Higher-Order Programming » Lab Sessions

Session 0 (Solutions)

Lecturer: Jens Nicolay (jens.nicolay@vub.be) Assistant: Bjarno Oeyen (bjarno.oeyen@vub.be)

Numbers, Strings, Booleans...

Exercise 1

123 ; an exact number -42 ; an exact number 0.33333 ; an inexact number 1/3 ; an exact number #t ; a boolean #f ; a boolean "hello" ; a string "" ; a string "world" ; a string modulo ; a procedure even? ; a procedure + ; a procedure >= ; a procedure string-length ; a procedure

Each of these expressions evaluates to itself, with the exception of the procedures.

modulo, even?, +, >= and string-length are symbols that evaluate to a procedure.

Combinations

Exercise 2

(string-length "VUB") ; -> 3 (abs -7) ; -> 7 (modulo 13 4) ; -> 1 (even? 19) ; -> #f (string-length (string-append "Hello" " " "World")) ; -> 11 (string? "Guy L. Steele") ; -> #t (number? "Gerald Jay Sussman") ; -> #f (procedure? modulo) ; -> #t (procedure? procedure?) ; -> #t (boolean? (string? 5)) -> #t (+ 10 15) ; -> 10 + 15 = 25 (- 5) ; -> -(5) = -5 (/ 6 2) ; -> 6 / 2 = 3 (+) ; -> 0 (- 100 (* 5 5)) ; -> 100 - (5 * 5) = 100 - 25 = 75 (/ (+ 100 200 300) 3) ; -> (100 + 200 + 300) / 3 = 600 / 3 = 200

Side note: Guy L. Steele and Gerald Jay Sussman are the names of the original designers of the Scheme programming language.

Exercise 3

$$e_1 = \frac{a + b}{2}$$

(define e1 (/ (+ a b) 2))

$$e_2 = \frac{a + b}{e} - \frac{c + d}{f}$$

(define e2 (- (/ (+ a b) e) (/ (+ c d) f)))

$$e_3 = a\times{}a + 2\times{}a\times{}b + b\times{}b$$

(define e3 (+ (* a a) (* 2 a b) (* b b)))

$$e4 = \frac{a + \frac{b}{c}}{d} \times \frac{e}{\frac{g}{i} - h}$$

(define e4 (* (/ (+ a (/ b c)) d) (/ e (- (/ g i) h))))

Procedures

Exercise 4

(define (double a) (* a 2))

Exercise 5

(define (square a) (* a a))

Exercise 6

(define (celsius-to-fahrenheit c) (- (* (+ c 40) 1.8) 40))

And, the other way around.

(define (fahrenheit-to-celsius f) (- (/ (+ f 40) 1.8) 40))

Exercise 7

(define (average-of-three x y z) (/ (+ x y z) 3))