8.12
Lecture 8: Structures
This assignment is due on Tuesday, January 30 at 11:59pm. Submit it using Handin as assignment lecture8.
Exercise 1.
Copy the code below into your Definitions Window.
; Exercise 1 ; The line below is a ; A Posn is (make-posn Number Number) ; The line below is a ; make-posn : Number Number -> Posn ; The line below is a ; posn-x : Posn -> Number ; The line below is a ; posn-y : Posn -> Number ; The line below is a (define here (make-posn 30 50)) ; The line below is a (define there (make-posn 70 45))
At the end of each line “; The line below is a”,
write one of the following phrases:
write one of the following phrases:
constant definition
variable definition
function definition
data definition
signature
Don’t change anything else you copy.
Exercise 2.
Copy the expressions below into your Definitions Window.
What are their results? Try to predict the results before asking DrRacket.
; Exercise 2 ; (posn-x there) ; = (posn-x (make-posn 70 45)) ; = ??? ; (posn-y here) ; = ??? ; = ...
Show step-by-step calculations by adding comments.
Use the Stepper to confirm that your steps are correct.
Exercise 3.
Copy the expressions below into your Definitions Window.
What are their results? Try to predict the results before asking DrRacket.
(If it runs into an error, write “error” without quotes at the end.)
; Exercise 3 ; (+ 1 (posn-y there)) ; = (+ 1 (posn-y (make-posn 70 45))) ; = ??? ; = ... ; (+ 1 there) ; = ??? ; = ... ; (- (posn-x there) (posn-x here)) ; = ??? ; = ... ; (make-posn (posn-x there) (posn-y here)) ; = ??? ; = ... ; (posn-y (posn-x here)) ; = ??? ; = ...
Show step-by-step calculations by adding comments.
Use the Stepper to confirm that your steps are correct.
Exercise 4.
Design a function called size that takes a Posn as input
and computes the sum of the absolute values of its x and y.
For example, the size of (make-posn 2 -3) is 5.
Remember to follow the design recipe whenever you design or write a function. In particular, every type mentioned in a signature must be introduced by a data definition, except for these well-known types: Number, Image, String, Color, Boolean, Posn.
Exercise 5.
Design a function called normalize that takes a Posn as input
and produces a new Posn:
The produced x should be the given x divided by the size of the given Posn.
The produced y should be the given y divided by the size of the given Posn.
(normalize (make-posn 2 -3))
The code written in the videos above is
available for your reference.
To download it, don’t use “Save Page As” or “Save As”;
use “Save Link As” or “Download Linked File” in your Web browser.
If you can’t find the command, try right-clicking or two-finger-tapping or
long-pressing.
Optional: Read Chapter 5 of the textbook.