%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Code for Sample Lattices
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

lub(max,A,B,Max):-	max(A,B,Max).
bottom(max,0).
gt1(max,A,B):- max(A,B,A).

max(One,Two,Max):- One > Two -> Max = One ; Max = Two.


lub(min,A,B,Min):-	min(A,B,Min).
bottom(min,infinity).
gt1(min,A,B):- min(A,B,A).

min(One,infinity,One):-!.
min(infinity,Two,Two):-!.
min(One,Two,Min):- One > Two -> Min = Two ; Min = One.

lub(set,A,B,Union):-	append(A,B,App),sort(App,Union).
bottom(set,[]).
gt1(set,A,B):- subset(B,A).

subset([],_).
subset([H|T],List):-
	memberchk(H,List),
	subset(T,List).