4.2. ARITHMETIC EXPRESSIONS IN SCHEME

49

; hypotenuse34.servlet    this returns the length

; of the hypotenuse of a right triangle who other sides

; have length 3 and 4

(sqrt (+ (* 3 3) (* 4 4)))

This servlet contains a more complex scheme expression with four operators (two

multiplication operators  * , one addition  + , and one square root  sqrt ).

The Scheme server evaluates such an expression by first evaluating the innermost

expressions (* 3 3) and (* 4 4) to get 9 and 16 respectively. These values

are subsituted back into the expression to yield the simpler expression:

(sqrt (+ 9 16))

Next the sum is evaluated to yield 25 which is substituted back into the expres 

sion to get:

(sqrt 25)

which evaluates to

5.0

and this is sent back to the browser.

Scheme provides a large set of arithmetic operators including the following

(+ a b ... c) addition

(  a b) subtraction

(* a b ... c) multiplication

(/ a b) division

(sqrt a) square root

(exp a) exponential function

(log a) natural logarithm

(sin a) sine (in radians)

(cos a) cosine (in radians)

(tan a) tangent (in radians)

(asin a) arcsin

(acos a) arccosine

(atan a) arctangent

(round a) rounds to the nearest integer

(expt a b) raise a to the b power

Exercise 2 What is the result of evaluating the following Scheme expressions:

(* 1 2 3 4 5)

(+ 5 (* 3 (+ 6 (* 7 2))))

(+ (* 1 1) (* 2 2) (* 3 3) (* 4 4) (* 5 5))