CSI 2120

Lab 9: Scheme

Exercise 1: Prefix Notation

Use Racket as an interactive Scheme calculator. Scheme uses prefix notation. Example:


(* 6 (- 10 5))

This expression will evaluate to 30 because 6 * (10 - 5) = 30.

Calculate the sum of the squares for the numbers 1 to 4. Hint: Your result should be 30.

Calculate both solutions to 2x^2 + 5x - 3 = 0.

Calculate the result of the sin(pi/4) cos(pi/3) + cos(pi/4) sin(pi/3)

Exercise 2: Local and Global Definitions

Global definition use define and local definition use let bindings.

Define a global constant


(define myFavorite 42)

Verify that you can use the definition.

Define locals with let


(let ((x 1) (y 2))
  (+ x y))

Verify that after the evaluation x and y are no longer defined, e.g. by using (* x y)

Use a local let binding for the angles to calculate sin(pi/4) cos(pi/3) + cos(pi/4) sin(pi/3) again.

Exercise 3: Procedures

Lambda expressions create local procedures.


((lambda (x y) (+ x y)) 1 2)

This code defines the lambda and then uses it with the arguments 1 and 2.

Use a lambda with the angles as arguments to calculate sin(pi/4) cos(pi/3) + cos(pi/4) sin(pi/3) again.

We can also define global procedures.


(define foo (lambda (x y) (+ x y)))

Call the function foo with 1 and 2 as arguments.

Note that the syntax of Scheme follows strict form. The first entry in a list is treated as a function. Lists are written with round brackets. In fact all the above calculations used a list to express the calculation.

You can find more information in our textbook The Scheme Programming Language by R. Kent Dybvig, especially, Section 2.5 Lambda Expressions.

Define a global function to calculate sin(alpha) cos(beta) + cos(alpha) sin(beta) with alpha and beta as parameters.

Exercise 4: Quadratic equation

Define a global function that finds both roots of a quadratic equation ax^2+bx+c = 0 with a,b,c as arguments. Note that you can calculate two solutions and return them as a list as follows:


(define foo (lambda (x y) (list (+ x y) (- x y))))