Description
References
Structure and Interpretation of Computer Programs
● Section 2.1.1 – the subsection titled Pairs describes cons, car and cdr
● Section 2.2 up to the end of Section 2.2.1, describes how lists are represented and
processed in Scheme/Racket
Two documents at the Racket website provide plenty of information about the Racket dialect of
Scheme:
The Racket Guide, https://docs.racket-lang.org/guide/index.html
● See Section 3.8, Pairs and Lists
The Racket Reference, https://docs.racket-lang.org/reference/index.html
● Section 4.9, Pairs and Lists, summarizes the Racket procedures that operate on
immutable lists and pairs.
A guide to the DrRacket IDE can be found here:
http://docs.racket-lang.org/drracket/index.html
Racket Coding Conventions
Please adhere to the conventions described in the Lab 1 handout.
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))
2
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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