prolog sum & sub using successors ?

Question

Hi , what is substraction and summation using successors , can any one show me an example for that i know how to do it the normal way .

/* sub(X, Y, Z) ---subtraction */

sub(X, Y, Z) :- add(Y, Z, X).

Answer 1

First, you need to have a predicate succ. This is how SWI-Prolog defines it:

succ(?Int1, ?Int2)
    True  if  Int2 = Int1+ 1  and  Int1>=0.     At  least  one  of  the
    arguments must be  instantiated to a natural number.  This predicate
    raises the domain-error not_less_than_zero if called with a negative
    integer.   E.g. succ(X, 0)  fails silently and succ(X, -1) raises  a
    domain-error.

Given that, we can define add like this:

add(0, Y, Y).
add(X, Y, Z) :-
  succ(PredX, X),
  add(PredX, Y, PredZ),
  succ(PredZ, Z).

And subtract like this:

subtract(X, 0, X).
subtract(X, Y, Z) :-
  succ(PredY, Y),
  succ(PredX, X),
  subtract(PredX, PredY, Z).

Note that neither one of these will handle negative numbers (because succ doesn't), and therefore I haven't bothered to make subtract function when Y > X.

---

EDIT:

Here's a version of add and subtract that work on any instantiation pattern. I still didn't bother with type-checking (as mentioned by Kaarel in the comments), or negative numbers.

add(0, 0, 0).
add(0, Y, Y).
add(X, 0, X).
add(X, Y, Z) :-
  nonvar(X),
  succ(PredX, X),
  (nonvar(Z) -> 
    succ(PredZ, Z), add(PredX, Y, PredZ) 
  ; 
    add(PredX, Y, PredZ), succ(PredZ, Z)
  ).
add(X, Y, Z) :-
  nonvar(Y),
  add(Y, X, Z).

subtract(0, 0, 0).
subtract(X, 0, X).
subtract(X, X, 0).
subtract(X, Y, Z) :-
  add(Y, Z, X).