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
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 fromdiv
?Try
showDiv
on some examples. Describe in words what it does.What does the
a
in the definition ofMaybe
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 areJust
, and returnsNothing
otherwise.
(You know the drill) The reporter 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
andlength noInts
.Explain what
[]
means.Evaluate
moreInts
andlength moreInts
.Do the same for
yetMoreInts
.Now evaluate
ints
. Has it changed?Write an expression
e
such thatlength e
evaluates to6
.Explain what the
(:)
operator does.What will
someInts
evaluate to? How aboutlength someInts
? Write down your guesses before typing them into GHCi.Now check your guesses.
Evaluate
ints2
. What do you notice?
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
, andgreeting3
. 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
andeveryone
which evaluates to"Hello, world!"
.
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, liket
ora
. Explain what the type oflistLength
means.Evaluate
startsWith "cat" "catastrophe"
. What happens?Complete the definition of
startsWith
by replacingundefined
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.