Lab 2: Representing Data using Functions

Usually we are taught that programs consist of code and data. In Scheme, we will gradually be observing that both are essentially the same – text surrounded by a forest of parentheses! :-)

In the last lab we saw that we could represent numbers and operations over numbers with lambdas themselves (as Church numerals). Today let us use lambdas to build complex data items, in a way realizing that like di erent special forms (such as let), even di erent data items could be expressed using functions.

Recall coordinate geometry. What’s a point in a 2D plane? A pair of x and y coordinates. Do we know how to represent coordinates together as a point in Scheme? Not yet. But we know that this stu is very powerful, so let’s try representing a point using a lambda:

(define (make-point x y)

(lambda (bit)

(if (= bit 0) x y)))

Notice what do we have above. The function make-point returns a lambda (read ‘point’), such that the parameters (read ‘coordinates’) x and y are encapsulated1 in the closure of the returned function. The next task is to be able to access the x and y coordinates. Our point lambda takes a bit to either return the x or the y coordinate, so we could do something like this:

(define (get-x point) (point 0))

(define (get-y point) (point 1))

Convince yourself that the following code will work:

(define p (make-point 2 3))

(get-x p)

> 2

(get-y p)

> 3

What’s the simplest combination we can build up using points? A straight line! Which gives the rst exercise for today’s lab:

Q1. Write a make-line function that constructs a line.



1You might get a co ee if you can build-up on this fact when we later learn about the OO paradigm!


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CS302: Paradigms of Programming    Lab 2: Representing Data using Functions



You know what’s coming next:

Q2. Write functions get-first-point and get-second-point that take a line and return its start and end points, respectively.

There is no end to abstraction. So next:

Q3. Write functions get-x1, get-y1, get-x2 and get-y2 that should take a line and use the above functions to retrieve the respective coordinates of each end point of the line.

Now let’s start creating more points and more lines. De ne the following:

Q4. A function mid-point that takes a line and returns a point consisting of the x and y coordinates of the center of that line.

Q5. A function length that returns the length of the line taken as input.

Q6. A function rotated-line that rotates a line {(x1,y1),(x2,y2)} clock-wise by 90 , such that the start point of the new line is (x2,y2).

Q7. Two points p1 and p2, a line ln between p1 and p2, and the mid-point pmid of ln.

Q8. Play with the de ned lines and points to make sure they work as expected.

Finally, replace the header #lang sicp with the following:

#lang racket

(require 2htdp/image)

and paste the following in the interpreter:

(define (draw-p lnV lnH pMid length)

(let ((vx2 (get-x2 lnV))

(vy2 (get-y2 lnV))

(hx2 (get-x2 lnH))

(hy2 (get-y2 lnH)))

(let ((i1 (line vx2 vy2 "black")))

(let ((i2 (add-line i1 0 0 hx2 hy2 "black")))

(let ((i3 (add-line i2 hx2 hy2 hx2 (- vy2 (/ length 2)) "black")))

(add-line i3 hx2 (- vy2 (/ length 2)) (get-x pMid) (get-y pMid) "black"))))))

Call the above (poorly written) function as follows:

(draw-p ln (rotated-line ln) pmid (length ln))

Report what shape does DrRacket react with. Change the above function to get di erent shapes. If further enthusiastic, Google/DDG “drawings in drracket” and enjoy!










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