1. dr Robert Kowalczyk WMiI UŁ
Summer School
Haskell 2
dr Robert Kowalczyk WMiI UŁ

2. dr Robert Kowalczyk WMiI UŁ
Syntax in Haskell
pattern matching
f : Z -> Z
f(0) = 1
f(1) = 3
f(2) = 6
f(x) = 0 if only x<>0 and x<>1 and x<>2
f :: Int -> Int
f(0) = 1
f(1) = 3
f(2) = 6
f(x) = 0 (or f(_)=0)
dr Robert Kowalczyk WMiI UŁ

3. dr Robert Kowalczyk WMiI UŁ
Syntax in Haskell
case of
f : Z -> Z
f(0) = 1
f(1) = 3
f(2) = 6
f(x) = 0 if only x<>0 and x<>1 and x<>2
f :: Int -> Int
f x = case x of
0 -> 1
1 -> 3
2 -> 6
_ -> 0
dr Robert Kowalczyk WMiI UŁ

4. dr Robert Kowalczyk WMiI UŁ
Syntax in Haskell
if ... else ...
sgn : Z -> Z
sgn(x) = -1 if only x<0
sgn(0) = 0
sgn(x) = 1 if only x>0
sgn:: Int -> Int
sgn x = if x > 0 then 1 else if x == 0 then 0 else -1
sgn:: Int -> Int
sgn x = if x > 0
then 1
else if x == 0
then 0
else -1
dr Robert Kowalczyk WMiI UŁ

5. dr Robert Kowalczyk WMiI UŁ
Syntax in Haskell
guards ...
sgn : Z -> Z
sgn(x) = -1 if only x<0
sgn(0) = 0
sgn(x) = 1 if only x>0
sgn:: Int -> Int
sgn x
| x < 0 = -1
| x == 0 = 0
| otherwise = 1
sgn:: Int -> Int
sgn x
| x > 0 = 1
| x == 0 = 0
| x < 0 = -1
sgn:: Int -> Int
sgn 0 = 0
sgn x
| x > 0 = 1
| x < 0 = -1
dr Robert Kowalczyk WMiI UŁ

6. dr Robert Kowalczyk WMiI UŁ
Syntax in Haskell
where
bmiTell :: Float -> Float -> String  
bmiTell weight height  
    | bmi <= skinny = ”You're underweight”  
    | bmi <= normal = ”You're normal” 
    | bmi <= fat    = ”You're overweight”  
    | otherwise     = ”You have a problem”  
    where bmi = weight / height ^ 2  
          skinny = 18.5  
          normal = 25.0  
          fat = 30.0  
dr Robert Kowalczyk WMiI UŁ

7. dr Robert Kowalczyk WMiI UŁ
Syntax in Haskell
let ... in ...
cylinder :: (RealFloat a) => a -> a -> a cylinder r h = let sideArea = 2 * pi * r * h topArea = pi * r ^2 in sideArea + 2 * topArea
dr Robert Kowalczyk WMiI UŁ

8. dr Robert Kowalczyk WMiI UŁ
Recursion
Recursion in computer science is a method where the solution to a problem depends on solutions to smaller instances of the same problem (as opposed to iteration). The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science.
dr Robert Kowalczyk WMiI UŁ

9. dr Robert Kowalczyk WMiI UŁ
Recursion
factorial :: Integer-> Integer
factorial 0 = 1
factorial n = n * factorial (n-1)
mult:: Int -> Int ->Int
mult 0 n = 0
mult m n = n + mult (m-1) n
dr Robert Kowalczyk WMiI UŁ

10. dr Robert Kowalczyk WMiI UŁ
Recursion
fib :: Int -> Int
fib 0 = 0
fib 1 = 1
fib n = fib (n – 2) + fib (n - 1)
length’ :: [a] -> Integer
length’ [] = 0
length’ (_:xs) = 1 + length’ xs
dr Robert Kowalczyk WMiI UŁ

11. dr Robert Kowalczyk WMiI UŁ
Recursion
maximum' :: (Ord a) => [a] -> a 
maximum' [] = error ”list is empty”  
maximum' [x] = x  
maximum' (x:xs) = max x (maximum' xs)
reverse' :: [a] -> [a]  
reverse' [] = []  
reverse' (x:xs) = reverse' xs ++ [x]
dr Robert Kowalczyk WMiI UŁ

12. dr Robert Kowalczyk WMiI UŁ
Recursion
zip' :: [a] -> [b] -> [(a,b)]  
zip' _ [] = []  
zip' [] _ = []  
zip' (x:xs) (y:ys) = (x,y):zip' xs ys
quicksort :: (Ord a) => [a] -> [a]  
quicksort [] = []  
quicksort (x:xs) =  smallerSorted ++ [x] ++ biggerSorted
where
smallerSorted = quicksort [a | a <- xs, a <= x]  
        biggerSorted = quicksort [a | a <- xs, a > x]   
dr Robert Kowalczyk WMiI UŁ

13. dr Robert Kowalczyk WMiI UŁ
Read from keyboard
readFromKeyboard = do
putStr "Podaj x: "
x <- getLine
putStr "Podaj y: "
y <- getLine
putStrLn (show((read x::Float)+(read y::Float)))   
show :: Show a => a -> String
read :: Read a => String -> a
dr Robert Kowalczyk WMiI UŁ

14. Higher order functions
map :: (a -> b) -> [a] -> [b]  
map _ [] = []  
map f (x:xs) = f x : map f xs    
map (+2) [1,2,3,4] -> [3,4,5,6]
map (length) [”I”,”love”,”Haskell”] -> [1,4,8]   
filter :: (a -> Bool) -> [a] -> [a]  
filter _ [] = []  
filter p (x:xs)   
    | p x       = x : filter p xs  
    | otherwise = filter p xs  
filter (>0) [ ] -> [1,2,3,4,5,6,7,8,9,10]
filter (not.null) [[1,2,3],[],[3,4,5],[2,2],[],[]] ->
[[1,2,3],[3,4,5],[2,2]]  
dr Robert Kowalczyk WMiI UŁ

15. dr Robert Kowalczyk WMiI UŁ
Lambdas
\ variables -> result     
calculateOnList x = map (\a -> 2*a + 1) x   
calculateOnLists x y = zipWith (\a b -> 2*a + 3*b + 1) x y   
dr Robert Kowalczyk WMiI UŁ

16. Excercises with Teacher
Define the function
max3 :: Float-> Float -> Float -> Float
which returns maximum from any three real numbers.
Ex. 2
Define two sequences {a_n} and {b_n} by formula
a_{n}=a_{n-1}+b_{n-1}, a_{0}=1
and
b_{n}=a_{n-1}*b_{n-1}, b_{0}=1.
Then create two lists:
- the list of k elements of sequence {a_n},
- the list of k elements of sequence {b_n}.
dr Robert Kowalczyk WMiI UŁ

17. Excercises with Teacher and without 
Write the functions:
firstFromList :: [a] -> a
secondFromList :: [a] -> a
lastFromList :: [a] -> a
beforelastFromList :: [a] -> a
which reads: first, second, last and before last element in any list.
Ex. 4
Define the function
sumPositiveElementsOnList :: [Int] -> Int
which returns sum of all positive integer numbers from this list.
dr Robert Kowalczyk WMiI UŁ

18. Excercises with Teacher’s help
Write the function
howManyTimes :: a -> [a] -> Int
which returns the number of how many times the element is on the list.
Ex. 6
isPrimeNumber :: Int -> Bool
which returns True or False depending on whether the number given as the argument is the prime number or not the prime number. Then write the function
nPrimeNumbers :: Int -> [Int]
which returns the first n primes numbers.
dr Robert Kowalczyk WMiI UŁ

19. Excercises without Teacher’s help
Define functions
toUpperString and toLowerString
which will convert each letter in a string to a large (small) one.
For example:
toUpperString ”Helooo Haskell” -> ”HELOOO HASKELL”
toLowerString ”Hello Haskell” -> ”hello haskell”
Hint. Import functions toUpper and toLower from the module Data.Char.
Ex. 8
Write the program
palindrom
which reads any string from the keyboard and check (True or False) if this string is a palindrom or not.
dr Robert Kowalczyk WMiI UŁ

20. dr Robert Kowalczyk WMiI UŁ
Sites about Haskell   
dr Robert Kowalczyk WMiI UŁ

21. Thank you for your attention
dr Robert Kowalczyk WMiI UŁ