% terms are either:
% atoms:
% green, sokrates, appl3, ',' 

% variables:
% X, Xs, _ , _Argument

% functions applied to arguments (functors)
% human(sokrates), human(X), cons(Head, Tail)

% facts
colour(green).
colour(red).

% rules.
colour(X) :- X = green
          ;   X = red.

colour(X) :- X = green
          ;   X = red.

human(sokrates).
human(plato).
human(aristoteles).

% Think about ':-' as a reversed implication arrow '<-'

mortal(X) :- human(X).

adjacent(a, b).
adjacent(b, c).
adjacent(c, d).
adjacent(d, a).

connected(X, Y) :-
    adjacent(X, Y).

connected(X, Y) :-
    adjacent(Y, X).

% member(X, L) : true if X is a member of L

memberP(X , [X | _]).
memberP(X , [H | T]) :-
    dif(X, H),
    memberP(X, T).

% appendP(Xs, Ys, Zs) : true if Zs is the concat of Xs and Ys

myReverse([], []).
myReverse([H | T], Ys) :-
    myReverse(T, Tr),
    append(Tr, [H], Ys).

myReverseAcc(Xs, Ys) :-
    myReverseAcc(Xs, [], Ys).

myReverseAcc([], X, X).
myReverseAcc([H | T], Acc, Ys) :-
    myReverseAcc(T, [H | Acc], Ys).


%myDelete(X, L, R) holds if R is the list where all occurences of X have been removed
myDelete(_ , [], []).
myDelete(X , [X | T], R ) :-
    myDelete(X, T, R).
myDelete(X, [H | T], [H | R]) :-
    dif(X, H),
    myDelete(X, T, R).

removeDuplicates([], []).
removeDuplicates([H | T], [H | Ys]) :-
    myDelete(H, T, R),
    removeDuplicates(R, Ys).

% takeout(X, L, R) holds if R is the list where the first occurence of X in L (that must exist) is removed.
% alternatively: holds if L is a list that is the result of inserting X somewhere in R.
takeout(X, [X | T], T).
takeout(X, [H | T], [H | Ys]) :-
    dif(X, H),
    takeout(X, T, Ys).

myPermutations([], []).
myPermutations([H | T], Ys) :-
    myPermutations(T, T1),
    takeout(H, Ys, T1).

% Collect all solutions to myPermutations([a,b,c], X) in a list Xs:
% ?- findall(X, myPermutations([a,b,c], X), Xs).