% XY Example 2. Floyd's Algorithm 
% "Negation and Aggregates in Recursive Rules: the LDL++ Approach", DOOD 93.

database ( {
        g(X:string, Y:string, C:integer)
}).

export delta(I, X, Y, C).

delta(0, X, X, 0)	<-	g(X,_,_).
delta(0, Y, Y, 0)	<-	g(_,Y,_).

delta(J+1, X, Z, min_all<C>) <- delta(J,X,Y,C1),
				g(Y,Z,C2), C=C1+C2,
				if (all(J,X,Z,C3) then C3>C).
all(J+1, X, Z, C)	<-	all(J,X,Z,C), ~delta(J+1, X, Z, _).
all(J, X, Z, C)		<-	delta(J, X, Z, C).