An Introduction to Functional Programming Through Lambda Calculus

- 137 -TFIND 5 [4,[3,EMPTY,EMPTY],[5,EMPTY,EMPTY]] -> ... ->TFIND 5 [5,EMPTY,EMPTY] -> ... ->TRUEFor example:TFIND 2 [7,[4,[3,EMPTY,EMPTY],[5,EMPTY,EMPTY]],[9,EMPTY,EMPTY]] -> ... ->TFIND 2 [4,[3,EMPTY,EMPTY],[5,EMPTY,EMPTY]] -> ... ->TFIND 2 [3,EMPTY,EMPTY] -> ... ->TFIND 2 EMPTY -> ... ->FALSE7.13. Binary trees of composite valuesBinary trees, like linear lists, may be used to represent ordered sequences of composite values. Each node holds onecomposite value from the sequence and the ordering is determined by one sub-value.The tree addition functions above may be modified to work with composite values. For example, we might hold thecirculation list of names in a binary tree in surname order. Adding a new name to the tree involves comparing the newsurname with the node surnames:rec CTADD N EMPTY = [N,EMPTY,EMPTY]or CTADD [F,S] [[NF,NS],L,R] =IF STRING_LESS S NSTHEN [[NF,NS],(CTADD [F,S] L),R]ELSE [[NF,NS],L,(CTADD [F,S] R)]rec CTADDLIST [] TREE = TREEor CTADDLIST (H::T) TREE = CTADDLIST T (CTADD H TREE)For example:CTADDLIST[["Mark","Monkey"],["Graham","Goat"],["Quentin","Quail"],["James","Jaguar"],["David","Duck]] EMPTY -> ... ->