Homework 9 Solutions

Solution Files

You can find the solutions in hw09.scm.

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.

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


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

Programs as Data: Chef Curry

Recall that currying transforms a multiple argument function into a series of higher-order, one argument functions. In the next set of questions, you will be creating functions that can automatically curry a function of any length using the notion that programs are data!

Q1: Cooking Curry

Implement the function curry-cook, which takes in a Scheme list formals and a quoted expression body. curry-cook should generate a program as a list which is a curried version of a lambda function. The outputted program should be a curried version of a lambda function with formal arguments equal to formals, and a function body equal to body. You may assume that all functions passed in will have more than 0 formals; otherwise, it would not be curry-able!

For example, if you wanted to curry the function (lambda (x y) (+ x y)), you would set formals equal to '(x y), the body equal to '(+ x y), and make a call to curry-cook: (curry-cook '(x y) '(+ x y)).

scm> (curry-cook '(a) 'a)
(lambda (a) a)
scm> (curry-cook '(x y) '(+ x y))
(lambda (x) (lambda (y) (+ x y)))
(define (curry-cook formals body)
(if (null? formals) body `(lambda (,(car formals)) ,(curry-cook (cdr formals) body)) )
)

Use Ok to test your code:

python3 ok -q curry-cook

Q2: Consuming Curry

Implement the function curry-consume, which takes in a curried lambda function curry and applies the function to a list of arguments args. You may make the following assumptions:

  1. If curry is an n-curried function, then there will be at most n arguments in args.
  2. If there are 0 arguments (args is an empty list), then you may assume that curry has been fully applied with relevant arguments; in this case, curry now contains a value representing the output of the lambda function. Return it.

Note that there can be fewer args than formals for the corresponding lambda function curry! In the case that there are fewer arguments, curry-consume should return a curried lambda function, which is the result of partially applying curry up to the number of args provdied. See the doctests below for a few examples.

scm> (define three-curry (lambda (x) (lambda (y) (lambda (z) (+ x (* y z)))) ))
three-curry
scm> (define eat-two (curry-consume three-curry '(1 2))) ; pass in only two arguments, return should be a one-arg lambda function!
eat-two
scm> eat-two
(lambda (z) (+ x (* y z)))
scm> (eat-two 3) ; pass in the last argument; 1 + (2 * 3)
7
scm> (curry-consume three-curry '(1 2 3)) ; all three arguments at once
7
(define (curry-consume curry args)
(if (null? args) curry (curry-consume (curry (car args)) (cdr args)) )
)

Use Ok to test your code:

python3 ok -q curry-consume

Macros

Q3: Switch to Cond

switch is a macro that takes in an expression expr and a list of pairs, options, where the first element of each pair is some value and the second element is a single expression. switch evaluates the expression contained in the list of options that corresponds to the value that expr evaluates to.

scm> (switch (+ 1 1) ((1 (print 'a))
                      (2 (print 'b)) ; (print 'b) is evaluated because (+ 1 1) evaluates to 2
                      (3 (print 'c))))
b

switch uses another procedure called switch-to-cond in its implementation:

scm> (define-macro (switch expr options)
                   (switch-to-cond (list 'switch expr options))
     )

Your task is to define switch-to-cond, which is a procedure (not a macro) that takes a quoted switch expression and converts it into a cond expression with the same behavior. An example is shown below.

scm> (switch-to-cond `(switch (+ 1 1) ((1 2) (2 4) (3 6))))
(cond ((equal? (+ 1 1) 1) 2) ((equal? (+ 1 1) 2) 4) ((equal? (+ 1 1) 3) 6))
(define-macro (switch expr options) (switch-to-cond (list 'switch expr options)))

(define (switch-to-cond switch-expr)
(cons 'cond
(map
(lambda (option) (cons `(equal? ,(car (cdr switch-expr)) ,(car option)) (cdr option)))
(car (cdr (cdr switch-expr))))))

Use Ok to test your code:

python3 ok -q switch-to-cond

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.

Exam Practice

Homework assignments will also contain prior exam questions for you to try. These questions have no submission component; feel free to attempt them if you'd like some practice!

Macros

  1. Fall 2019 Final Q9: Macro Lens
  2. Summer 2019 Final Q10c: Slice
  3. Spring 2019 Final Q8: Macros