An Introduction to Functional Programming Through Lambda Calculus

- 199 -(tadd 7 nil) ->(7 nil nil)(tadd 4 ’(7 nil nil)) ->(7(4 nil nil)nil)(tadd 10 ’(7 (4 nil nil) nil)) ->(7(4 nil nil)(10 nil nil))(tadd 2 ’(7 (4 nil nil) (10 nil nil))) ->(7(4(2 nil nil)nil)(10 nil nil))(tadd 5 ’(7 (4 (2 nil nil) nil) (10 nil nil))) ->(7(4(2 nil nil)(5 nil nil))(10 nil nil))Hence, to add a list of numbers to an ordered binary tree:(defun taddlist (l tree)(if (null l)tree(taddlist (cdr l) (tadd (car l) tree))))Finally, to traverse a binary tree in ascending order:(defun traverse (tree)(if (null tree)nil(append (traverse (left tree))(cons (item tree) (traverse (right tree))))))For example:(traverse ’(7 (4 (2 nil nil) (5 nil nil) (10 nil nil))) ->(2 4 5 7 10)10.15. Dynamic and lexical scopeLISP is often presented as if it were based on the λ calculus but this is somewhat misleading. LISP functionabstraction uses a notation similar to the λ abstraction but the relationship between bound variables and variables inexpressions is rather opaque.In our presentation of λ calculus, names have lexical or static scope. That is, a name in an expression corresponds tothe bound variable of the innermost enclosing function to define it.