Find max integer in a list in prolog

Question

I am trying to find the max number in a list. I know there are several solutions available online but I feel the best way to learn is to implement on my own.

I wrote

Answer 1

Consider the code presented in my answer to related question "Finding the max in a list - Prolog".

The code in mentioned answer is based on the meta-predicate foldl/4.

Here, I show how to do it with the meta-predicates combine/3 and reduce/3. First, combine/3:

:- meta_predicate combine(3,?,?).
combine( _ ,[]    ,[]).
combine(P_3,[X|Xs],Ys) :-
   list_prev_combined_(Xs,X,Ys,P_3).

:- meta_predicate list_combined_(?,?,3).
list_combined_([]    ,[], _ ).
list_combined_([X|Xs],Ys,P_3) :-
   list_prev_combined_(Xs,X,Ys,P_3).

:- meta_predicate list_prev_combined_(?,?,?,3).    
list_prev_combined_([]     ,X ,[X]   , _ ).
list_prev_combined_([X1|Xs],X0,[Y|Ys],P_3) :-
   call(P_3,X0,X1,Y),
   list_combined_(Xs,Ys,P_3).

Building on combine/3 we can define reduce/3 as follows:

:- meta_predicate reduce(3,?,?).
reduce(P_3,[X|Xs],V) :- 
   list_aka_prev_reduced_(Xs,Xs,X,V,P_3).

:- meta_predicate list_aka_prev_reduced_(?,?,?,?,3).
list_aka_prev_reduced_([]   ,_ ,V ,V, _ ).
list_aka_prev_reduced_([_|_],Xs,X0,V,P_3) :-
   list_prev_combined_(Xs,X0,Ys,P_3),
   reduce(P_3,Ys,V).

Regarding the shape of their respective proof trees, foldl/4 is similar to lists, while combine/3 and reduce/3 are similar to balanced binary trees.

Consider the following queries:

:- use_module(library(lambda)).

?- foldl(\X^Y^f(X,Y)^true, [1,2,3,4,5,6,7], 0,S).
S = f(7,f(6,f(5,f(4,f(3,f(2,f(1,0))))))).

?- combine(\X^Y^f(X,Y)^true, [1,2,3,4,5,6,7], S).
S = [f(1,2),f(3,4),f(5,6),7].

?- reduce(\X^Y^f(X,Y)^true, [1,2,3,4,5,6,7], S).
S = f(f(f(1,2),f(3,4)),f(f(5,6),7)).

reduce/3 is based on combine/3 and applies it until all items have been combined to one:

?- combine(\X^Y^f(X,Y)^true, [1,2,3,4,5,6,7], S).
S = [f(1,2),f(3,4),f(5,6),7].

?- combine(\X^Y^f(X,Y)^true, [f(1,2),f(3,4),f(5,6),7], S).
S = [f(f(1,2),f(3,4)),f(f(5,6),7)].

?- combine(\X^Y^f(X,Y)^true, [f(f(1,2),f(3,4)),f(f(5,6),7)], S).
S = [f(f(f(1,2),f(3,4)),f(f(5,6),7))].

?- reduce(\X^Y^f(X,Y)^true, [1,2,3,4,5,6,7], S).
S =  f(f(f(1,2),f(3,4)),f(f(5,6),7)).

Let's use it for getting the maximum integer Max in list [1,5,2,4,3,8,7,2]:

:- use_module(library(clpfd)).

?- reduce(\X^Y^XY^(XY #= max(X,Y)), [1,5,2,4,3,8,7,2], Max).
Max = 8.

℅ If you can't use clpfd, simply use is/2 instead of (#=)/2:
?- reduce(\X^Y^XY^(XY is max(X,Y)), [1,5,2,4,3,8,7,2], Max).
Max = 8.