (probably wrong) is that the answer will be:

73 - 119 - 177 + 102 = - 121

I’d be very glad to know the right answer.

Your task is to write a program that computes the right answer. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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