Module 03: Polymorphism and Lists
=================================
* Record your team members here:
In this module we will complete our initial exploration of the Haskell
programming language. For today, choose whoever you wish to start as
the driver.
Maybe
-----
```{.haskell}
data Maybe a where
Nothing :: Maybe a
Just :: a -> Maybe a
```
Note that the above definition of `Maybe` does not have bird tracks in
front of it since it is already defined in the standard library; I
just wanted to show you its definition.
> w :: Maybe Int
> w = Just 3
>
> x :: Maybe String
> x = Just "hello"
>
> y :: Maybe Char
> y = Nothing
>
> z :: Maybe (Maybe Int)
> z = Just Nothing
>
> safeDiv :: Integer -> Integer -> Maybe Integer
> safeDiv _ 0 = Nothing
> safeDiv x y = Just (x `div` y)
>
> showDiv :: Integer -> Integer -> String
> showDiv x y = case safeDiv x y of
> Nothing -> "Division by zero"
> Just z -> "Result is " ++ show z
* Give two example values of type `Maybe Bool`.
* How many distinct values of type `Maybe (Maybe Bool)` are there?
List all of them.
* How is `safeDiv` different from `div`?
* Try `showDiv` on some examples. Describe in words what it does.
* What does the `a` in the definition of `Maybe` represent?
* What Java feature does the `a` remind you of?
* Write a function `plusMaybe :: Maybe Integer -> Maybe Integer ->
Maybe Integer` which performs addition if both arguments are `Just`,
and returns `Nothing` otherwise.
![](../images/stop.gif) **(You know the drill)** You should be
prepared to share your version of `plusMaybe` with another group.
Lists
-----
**ROTATE ROLES**
> ints :: [Integer]
> ints = [3, 5, 92]
>
> noInts :: [Integer]
> noInts = []
>
> moreInts :: [Integer]
> moreInts = 7 : ints
>
> yetMoreInts :: [Integer]
> yetMoreInts = 4 : 2 : ints
>
> someInts :: [Integer]
> someInts = 8 : 42 : noInts
>
> ints2 :: [Integer]
> ints2 = 3 : 5 : 92 : []
* Evaluate `length ints` and `length noInts`.
* Explain what `[]` means.
* Evaluate `moreInts` and `length moreInts`.
* Do the same for `yetMoreInts`.
* Now evaluate `ints`. Has it changed?
* Write an expression `e` such that `length e` evaluates to `6`.
* Explain what the `(:)` operator does.
* What will `someInts` evaluate to? How about `length someInts`?
Write down your guesses *before* typing them into GHCi.
* Now check your guesses.
* Evaluate `ints2`. What do you notice?
![](../images/stop.gif)
Strings
-------
**ROTATE ROLES**
> greeting :: String
> greeting = "Hello"
>
> greeting2 :: String
> greeting2 = ['H','e','l','l','o']
>
> greeting3 :: [Char]
> greeting3 = ['H','e','l','l','o']
>
> everyone :: String
> everyone = "world"
* Evaluate `greeting`, `greeting2`, and `greeting3`. What
differences do you notice? What can you conclude? (Hint: try typing
`:info String` at the GHCi prompt.)
* Try evaluating `greeting : everyone`. What happens?
* Now try evaluating `greeting ++ everyone`. What happens?
* Explain the difference between `(:)` and `(++)`.
* What are the types of `(:)` and `(++)`? Do they match your
explanation above?
* Explain the difference between `'a'` and `"a"`.
* Write an expression using `greeting` and `everyone` which evaluates
to `"Hello, world!"`.
![](../images/stop.gif)
List pattern matching
---------------------
**ROTATE ROLES**
> listLength [] = 0 :: Integer
> listLength (_:xs) = 1 + listLength xs
>
> startsWith :: String -> String -> Bool
> startsWith [] _ = undefined
> startsWith (_:_) [] = undefined
> startsWith (x:xs) (y:ys) = undefined
* What is the type of `listLength`? (Feel free to ask GHCi.)
* The type of `listLength` probably has a lowercase letter in it, like
`t` or `a`. Explain what the type of `listLength` means.
* Evaluate `startsWith "cat" "catastrophe"`. What happens?
* Complete the definition of `startsWith` by replacing `undefined`
with appropriate expressions. `startsWith` should test whether the
second argument has the first argument as a prefix. For example:
```
startsWith "cat" "catastrophe" -> True
startsWith "car" "catastrophe" -> False
startsWith "ban" "banana" -> True
startsWith "" "dog" -> True
startsWith "at" "catastrophe" -> False
startsWith "dog" "" -> False
```
* Write a function `contains :: String -> String -> Bool`, which tests
whether the second argument contains the first argument as a
(contiguous) substring. For example,
```
contains "cat" "catastrophe" -> True
contains "cat" "concatenate" -> True
contains "cat" "create" -> False
contains "fly" "old lady" -> False
```
Hint: use `startsWith`.
* Write a function `listReverse :: [a] -> [a]` which reverses a list.
For example,
```
listReverse [] -> []
listReverse [1,2,3] -> [3,2,1]
listReverse "Hello" -> "olleH"
```
**DO NOT** look at any existing implementation of reverse.