"Search new states f i r s t until goal is reached."

(tree-search ( l i s t start) goal-p successors #'append))

Let's see how we can search through the binary tree defined previously. First, we define the successor function b i nary- tree. It returns a list of two states, the two numbers that are twice the input state and one more than twice the input state. So the successors of 1 will be 2 and 3, and the successors of 2 will be 4 and 5. The b i na ry - t r e e function generates an infinite tree of which the first 15 nodes are diagrammed in our example.

(defun b i n a r y -tree (x) ( l i s t (* 2 x) (+ 1 (* 2 x))))