%%% Assignment 5
%%% Extra Credit
%%% Out: Wed 24 Oct
%%% Due: Mon 29 Oct 
%%% Author : Brigitte Pientka
%
% (25 points) Implement the maximum function max : nat -> nat -> nat
% that returns the maximum of two natural numbers.

% auxiliary function

% x greater or equal to y

% geq 0 y = true
% geq (s x) (s y) = geq x y

val geq : nat -> nat -> bool =
 fn x => rec x
  of g 0      => fn y => true
  |  g (s x') => fn y => rec y
                    of g' 0      => false
                    |  g' (s y') => g x' y' end
end;

% maximum function

val max : nat -> nat -> nat =
 fn x => fn y => if (geq x y) then x else y;