% comment the next two lines out when testing - put back in to submit
:- initialization(q1).
:- initialization(q2).
:- initialization(q3).
:- initialization(end).

% FACTS.
mammal(kitty).
mammal(ratatat).
mammal(fido).
claws(kitty).
tail(ratatat).
bestfriend(fido).
feathers(tweety).

% 9 RULES.
% If X is a mammal then X has fur.
fur(X) :- mammal(X).

% If X has fur and X has a tail then X is a rat.
rat(X) :-
    fur(X),                                                                                                                                                                                                                                       fur(X),
    tail(X).

% If X has claws and X has fur then X is a cat.
cat(X) :-
    claws(X),
    fur(X).
% If X is a cat then X meows.
meows(X) :- cat(X).
% If X has feathers then X is a bird.
bird(X) :- feathers(X).
% If X is a bestfriend and X has fur then X is a dog.
dog(X) :-
    fur(X),
    bestfriend(X).
% If X is a dog and Y meows then X likes Y.
likes(X, Y) :-
    dog(X),
    meows(Y).
% If X is a cat and Y is a bird then X likes Y.
likes(X, Y) :-
    cat(X),
    bird(Y).
% If X is a cat and Y is a rat then X likes Y.
likes(X, Y) :-
    cat(X),
    rat(Y).

writeln(T) :- write(T), nl.

% QUERY. Uncomment after you have written all predicates.
q1 :- writeln('Who likes whom? '),
    findall(X, (likes(X,Y), format('~w ~w~n',[X,Y])),_).
q2 :- write('Move cnt for 5: '),
    findall(X, (moves(5,X), format('~w',[X])),_).
q3 :- nl, write('Max(7,3,9)? '),
    findall(X, (max3(7,3,9,X), format('~w ~n',[X])),_).
end :- writeln('done'), halt.

% Part B
max3(X, Y, Z, W) :-
    max2(X, Y, R),
    max2(X, Z, R2),
    max2(R, R2, R3),
    W is R3.

max2(X, Y, R) :-
    X > Y,
    R is X, !.
max2(_, Y, R) :-
    R is Y.

moves(X, R) :-
    X = 1,
    R is 1.
moves(X, R) :-
    X > 1, T1 is X - 1, T2 is X - 1,
    moves(T1, R1),
    moves(T2, R2),
    U is R1 + R2,
    R is U + 1.