Homework 8🔗

Last updated: Tue, 31 Mar 2026 09:51:35 -0400

Out: Tue Mar 31 2026, 11am EST

Due: Tue Apr 07 2026, 11am EST

Overview🔗

This assignment continues to look at intertwined data, specifically the multidimensional Array, which will help us create our own programming language.

This hw will be graded accordingly:

Setup🔗

Create a new repository for this assignment by going to the CS450 Spring 2026 GitHub Organization and clicking "New".

Note: The CS450 Spring 2026 GitHub Organization must be the owner of the repository. Please do not create the repository in your own account.

On the "Create a new repository" screen:

• Name the repository hw<X>-<LASTNAME>-<FIRSTNAME> where <X> is the current homework number.

  For example, I would name my hw8 repository hw8-Chang-Stephen.

• Mark the repository as Private.

• Check "Add a README file".

• Select the Racket template for the .gitignore.

• Choose whatever you wish for the license.

When done click "Create repository".

Updating Racket450🔗

Make sure you have the latest version of racket450.

To do this from DrRacket, go to File -> Package Manager -> Currently Installed, search for "racket450", and then click "Update".

Alternatively, if you prefer the command line, run:

raco pkg update racket450

Reading🔗

Review Chapters 19-20 of the Textbook, and also Chapter 23 for multi-argument functions (where reading means trying to work through the examples and exercises interactively).

NOTE: The textbook will refer to "Student Languages" which we do not use in this course (and a "Stepper" that only works with the Student Languages). Instead, we use a version of Racket tailored for this course, which is invoked by putting #lang racket450 at the top of a file (see also Before Submitting).

Also, read any relevant sections of the The Design Recipe section of the course website (topics that will be covered in future lectures are marked as such).

Tasks🔗

The main code should go in a file named hw8.rkt that uses #lang racket450, as described previously.

NOTE, on using previous code: All assignments are designed so that it is quicker to complete them if you start from scratch and follow the Design recipe. No previous code or "solutions" to previous assignments are needed to complete any assignment. Do not attempt to complete this assignment by starting with some pile of code (from a previous assignment or anywhere else) and trying to "make it work". Doing this is almost always slower and you might not be able to finish the assignment on time if you do it this way (it also leads to tedious bugs that are hard to find and impossible to give help to). Finally, not following these instructions demonstrates a lack of understanding of course concepts—which focuses on the high-level programming process and not the final code—and thus will receive a low grade.

NOTE, on not automatically running code: The submitted program must be only a series of defines (both constants and function definitions are allowed). It should not run any code other than check-equal? Examples. Not following this will result in GradeScope errors and/or timeouts.

As usual, all submitted code must follow the The Design Recipe. This means that language features may only be used in the correct scenarios, as called for by The Design Recipe.

• For example, set! and other "imperative" features are not allowed ever.

• Conditionals such as if and cond are only to be used with the appropriate Data Definitions or in other appropriate scenarios described in class.

• Signatures should use define/contract and the predicates defined in the Data Design Recipe step. In this assignment, you may use the listof contract constructor where appropriate.

• For Examples and Tests, do not use check-expect from the Beginning Student Language (even though the textbook says to). Instead, use check-equal? or other testing forms from rackunit (which are built into racket450, so do not explicitly require rackunit).

• Examples for a function definition should be put before the define in hw8.rkt.

• Tests should be put a into hw8-tests.rkt file that uses #lang racket450/testing. Try to think about corner cases and code coverage.

• NOTE, on one-line helper functions: If the name and description of a "helper" function clearly describe what it does, and it clearly follows some Data Definition and all other Design Recipe steps (the course staff is the final arbiter of this), it does not need to be submitted with Examples and Tests if they are covered by other tests. ("Helper" functions are defined as functions not described in the homework assignment description.) NOTE: This does not change the Design Recipe. It is only changing submission requirements. As usual, however, we will not be able to help debug code that does not follow the Design Recipe, so omit these steps at your own risk.

• All other functions should have at minimum one Example and "sufficient" Tests.

Data Definitions

This HW will continue exploring multidimensional "arrays", as found in popular libraries like Python’s NumPy library. Specifically, define the following Data Definitions for this assignment:

• An Atom is one of:

  • Number

  • Bool

• An Array is one of:

  • Atom

  • ArrayList

  An ArrayList is one of:

  • empty

  • (cons Array ArrayList)

  Further, an Array has an additional invariant that it is "rectangular", meaning that along any one dimension, each element must have the same length. For example, in a 2d Array, all the rows must have the same length.

  Together, these intertwined data definitions, plus the invariants, represent all possible rectangular multi-dimensional array values.

  Though we have defined Array as a (potentially nested) list (of lists), to show the connection to existing libraries (and introduce some new Racket features), we will use an alternate constructor that resembles the array constructor in NumPy (Note: familiarity with this library it not needed to do this assignment).

  Specifically, in python, one might write:

  arr = numpy.array([1, 2, 3, 4, 5])

  In this assignment, define an alternate mk-array constructor that returns its argument unchanged (for now, though we can later add other parameters like the python constructor has). When used, the given argument should use the racket quote constructor (with square brackets, which are the same as round ones in Racket). So to define the same array as above in racket450, we write:

  (define arr (mk-array '[1 2 3 4 5]))

  Multi-dimensional arrays are just as straightforward.

  In python:

  arr = numpy.array([[1, 2, 3], [4, 5, 6]])

  arr = numpy.array([[[1, 2, 3], [4, 5, 6]], [[1, 2, 3], [4, 5, 6]]])

  In this assignment;

  (define arr (mk-array '[[1 2 3] [4 5 6]]))

  (define arr (mk-array '[[[1 2 3] [4 5 6]] [[1 2 3] [4 5 6]]]))

• You are allowed to define any other Data Defintions as you see fit

Array Functions

You will need to write the following functions that compute on Array.

To make things easier, we will use NumPy as a reference for expected behavior. Thus, you can refer to any implementation, e.g. this online demo, to help you understand the required functions and create Examples.

Note that this assignment does not require writing a lot of code and should be straightforward if you follow the The Design Recipe. In particular, you’ll need to spend a good amount of timing coming up with and understanding many different Examples. If you are still ignoring the Design Recipe, however, then it may be difficult to complete the assignment.

• a function array+ with Signature represented by contract (-> Array? Array? Array?)

  When two Arrays are the same dimensions, then the result should be the elementwise addition of the inputs, producing an output Array of the same dimensions.

  But two different-size Arrays may be added if the smaller one can be broadcast across the larger one. The smallest example of this is adding a single scalar number to an Array, which increments every element of the Array by that number.

  More generally, before attempting to add different-size Arrays, their dimensions (i.e., the result of a shape function from Homework 7) should be compared, in reverse order (you’ll likely need an accumulator function to do this). The two Arrays may be added if for each pair of dimensions (the following is taken from the NumPy docs on broadcasting):

  • they are equal

  • one of them is 1

  • one of them doesnt have that dimension, in which the missing dimension of that Array should be set to 1 by wrapping the Array in an additional outer Array (i.e., list in Racket)

  Hint: you should define a separate helper function that uses an accumulator to compute the broadcast.

  When one of the above conditions is not satisfied when comparing two dimensions, then the result should be an exception that is raised using error. You should define a struct named exn:fail:cs450:broadcast for this situation.

  Further, it should be possible to add non-numeric Arrays. More specifically, when adding a Boolean, it should first be coerced to a number as follows: true = 1 and false = 0. Make sure to define appropriate helper functions to help do the conversions.

API for Grading

Here is a summary of the required functions that are needed to properly grade the assignment

• mk-array

• array+

• exn:fail:cs450:broadcast?

Before Submitting🔗

Testing (and Autograders)

Before submitting, note:

• Each programmer is solely responsible for testing their program to make sure it’s correct. Do not submit until all code has been has a "sufficient" number of Test cases that verify its correctness.

• Note that there is no GradeScope "Autograder" available for students to use (an Autograder is not a software development/testing tool anyways, so it should not be used as one).

  Thus, no questions mentioning an Autograder will be answered, e.g., posts asking "why is the Autograder giving an error?" are not allowed.

  If you happen to find an Autograder and decide to look at its output despite this warning, please understand that it may be incorrect or incomplete, change at any time, or have random behavior, and that it in no way indicates the grade of the submitted hw.

  Anyone that does get useful information from an Autograder, e.g., a failing test case or crashing code report, should treat it as bonus information (that you otherwise would not have had) that you and you alone must determine what to do with.

  Regardless of what any Autograder might say, all code must still be independently tested to be correct before it is submitted.

• The proper way to ask questions is with small code examples. This means that each question must include a small example code snippet along with what the "expected" result should be!

  Further, any posted examples should contain the minimal amount of code needed to explain the question. Full file dumps or anything more than a few lines will not be accepted. More is not better. In fact it’s worse because it takes longer to read and is less likely to get a good answer.

Style

All code should follow proper Racket Style.

Also, the repository itself must follow proper style. Specifically, it must have appropriate commit messages. See How to Write a Git Commit Message if you are unsure how to write a commit message.

Note: Do not use the "file upload" feature on Github. The course staff may not accept hw uploaded in this way.

Files

A submission must have the following files in the repository root:

• hw8.rkt: Contains the hw solution code.

  The first line should be #lang racket450.

  All defines should use the name specified in the exercise (ask if you are unsure).

• hw8-tests.rkt: This file should use the #lang racket450/testing language.

  It should also require hw8.rkt and define tests for it.

  Specifically, it should contain "sufficient" Test cases (e.g., check-equal?, etc.) for each defined function.

• README.md: Contains the required README information, including the GitHub repo url.

Submitting🔗

When you are done, submit your work to Gradescope hw8. You must use the "GitHub" Submission Method and select your hw<X>-<LASTNAME>-<FIRSTNAME> repository.

Note that this is the only acceptable way to submit homework in this course. (Do not manually upload files and do not email files to the course staff. Homework submitted via any unapproved methods will not be graded.)