CS 3540: Programming Languages and Paradigms

Instructions

• The quiz consists of five questions and one image.
• Read all the questions thoroughly before you begin. It is worth your time to plan ahead!
• The quiz is worth 60 points. Each question is worth twelve points.
• Partial credit will be given where possible, so show your work.
• The quiz lasts thirty (30) minutes. It is due at 1:45 PM.

Problem 1

Write brief answers for each of the following items (two sentences each, max).

• One of the three things that every programming language has is a means of combination. What is Racket's only means of combination? Give an example to illustrate your answer.
• What are the other two things that every programming language has? Give an example of each from Racket.
• We say that define is a special form. What does that mean? List one way we can know that is true from define's behavior.
• What does it mean to say that that map is a higher-order function?

Problem 2

Answer each of these questions about the structure of Racket lists.

• Draw a box-and-pointer diagram that shows the structure of this Racket list:

  (list 3 (cons 1 6) (cons 2 (cons 4 '())))
  
• Write the Racket literal corresponding to the list shown in this box-and-pointer diagram.

Problem 3

When we go to the store, we pay a small sales tax on each item. we buy. The total price for any particular item is (the price of the item) × (the number of items bought) × (1 + the tax rate).

Write a Racket function named line-item-cost that takes three arguments, all numbers: the item price, the number of items purchased, and the tax rate.

line-item-cost returns the total cost for this purchase, including sales tax. For example:

> (line-item-cost 1.00 1 0.05)      ; $1.00 x 1, plus 5%
1.05

> (line-item-cost 5.00 4 0.07)      ; $5.00 x 4, plus 7%
21.40

> (line-item-cost 10.00 6 0.15)     ; $10.00 x 6, plus 15%
69.00

Problem 4

In Session 7, we worked with lists of daily weather data. Each day's weather entry looked like this:
(city date high-temp low-temp precipitation wind-speed snow).
The first two items are strings, and the rest are numbers.

Write a Racket function named amount-over that takes one argument, a number baseline.

amount-over returns a function as its value. That function takes one argument, a day's weather entry, and returns how much the day's high temperature is above baseline. For example:

> (define jan01 '("ALO" "2024-01-01" 27.0 22.0 0.0 6.430424 0.0))
> (define oct27 '("ALO" "2024-10-27" 65.0 36.0 0.0 10.25392 0.0))

> ( (amount-over 50) oct27 )
15.0
> ( (amount-over 0) jan01 )
27.0
> (define amount-above-average (amount-over 58))
> (map amount-above-average (list jan01 oct27))
'(-31.0 7.0)

Recall that Racket has list accessors first through tenth.

Problem 5

Suppose that we have a list of pixels from an image, where each pixel is a list (r g b) containing the red, green, and blue (RGB) values of the pixel. (76 195 202) is an example of a pixel. For example, an image might look like this:

  ( (76 195 202) (255 71 208) (175 81 214) (0 165 81) ... )

Write a Racket function named least-red-green that takes one argument, a list of pixels lst in this form.

least-red-green computes the sum of the red and green values for every pixel in lst and returns the smallest of the sums. For example:

> (least-red-green '( (1 3 5) ))
4

> (least-red-green '( (0 0 240) (100 120 140) ))
0

; trust me: this pixel has smallest red + green
;                                                vvvvvv
> (least-red-green '( (76 195 202) (255 71 208) (175 81 214) ))
256

Remember: Racket has a variable-arity function named min.

Use the higher-order functions apply and map as needed to implement your function. No recursion, looping, or sorting are allowed.