Due by 11:59pm on Thursday, April 4

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, submit the assignment by uploading all code files you've edited to Gradescope. You may submit more than once before the deadline; only the final submission will be scored. Check that you have successfully submitted your code on 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:

• Scheme Specification
• Scheme Built-in Procedure Reference

Grading: Homework is graded based on correctness. Each incorrect problem will decrease the total score by one point. This homework is out of 2 points.

The 61A Scheme interpreter is included in each Scheme assignment. To start it, type python3 scheme in a terminal. To load a Scheme file called f.scm, type python3 scheme -i f.scm. To exit the Scheme interpreter, type (exit).

Scheme Editor

All Scheme assignments include a web-based editor that makes it easy to run ok tests and visualize environments. Type python3 editor in a terminal, and the editor will open in a browser window (at http://127.0.0.1:31415/). To stop running the editor and return to the command line, type Ctrl-C in the terminal where you started the editor.

The Run button loads the current assignment's .scm file and opens a Scheme interpreter, allowing you to try evaluating different Scheme expressions.

The Test button runs all ok tests for the assignment. Click View Case for a failed test, then click Debug to step through its evaluation.

Recommended VS Code Extensions

If you choose to use VS Code as your text editor (instead of the web-based editor), install the vscode-scheme extension so that parentheses are highlighted.

Before:

After:

In addition, the 61a-bot (installation instructions) VS Code extension is available for Scheme homeworks. The bot is also integrated into ok.

Required Questions

Q1: Pow

Implement a procedure pow that raises a base to the power of a nonnegative integer exp. The number of recursive pow calls should grow logarithmically with respect to exp, rather than linearly. For example, (pow 2 32) should result in 5 recursive pow calls rather than 32 recursive pow calls.

Hint:

1. x^2y = (x^y)²
2. x^2y+1 = x(x^y)²

For example, 2¹⁶ = (2⁸)² and 2¹⁷ = 2 * (2⁸)².

You may use the built-in predicates even? and odd?. Also, the square procedure is defined for you.

Scheme doesn't have while or for statements, so use recursion to solve this problem.

(define (square n) (* n n))

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

Use Ok to test your code:

python3 ok -q pow
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Q2: Repeatedly Cube

Implement repeatedly-cube, which receives a number x and cubes it n times.

Here are some examples of how repeatedly-cube should behave:

scm> (repeatedly-cube 100 1) ; 1 cubed 100 times is still 1
1
scm> (repeatedly-cube 2 2) ; (2^3)^3
512
scm> (repeatedly-cube 3 2) ; ((2^3)^3)^3
134217728

For information on let, see the Scheme spec.

(define (repeatedly-cube n x)
    (if (zero? n)
        x
        (let
            (_________________)
            (* y y y))))

Use Ok to test your code:

python3 ok -q repeatedly-cube
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Q3: Cadr

Note: Scheme lists are covered in the lecture videos for Wednesday, April 3.

Define the procedure cadr, which returns the second element of a list. Also define caddr, which returns the third element of a list.

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

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

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

Use Ok to test your code:

python3 ok -q cadr-caddr
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