%%%% File: combosets.pro
%%%% Line: Generate Combos and Permutations
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% The permutation facts
% Permutations of Order 2
perm(s(A,B),p(A,B)).
perm(s(A,B),p(B,A)).
% Permutations of Order 3
perm(s(A,B,C),p(A,X,Y)) :- perm(s(B,C),p(X,Y)).
perm(s(A,B,C),p(B,X,Y)) :- perm(s(A,C),p(X,Y)).
perm(s(A,B,C),p(C,X,Y)) :- perm(s(A,B),p(X,Y)).
% Permutations of Order 4
perm(s(A,B,C,D),p(A,X,Y,Z)) :- perm(s(B,C,D),p(X,Y,Z)).
perm(s(A,B,C,D),p(B,X,Y,Z)) :- perm(s(A,C,D),p(X,Y,Z)).
perm(s(A,B,C,D),p(C,X,Y,Z)) :- perm(s(A,B,D),p(X,Y,Z)).
perm(s(A,B,C,D),p(D,X,Y,Z)) :- perm(s(A,B,C),p(X,Y,Z)).
% Permutations of Order 5
perm(s(A,B,C,D,E),p(A,X,Y,Z,W)) :- perm(s(B,C,D,E),p(X,Y,Z,W)).
perm(s(A,B,C,D,E),p(B,X,Y,Z,W)) :- perm(s(A,C,D,E),p(X,Y,Z,W)).
perm(s(A,B,C,D,E),p(C,X,Y,Z,W)) :- perm(s(B,A,D,E),p(X,Y,Z,W)).
perm(s(A,B,C,D,E),p(D,X,Y,Z,W)) :- perm(s(B,C,A,E),p(X,Y,Z,W)).
perm(s(A,B,C,D,E),p(E,X,Y,Z,W)) :- perm(s(B,C,D,A),p(X,Y,Z,W)).
%% Permutation rules
% Permutations of Order 2
permutation(A,B) :-
perm(s(A,B),p(V,W)),
write(V),write(' '),write(W),nl,
fail.
% Permutations of Order 3
permutation(A,B,C) :-
perm(s(A,B,C),p(V,W,X)),
write(V),write(' '),write(W),write(' '),write(X),nl,
fail.
% Permutations of Order 4
permutation(A,B,C,D) :-
perm(s(A,B,C,D),p(V,W,X,Y)),
write(V),write(' '),write(W),write(' '),write(X),write(' '),write(Y),nl,
fail.
% Permutations of Order 5
permutation(A,B,C,D,E) :-
perm(s(A,B,C,D,E),p(V,W,X,Y,Z)),
write(V),write(' '),write(W),write(' '),write(X),write(' '),write(Y),write(' '),write(Z),nl,
fail.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% The combination facts
% Combin of 3
combos(set(N1,N2,N3),combo(N1,N2),extras(N3)).
combos(set(N1,N2,N3),combo(N2,N3),extras(N1)).
combos(set(N1,N2,N3),combo(N1,N3),extras(N2)).
% Combin of 4
combos(set(N1,N2,N3,N4),combo(N1,N2),extras(N3,N4)).
combos(set(N1,N2,N3,N4),combo(N1,N3),extras(N2,N4)).
combos(set(N1,N2,N3,N4),combo(N1,N4),extras(N2,N3)).
combos(set(N1,N2,N3,N4),combo(N2,N3),extras(N1,N4)).
combos(set(N1,N2,N3,N4),combo(N2,N4),extras(N1,N3)).
combos(set(N1,N2,N3,N4),combo(N3,N4),extras(N1,N2)).
% Combin of 5
combos(set(N1,N2,N3,N4,N5),combo(N1,N2),extras(N3,N4,N5)).
combos(set(N1,N2,N3,N4,N5),combo(N1,N3),extras(N2,N4,N5)).
combos(set(N1,N2,N3,N4,N5),combo(N1,N4),extras(N2,N3,N5)).
combos(set(N1,N2,N3,N4,N5),combo(N1,N5),extras(N2,N3,N4)).
combos(set(N1,N2,N3,N4,N5),combo(N2,N3),extras(N1,N4,N5)).
combos(set(N1,N2,N3,N4,N5),combo(N2,N4),extras(N1,N3,N5)).
combos(set(N1,N2,N3,N4,N5),combo(N2,N5),extras(N1,N3,N4)).
combos(set(N1,N2,N3,N4,N5),combo(N3,N4),extras(N1,N2,N5)).
combos(set(N1,N2,N3,N4,N5),combo(N3,N5),extras(N1,N2,N4)).
combos(set(N1,N2,N3,N4,N5),combo(N4,N5),extras(N1,N2,N3)).