sumPoly(P1, [], P1).
sumPoly([], P2, P2).
sumPoly([H1 | P1], [H2 | P2], [H3 | P3]) :- sumPoly(P1, P2, P3), 
                                            H3 is  H1 + H2.


sumDense(P1, [], P1).
sumDense([], P2, P2).
sumDense([[C1, E1] | P1], [[C2, E2] | P2], [[C3, E3] | P3]) :- 
                               E1 < E2, C3 = C1, E3 = E1,
                               sumDense(P1, [[C2, E2] | P2], P3).
sumDense([[C1, E1] | P1], [[C2, E2] | P2], [[C3, E3] | P3]) :- 
                               E1 > E2, C3 = C2, E3 = E2,
                               sumDense([[C1, E1] | P1] , P2, P3).
sumDense([[C1, E1] | P1], [[C2, E2] | P2], [[C3, E3] | P3]) :- 
                               E1 = E2, C3 is C1 + C2, E1 = E3,
                               sumDense(P1, P2, P3).

wineList([[1996, chardonnay, gallo, 6.95], 
              [1997, pinotnoir, gallo, 5.95],
              [1995, burgundy, ripple, 3.95],  
              [1996, cabernet, gallo, 4.95],
              [1997, pinotnoir, maddog, 3.95],
              [1997, chardonnay, nighttrain, 4.99],
              [1996, bordeaux, ripple, 2.99],
              [1997, bordeaux, ripple, 2.95],
              [1997, chardonnay, gallo, 5.95],
              [1994, chardonnay, gallo, 16.99],
              [1997, pinotnoir, oldtavern, 2.95],
              [1996, burgundy, maddog, 3.95]]).

vintage(_, [], []).
vintage(Y, [[Y, V, W, P] | W1],  [[Y, V, W, P] | W2]) :- 
 			       vintage(Y, W1, W2).
vintage(Y, [_ | W1], W2) :- vintage(Y, W1, W2).

wineType(_, _, [], []).
wineType(V, W, [[Y, V, W, P] | W1],  [[Y, V, W, P] | W2]) :- 
 			       wineType(V, W, W1, W2).
wineType(V, W, [_ | W1], W2) :- wineType(V, W, W1, W2).

minPrice([[_, _, _, P]], P).
minPrice([[_, _, _, P] | W], P) :- minPrice(W, P1), P =< P1.
minPrice([[_, _, _, P] | W], P1) :- minPrice(W, P1), P1 =< P.

price([_, _, _, P], P).

minPriceWine([W], W).
minPriceWine([W | L], W) :- minPriceWine(L, W1), price(W, P), 
                            price(W1, P1), P =< P1.
minPriceWine([W | L], W1) :- minPriceWine(L, W1), price(W, P), 
                            price(W1, P1), P1 =< P.