/* Exercice 2*/

inf(M,P):-M>0, Q is M-1, inf(Q,P).
inf(M,P):-M>0, P is M-1.


aux1(_,[],0):-!.
aux1(N,[X|L],M):-inf(N,X), P is M-1, aux1(N,L,P).
genere(N,L):-aux1(N,L,N).

compte([],_,0).
compte([X|L],X,N):- !,compte(L,X,M), N is M+1.
compte([_|L],X,N):-compte(L,X,N).

ar(L):-aux(L,0,L).
aux([],_,_).
aux([X|L],N,G):-compte(G,N,X),M is N+1, aux(L,M).

genar(N,G):-genere(N,G), ar(G).

    
inf1(M,M).
inf1(M,N):-M>0, P is M-1, inf1(P,N).
        
genere1(N,L):-genereaux(N,N,L,N).
genereaux(0,_,[],0).
genereaux(K,N,[X|L],S):- K>0,inf(N,X),
inf1(S,X), R is S-X, J is K-1, genereaux(J,N,L,R).


genere2(N,L):-gaux(N,N,L,N,0,N).
gaux(0,_,[],0,_,0).
gaux(K,N,[X|L],S,I,P):-K>0, inf(N,X), inf1(S,X), F is I*X, inf1(P, F), J is K-1, R is S-X, T is P - I*X, O is I+1, gaux(J,N,L,R,O,T).

/* Exercice 3 */
  

printSum([],[]).
printSum([X|L],[Y|G]):- S is X+Y, writeln(S), printSum(L,G).

printAppend([],[]).
printAppend([X|L],[Y|G]):- string_concat(X,Y,Z), writeln(Z), printAppend(L,G).

twoListIter(_,[],[]).
twoListIter(P,[X|L],[Y|G]):-Q=..[P,X,Y],Q,twoListIter(P,L,G).