Write a lookup predicate that looks up a value in a binary search tree like the kind defined in example 7.10.

As mentioned earlier in the text, Prolog originated out of Colmerauer’s interest in using logic to express grammar rules and to formalize the parsing of natural language sentences. Kowalski and Comerauer solved this problem together and Colmerauer figured out how to encode the grammar as predicates so sentences could be parsed efficiently. The next sections describe the implementation of parsing Colmerauer devised in 1972.

example 7.10.

Consider implementing a lookup predicate for a binary search tree in Prolog. A tree may be defined recursively as either nil or a btnode(Val,Left,Right) where Val is the value stored at the node and Left and Right represent the left and right binary search trees. The recursive definition of a binary search tree says that all values in the left subtree must be less than Val and all values in the right subtree must be greater than Val. For this example, let’s assume that binary search trees don’t have duplicate values stored in them. A typical binary search tree structure might look something like this:

which corresponds to the tree shown graphically here.

Items may be inserted into and deleted from a binary search tree. Since Prolog programmers write predicates, the code to insert into and delete from a binary search tree must reflect the before and after picture. Because a binary search tree is recursively defined, each part of the definition will be part of a corresponding case for the insert and delete predicates. So, inserting into a search tree involves the value to insert, the tree before it was inserted, and the tree after it was inserted. Similarly, a delete predicate involves the same three arguments. Looking up a value in a binary search tree results in a true or false response, which is the definition of a predicate. Writing a lookup predicate requires the value and the search tree in which to look for the value.