Finding the max in a list - Prolog

Question

I was just introduced to Prolog and am trying to write a predicate that finds the Max value of a list of integers. I need to write one that compares from the beginning and the other that compares from the end. So far, I have:

max2([],R).
max2([X|Xs], R):- X > R, max2(Xs, X).
max2([X|Xs], R):- X <= R, max2(Xs, R).

I realize that R hasn't been initiated yet, so it's unable to make the comparison. Do i need 3 arguments in order to complete this?

Answer 1

As an alternative to BLUEPIXY' answer, SWI-Prolog has a builtin predicate, max_list/2, that does the search for you. You could also consider a slower method, IMO useful to gain familiarity with more builtins and nondeterminism (and then backtracking):

slow_max(L, Max) :-
   select(Max, L, Rest), \+ (member(E, Rest), E > Max).

yields

2 ?- slow_max([1,2,3,4,5,6,10,7,8],X).
X = 10 ;
false.

3 ?- slow_max([1,2,10,3,4,5,6,10,7,8],X).
X = 10 ;
X = 10 ;
false.

edit

Note you don't strictly need three arguments, but just to have properly instantiated variables to carry out the comparison. Then you can 'reverse' the flow of values:

max2([R], R).
max2([X|Xs], R):- max2(Xs, T), (X > T -> R = X ; R = T).

again, this is slower than the three arguments loops, suggested in other answers, because it will defeat 'tail recursion optimization'. Also, it does just find one of the maxima:

2 ?- max2([1,2,3,10,5,10,6],X).
X = 10 ;
false.