CS374: Principles of Programming Languages - Functional Programming (100 Points)

Assignment Goals

The goals of this assignment are:
  1. To explore the functional programming paradigm using the Scheme language

Background Reading and References

Please refer to the following readings and examples offering templates to help get you started:

The Assignment

The purpose of this assignment is to explore the functional programming paradigm in Scheme.


If you have not already, install scheme on your computer. If you can type scheme and hit Enter, and see Scheme load, you are ready to proceed. If you need to install Scheme on Ubuntu, you can execute this command:

sudo apt update && sudo apt install mit-scheme

or install Homebrew on the mac, and run this command from the Mac terminal:

brew install mit-scheme

Alternatively, you can use a web-based IDE such as repl.it.

When you run scheme, you’ll be presented with an interpreter where you can write or paste code directly, or use the following command to load a file (here, called myfile.scm, from your current directory (from which you started scheme):

(load "myfile.scm")

Part 1: Warmup with Lambda Procedures

Using lambda, define a procedure that computes a value on a line according to the classic formula:

\(y = mx + b\)

Part 2: Warmup with Anonymous Lambda Procedures

Define an anonymous or secondary lambda procedure to compute the discriminant of a quadratic function:

\(x1, x2 = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\)

Specificaly, your anonymous lambda should compute:

\(\sqrt{b^{2} - 4ac}\)

And you can compose and return a list from your main lambda procedure that adds to, and subtracts from, the discriminant to obtain your two roots.

Part 3: Mapping

Using an anonymous lambda procedure, create a map that applies your anonymous lambda to two lists. map works like this:

(map <your lambda procedure> '(1 2 3) '(4 5 6))

This map will apply your lambda procedure to each pair of items in the list (1 and 4, 2 and 5, and 4 and 6). Your lambda should accept, then, two parameters. Modify this map to multiply each pair of items together.

Next, you can use apply to reduce this list. Prepend the following (and balnace the parentheses on the right) to compute the dot product of the two lists by adding together all the items in the resulting list:

(apply + <your map here>)

Part 4: Working with Lists

Write a lambda procedure called czr which returns the last item in the list. If the cdr of the list is null, then you have found the last item: otherwise, you can recurse into czr on the cdr of the list until the last item is found.

Write a second lambda function called cxr that returns everything except the last item in the list. You may write or find (and cite) a procedure to reverse a list, and note that cxr is the cdr of the reverse of a list, reversed again.

You can append two lists together as follows (where '(1 2 3) and '(4 5 6) are lists that can also be variables or recursive function calls that return lists! The result is (1 2 3 4 5 6)):

(append (list 1 2 3) (list 4 5 6))


In your submission, please include answers to any questions asked on the assignment page in your README file. If you wrote code as part of this assignment, please describe your design, approach, and implementation in your README file as well. Finally, include answers to the following questions:
  • Describe what you did, how you did it, what challenges you encountered, and how you solved them.
  • Please answer any questions found throughout the narrative of this assignment.
  • If collaboration with a buddy was permitted, did you work with a buddy on this assignment? If so, who? If not, do you certify that this submission represents your own original work?
  • Please identify any and all portions of your submission that were not originally written by you (for example, code originally written by your buddy, or anything taken or adapted from a non-classroom resource). It is always OK to use your textbook and instructor notes; however, you are certifying that any portions not designated as coming from an outside person or source are your own original work.
  • Approximately how many hours it took you to finish this assignment (I will not judge you for this at all...I am simply using it to gauge if the assignments are too easy or hard)?
  • Your overall impression of the assignment. Did you love it, hate it, or were you neutral? One word answers are fine, but if you have any suggestions for the future let me know.
  • Using the grading specifications on this page, discuss briefly the grade you would give yourself and why. Discuss each item in the grading specification.
  • Any other concerns that you have. For instance, if you have a bug that you were unable to solve but you made progress, write that here. The more you articulate the problem the more partial credit you will receive (it is fine to leave this blank).

Assignment Rubric

Description Pre-Emerging (< 50%) Beginning (50%) Progressing (85%) Proficient (100%)
Algorithm Implementation (60%) The algorithm fails on the test inputs due to major issues, or the program fails to compile and/or run The algorithm fails on the test inputs due to one or more minor issues The algorithm is implemented to solve the problem correctly according to given test inputs, but would fail if executed in a general case due to a minor issue or omission in the algorithm design or implementation A reasonable algorithm is implemented to solve the problem which correctly solves the problem according to the given test inputs, and would be reasonably expected to solve the problem in the general case
Code Quality and Documentation (30%) Code commenting and structure are absent, or code structure departs significantly from best practice, and/or the code departs significantly from the style guide Code commenting and structure is limited in ways that reduce the readability of the program, and/or there are minor departures from the style guide Code documentation is present that re-states the explicit code definitions, and/or code is written that mostly adheres to the style guide Code is documented at non-trivial points in a manner that enhances the readability of the program, and code is written according to the style guide
Writeup and Submission (10%) An incomplete submission is provided The program is submitted, but not according to the directions in one or more ways (for example, because it is lacking a readme writeup) The program is submitted according to the directions with a minor omission or correction needed, and with at least superficial responses to the bolded questions throughout The program is submitted according to the directions, including a readme writeup describing the solution, and thoughtful answers to the bolded questions throughout

Please refer to the Style Guide for code quality examples and guidelines.