2023 Exam Review I

I. Class and Instance

The Dilate class requires a function dilate that takes in a double (the dilation factor) and an instance of the Dilate class, and puts out a new instance of the dilate class.

1. Write the Dilate class declaration.

2. A Point3D is defined as below. Make Point3D an instance of the Dilate class.

    newtype Point3D = Point3D (Double, Double, Double)
    exA = Point3D (5,12,13)
   

3. Write the function dilateList which takes in double and a list of items in a class that can Dilate, and puts out a list of the dilated items.

   1. What is the type signature of dilateList?
   2. Write the function dilateList.

4. (Advanced, optional.) If you can Dilate a class, you can also Dilate the Maybe version of that class. Write an instance declaration that conveys this fact.

5. Suppose that a kind of line is determined by a point (Double, Double) and a slope Double. Write a data definition for Line with accessors pt and slope.

6. When you dilate a line the point changes but the slope does not. Write an instance declaration for this fact.

II. Stone Age

7. The mynub function removes duplicates from a list, not otherwise changing the order. Write the mynub function using only “stone age” tools.

   check_mynub = ([1,2,3,5] == mynub [1,2,3,2,2,2,2,5,1])
   

8. The dropUnwrap function takes in a list of Maybe b and puts out a list of b. Items that are Nothing are eliminated.

    check_du = ([5,30] == dropUnwrap [Just 5, Nothing, Just 30, Nothing])
   

III. Iron Age

In this section you are supposed to use map, filter and foldl (or any of its variants).

9. (findy :: Int -> [(Int,Int)] -> [(Int,Int)]). Return all of the points that have the given y value.

10. (pythagsum :: [(Int,Int)] -> Int) Find the sum of (x squared + y squared) for each point in the input list.