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1. 1. Refresher Sebastian Rettig“Work on Haskell began in 1987 when aa committee of “Work on Haskell began in 1987 when committee ofresearchers got together to design aa kick-asslanguage.” ([1]) researchers got together to design kick-ass language.” ([1])
2. 2. Imperative Programming● Variables (value placeholder) – Value can change during program flow● Modules, Classes, Functions, Procedures● Control Flow Structures (IF THEN ELSE, Loops (WHILE), Goto)
3. 3. Functional Programming● No Variables● Functions only, eventually stored in Modules – Behavior do not change, once defined – → Function called with same parameter calculates always the same result● Function definitions (Match Cases)● Recursion
4. 4. Haskell Refresher Quiz● Whats the red one ?●maxList :: (Ord a) => [a] -> amaxList [] = error “empty”maxList [x] = xmaxList (x:xs) | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
5. 5. Haskell Refresher Quiz● Whats the red one ?●maxList :: (Ord a) => [a] -> a FunctionmaxList [] = error “empty”maxList [x] = xmaxList (x:xs) | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
6. 6. Haskell Refresher Quiz● Whats the red one ?●maxList :: (Ord a) => [a] -> amaxList [] = error “empty”maxList [x] = xmaxList (x:xs) | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
7. 7. Haskell Refresher Quiz● Whats the red one ?●maxList :: (Ord a) => [a] -> a Function HeadermaxList [] = error “empty”maxList [x] = xmaxList (x:xs) | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
8. 8. Haskell Refresher Quiz● Whats the red one ? maxList :: [Int] -> Int maxList [] = error “empty” maxList [x] = x maxList (x:xs) | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
9. 9. Haskell Refresher Quiz● Whats the red one ?● maxList :: [Int] -> Int● maxList [] = error “empty” maxList [x] = x maxList (x:xs) | x > maxTail = x Function Body | otherwise = maxTail where maxTail = maxList xs
10. 10. Haskell Functions● function contains header and body● header consists of type definition: <funcname> :: <param> [ -> <param_n>] -> <result>● body consists of pattern rules and calculation <funcname> <paramalias_1> [<paramalias_n>] = {calc}● Example (2 params if type [Int] & Int, result Bool): isHead :: [Int] -> Int -> Bool isHead xs i = i==head xs
11. 11. Haskell Refresher Quiz● Whats the red one ?● maxList :: [Int] -> Int maxList [] = error “empty” maxList [x] = x maxList (x:xs) | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
12. 12. Haskell Refresher Quiz● Whats the red one ?● maxList :: [Int] -> Int Type maxList [] = error “empty” maxList [x] = x maxList (x:xs) | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
13. 13. Types in Haskell (1)Starts with uppercase first character● Int bounded from -2147483648 to 2147483647● Integer unbounded (for big numbers) but slower than Int● Float floating point (single precision)● Double floating point (double precision)● Bool boolean● Char character● String list of Char (String == [Char])
14. 14. Types in Haskell (2)● Lists: must be homogenous (entries from the same type) – [] empty List – [Int] List of Int – But e.g. [Int, Bool] not allowed (not homogenous)!● Tuples: can contain different types BUT have fixed length – () empty tuple (has only 1 value) – (Int, Bool) tuple of a pair Int, Bool – (Int, Bool, Bool) tuple of Int, Bool, Bool
15. 15. Lists & List Comprehension● Example: double entries in list doubleList [] = [] doubleList (x:xs) = x:x:doubleList xs – e.g. [1,2,3] → x=1; xs=[2,3]● Multiplication of a list of values: Hugs> product [1..5] 120● or in a function: fac n = product [1..n]
16. 16. Haskell Refresher Quiz● Whats the red one ?●maxList :: [Int] -> IntmaxList [] = error “empty”maxList [x] = xmaxList (x:xs) | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
17. 17. Haskell Refresher Quiz● Whats the red one ?●maxList :: [Int] -> IntmaxList [] =maxList [x] = x error “empty” PatternmaxList (x:xs) Matching | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
18. 18. Haskell Refresher Quiz● Whats the red one ?● maxList :: [Int] -> Int maxList [] = error “empty” maxList [x] = x maxList (x:xs) | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
19. 19. Haskell Refresher Quiz● Whats the red one ?● maxList :: [Int] -> Int maxList [] = error “empty” maxList [x] = x maxList (x:xs) | x > maxTail = x | otherwise = maxTail Guards where maxTail = maxList xs
20. 20. Haskell Refresher Quiz● Whats the red one ?● maxList :: [Int] -> Int maxList [] = error “empty” maxList [x] = x maxList (x:xs) | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
21. 21. Haskell Refresher Quiz● Whats the red one ?● maxList :: [Int] -> Int maxList [] = error “empty” maxList [x] = x maxList (x:xs) | x > maxTail = x | otherwise = maxTail Additional where maxTail = maxList xs where clause
22. 22. Pattern Matching (1)● create matching rules: fac 0 = 1 fac n = n * fac (n-1)● use wildcards to ignore parameters in pattern: take 0 _ = [] take _ [] = [] take n (x:xs) = [x] ++ take (n-1) xs
23. 23. Pattern Matching (2)● use Guards to separate a matching case deeper: myFilter _ [] = [] myFilter f (x:xs) | f==x = x:myFilter g xs | otherwise = myFilter f xs where g = 2*f – like an IF THEN ELSE – Guard Condition evaluate to Bool (True/False)● eventually define values with where-clause myFilter 2 [1,2,3,4,5,6] results to [2,4]
24. 24. Recursion● Recursion vs. Final Recursion:countX :: Int -> [Int] -> Int ● Hugs> countX 3 [1,4,3,5,3]countX x [] = 0 2countX x (y:ys) | x==y = 1 + countX x ys | otherwise = countX x ys countXFinal :: Int -> [Int] -> Int -> Int countXFinal x [] accu = accu countXFinal x (y:ys) accu | x==y = countXFinal x ys accu+1 | otherwise = countXFinal x ys accu● use accumulator to reduce stack usage● Hugs> countXFinal 3 [1,4,3,5,3] 0 2
25. 25. Haskell Refresher Quiz ● Whats the red one ? ●maxList :: (Ord a) => [a] -> amaxList [] = error “empty”maxList [x] = xmaxList (x:xs) | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
26. 26. Haskell Refresher Quiz ● Whats the red one ? ●maxList :: (Ord a) => [a] -> a TypeclassmaxList [] = error “empty”maxList [x] = xmaxList (x:xs) | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
27. 27. Haskell Refresher Quiz ● Whats the red one ? ●maxList :: (Ord a ) => [a] -> amaxList [] = error “empty”maxList [x] = xmaxList (x:xs) | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
28. 28. Haskell Refresher Quiz ● Whats the red one ? ●maxList :: (Ord a ) => [a] -> a Type variablemaxList [] = error “empty”maxList [x] = xmaxList (x:xs) | x > maxTail = x | otherwise = maxTail where maxTail = maxList xs
29. 29. Type Polymorphism (1)● Statically typed, but Compiler can read type from context (type inference)● → no need to set type explicitly● → makes function more generic for different kinds of types (type polymorphism) – Why should I use quicksort :: [Int] -> [Int] – even if I also want to sort character? Hugs> quicksort [f,a,d,b] "abdf"
30. 30. Type Polymorphism (2)● the header of our previous implementations could be fact :: Int -> Int maxList :: [Int] -> Int● but is only limited to Int, but maxList could also handle Char● → why not make it generic? maxList :: [a] -> a● but what happens, if the corresponding Type is not comparable or cannot be ordered?
31. 31. Type Polymorphism (3)● Solution: use Typeclasses maxList :: (Ord a) => [a] -> a● then we can be sure to use (<,<=, ==, /=, >=, >)● function header can contain multiple typeclasses maxList :: (Ord a, Eq b) => [a] -> [b] -> a● In Haskell-Interpreter: to list the function header :t <function_name>
32. 32. Typeclasses (1)● define properties of the types● like an interface● Typeclasses: – Eq can be compared – Ord can be ordered (>, <, >=, <=) (extending Eq) – Show can be shown as string – Read opposite of Show – Enum sequentially ordered types (can be enumerated and usable in List-Ranges [a..e])
33. 33. Typeclasses (2)● Typeclasses: – Bounded upper/lower bound (minBound, maxBound) – Num types behave like numbers (must already be Show, Eq) – Integral contains only integrals (subclass of Num) – Floating corresponding real numbers (subclass of Num)● if all Types of tuple are in same Typeclass → Tuple also in Typeclass
34. 34. Haskell Refresher Quiz● Which will terminate? (1) head [1..] (2) last [1..] (3) tail [1,2,3,4,5,6] (4) init (take 5 (cycle [1..]))
35. 35. Haskell Refresher Quiz● Which will terminate? (1) head [1..] (2) last [1..] (3) tail [1,2,3,4,5,6] (4) init (take 5 (cycle [1..]))● (1), (3) and (4) because of Lazy Evaluation
36. 36. Lazy Evaluation● Function execution only if result is needed● → Program = series of data-transformations● Example: A(B(C(x))) – If A needs result from B → call B – If B needs result from C → call C
37. 37. Haskell Refresher Quiz● Which one is faster? (1) head (take 5 [1,2,3,4,5,6]) (2) head (take 5 [1..10]) (3) head (take 5 [1..]) (4) head (take 5 (cycle [1..10]))