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

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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

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(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

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

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

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

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

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

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

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

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

Procedures

Exercise 4

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

Exercise 5

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

Exercise 6

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

And, the other way around.

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

Exercise 7

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