2020 Sem.II Final

You may use the Picturing Programs book and the Racket Help Desk. You may not use your old work. Please do not discuss this test with other people until after 1:30pm on the day after the exam.

1. Signatures

(define-struct tstm (p n c ell))

In this section all models are assumed and required to have their parts with the correct types above. You do not need to check that models you are given are correct, and models you produce must also have the correct types in each spot.

1a. Give a signature for this function

(define (mystery-1a g h)
  (make-tstm (make-posn 5 g)
             (sqrt g)
             h
             empty))

1b. Give a signature for this function

(define (mystery-1b t)
  (cond [(empty? (tstm-ell t))
         (tstm-p t)]
        [else
         (make-posn (tstm-n t)
                    (string-length (tstm-c t)))]))

2. Structures

Using the same structure tstm from above, write a function to be used as a tick handler - add 1 to the number in the model.

There are check-expects in the provided starter code.

(define (tstm-tick model)
  model)

3. Quality Design

In this section, the model needs to represent a position, speed, and score. For example: point=(40,75), speed=10, score=13.

Two different students “argh” and “oof” present different possible models.

(define ex-argh (make-posn (make-posn 40 75)
                           (make-posn 10 13)))
(define ex-oof (make-posn 13
                          (make-posn 10
                                     (make-posn 40 75))))

3a. Neither one of these is correct. Write the same example doing what they should be doing. Call your approach good.

3b. Write two functions to translate from the argh method to the oof method using your good method.

(define (argh->good a)
  "todo")
(define (good->oof g)
  "fixme")

4. Check-Expects

The in-triangle? function takes in four posns: the first three specify corners of a triangle, and the fourth one is a point Q. The function returns true if Q is in the triangle made by connecting the other three points, and false otherwise. (On the edge counts as in.)

Write three good check-expects for this function. Do not write the actual function. You check expects should cover a range of possible mistakes in the bad function given:

• bad function gives correct answer true
• bad function gives correct answer false
• bad function gives true but correct answer is false

Draw a picture and/or explain in words why the answers you give for the checks are correct.

(define (in-triangle? p1 p2 p3 q) ;; BAD!
  (and (<= (posn-x p1) (posn-x q) (posn-x p3))
       (<= (posn-y p1) (posn-y q) (posn-y p2))))

Common questions:

• Does on the edge of the triangle count as “in” it? Yes.
• Is the given in-triangle? function supposed pass all of the check-expects that I write? NO. Checks are written based on the purpose statement, not what the function actually does. The third bullet point above means you should have one failing check.

5. Lists

Use the same tstm from question 1 above.

In this section you are writing a function in-tol that takes in a tstm and a tolerance number. Return all of the numbers from the ell part of tstm that are within tolerance of the n part

Of course you may use helper functions.

There are check-expects in the starter code provided.

Example: when the model is

(make-tstm (make-posn 1 2) 18 "red"
           (list 13 14 21 22 23))

and the tolerance is 4, your function should output the (list 14 21 22) because those numbers from the list are within 4 of 18. Notice that the tolerance is from -4 to +4!

(define (in-tol model tolerance)
  empty)