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.
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.
Maybe (Maybe Bool)
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.
plusMaybe :: Maybe Integer -> Maybe Integer -> Maybe Integer
(You know the drill) You should be prepared to share your version of plusMaybe with another group.
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?
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?
greeting : everyone
Now try evaluating greeting ++ everyone. What happens?
greeting ++ everyone
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!".
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?
startsWith "cat" "catastrophe"
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 :: String -> String -> Bool
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 :: [a] -> [a]
listReverse  -> 
listReverse [1,2,3] -> [3,2,1]
listReverse "Hello" -> "olleH"
DO NOT look at any existing implementation of reverse.