fact1(0,1).
fact1(N,R) :- N>0, P is N-1, fact1(P,V), R is N*V.
fact2(X,1) :- X=:=0.
fact2(N,R) :- N>0, P is N-1, fact2(P,V), R is N*V.

a(0,1).
b(X,1):-X=0.
c(X,1):-X=:=0.
d(X,1):-X==0.

if_1(T,P,Q):-T,!,P.
if_1(T,P,Q):-Q.
if_2(T,P,Q):-T,P,!.
if_2(T,P,Q):-Q.
if_3(T,P,Q):-!,T,P.
if_3(T,P,Q):-Q.


/* pour distinguer if_1 et if_2: (true,false,true)  
1 et 3: (fail,fail,true)  
2 et 3 idem
*/

p(1).
p(2).
p(3).
p(4).

p_aux(X,Y) :- p(X), p(Y), X\==Y, !.
p2(X) :- p_aux(X,_).
p2(X) :- p_aux(_,X).
/*********/
p_auxb(X) :- p(X) , !.
p2b(X):- p_auxb(X) ; p_auxb(X).

/* recurrence*/


est_formule(X):-atomic(X),!.
est_formule(neg(X)):-est_formule(X).
est_formule(et(X,Y)):-est_formule(X),est_formule(Y).
est_formule(ou(X,Y)):-est_formule(X),est_formule(Y).


symboles(X,1,0,0,0):-atomic(X).
symboles(neg(P),A,N,E,O):-symboles(P,A,M,E,O), N is M+1.
symboles(et(P,Q),A,N,E,O):-symboles(P,Aa,Na,Ea,Oa),
    symboles(Q,Ab,Nb,Eb,Ob), A is Aa+Ab, N is Na+Nb, E is Ea+Eb+1,O is Oa+Ob.
symboles(ou(P,Q),A,N,E,O):-symboles(P,Aa,Na,Ea,Oa),
    symboles(Q,Ab,Nb,Eb,Ob), A is Aa+Ab, N is Na+Nb, E is Ea+Eb,O is Oa+Ob+1.


variables(X,[X]):-atomic(X),!.
variables(neg(X),L):-variables(X,L).
variables(et(X,Y), L):-variables(X,L1),variables(Y,L2),union(L1,L2,L).
variables(ou(X,Y), L):-variables(X,L1),variables(Y,L2),union(L1,L2,L).

combine([],[],[]).
combine([X|L],[Y|G],[(X,Y)|H]) :- combine(L,G,H).

assoc(X,[(X,Y)|_],Y):-!.
assoc(X,[_|L],Y):-assoc(X,L,Y).

combiner([],[]).
    combiner([X|L],[(X,Y)|R]):-combiner(L,R),(Y=1;Y=0).

evaluer(X,A):-atomic(X),  assoc(X,A,1).
evaluer(neg(X),A):-not(evaluer(X,A)).
evaluer(et(X,Y),A):-evaluer(X,A),evaluer(Y,A).
evaluer(ou(X,Y),A):-(evaluer(X,A), !); evaluer(Y,A).


/* sat(F,A):-variables(F,L), length(L,N), engendre(N,H), combine(L,H,A),
evaluer(F,A,1).*/

satisfait(F,A):-variables(F,L), combiner(L,A),
evaluer(F,A).


/*ordre superieure*/

map2_somme([],[],[]):-!.
map2_somme([],_,_):-write("Arguments non valides"), fail.
map2_somme(_,[],_):-write("Arguments non valides"), fail.
    map2_somme([X|L],[Y|G],[Z|R]):-(integer(X),integer(Y)) -> (Z is X+Y, map2_somme(L,G,R)); (write("Arguments non valides"), fail).

map2(_,[],[],[]):-!.
map2(_,[],_,_):-write("Arguments non valides"), fail.
map2(_,_,[],_):-write("Arguments non valides"), fail.

map2(P,[X|L],[Y|G],[Z|H]):-(integer(X),integer(Y)) -> (Q=..[P,X,Y,Z],Q,map2(P,L,G,H));  (write("Arguments non valides"), fail).

produit(X,Y,Z):- Z is X*Y.

map3(_,[],[],[],[]):-!.
map3(_,[],_,_,_):-write("Arguments non valides"), fail.
map3(_,_,[],_,_):-write("Arguments non valides"), fail.
map3(_,_,_,[],_):-write("Arguments non valides"), fail.

map3(P,[X|L],[Y|G],[W|K],[Z|H]):-(integer(X),integer(Y),integer(W)) -> (Q=..[P,X,Y,W,Z],Q,map3(P,L,G,K,H));  (write("Arguments non valides"), fail).


somme_3(A,B,C,D):-D is A+B+C.
/*jeux*/

move([X|L],[SX|L1]):- SX is X+1, takeone(L,L1).
move([X|L],[X|T]):-move(L,T).

takeone([X|L],[P|L]):-X>0, P is X-1.
takeone([X|L],[X|L1]):-takeone(L,L1).

gagne(X):-move(X,Y),not(gagne(Y)),!.

gagnebis([_,M,D]):- D mod 2 =\= 0,!; M mod 2 =\= 0.