1.
An Introduction to
Functional Programming
using Haskell
Michel Rijnders <mies@tty.nl>

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
...

13.
List Patterns
[]
xs
(x:xs)
(x:_)
(_:xs)
(_:_)

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

29.
Built-In Classes
Eq
Ord
Enum
Show
Read

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)