Homework 10: Testing

CIS 194: Homework 10
Due Tuesday, November 8

The is just small, 10 points, finger exercise to reinforce the lecture material. Your main task is to work on the project.

Exercise 1

From your or the example solution of week 7, extract the Tree data type and the labelTree function. You can add Eq to the derived classes of Tree.

Declare an Arbitrary instance for trees:

instance Arbitrary a => Arbitrary (Tree a) where …

You do not have to implement a shrink function.

Use sample in GHCi to visually assess whether you generate useful looking trees.

Exercise 2

Implement these functions:

size :: Tree a -> Int
toList :: Tree a -> [a]

where size counts the number of leaves in the tree, and toList contains all the values in the leafs, from left to right.

Exercise 3

Create these QuickCheck properties:

```
prop_lengthToList :: Tree Integer -> Bool
```
The length of the list produced by toList is the size of the given tree.

prop_sizeLabelTree :: Tree Integer -> Bool

labelTree does not change the size of the tree.

```
prop_labelTree :: Tree Integer -> Bool
```
For every tree t, toList (labelTree t) is the expected list.

Hint: [0..n] denotes the list of numbers from 0 to n, inclusively.
```
prop_labelTreeIdempotent :: Tree Integer -> Bool
```
Applying labelTree to a list twice does yield the same list as applying it once.