1)

date(M, D, Y) :- integer(Y), Y >= 0, integer(D), D > 0,
                 daysmonth(M, MaxDay, Y), D =< MaxDay.

leapyear(Y) :- integer(Y), Y > 0, 0 is Y mod 4, 
               Z is Y mod 100, Z > 0.

leapyear(Y) :- integer(Y), Y > 0, 0 is Y mod 4, 
               Z is Y mod 400, Z = 0.

daysmonth(jan, 31, _).
daysmonth(feb, 28, Y) :- not(leapyear(Y)).
daysmonth(feb, 29, Y) :- leapyear(Y).
daysmonth(mar, 31, _).
daysmonth(apr, 30, _).
daysmonth(may, 31, _).
daysmonth(jun, 30, _).
daysmonth(jul, 31, _).
daysmonth(aug, 31, _).
daysmonth(sep, 30, _).
daysmonth(oct, 31, _).
daysmonth(nov, 30, _).
daysmonth(dec, 31, _).