lab09

Lab 9: Scheme | CS 61A Spring 2024

Lab 9: Scheme​

• lab09.zip

Due by 11:59pm on Wednesday, April 3.

Starter Files​

Download lab09.zip. Inside the archive, you will find starter files for the questions in this lab, along with a copy of the Ok autograder.

Scheme Introduction​

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:

Required Questions​

Getting Started Videos​

These videos may provide some helpful direction for tackling the coding problems on this assignment.

To see these videos, you should be logged into your berkeley.edu email.

YouTube link

Consult the drop-downs below if you need a refresher on Scheme. It's okay to skip directly to the questions and refer back here should you get stuck.

Atomic expressions (also called atoms) are expressions without sub-expressions, such as numbers, boolean values, and symbols.

scm> 1234    ; integer1234scm> 123.4   ; real number123.4scm> #f      ; the Scheme equivalent of False in Python#f

A Scheme symbol is equivalent to a Python name. A symbol evaluates to the value bound to that symbol in the current environment. (They are called symbols rather than names because they include + and other arithmetic symbols.)

scm> quotient      ; A symbol bound to a built-in procedure#[quotient]scm> +             ; A symbol bound to a built-in procedure#[+]

In Scheme, all values except #f (equivalent to False in Python) are true values (unlike Python, which has other false values, such as 0).

scm> #t#tscm> #f#f

Scheme uses Polish prefix notation, in which the operator expression comes before the operand expressions. For example, to evaluate 3 * (4 + 2), we write:

scm> (* 3 (+ 4 2))18

Just like in Python, to evaluate a call expression:

1. Evaluate the operator. It should evaluate to a procedure.
2. Evaluate the operands, left to right.
3. Apply the procedure to the evaluated operands.

Here are some examples using built-in procedures:

scm> (+ 1 2)3scm> (- 10 (/ 6 2))7scm> (modulo 35 4)3scm> (even? (quotient 45 2))#t

Define: The define form is used to assign values to symbols. It has the following syntax:

(define <symbol> <expression>)

scm> (define pi (+ 3 0.14))piscm> pi3.14

To evaluate the define expression:

1. Evaluate the final sub-expression (<expression>), which in this case evaluates to 3.14.
2. Bind that value to the symbol (symbol), which in this case is pi.
3. Return the symbol.

The define form can also define new procedures, described in the "Defining Functions" section.

If Expressions: The if special form evaluates one of two expressions based on a predicate.

(if <predicate> <if-true> <if-false>)

The rules for evaluating an if special form expression are as follows:

1. Evaluate the <predicate>.
2. If the <predicate> evaluates to a true value (anything but #f), evaluate and return the value of the <if-true> expression. Otherwise, evaluate and return the value of the <if-false> expression.

For example, this expression does not error and evaluates to 5, even though the sub-expression (/ 1 (- x 3)) would error if evaluated.

scm> (define x 3)xscm> (if (> (- x 3) 0) (/ 1 (- x 3)) (+ x 2))5

The <if-false> expression is optional.

scm> (if (= x 3) (print x))3

Let's compare a Scheme if expression with a Python if statement:

Scheme

Python

|

scm> (if (> x 3) 1 2)

|

>>> if x > 3:...     1... else:...     2

|

The Scheme if expression evaluates to a number (either 1 or 2, depending on x). The Python statement does not evaluate to anything, and so the 1 and 2 cannot be used or accessed.

Another difference between the two is that it's possible to add more lines of code into the suites of the Python if statement, while a Scheme if expression expects just a single expression in each of the <if-true> and <if-false> positions.

One final difference is that in Scheme, you cannot write elif clauses.

Cond Expressions: The cond special form can include multiple predicates (like if/elif in Python):

(cond    (<p1> <e1>)    (<p2> <e2>)    ...    (<pn> <en>)    (else <else-expression>))

The first expression in each clause is a predicate. The second expression in the clause is the return expression corresponding to its predicate. The else clause is optional; its <else-expression> is the return expression if none of the predicates are true.

The rules of evaluation are as follows:

1. Evaluate the predicates <p1>, <p2>, ..., <pn> in order until one evaluates to a true value (anything but #f).
2. Evalaute and return the value of the return expression corresponding to the first predicate expression with a true value.
3. If none of the predicates evaluate to true values and there is an else clause, evaluate and return <else-expression>.

For example, this cond expression returns the nearest multiple of 3 to x:

scm> (define x 5)xscm> (cond ((= (modulo x 3) 0) x)            ((= (modulo x 3) 1) (- x 1))            ((= (modulo x 3) 2) (+ x 1)))6

Lambdas: The lambda special form creates a procedure.

(lambda (<param1> <param2> ...) <body>)

This expression will create and return a procedure with the given formal parameters and body, similar to a lambda expression in Python.

scm> (lambda (x y) (+ x y))        ; Returns a lambda procedure, but doesn't assign it to a name(lambda (x y) (+ x y))scm> ((lambda (x y) (+ x y)) 3 4)  ; Create and call a lambda procedure in one line7

Here are equivalent expressions in Python:

>>> lambda x, y: x + y<function <lambda> at ...>>>> (lambda x, y: x + y)(3, 4)7

The <body> may contain multiple expressions. A scheme procedure returns the value of the last expression in its body.

The define form can create a procedure and give it a name:

(define (<symbol> <param1> <param2> ...) <body>)

For example, this is how we would define the double procedure:

scm> (define (double x) (* x 2))doublescm> (double 3)6

Here's an example with three arguments:

scm> (define (add-then-mul x y z)        (* (+ x y) z))scm> (add-then-mul 3 4 5)35

When a define expression is evaluated, the following occurs:

1. Create a procedure with the given parameters and <body>.
2. Bind the procedure to the <symbol> in the current frame.
3. Return the <symbol>.

The following two expressions are equivalent:

scm> (define add (lambda (x y) (+ x y)))addscm> (define (add x y) (+ x y))add

Q1: Over or Under​

Define a procedure over-or-under which takes in a number num1 and a number num2 and returns the following:

• -1 if num1 is less than num2
• 0 if num1 is equal to num2
• 1 if num1 is greater than num2

Challenge: Implement this in 2 different ways using if and cond!

(define (over-or-under num1 num2)  'YOUR-CODE-HERE)

Use Ok to test your code:

python3 ok -q over_or_under

Q2: Make Adder​

Write the procedure make-adder which takes in an initial number, num, and then returns a procedure. This returned procedure takes in a number inc and returns the result of num + inc.

Hint: To return a procedure, you can either return a lambda expression or define another nested procedure. Remember that Scheme will automatically return the last clause in your procedure.

You can find documentation on the syntax of lambda expressions in the 61A scheme specification!

(define (make-adder num)  'YOUR-CODE-HERE)

Use Ok to test your code:

python3 ok -q make_adder

Q3: Compose​

Write the procedure composed, which takes in procedures f and g and outputs a new procedure. This new procedure takes in a number x and outputs the result of calling f on g of x.

(define (composed f g)  'YOUR-CODE-HERE)

Use Ok to test your code:

python3 ok -q composed

Q4: Repeat​

Write the procedure repeat, which takes in a procedure f and a number n, and outputs a new procedure. This new procedure takes in a number x and outputs the result of applying f to x a total of n times. For example:

scm> (define (square x) (* x x))squarescm> ((repeat square 2) 5) ; (square (square 5))625scm> ((repeat square 3) 3) ; (square (square (square 3)))6561scm> ((repeat square 1) 7) ; (square 7)49

Hint: The composed function you wrote in the previous problem might be useful.

(define (repeat f n)  'YOUR-CODE-HERE)

Use Ok to test your code:

python3 ok -q repeat

Q5: Greatest Common Divisor​

The GCD is the the greatest common divisor of two positive integers.

Write the procedure gcd, which computes the GCD of numbers a and b using Euclid's algorithm, which uses the fact that the GCD of two values is either of the following:

• the smaller value if it evenly divides the larger value, or
• the greatest common divisor of the smaller value and the remainder of the larger value divided by the smaller value

In other words, if a is greater than b and a is not divisible by b, then

gcd(a, b) = gcd(b, a % b)

You may find the provided procedures min and max helpful. You can also use the built-in modulo and zero? procedures.

scm> (modulo 10 4)2scm> (zero? (- 3 3))#tscm> (zero? 3)#f

(define (max a b) (if (> a b) a b))(define (min a b) (if (> a b) b a))(define (gcd a b)  'YOUR-CODE-HERE)

Use Ok to test your code:

python3 ok -q gcd

Check Your Score Locally​

You can locally check your score on each question of this assignment by running

python3 ok --score

This does NOT submit the assignment! When you are satisfied with your score, submit the assignment to Gradescope to receive credit for it.

Submit​

Submit this assignment by uploading any files you've edited to the appropriate Gradescope assignment. Lab 00 has detailed instructions.

In addition, all students who are not in the mega lab must complete this attendance form. Submit this form each week, whether you attend lab or missed it for a good reason. The attendance form is not required for mega section students.