Homework 7: Scheme

Instructions

Download hw07.zip. Inside the archive, you will find a file called hw07.scm, along with a copy of the ok autograder.

Submission: When you are done, zip up your assignment and submit it through Gradescope. See Lab 0 for more instructions on submitting assignments.

Using Ok: If you have any questions about using Ok, please refer to this guide.

Readings: You might find the following references useful:

Grading: Homework is graded based on correctness. Each incorrect problem will decrease the total score by one point. There is a homework recovery policy as stated in the syllabus. This homework is out of 2 points.

Scheme is a famous functional programming language from the 1970s. It is a dialect of Lisp (which stands for LISt Processing). The first observation most people make is the unique syntax, which uses a prefix notation and (often many) nested parentheses (see http://xkcd.com/297/). Scheme features first-class functions and optimized tail-recursion, which were relatively new features at the time.

You may find it useful to try code.cs61a.org/scheme when working through problems, as it can draw environment and box-and-pointer diagrams and it lets you walk your code step-by-step (similar to Python Tutor). Don't forget to submit your code through Ok though!

Scheme Editor

As you're writing your code, you can debug using the Scheme Editor. In your scheme folder you will find a new editor. To run this editor, run python3 editor. This should pop up a window in your browser; if it does not, please navigate to localhost:31415 and you should see it.

Make sure to run python3 ok in a separate tab or window so that the editor keeps running.

If you find that your code works in the online editor but not in your own interpreter, it's possible you have a bug in code from an earlier part that you'll have to track down. Every once in a while there's a bug that our tests don't catch, and if you find one you should let us know!

Required Questions

Q1: Thane of Cadr

Define the procedures cadr and caddr, which return the second and third elements of a list, respectively. If you would like a quick refresher on scheme syntax consider looking at Lab 10 Scheme Refresher.

(define (cddr s)
  (cdr (cdr s)))

(define (cadr s)
  'YOUR-CODE-HERE
)

(define (caddr s)
  'YOUR-CODE-HERE
)

Use Ok to unlock and test your code:

python3 ok -q cadr-caddr -u

python3 ok -q cadr-caddr

Q2: Ordered

Implement a procedure called ordered?, which takes a list of numbers and returns True if the numbers are in nondescending order, and False otherwise. Numbers are considered nondescending if each subsequent number is either larger or equal to the previous, that is:

1 2 3 3 4

Is nondescending, but:

1 2 3 3 2

Is not.

Hint: The built-in null? function returns whether its argument is nil.

(define (ordered? s)
  'YOUR-CODE-HERE
)

Use Ok to unlock and test your code:

python3 ok -q ordered -u

python3 ok -q ordered

Q3: Pow

Implement a procedure pow for raising the number base to the power of a nonnegative integer exp for which the number of operations grows logarithmically, rather than linearly (the number of recursive calls should be much smaller than the input exp). For example, for (pow 2 32) should take 5 recursive calls rather than 32 recursive calls. Similarly, (pow 2 64) should take 6 recursive calls.

Hint: Consider the following observations:

\( x^{2y} = (x^y)^2 \)

\( x^{2y + 1} = x(x^y)^2 \)

For example we see that \( 2^{32} = (2^{16})^2 \), \( 2^{16} = (2^8)^2 \), etc. You may use the built-in predicates even? and odd?. Scheme doesn't support iteration in the same manner as Python, so consider another way to solve this problem.

(define (square x) (* x x))

(define (pow base exp)
  'YOUR-CODE-HERE
)

Use Ok to unlock and test your code:

python3 ok -q pow -u

python3 ok -q pow