Lists in Prolog - Thinking as Computation - page 147

The append predicate can also be used to generate lists:
% What pairs of lists when joined give [a,b,c]?
?- append(X,Y,[a,b,c]).
X = [],

Y = [a, b, c] ;

X = [a], Y = [b, c] ;

X = [a, b], Y = [c] ;

X = [a, b, c], Y = [] ;

No
Using append to generate a pair of lists in this way is a very useful technique. (In
chapter 8, it is used to break up a list of words into phrases.) Variables can also be
used freely within the arguments to append :

% [a,b] joined to what list L gives [a,b,c,d,e,f]?
?- append([a,b],L,[a,b,c,d,e,f]).
L = [c, d, e, f]
% Solve for the variables X, Y, and L.
?- append([X,b],[d|L],[a,_,Y,e,f]).
X=a, L=[e,f],Y=d

The append predicate is quite powerful, and a number of additional predicates can be
defined with it. Here are some one-line examples:
The predicate front(L1,L2) holds if the list L1 is the start of list L2 :
front(L1,L2) :- append(L1,_,L2).

The predicate last(E,L) holds if E is the last element of list L :
last(E,L) :- append(_,[E],L).

Yet another version of the member predicate:
elem2(E,L) :- append(_,[E|_],L).
This definition of elem2 says that E is an element of list L if L is the result of joining
something (the first _ ) with a list whose head is E and whose tail is something (the
second _ ). In other words, E is an element of L if L is a list that has some number of
elements, then E , then some number of other elements.
As with the member predicate, one needs to be careful not to generate an infinite set
of candidate values. Consider this version of a predicate that determines whether one
element appears before another in a list:
% A first version
before(X,Y,L) :- append(_,[X|_],Z), append(Z,[Y|_],L).