Typed Exercises 2

Additional practice writing typed functions, includes lists and recursion.

  1. ezn: Create a list of n numbers, counting from n down to 0.

     (check-expect (ezn 5) (list 5 4 3 2 1 0))
 (check-expect (ezn 7) (list 7 6 5 4 3 2 1 0))

  2. rpt: Given a word and a number, make a list containing that word the given number of times, except chop off one more letter at the start of the word each time you repeat it.

     (check-expect (rpt "word" 4) (list "word" "ord" "rd" "d"))
 (check-expect (rpt "cat" 2) (list "cat" "at"))

  3. perfect-squares: Given a list of integers, return a list of all of the perfect squares contained in that list. If you work with real numbers, you probably want Nonnegative-Real numbers.

  4. grow-sq: Given a start and end integer, make a list of images, all outline squares beginning at side length start, and ending at side length <= end.

    (grow-sq 10 17)

  5. sqc: Given two integers start and end, draw one image which is an overlay of images as n goes from start to end increasing by 1 each time. The image is an outline circle of radius 10*n when n is even and an outline square of side length 20*n when n is odd.

    (sqc 5 11)

Facts about Numbers

There are many number types, including:

  • Number
  • Real
  • Integer
  • Nonnegative-Real
  • Nonnegative-Integer
  • Positive-Integer

Pick the most appropriate one. For example, if you are taking the square root of a number, Nonnegative-Real might be a good choice. If that number is also an integer, then use Nonnegative-Integer.

The type Number actually means complex number (like 5+12i from math class), so lots of the time you really want to use Real.

Trouble spots

When you subtract one from a positive integer, Racket no longer knows it is positive (could have turned into zero). However, adding one to a positive integer gives you something that is definitely positive. That means when you are working with positive numbers and you have a choice between counting up or counting down, count up.

Pro tip: if you have an Integer and the error message tells you that a Positive-Real is needed, you should change your type to Positive-Integer.

Last modified August 18, 2023: 2022-2023 End State (7352e87)