Higher-Order Programming » Lab Sessions

Session 2 (Solutions)

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

Section 1: More Higher-Order Procedures

Exercise 1:

(define (flip f) (lambda (x y) (f y x)))

Exercise 2:

(define (iterate f n x) (if (= n 0) x (iterate f (- n 1) (f x)))) (define (iterate-until f p x) (if (p x) x (iterate-until f p (f x))))

Exercise 3:

(define (avg x y) (/ (+ x y) 2)) (define (pointwise-avg f g) (lambda (x) (avg (f x) (g x)))) (define (pointwise-min f g) (lambda (x) (min (f x) (g x)))) (define (pointwise-max f g) (lambda (x) (max (f x) (g x))))

Exercise 4:

(define (pointwise o) (lambda (f g) (lambda (x) (o (f x) (g x))))) (define pointwise-avg-2 (pointwise avg))

Bonus Exercises: Church Booleans

(define (c-choose b) (lambda (x y) (if b x y))) (define (c-not p) (lambda (x y) (p y x))) (define (c-or p q) (p p q)) (define (c-xor p q) (p (c-not q) q))