Higher-Order Programming » Lab Sessions

Session 6

Assistant: Steven Keuchel (steven.keuchel@vub.be)

Section 1: Environment Diagrams

Exercise 1: A Functional Environment Diagram

Using pen and paper, draw an environment diagram of evaluating (square 5) and (f 5) using the following definitions. You do not need to draw the definition of these 3 procedures.

(define (square x) (* x x)) (define (sum-of-squares x y) (+ (square x) (square y))) (define (f a) (sum-of-squares (+ a 1) (* a 2)))

Exercise 2: A Recursive Environment Diagram

The following is a solution of an earlier exercise.

(define (add-to-end lst a) (cond ((null? lst) (list a)) (else (cons (car lst) (add-to-end (cdr lst) a)))))

Draw an environment diagram when evaluating (add-to-end (list 1 2 3) 5).

Exercise 3: A Lexical Environment Diagram

Using pen and paper, draw an environment diagram of evaluating the following program.

(define c 3) (define (add-c x y) (+ x y c)) (define (sum x y c) (add-c x y)) (display (sum 20 30 40))

What is the displayed in the REPL? Is this the result you expected? What would be the result if Scheme had a dynamic scope (instead of a lexical scope)?

Exercise 4: A Functional Environment Diagram with Local Immutable State

Using pen and paper, draw an environment diagram of evaluating (increment10 20) and using the following definitions. Include the definitions of the two procedures in your diagram.

(define (make-incrementer c) (lambda (x) (+ x c))) (define increment10 (make-incrementer 10))