% Fractions and rational numbers in Prolog
gcd(X,X,X):-!.
gcd(X,1, 1):-!.
gcd(1,X,1):-!.
gcd(X,0, X):-!.
gcd(0,X,X):-!.
gcd(X,Y,Z):-X>Y,!, XY is X mod Y, gcd(XY,Y,Z).
gcd(X,Y,Z):-X<Y,!, YX is Y mod X, gcd(X,YX,Z).

lcm(X,Y,LCM):-gcd(X,Y,GCD), LCM is X*Y//GCD.

reduce(A/A,1/1):-!.
reduce(A/1,A/1):-!.
reduce(1/A,1/A):-!.
reduce(A/B,C/D):-gcd(A,B,G), C is A//G, D is B//G.

propper(A/B,A/B):-A<B,!.
propper(A/A,1):-!.
propper(A/B,I+E/B):-I is A // B, E is A mod B.

val(A/B+C/D, E/F):- !, lcm(B,D,Den), N is A*(Den//B) + C*(Den//D), reduce(N/Den,E/F).
val(X+Y, E/F):- val(X, C/D), val(Y,A/B), !, val(C/D+A/B, E/F).

val(A/B-C/D, E/F):- !, lcm(B,D,Den), N is A*(Den//B) - C*(Den//D), reduce(N/Den,E/F).
val(X-Y, E/F):- val(X, C/D), val(Y,A/B), !, val(C/D-A/B, E/F).

val((A/B)*(C/D), E/F):- !, N is A*C, Den is B*D, reduce(N/Den,E/F).
val(X*Y, E/F):- val(X, C/D), val(Y,A/B), !, val((C/D)*(A/B), E/F).

val((A/B)/(C/D), E/F):- !, N is A*D, Den is B*C, reduce(N/Den,E/F).
val(X/Y, E/F):- val(X, C/D), val(Y,A/B), !, val((C/D)/(A/B), E/F).

val(-(A/B), MA/VB):- val(A/B,VA/VB), !, MA is - VA.
val(+(A/B), VA/VB):- val(A/B,VA/VB), !.

val(A/B, RA/RB):- VA is A, VB is B, !, reduce(VA/VB, RA/RB).

val(A, VA/1):-VA is A.

go:-prompt(_, 'Expression=? '), repeat, read(Term), val(Term,Val),  write(Val), nl,	propper(Val,PVal),  write(PVal), nl.
:- write('Input "go."... end the expression with a period.'), nl.