Modified Julian Day calculations in Prolog. This experiment might form the basis of a date library someday.

julian.pl

:- module(julian, [ date_name/2
                  , day_of_week/2
                  , gregorian/3
                  ]).
:- use_module(library(clpfd)).

%%    gregorian(?Year, ?Month, ?Day) is det.
%
%	True if Year, Month and Day form a valid date in the Gregorian
%	calendar.  For example, one could iterate all leap years with
%
%	==
%	gregorian(Y, 2, 29), Y #> 1776, indomain(Y).
%	==
gregorian(Y,M,D) :-
    Y in -4713..3267,
    M in 1..12,
    (   (D in 1..28)
    #\/ (M #\= 2 #/\ D in 29..30)
    #\/ (M in 1 \/ 3 \/ 5 \/ 7 \/ 8 \/ 10 \/ 12 #/\ D #= 31)
    #\/ (M #= 2 #/\ D #= 29 #/\ Y mod 400 #= 0)
    #\/ (M #= 2 #/\ D #= 29 #/\ Y mod 4 #= 0 #/\ Y mod 100 #\= 0)
    ).

%%	mjd(?MJD:integer) is det.
%
%	True if MJD is a valid modified Julian day number.
mjd(MJD) :-
    MJD in -2400328 .. 514671.

%%	day_of_week(?Datetime, ?DayOfWeek:atom) is det.
%
%	True Datetime occurs on the given day of the week.
day_of_week(datetime(MJD, _), DayOfWeek) :-
    (MJD+2) mod 7 #= DayNumber,
    day_name(DayNumber, DayOfWeek).

%%	day_name(?Number:integer, ?DayOfWeek:atom)
%
%	True if Number is the ISO number for DayOfWeek.
%	0 is Monday, 6 is Sunday.
day_name(0, monday).
day_name(1, tuesday).
day_name(2, wednesday).
day_name(3, thursday).
day_name(4, friday).
day_name(5, saturday).
day_name(6, sunday).


date_name(datetime(MJD,_Nano), gregorian(Year, Month, Day)) :-
    gregorian(Year, Month, Day),
    mjd(MJD),
    !,
    Y = 4716,
    V = 3,
    J = 1401,
    U = 5,
    M = 2,
    S = 153,
    N = 12,
    W = 2,
    R = 4,
    B = 274277,
    P = 1461,
    C = -38,
    F0 #= JD + J,
    F1 #= F0 + (((4 * JD + B)/146097) * 3)/4 + C,
    E #= R * F1 + V,
    G #= mod(E, P)/R,
    H #= U * G + W,
    Day #= (mod(H, S))/U + 1,
    Month #= mod(H/S + M, N) + 1,
    Year #= E/P - Y + (N + M - Month)/N,
    MJD #= JD - 2400001,
    ( ground(MJD) ->
        labeling([leftmost, up, step], [Year, Month, Day])
    ; ground(Year), ground(Month), ground(Day) ->
        labeling([leftmost, up, step], [MJD])
    ; true
    ).
date_name(Datetime, july_fourth) :-
    Y #>= 1776,
    date_name(Datetime, gregorian(Y,7,4)).


:- begin_tests(acceptable_gregorian_dates).
test(march_16_2013) :-
    gregorian(2013,3,16).

% leap year rules
test(1900, [fail]) :-
    gregorian(1900,2,29).
test(2000) :-
    gregorian(2012,2,29).
test(2012) :-
    gregorian(2012,2,29).
test(2013, [fail]) :-
    gregorian(2013,2,29).
test(2014, [fail]) :-
    gregorian(2014,2,29).
test(2016) :-
    gregorian(2016,2,29).
:- end_tests(acceptable_gregorian_dates).


:- begin_tests(gregorian_conversion).
test(march_16_2013) :-
    date_name(datetime(56367, _), gregorian(2013,3,16)).
test(unix_epoch) :-
    date_name(datetime(40587, _), gregorian(1970,1,1)).
:- end_tests(gregorian_conversion).

Find Fourth of July on a Sunday during Dwight Eisenhower's presidency:

?- use_module(library(clpfd)).
true.
?- Y in 1953..1961, date_name(Dt, (sunday,july_fourth,gregorian(Y,_,_))).
Y = 1954,
Dt = datetime(34927, _G44).