L4 v2 BIA

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%tree(5, tree(3, tree(1, null, null), tree(4, null, null)), tree(7,
% null, null)).

%1.
add(null, S) :- S is 0.
add(tree(X,Y,Z), S) :- add(Y, S1), add(Z, S2), S is X + S1 + S2.

%2.
count_leaves(null, Count) :- Count is 0.
count_leaves(tree(_, null, null), Count) :- !, Count is 1.
count_leaves(tree(_,Y,Z), Count) :- count_leaves(Y, Count1), count_leaves(Z, Count2), Count is Count1 + Count2.

%3.
rootValue(tree(X, _, _), Y) :- Y is X.
compute(tree(X, null, null), Result) :- number(X), !, Result is X.
compute(tree(+, X, Y), Result) :- compute(X, Op1), compute(Y, Op2), Result is Op1 + Op2.
compute(tree(-, X, Y), Result) :- compute(X, Op1), compute(Y, Op2), Result is Op1 - Op2.
compute(tree(*, X, Y), Result) :- compute(X, Op1), compute(Y, Op2), Result is Op1 * Op2.
compute(tree(/, X, Y), Result) :- compute(X, Op1), compute(Y, Op2), Result is Op1 / Op2.

%4.
%
convert(X, Result) :- Result = tree(X, null, null),number(X).
convert(X+Y, Result) :- Result = tree(+, X1, Y1),convert(X, X1), convert(Y, Y1) .
convert(X-Y, Result) :-Result = tree(-, X1, Y1), convert(X, X1), convert(Y, Y1).
convert(X*Y, Result) :- Result = tree(*, X1, Y1),convert(X, X1), convert(Y, Y1).
convert(X/Y, Result) :- Result = tree(/, X1, Y1),convert(X, X1), convert(Y, Y1) .