Due by 11:59pm on Tuesday, November 28

Instructions

Download hw09.zip. Inside the archive, you will find a file called hw09.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. There is a homework recovery policy as stated in the syllabus. This homework is out of 2 points.

Macros are a method of programming that allow programmers to treat expressions as data and create procedures of a language using the language itself. Macros open the door to many clever tricks of creating "shortcuts", and with Scheme, allow us to build our own special forms other than the ones that are built in.

Required Questions

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)
    'YOUR-CODE-HERE
)

Use Ok to test your code:

python3 ok -q curry-cook
Copy
✂️

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)
    'YOUR-CODE-HERE
)

Use Ok to test your code:

python3 ok -q curry-consume
Copy
✂️

Macros

Q3: Switch to Cond

switch is a macro that takes in an expression expr and a list of pairs, cases, 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 cases 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 cases)
                   (switch-to-cond (list 'switch expr cases))
     )

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 cases) (switch-to-cond (list 'switch expr cases)))

(define (switch-to-cond switch-expr)
  (cons _________
    (map
	  (lambda (case) (cons _______________ (cdr case)))
	  (car (cdr (cdr switch-expr))))))

Use Ok to test your code:

python3 ok -q switch-to-cond
Copy
✂️

Q4: Factor Switch

Note: This question assumes you finished implementing switch-to-cond in the previous problem.

Define the procedure switch-factors, which uses the switch macro to determine whether a number is one, prime, or composite.

• A prime number n is a number that is not divisible by any numbers other than 1 and n itself.
• A composite number n is a number that is divisible by at least one number other than 1 and n.

scm> (switch-factors 1)
one
scm> (switch-factor 17)
prime
scm> (switch-factor 9)
composite

You may use the min, count, and is-factor procedures, which have already been defined for you.

Hint: switch doesn't have an else case. In other words, switch only returns an expression when expr equals the value correponding to that expression. Knowing this, how can the min procedure be useful?

(define (min x y) (if (< x y) x y))

(define (count f n i) (if (= i 0) 0 (+ (if (f n i) 1 0) (count f n (- i 1)))))

(define (is-factor dividend divisor) (if (equal? (modulo dividend divisor) 0) #t #f))

(define (switch-factors n)
  (switch _________ __________________)
)

Use Ok to test your code:

python3 ok -q switch-factors
Copy
✂️

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

Make sure to submit this assignment by uploading any files you've edited to the appropriate Gradescope assignment. For a refresher on how to do this, refer to Lab 00.

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