## Description

Getting Started

Launch the DrRacket IDE.

If necessary, configure DrRacket so that the programming language is Racket. To do this, select

Language > Choose Language from the menu bar, then select The Racket Language in the

Choose Language dialog box.

#lang racket should appear at the top of the definitions area. Don’t delete this line.

“The Rules”

Do not use special forms that have not been presented in lectures. Specifically,

● Do not use set! to perform assignment; i.e., rebind a name to a new value.

● Do not use any of the Racket procedures that support mutable pairs and lists (mpair,

mcons, mcar, mcdr, set-mcar!, set-mcdr!), as described in Section 4.10 of The

Racket Reference.

● Do not use begin expressions to group expressions that are to be evaluated in sequence.

You can use lambda expressions to create procedures and let expressions to create local

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variables, but they aren’t required.

You are allowed to use the procedures that are described in these sections of The Racket

Reference:

● Section 4.9.1, Pair Constructors and Selector

● Section 4.9.2, List Operations

● Section 4.9.6, Pair Accessor Shorthands

● Section 4.9.7, Additional List Functions and Synonyms: empty, cons?, empty?, first,

rest, second through tenth, last, last-pair.

Unless otherwise noted, you are not allowed to use the procedures that are described in these

sections of The Racket Reference:

● Section 4.9.3, List Iteration

● Section 4.9.4, List Filtering

● Section 4.9.5, List Searching

● Section 4.9.7, Additional List Functions and Synonyms: with the exception of the

permitted procedures listed earlier.

● Section 4.9.8, Immutable Cyclic Data

You can save your solutions to the exercises in a single file; for example, lab2.rkt, or you can

create a different file for each exercise.

Exercise 1

Part (a) Define procedure (sum-numbers numbers). It takes a list of numbers as an argument

and returns their sum. Do not use Racket’s apply procedure to apply + to the list. Your

procedure must recursively sum the numbers.

Part (b) Define procedure (average numbers). It takes a list of numbers and returns their

average. This procedure must call the sum-numbers procedure you defined for part (a).

Exercise 2

Define procedure (occurrences numbers n). It takes a list of numbers and a number, and

calculates how many times the number occurs in the list. For example:

> (occurrences ‘(1 3 5 2 7 5 8 9 5) 5)

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Remember, you are not allowed to use any of Racket’s list searching procedures (The Racket

Reference, Sections 4.9.5 and 4.9.7).

Hint: review the contains? procedure posted on cuLearn before you attempt this exercise.

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Exercise 3

Define procedure convert. It takes a list of decimal digits and produces the corresponding

integer number. The first digit in the list is the least significant. For example:

> (convert (cons 1 (cons 2 (cons 3 empty))))

321

> (convert (list 4 5 6))

654

> (convert ‘(2))

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Exercise 4

Define procedure convertFC. It takes a list of temperature measurements in degrees Fahrenheit

and returns a list of the equivalent Celsius temperatures. Feel free to define “helper” procedure(s)

that are called by convertFC.

Remember, you are not allowed to use map or any of the other list iteration procedures provided

by Racket (The Racket Reference, Sections 4.9.3 and 4.9.7).

Exercise 5

Define procedure eliminate-threshold. This procedure takes a list of numbers and a

threshold value. It returns a list containing all numbers that are below or equal to the threshold.

For example,

> (eliminate-threshold (list 3 7 0 4 1 5) 4)

‘(3 0 4 1)

> (eliminate-threshold (list 3 7 0 4 1 5) -1)

‘() ; returns the empty list

Remember, you are not allowed to use map, filter, or any of the other “forbidden” procedures

listed in “The Rules” on Page 2.

Revised Feb. 8, 2018: In Exercises 1 and 2, changed the name of parameter list to numbers.

(list will be bound to a list of numbers when the procedure is called, which means the function

cannot call Racket’s list procedure).

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