Lists Write the following predicates on lists.

• equal/2 meaning that both given lists are equal:

?- equal([3, 5, 2, 1], [3, 5, 2, 1]).

true

?- equal([3, 5, 2, 1], [1, 2, 3, 5]).

false

?- equal(bob, bob).

false

• contains/2 meaning that the list contains an element:

?- contains([3, 5, 2, 1], 2).

true

?- contains([3, 5, 2, 1], 4).

false

• reverse/2 meaning the first list is the reverse of the second.

?- reverse([3, 5, 2, 1], X).

X = [1, 2, 5, 3]

?- reverse (bob, X).

false

• sum/2 meaning the second member is the sum of elements in the first.

?- sum([3, 5, 2, 1], S).

S = 11

?- sum([], S).

S = 0

Binary trees
We will create a data structure that represents binary trees. Each node will be represented as bt(L, E, R), where L is the left subtree, R is the right subtree, and E is the element at the given note. An empty tree is denoted as the atom nil.

• Write the predicate binary_treee/1, that returns true if the argument is a binary tree:
?- binary_treee(nil)
true
?- binary_tree(bt(nil, 3, nil))
true
?- binary_tree(bt(bt(nil, 4, bt(nil, 5, nil)), 3, nil))
true
?- binary_tree(bt(nil, 3))
false

• Write the predicate in_order/2, that returns the list of arguments ordered by the in-order traversal (left-to-right: https://www. geeksforgeeks. org/tree-traversals-inorder-preorde r-and-postorder/ ):
?- in_order(bt(bt(nil, 4, bt(nil, 5, nil)), 3, nil), L)
L = [4, 5, 3]