Moving in Two Dimensions

# update-danger :: Number -> Number # takes in danger’s x-coordinate and produces the next one

This function takes in the danger’s x-coordinate and produces the next one, but it doesn’t do anything with the y-coordinate. That’s why our DANGER can only move left or right! Suppose we wanted to change the function, so it updates the character by moving diagonally…​

1 Stop and think! What, if anything, will have to change about the Domain?

2 To move diagonally, we need the function to be aware of both the x and the y-coordinate. It will have to consume both x and y, so the Domain will change to Number Number. What other functions have you used that consume two Numbers?

3 Stop and think! What, if anything, will have to change about the Range?

The Range can’t just be one Number, since an (x, y) coordinate has two Numbers. One idea might be to write the contract this way:

# update-danger :: Number Number -> Number Number # take in danger’s x- and y-coordinate, and produces the next x- and next y-coordinate

Unfortunately, that contract breaks an important rule about functions: Given an input, all functions must produce one output!

Fortunately, our programming language has another data type, called a Posn. A Posn - short for "position" - is a piece of data that contains two Numbers! We can make a posn to represent the position (100, 200) with the following code:

make-posn​(​100, 200​)

4 On the computer, try making a Posn or two. What expression will make a Posn representing the origin?

5 Write the contract for the make-posn function on the line below.

6 On the lines below, write the new contract and purpose for update-danger, so that it produces a Posn instead of a Number.

7 In your game file, change your contract, purpose, examples, and definition to make your DANGER and TARGET move in two dimensions!