% define a predicate app(Xs,Ys,Zs)
% <=> Zs contains all elements of Xs and Ys in the same order.
% e.g., app([1,2],[3,4],[1,2,3,4]) is true

%app([],Ys,Zs) :- Zs=Ys.
app([],Ys,Ys).
app([X|Xs],Ys,[X|Zs]) :- app(Xs,Ys,Zs).

% musterorientiert: falls das erste Argument eine Liste ist, dann passt
% hoechstens eine der beiden Klauseln
%
% ?- app([1,2],[3,4],[1,2,3,4]).
% |-
% ?- app([2],[3,4],[2,3,4]).
% |-
% ?- app([],[3,4],[3,4]).
% |-
% ?- .
%
% Suchraum: 1-elementig
% Berechnung: deterministisch

% Add an element at the end of a list:
add_list(L, E, LwithE) :- app(L,[E],LwithE).

% Last element E of a list L:
last(L,E) :- app(_,[E],L).

% Is E an element of a list L:
elem(E,L) :- app(_,[E|_],L).

% deletes an occurrence of an element E in a list Xs, Ys is the remaining list
delete(Xs,E,Ys) :- app(L1,[E|L2],Xs), app(L1,L2,Ys).

% sublist(Xs,Ys) <=> Xs is a list occurring in Ys
sublist(Xs,Ys) :- app(_,L2,Ys), app(Xs,_,L2).