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.

Preparation

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")

Finally, you can clone this git repository that provides a scheme.py Python interpreter: git clone https://github.com/BillJr99/scheme-interpreter.git. You can run it via python scheme.py 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:

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

Specifically, your anonymous lambda should compute:

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

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.

For your convenience, you may wish to also calculate the square root of the discriminant within this anonymous procedure (and you should feel free to do so!):

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

Note that the sqrt function is built into Scheme, so you can (sqrt x) for some expression x.

What to Do

Begin by writing the quadratic formula as a function that calls subfunctions. Define each of these functions. For example, you might have quadratic call discriminant and plusminus. discriminant computes the discriminant, and plusminus returns a list of values consisting of a + b and a - b for paramaters a and b. Note that when dividing a list of values by a scalar (i.e., dividing the plusorminus by 2 * a, you’ll need a function that dividies a list of two items by a scalar. The division operator does not do this natively. Here is a function you can use for this purpose:

(define div2 (lambda (L x)
   (list (/ (car L) x) (/ (car (cdr L)) x))
))

Test this function by calling quadratic with example values. Then, modify your program by replacing each function call with the lambda of the function (i.e., everything inside the define statement). Repeat this process until you have no more function calls, but only anonymous inner lambda statements. You should have a one-line main function that composes all your lambdas together! Run this, and you should obtain the same results as before.

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))

Your lambda procedure could be a function or an operator like * (which, if used in combination with + below, gives you the dot product of two vectors!).

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. Note that cxr is the cdr of the reverse of a list, reversed again. If you get an error that reverse cannot be found in your interpreter, you can paste the below code into your own program to provide that functionality. Note that you should only do this if your interpreter doesn’t have a native reverse function built in.:

(define reverse-helper (lambda (remaining reversed)
    (if (null? remaining)
        reversed
        (reverse-helper (cdr remaining) (cons (car remaining) reversed))
	)
))

(define reverse (lambda (lst)
  (reverse-helper lst '())
))

Submission

In your submission, please include answers to any questions asked on the assignment page, as well as the questions listed below, in your README file. If you wrote code as part of this assignment, please describe your design, approach, and implementation in a separate document prepared using a word processor or typesetting program such as LaTeX. This document should include specific instructions on how to build and run your code, and a description of each code module or function that you created suitable for re-use by a colleague. In your README, please 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.