%:- use_module(library(lists)). % This library provides e.g. append(X, Y, Z)
                                % and other built-in predicates concerning lists



/************************ ex1:family *******************************/
male(andrew).
male(todd).
male(mike).
male(peter).
male(john).
male(jason).
male(william).
male(ian).

female(susan).
female(ann).
female(elizabeth).
female(mary).
female(jenny).
female(josephine).
female(vicky).

parent(mary,andrew).
parent(mary,todd).
parent(mary,susan).
parent(jason,andrew).
parent(jason,todd).
parent(jason,susan).
parent(vicky,mike).
parent(vicky,peter).
parent(john,mike).
parent(john,peter).
parent(jenny,ann).
parent(jenny,elizabeth).
parent(william,ann).
parent(william,elizabeth).
parent(josephine,mary).
parent(josephine,john).
parent(josephine,jenny).
parent(ian,mary).
parent(ian,john).
parent(ian,jenny).

child(A,B) :- parent(B,A).
son(A,B) :- male(A),parent(B,A).
daughter(A,B) :- female(A),parent(B,A).

mother(A,B) :- parent(A,B),female(A).
father(A,B) :- parent(A,B),male(A).

grandparent(A,B) :- parent(A,C),parent(C,B).

% All solutions occur twice, because parent(C,A) matches with
% father and mother.
% A \== B ensures that brother(X, X) is _not_ a solution.
brother(A, B) :- parent(C, A), parent(C, B), male(A), A \= B.

% Solutions occur only ones because parents(C, A) is replaced by
% mother(C, A) or father(C, A) resp.
brother2(A, B) :- mother(C, A), mother(C, B), male(A), A \= B.
brother3(A, B) :- father(C, A), father(C, B), male(A), A \= B.

/************************ ex2:factorial *******************************/
factorial(0,1).
factorial(N,F) :-
	N > 0,
	N1 is N-1,
	factorial(N1,F1),
	F is N*F1.

/************************ ex3:exponential *******************************/
exp(X, 0, 1).
exp(X, N, Y) :-
	N > 0,
	N1 is N-1,
	exp(X, N1, Y1),
	Y is X*Y1.
	
/************************ ex4:reverse *******************************/
reverse(X, Y) :- reverse(X, [], Y).

reverse([], Y, Y).
reverse([H|T], Y0, Y) :-
		reverse(T, [H|Y0], Y).
/************************ ex5:append *******************************/
append([], Ys, Ys).
append([X|Xs], Ys, [X|Zs]) :-
	append(Xs, Ys, Zs).

prefix(Xs, Ys) :-
	append(Xs, As, Ys).
suffix(Xs, Ys) :-
	append(As, Xs, Ys).
last(X, Xs) :-
	append(As, [X], Xs).

/************************ ex6:delete *******************************/
delete(X, [X|Tail], Tail).
delete(X, [Y|Tail], [Y|Tail1]) :-
	delete(X, Tail, Tail1).

/************************ ex7:permutation *******************************/
permutation([], []).
permutation(L, [X| P]) :-
	delete(X, L, L1),
	permutation(L1, P).
/************************ ex8:subset *******************************/
member(X, [X|_Tail]).
member(X, [_Y|Tail]) :-
	member(X, Tail).

subset([], _).
subset([X|Tail], Set) :-
	member(X, Set),
	subset(Tail, Set).