Better termination for s(X)-sum

Question

(Let me sneak that in within the wave of midterm questions.)

A common definition for the sum of two natural numbers is nat_nat_sum/3:

na         


        

Answer 1

Take the following two definitions:

Definition 1:

add(n,X,X).
add(s(X),Y,s(Z)) :- add(X,Y,Z).

Definition 2:

add(n,X,X).
add(s(X),Y,Z) :- add(X,s(Y),Z).

Definition 1 terminates for pattern add(-,-,+), whereas definition 2 does not terminate for pattern add(-,-,+). Look see:

Definition 1:

?- add(X,Y,s(s(s(n)))).
X = n,
Y = s(s(s(n))) ;
X = s(n),
Y = s(s(n)) ;
X = s(s(n)),
Y = s(n) ;
X = s(s(s(n))),
Y = n
?- 

Definition 2:

?- add(X,Y,s(s(s(n)))).
X = n,
Y = s(s(s(n))) ;
X = s(n),
Y = s(s(n)) ;
X = s(s(n)),
Y = s(n) ;
X = s(s(s(n))),
Y = n ;
Error: Execution aborted since memory threshold exceeded.
    add/3
    add/3
?- 

So I guess definition 1 is better than definition 2.

Bye