Overview of the Haskell 98 Programming Language

1. Overview of the Haskell 98 Programming Language (Condensed from Haskell Document by Godisch and Sturm)

2. How to Run Haskell Programs • Use the Hugs interpreter downloaded from www.haskell.org/hugs/ • At the command line, enter hugs • Haskell script files usually end with a ".hs" extension • -- indicates a single-line comment • {- -} enclose multi-line comments • : <command> executes a Haskell command • All variables and functions start with a lowercase letter • All types and constructors start with an uppercase letter

3. Summary of Commands Used in Hugs

4. Built-in Haskell Data Types • Int • Integer • Float • Double • Bool • Char • String

5. Using the Data Type Int myFile.hs functionF :: Int -> Int -> Int functionF x y = x + y Inside Hugs Interpreter Prelude> :load myFile.hs Main> functionF 1 2 3

6. Operators Available for Type Int • 5 + 3 • 5 - 3 • 5 * 3 • 5 `div` 3 Integer division (backquotes) • div 5 3 • 5 `mod` 2 Modulo division • mod 5 2 • 5 ^ 3 3rd power of 5 • abs (-5) Absolute value, parentheses are needed • Negate (-5) Negation of -5 • -5 Negative 5

7. Using the Data Type Bool • Values of type Bool are True or FalsefunctionF :: Int -> BoolfunctionF = (>= 7) • Boolean Operators True && False – logical AND True || False - logical OR not True - logical negation True == False - equality True /= False - inequality

8. Using the Data Type Char • A character is enclosed in a single quotec :: Charc = 'a' • A character can be converted to its ASCII integer value and vice versa using predefined functions> ord 'a'97> chr 97'a'

9. Using the Data Type String • A string is a (possibly empty) sequence of characters and is enclosed in double quotes • It is type synonym for a list of type CharfunctionS :: StringfunctionS = "A string example"

10. Guards and Pattern Matching functionG :: Int -> Int functionG n | n == 0 = 0 | otherwise = n - 1 functionH :: Int -> Int functionH 0 = 0 functionH (n + 1) = n

11. Precedence and Binding • Function application has the highest precedence • Example: functionF n + 1 • Correct binding: (functionF n) + 1 • Wrong binding: functionF (n + 1)

12. Indentation and the Offside Rule • Haskell reduces the need for parentheses to a minimum by using the offside rule • To detect the start of another function definition, Haskell looks for the first piece of text that lies at the same indentation or to the left of the start of the current function • Also, a semicolon can be used to separate several definitions on the same line

13. where and let keywords • Each expression may be followed by a local definitions using the keyword where • A similar approach can be done using the keywords let and in functionF :: Int -> Int functionF x = g (x + 1) where g = (^2) functionM :: Int -> Int functionM x = let functionP = (^2) in functionP (x + 1)

14. Tuples • A tuple is a grouping of two or more possibly different types representing a record or structure person :: (String, Int)person = ("Bill", 24) • A type synonym using the keyword type can be used to give an alternative name to a typetype Person = (String, Int)

15. Polymorphic Functions • A polymorphic function has one definition. It accepts variables of different types as input at runtime • Polymorphic types begin with a lowercase letterfunctionF :: a -> b -> c -> afunctionF x _ _ = x • This is different from overloaded functions • They have many different definitions • Example is the equality function, which is defined differently for type Int compared to type Bool

16. Type Classes • Members of a type classe are called instances • Predefined instances of class Eq are Int, Float, Double, Bool, Char, and String • Haskell has other built-in classes • Eq - equality and inequality • Ord - ordering over elements of a type • Enum - enumeration of a type • Show - conversion of the elements of a type into text • Read - conversion of values to a type from a string

17. Function Composition • The function composition operator is the dot (.) • It type of the dot is (b -> c) -> (a -> b) -> (a -> c) • ExamplefunctionF :: Char -> CharfunctionF c = chr (succ (ord c))functionG :: Char -> CharfunctionG = chr . succ . ord

18. Using Lists • A list is an ordered set of values of the same type • It is enclosed in brackets with each element separated by a comma listOfInt :: [Int] listOfInt = [1,2,3,4] listOfChar :: [Char] listOfChar = ['h', 'e', 'l', 'l', 'o'] listOfString :: [ [Char] ] listOfString = [['o', 'n', 'e'], "two", "three"]

19. Construction of Lists • A list can be written as x:xs, where x is the head of the list, xs is the tail, and : is the cons operator • Every list is built up recursively using the cons operator whose type is a -> [a] -> [a][] == []1:[] == [1]2:[1] == [2, 1]3:[2,1] == 3:2:1:[] == [3, 2, 1] • The list concatenation operator is ++ and its type is[a] -> [a] -> [a][1,2] ++ [] ++ [3,4,5] == [1, 2, 3, 4, 5] • Lists of elements can be denoted by giving a range[2 .. 8 ] == [2, 3, 4, 5, 6, 7, 8][1, 3 .. 12] == [1, 3, 5, 7, 9, 11]

20. Pattern Matching Over Lists • An unstructured variable xs matches any list • (_:_) matches any non-empty list without binding of list elements • (x:xs) matches any non-empty list; however, x is bound to the head and xs to the tail • (_:[]) is identical to [_] and matches any list with one and only one element • (x1:x2:xs) extracts the first two elements of a list containing two or more elements, with x1 and x2 bound to the first two elements and xs bound to the tail

21. List Comprehension • A subset of a list can be generated using list comprehension in a common mathematical set notation[x | x<-g, even x] generator guard(Translated as: x such that x is a member of the list g and x is even) • Generate a list of all possible pairs out of two setspairs :: [a] -> [b] -> [(a,b)]pairs xs ys = [(x,y) | x <- xs, y <- ys]

22. Recursion over Lists • Example: Sum up the elements of a listsum :: [Int] -> Intsum [] = 0sum (x:xs) = x + sum xs • Example: Filter a list according to a selection criteriafilter :: (a -> Bool) -> [a] -> [a]filter p [] = []filter p (x:xs) | p x = x : filter p xs | otherwise = filter p xs Note: sum and filter are both predefined functions in Haskell

23. Some Predefined List Functions • (:) :: a -> [a] -> [a] • (++) :: [a] -> [a] -> [a] • (!!) :: [a] -> Int -> a • map :: (a->b) -> [a] -> [b] • filter :: (a -> Bool) -> [a] -> [a] • head :: [a] -> a • tail :: [a] -> [a] • last :: [a] -> a • init :: [a] -> [a] • length :: [a] -> Int • null :: [a] -> Bool • take :: Int -> [a] -> [a] • drop :: Int -> [a] -> [a]

24. Algebraic Data Types: Enumeration • This is the simplest kind of algebraic typedata Color = Red | Green | Bluedata RoomNumber = 102 | 214 | 228 | 233 | 245assignColor :: RoomNumber -> Color

25. Algebraic Data Types: Product • This is used to combine two or more typestype Name = Stringtype Age = Intdata People = Person Name Age • Person is referred to as the constructor of type People. Its type is Name -> Age -> People • Person is a function that generates an element of type People out of the types Name and Age

26. Algebraic Data Types: Alternatives • This is used to combine two or more types but allows some choicestype Name = Stringdata Year = Freshman | Sophomore | Junior | Seniordata Dept = Bus | Eng | LA | Mathdata People = Student Name Year | Staffer Name Dept

27. Algebraic Data Types: Recursive • A recursive type can be created from an alternative typedata Tree = Nil | Node Int Tree TreemyTree :: TreemyTree = Node 1 (Node 2 (Node 4 Nil Nil) (Node 5 Nil Nil)) (Node 3 Nil Nil)depth :: Tree -> Intdepth Nil = 0depth (Node _ t1 t2) = 1 + max (depth t1) (depth t2)

28. Instances of Classes • When creating a new algebraic type, you may need to inherit operations from other type classes. This is done using the deriving keyworddata Color = Red | Green | Blue deriving (Eq, Ord, Enum, Show, Read)

29. Example of an Abstract Data Type Module Stack (Stack, isEmpty, push, pop) where data Stack a = Empty | MyStack a (Stack a)isEmpty :: Stack a -> Bool isEmpty Empty = True isEmpty (MyStack _ _) = False push :: a -> Stack a -> Stack a push element aStack = MyStack element aStack pop :: Stack a -> (a, Stack a) pop Empty = error "Empty stack" pop (MyStack element aStack) = (element, aStack)