EXAM
Introduction to Functional Programming
TDA555/DIT440

 DAY: October 27, 2015 TIME: 14:00–18:00 PLACE: H-salar

 Responsible: Aids: Grade: David Sands, D&IT, Tel: 0737 20 76 63 An English (or English-Swedish, or English-X) dictionary Completing Part I gives a 3 or a G;Part I and Part II are both needed for a 4, 5, or VG

This exam consists of two parts:
 Part I   (5 small assignments) Give good enough answers for 4 assignments here and you will get a 3 or a G (Points on Part II can be counted towards Part I if needed, but this is very unlikely to happen in practice.) Part II   (2 larger assignments) You do not need to solve this part if you are happy with a 3 or a G! Do Part I and one assignment of your choice here and you will get a 4 Do Part I and both assignments here and you will get a 5 or a VG

 Please read the following guidelines carefully: Answers can be given in Swedish or English Begin each assignment on a new sheet Write your number on each sheet Write clearly; unreadable = wrong! You can make use of the standard Haskell functions and types given in the attached list (you have to implement other functions yourself if you want to use them) You do not have to import standard modules in your solutions

Good Luck!

Part I

You have to complete 4 out of the following 5 assignments to get a pass on the exam.

1. Implement a function

``splitComma :: String -> (String,String)``

that splits a string at the first comma character. The comma itself should not be part of the result.

You don’t need to handle the case where the string does not contain a comma.

Examples:

``````*Main> splitComma "abc,123"
("abc","123")

*Main> splitComma "Jeffery Wilkie,15"
("Jeffery Wilkie","15")``````

Hint:

• Use the standard functions `takeWhile` and `dropWhile`.

2. Assume that you have a database of personal information stored as a text file in the following format:

``````Ginger Willard,45
Brandon Durand,23
Jeffery Wilkie,15
Judith Stevens,38``````

Each line consists of a name, followed by a comma, followed by that person’s age.

Implement a function

``parseDB :: String -> [(String,String)]``

that reads a string in the above format and returns a list of pairs, where each pair is the name and age of the person on the corresponding line in the file.

You can use the function `splitComma` from assignment 1 (don’t need to redefine it here).

Examples:

``````*Main> parseDB "abc,123"
[("abc","123")]

*Main> parseDB "Ginger Willard,45\nBrandon Durand,23\nJeffery Wilkie,15\n"
[("Ginger Willard","45"),("Brandon Durand","23"),("Jeffery Wilkie","15")]``````

(Note the newline characters `'\n'` in the input string.)

Hint:

• Use the standard function `lines`.

3. Consider the following recursive data type, modeling logical formulas in Haskell:

``````data Form
= And Form Form
| Or Form Form
| Not Form
| Val Bool``````

For example, the formula `not True || False` is represented as `Or (Not (Val True)) (Val False)`.

Now, implement a function

``eval :: Form -> Bool``

that evaluates a given formula to its value, a Boolean.

Examples:

``````*Main> eval (And (Val True) (Or (Val False) (Val True)))
True

*Main> eval (Not (And (Val True) (Val False)))
True``````

Hint:

• Use the standard functions (`&&`), (`||`), and `not`.

4. Write a QuickCheck property that expresses the fact that concatenating two lists (i.e. `as ++ bs`) gives a new list that has the first list (i.e. `as`) as a prefix.

Hint:

• Use the standard function `isPrefixOf` to check that a list is a prefix of another list.

5. Recall the database format from assignment 2. Write a function

``lookupDB :: FilePath -> String -> IO String``

that given a database file name and a person name, looks up the age of the person in the database.

You can use the function `parseDB` from assignment 2 (don’t need to redefine it here).

You can assume that the person to lookup exists in the database.

For example, assume that the file `"db.txt"` has the following content:

``````Ginger Willard,45
Brandon Durand,23
Jeffery Wilkie,15
Judith Stevens,38``````

Then we get the following example runs of the function:

``````*Main> lookupDB "db.txt" "Judith Stevens"
"38"

*Main> lookupDB "db.txt" "Brandon Durand"
"23"``````

Hint:

• Use `readFile`, and `lookup`.

Part II

You do not need to work on this part if you only want to get a 3 or a G!

If you want to get a 4, you have to do Part I, plus one of the following assignments.

If you want to get a 5 or a VG, you have to do Part I, plus both of the following assignments.

6. Define a function that displays a table in the text terminal:

``showTable :: [[String]] -> IO ()``

The table is represented as a list of columns. We will use following table as an example:

``````myTable :: [[String]]
myTable = [ ["Adam",     "Bertil", "Cesar"]
, ["Lilla My", "E.T.",   "X"]
, ["1",        "2",      "3"]
]``````

The first (i.e. left-most) column in `myTable` is the list `["Adam", "Bertil", "Cesar"]`.

Each column should be printed next to the previous one, from left to right, and each element in a column should be printed below the previous one. Furthermore, the elements in a column should be left-aligned, and there should be at least one space between each adjacent column.

Printing `myTable` should give the following result:

``````*Main> showTable myTable
Bertil E.T.     2
Cesar  X        3``````

You can assume that all columns in the table have the same number of elements.

Hint:

• First fix the width of each column, then use `transpose` to get a list of rows.
• You might find `concat` and `unlines` useful for turning the list of rows into a single string.

7. Your task is to implement a part of a screen saver that shows a ball bouncing around on the screen. The ball can travel in four different directions: north-east, north-west, south-east and south-west, as represented by the following data type:

``data Dir = NE | NW | SE | SW``

Implement the following function, which returns an infinite list of positions for the ball:

``screenSaver :: (Int,Int) -> Dir -> (Int,Int) -> [(Int,Int)]``

A call to this function takes the form `screenSaver (w,h) dir (x,y)`, where `(w,h)` gives the width and height of the screen, `dir` gives the initial direction of the ball and `(x,y)` is the starting position.

The ball should move one pixel (in both x and y) in each step. Whenever the ball reaches the end of the screen, it should bounce. For example, if the current direction is `NE` and it reaches the eastern border, it should go on in the direction `NW`. If the ball reaches a corner, it should bounce backwards (i.e. `NE` becomes `SW`).

You do not need to take the width of the ball into account. The ball reaches a border when its center reaches the border.

Example:

``````*Main> take 20 \$ screenSaver (50,50) NW (3,5)
[(3,5),(2,4),(1,3),(0,2),(1,1),(2,0),(3,1),(4,2),(5,3),(6,4),(7,5),(8,6),(9,7),(10,8),(11,9),(12,10),(13,11),(14,12),(15,13),(16,14)]``````

Here is a picture that shows how the ball moves in the above example:

Appendix

``````
{-
This is a list of selected functions from the standard Haskell modules:

Prelude
Data.List
Data.Maybe
Data.Char
-}

--------------------------------------------------------------------------
-- standard type classes

class Show a where
show :: a -> String

class Eq a where
(==), (/=) :: a -> a -> Bool

class (Eq a) => Ord a where
(<), (<=), (>=), (>) :: a -> a -> Bool
max, min             :: a -> a -> a

class (Eq a, Show a) => Num a where
(+), (-), (*)    :: a -> a -> a
negate           :: a -> a
abs, signum      :: a -> a
fromInteger      :: Integer -> a

class (Num a, Ord a) => Real a where
toRational       ::  a -> Rational

class (Real a, Enum a) => Integral a where
quot, rem        :: a -> a -> a
div, mod         :: a -> a -> a
toInteger        :: a -> Integer

class (Num a) => Fractional a where
(/)              :: a -> a -> a
fromRational     :: Rational -> a

class (Fractional a) => Floating a where
exp, log, sqrt      :: a -> a
sin, cos, tan       :: a -> a

class (Real a, Fractional a) => RealFrac a where
truncate, round  :: (Integral b) => a -> b
ceiling, floor   :: (Integral b) => a -> b

--------------------------------------------------------------------------
-- numerical functions

even, odd        :: (Integral a) => a -> Bool
even n           = n `rem` 2 == 0
odd              = not . even

--------------------------------------------------------------------------

sequence     :: Monad m => [m a] -> m [a]
sequence     = foldr mcons (return [])
where mcons p q = do x <- p; xs <- q; return (x:xs)

sequence_    :: Monad m => [m a] -> m ()
sequence_ xs = do sequence xs; return ()

--------------------------------------------------------------------------
-- functions on functions

id               :: a -> a
id x             = x

const            :: a -> b -> a
const x _        = x

(.)              :: (b -> c) -> (a -> b) -> a -> c
f . g            = \ x -> f (g x)

flip             :: (a -> b -> c) -> b -> a -> c
flip f x y       = f y x

(\$) :: (a -> b) -> a -> b
f \$  x           = f x

--------------------------------------------------------------------------
-- functions on Bools

data Bool = False | True

(&&), (||)       :: Bool -> Bool -> Bool
True  && x       = x
False && _       = False
True  || _       = True
False || x       = x

not              :: Bool -> Bool
not True         = False
not False        = True

--------------------------------------------------------------------------
-- functions on Maybe

data Maybe a = Nothing | Just a

isJust                 :: Maybe a -> Bool
isJust (Just a)        =  True
isJust Nothing         =  False

isNothing              :: Maybe a -> Bool
isNothing              =  not . isJust

fromJust               :: Maybe a -> a
fromJust (Just a)      =  a

maybeToList            :: Maybe a -> [a]
maybeToList Nothing    =  []
maybeToList (Just a)   =  [a]

listToMaybe            :: [a] -> Maybe a
listToMaybe []         =  Nothing
listToMaybe (a:_)      =  Just a

--------------------------------------------------------------------------
-- functions on pairs

fst              :: (a,b) -> a
fst (x,y)        =  x

snd              :: (a,b) -> b
snd (x,y)        =  y

curry            :: ((a, b) -> c) -> a -> b -> c
curry f x y      =  f (x, y)

uncurry          :: (a -> b -> c) -> ((a, b) -> c)
uncurry f p      =  f (fst p) (snd p)

--------------------------------------------------------------------------
-- functions on lists

map :: (a -> b) -> [a] -> [b]
map f xs = [ f x | x <- xs ]

(++) :: [a] -> [a] -> [a]
xs ++ ys = foldr (:) ys xs

filter :: (a -> Bool) -> [a] -> [a]
filter p xs = [ x | x <- xs, p x ]

concat :: [[a]] -> [a]
concat xss = foldr (++) [] xss

concatMap :: (a -> [b]) -> [a] -> [b]
concatMap f = concat . map f

head, last       :: [a] -> a

last [x]         = x
last (_:xs)      = last xs

tail, init       :: [a] -> [a]
tail (_:xs)      = xs

init [x]         = []
init (x:xs)      = x : init xs

null             :: [a] -> Bool
null []          = True
null (_:_)       = False

length           :: [a] -> Int
length []        = 0
length (_:l)     = 1 + length l

(!!)             :: [a] -> Int -> a
(x:_)  !! 0      = x
(_:xs) !! n      = xs !! (n-1)

foldr            :: (a -> b -> b) -> b -> [a] -> b
foldr f z []     =  z
foldr f z (x:xs) =  f x (foldr f z xs)

foldl            :: (a -> b -> a) -> a -> [b] -> a
foldl f z []     =  z
foldl f z (x:xs) =  foldl f (f z x) xs

iterate          :: (a -> a) -> a -> [a]
iterate f x      =  x : iterate f (f x)

repeat           :: a -> [a]
repeat x         =  xs where xs = x:xs

replicate        :: Int -> a -> [a]
replicate n x    =  take n (repeat x)

cycle            :: [a] -> [a]
cycle []         =  error "Prelude.cycle: empty list"
cycle xs         =  xs' where xs' = xs ++ xs'

take, drop             :: Int -> [a] -> [a]
take n _      | n <= 0 =  []
take _ []              =  []
take n (x:xs)          =  x : take (n-1) xs

drop n xs     | n <= 0 =  xs
drop _ []              =  []
drop n (_:xs)          =  drop (n-1) xs

splitAt                :: Int -> [a] -> ([a],[a])
splitAt n xs           =  (take n xs, drop n xs)

takeWhile, dropWhile    :: (a -> Bool) -> [a] -> [a]
takeWhile p []          =  []
takeWhile p (x:xs)
| p x       =  x : takeWhile p xs
| otherwise =  []

dropWhile p []          =  []
dropWhile p xs@(x:xs')
| p x       =  dropWhile p xs'
| otherwise =  xs

lines, words     :: String -> [String]
-- lines "apa\nbepa\ncepa\n" == ["apa","bepa","cepa"]
-- words "apa  bepa\n cepa"  == ["apa","bepa","cepa"]

unlines, unwords :: [String] -> String
-- unlines ["apa","bepa","cepa"] == "apa\nbepa\ncepa"
-- unwords ["apa","bepa","cepa"] == "apa bepa cepa"

reverse          :: [a] -> [a]
reverse          =  foldl (flip (:)) []

and, or          :: [Bool] -> Bool
and              =  foldr (&&) True
or               =  foldr (||) False

any, all         :: (a -> Bool) -> [a] -> Bool
any p            =  or . map p
all p            =  and . map p

elem, notElem    :: (Eq a) => a -> [a] -> Bool
elem x           =  any (== x)
notElem x        =  all (/= x)

lookup           :: (Eq a) => a -> [(a,b)] -> Maybe b
lookup key []    =  Nothing
lookup key ((x,y):xys)
| key == x   =  Just y
| otherwise  =  lookup key xys

sum, product     :: (Num a) => [a] -> a
sum              =  foldl (+) 0
product          =  foldl (*) 1

maximum, minimum :: (Ord a) => [a] -> a
maximum []       =  error "Prelude.maximum: empty list"
maximum xs       =  foldl1 max xs

minimum []       =  error "Prelude.minimum: empty list"
minimum xs       =  foldl1 min xs

zip              :: [a] -> [b] -> [(a,b)]
zip              =  zipWith (,)

zipWith          :: (a->b->c) -> [a]->[b]->[c]
zipWith z (a:as) (b:bs)
=  z a b : zipWith z as bs
zipWith _ _ _    =  []

unzip            :: [(a,b)] -> ([a],[b])
unzip            =  foldr (\(a,b) ~(as,bs) -> (a:as,b:bs)) ([],[])

nub              :: Eq a => [a] -> [a]
nub []           = []
nub (x:xs)       = x : nub [ y | y <- xs, x /= y ]

delete           :: Eq a => a -> [a] -> [a]
delete y []      = []
delete y (x:xs)  = if x == y then xs else x : delete y xs

(\\)             :: Eq a => [a] -> [a] -> [a]
(\\)             = foldl (flip delete)

union            :: Eq a => [a] -> [a] -> [a]
union xs ys      = xs ++ (ys \\ xs)

intersect        :: Eq a => [a] -> [a] -> [a]
intersect xs ys  = [ x | x <- xs, x `elem` ys ]

intersperse      :: a -> [a] -> [a]
-- intersperse 0 [1,2,3,4] == [1,0,2,0,3,0,4]

transpose        :: [[a]] -> [[a]]
-- transpose [[1,2,3],[4,5,6]] == [[1,4],[2,5],[3,6]]

partition        :: (a -> Bool) -> [a] -> ([a],[a])
partition p xs   = (filter p xs, filter (not . p) xs)

group            :: Eq a => [a] -> [[a]]
-- group "aapaabbbeee" == ["aa","p","aa","bbb","eee"]

isPrefixOf, isSuffixOf   :: Eq a => [a] -> [a] -> Bool
isPrefixOf []     _      =  True
isPrefixOf _      []     =  False
isPrefixOf (x:xs) (y:ys) =  x == y && isPrefixOf xs ys

isSuffixOf x y           =  reverse x `isPrefixOf` reverse y

sort              :: (Ord a) => [a] -> [a]
sort              = foldr insert []

insert            :: (Ord a) => a -> [a] -> [a]
insert x []       = [x]
insert x (y:xs)   = if x <= y then x:y:xs else y:insert x xs

--------------------------------------------------------------------------
-- functions on Char

type String = [Char]

toUpper, toLower :: Char -> Char
-- toUpper 'a' == 'A'
-- toLower 'Z' == 'z'

digitToInt :: Char -> Int
-- digitToInt '8' == 8

intToDigit :: Int -> Char
-- intToDigit 3 == '3'

ord :: Char -> Int
chr :: Int  -> Char

isDigit :: Char -> Bool

--------------------------------------------------------------------------
-- input/output

putStr  :: String -> IO ()
getLine :: IO String

readFile  :: FilePath -> IO String
writeFile :: FilePath -> String -> IO ()

--------------------------------------------------------------------------``````