An Introduction to Functional Programming using Haskell
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The document provides an introduction to functional programming using Haskell. It discusses Haskell's main features such as being purely functional, lazy, strongly typed, and supporting higher-order functions. It also covers Haskell's history, types, functions, pattern matching, and common data structures like lists. Programming techniques like recursion, algebraic data types, and type classes are explained. Examples of list processing functions and higher-order functions are provided.
![Types
basic types: Char, Bool, Int, Integer,
Double
composite types
lists: [Char], [Int], [[Char]]
tuples: (String,Int)](https://image.slidesharecdn.com/ifpuh-091108054940-phpapp02/85/An-Introduction-to-Functional-Programming-using-Haskell-7-320.jpg)
![Function Types
square :: Integer -> Integer
(&&) :: Bool -> Bool -> Bool
length :: [a] -> Int
(:) :: a -> [a] -> [a]](https://image.slidesharecdn.com/ifpuh-091108054940-phpapp02/85/An-Introduction-to-Functional-Programming-using-Haskell-8-320.jpg)
![Exercises Template
-- file: Main.hs
module Main where
import Prelude hiding (sum,length)
sum :: [Int] -> Int
...
length :: [a] -> Int
...](https://image.slidesharecdn.com/ifpuh-091108054940-phpapp02/85/An-Introduction-to-Functional-Programming-using-Haskell-12-320.jpg)
![List Patterns
[]
xs
(x:xs)
(x:_)
(_:xs)
(_:_)](https://image.slidesharecdn.com/ifpuh-091108054940-phpapp02/85/An-Introduction-to-Functional-Programming-using-Haskell-13-320.jpg)
![List Comprehensions
> let xs = [2,4,7]
> [ 2 * x | x <- xs ]
[4,8,14]
> [ even x | x <- xs ]
[True,True,False]
> [ 2 * x | x <- xs, even x, x > 3]
[8]
> [ x + y | (x,y) <- [(2,3),(2,1)] ]
[5,3]
> [ x + y | (x,y) <- [(2,3),(2,1)],
x < y ]
[5]](https://image.slidesharecdn.com/ifpuh-091108054940-phpapp02/85/An-Introduction-to-Functional-Programming-using-Haskell-14-320.jpg)
![List Functions
(:) :: a -> [a] -> [a] tail, init :: [a] -> [a]
(++) :: [a] -> [a] -> [a] replicate ::
Int -> a -> [a]
(!!) :: [a] -> Int -> [a]
take, drop ::
concat :: [[a]] -> [a] Int -> [a] -> [a]
length :: [a] -> Int splitAt ::
Int -> [a] -> ([a],[a])
head, last :: [a] -> a](https://image.slidesharecdn.com/ifpuh-091108054940-phpapp02/85/An-Introduction-to-Functional-Programming-using-Haskell-17-320.jpg)
![More List Functions
repeat :: a -> [a] and, or ::
[Bool] -> Bool
reverse :: [a] -> [a]
sum, product ::
zip :: [Int] -> Int
[a] -> [b] -> [(a,b)] [Float] -> Float
unzip ::
[(a,b)] -> ([a],[b])](https://image.slidesharecdn.com/ifpuh-091108054940-phpapp02/85/An-Introduction-to-Functional-Programming-using-Haskell-18-320.jpg)
![Programming with Lists
Prelude> :load Sprite
*Sprite> print glider
.#.
..#
###
[(),(),()]
*Sprite> print (flipH glider)
###
..#
.#.
[(),(),()]](https://image.slidesharecdn.com/ifpuh-091108054940-phpapp02/85/An-Introduction-to-Functional-Programming-using-Haskell-19-320.jpg)
![Sprite.hs
flipH :: Picture -> Picture
flipH pic = reverse pic
flipV :: Picture -> Picture
flipV pic =
[ reverse line | line <- pic ]](https://image.slidesharecdn.com/ifpuh-091108054940-phpapp02/85/An-Introduction-to-Functional-Programming-using-Haskell-20-320.jpg)
![Mapping and Filtering
map :: (a -> b) -> [a] -> [b]
filter :: (a -> Bool) -> [a] -> [a]
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]](https://image.slidesharecdn.com/ifpuh-091108054940-phpapp02/85/An-Introduction-to-Functional-Programming-using-Haskell-23-320.jpg)
![Folding
foldl :: (a -> b -> a) -> a -> [b] -> a
foldl1 :: (a -> b -> a) -> [b] -> a
foldr :: (a -> b -> b) -> b -> [a] -> b
foldr1 :: (a -> a -> a) -> [a] -> a](https://image.slidesharecdn.com/ifpuh-091108054940-phpapp02/85/An-Introduction-to-Functional-Programming-using-Haskell-24-320.jpg)
![Defining an Instance
instance Visible Char where
toString ch = [ch]
size _ = 1
instance Eq Bool where
True == True = True
False == False = True
_ == _ = False](https://image.slidesharecdn.com/ifpuh-091108054940-phpapp02/85/An-Introduction-to-Functional-Programming-using-Haskell-27-320.jpg)
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An Introduction to Functional Programming using Haskell
- 1. An Introduction to Functional Programming using Haskell Michel Rijnders <[email protected]>
- 2. Administrativia Anglais? tuple programming skill level working ghci handouts breaks
- 3. Main Features purely functional lazy higher order strongly typed general purpose
- 4. History September 1987 FPCA “design by committee” P. Hudak, J. Hughes, S. Peyton Jones, and P. Wadler: “A History of Haskell: Being Lazy With Class” (2007)
- 5. Main Difference mainstream languages are all about state functional programming is all about values
- 6. Computation all computation is done via the evaluation of EXPRESSIONS to yield VALUES every value has an associated TYPE
- 7. Types basic types: Char, Bool, Int, Integer, Double composite types lists: [Char], [Int], [[Char]] tuples: (String,Int)
- 8. Function Types square :: Integer -> Integer (&&) :: Bool -> Bool -> Bool length :: [a] -> Int (:) :: a -> [a] -> [a]
- 9. Function Definitions fac :: Int -> Int fac n = if n == 0 then 1 else n * fac (n - 1)
- 10. Guards -- guards fac’ :: Int -> Int fac’ n | n == 0 = 1 | otherwise = n * fac’ (n - 1)
- 11. Pattern Matching -- pattern matching fac’’ :: Int -> Int fac’’ 0 = 1 fac’’ n = n * fac’’ (n - 1)
- 12. Exercises Template -- file: Main.hs module Main where import Prelude hiding (sum,length) sum :: [Int] -> Int ... length :: [a] -> Int ...
- 14. List Comprehensions > let xs = [2,4,7] > [ 2 * x | x <- xs ] [4,8,14] > [ even x | x <- xs ] [True,True,False] > [ 2 * x | x <- xs, even x, x > 3] [8] > [ x + y | (x,y) <- [(2,3),(2,1)] ] [5,3] > [ x + y | (x,y) <- [(2,3),(2,1)], x < y ] [5]
- 15. Summary computation types functions guards pattern matching list comprehensions
- 16. Coming Up programming with lists higher-order functions type classes algebraic types
- 17. List Functions (:) :: a -> [a] -> [a] tail, init :: [a] -> [a] (++) :: [a] -> [a] -> [a] replicate :: Int -> a -> [a] (!!) :: [a] -> Int -> [a] take, drop :: concat :: [[a]] -> [a] Int -> [a] -> [a] length :: [a] -> Int splitAt :: Int -> [a] -> ([a],[a]) head, last :: [a] -> a
- 18. More List Functions repeat :: a -> [a] and, or :: [Bool] -> Bool reverse :: [a] -> [a] sum, product :: zip :: [Int] -> Int [a] -> [b] -> [(a,b)] [Float] -> Float unzip :: [(a,b)] -> ([a],[b])
- 19. Programming with Lists Prelude> :load Sprite *Sprite> print glider .#. ..# ### [(),(),()] *Sprite> print (flipH glider) ### ..# .#. [(),(),()]
- 20. Sprite.hs flipH :: Picture -> Picture flipH pic = reverse pic flipV :: Picture -> Picture flipV pic = [ reverse line | line <- pic ]
- 21. Higher Order Functions functions as arguments functions as results or both
- 22. Higher Order Functions patterns of computation mapping: transforming elements filtering: selecting elements folding: combining elements
- 23. Mapping and Filtering map :: (a -> b) -> [a] -> [b] filter :: (a -> Bool) -> [a] -> [a] zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- 24. Folding foldl :: (a -> b -> a) -> a -> [b] -> a foldl1 :: (a -> b -> a) -> [b] -> a foldr :: (a -> b -> b) -> b -> [a] -> b foldr1 :: (a -> a -> a) -> [a] -> a
- 25. Type Classes type class: a collection of of types over which certain functions are defined equality class Eq (==) :: (Eq a) => a -> a -> Bool (/=) :: (Eq a) => a -> a -> Bool
- 26. Declaring a Class class Visible a where toString :: a -> String size :: a -> Int class Eq a where (==), (/=) :: a -> a -> Bool x /= y = not (x == y) x == y = not (x /= y)
- 27. Defining an Instance instance Visible Char where toString ch = [ch] size _ = 1 instance Eq Bool where True == True = True False == False = True _ == _ = False
- 28. Derived Classes class Eq a => Ord a where (<), (<=), (>), (>=) :: a -> Bool max, min :: a -> a -> a compare :: a -> a -> Ordering
- 30. Algebraic Types data Bool = False | True data Season = Spring | Summer | Autumn | Winter data Ordering = LT | EQ | GT
- 31. Product Types data People = Person Name Age type Name = String type Age = Int data Shape = Circle Double | Rectangle Float Float
- 32. Recursive Algebraic Types data Expr = Lit Int | Add Expr Expr | Sub Expr Expr data Tree a = Node (Tree a) (Tree a) | Leaf a
- 33. More? http://haskell.org/ G. Hutton: Programming in Haskell (Cambridge University Press) B. O’Sullivan, J. Goerzen, D. Stewart: Real World Haskell (O’Reilly)
Editor's Notes
- #2: Introductie Eduard
- #5: - FPCA: Conference on Functional Programming Languages and Computer Architecture - Paul Hudak: Yale - John Hughes: Chalmers (G&#xF6;teborg) - Simon Peyton Jones: Microsoft Cambridge - Philp Wadler: Edinburgh
- #8: - ghci demo - exercises (1. Expressions, Values, and Types)
- #13: - exercises 2
- #14: - exercises 3 - warn about repeated variables
- #15: - generator - one or more tests - pattern - exercises 4
- #21: - exercises 5
- #24: - exercises 6
- #26: - constraints
- #27: - default definitions
- #28: - exercises 8