====== Exp ======
{{tag>math arithmetic}}
===== Description =====
Exponentiation as repeated multiplication

**Source**:  The Art of Prolog
===== Download =====
Program source code: {{exp.pl}}
===== Listing =====
<code prolog>
/*
	exp(N,X,Y) :-
			N, X and Y are natural numbers
			such that Y equals X raised to the power N.
*/

	exp(s(N),0,0).
	exp(0,s(X),s(0)).
	exp(s(N),X,Y) :- exp(N,X,Z), times(Z,X,Y).

	times(0,Y,0).
	times(s(X),Y,Z) :- times(X,Y,XY), plus(XY,Y,Z).

	myplus(0,X,X) :- natural_number(X).
	myplus(s(X),Y,s(Z)):- myplus(X,Y,Z).

	natural_number(0).
	natural_number(s(X)) :- natural_number(X).

%	Program 3.5: Exponentiation as repeated multiplication
</code>
===== Comments =====