関数型プログラミングで重要となる高階関数と遅延評価について紹介。時間の関係で、遅延評価については Why Functional Programming Matters とその関連 URL の紹介しかしていない。

1. Welcome to the world of the functional programming
Kenta Murata 2011.06.11 #osc11do
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2. Monday, June 13, 2011 2

3. mrkn
Ruby
Ruby
http://www.flickr.com/photos/koichiroo/5244581973/
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4. Monday, 1
2010 3 June 13, 2011 4

5. Welcome to the world of the functional programming
Kenta Murata 2011.06.11 #osc11do
Monday, June 13, 2011 5

6. Functional Programming
Monday, June 13, 2011 6

7. Imperative Programming
Procedural Programming
Monday, June 13, 2011 7

8. Fortran
Basic
Cobol
Algol
C
C++
Java
LISP
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9. Monday, June 13, 2011 9

10. Functional Programming
Monday, June 13, 2011 10

11. High-order Functions
Lazy Evaluation
Monday, June 13, 2011 11

12. Functions
as Building Blocks
for constructing programs
http://www.flickr.com/photos/stevendepolo/5597111652
Monday, June 13, 2011 12

13. Functions as Glue
for bonding functions
http://www.flickr.com/photos/pseudoego/5417919481
Monday, June 13, 2011 13

14. A lot of programming
languages
available for
functional programming
http://www.flickr.com/photos/32712959@N07/3222623206
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15. Monday, June 13, 2011 15

16. Monday, June 13, 2011 16

17. Monday, June 13, 2011 17

18. High-order Functions
Monday, June 13, 2011 18

19. Monday, June 13, 2011 19

20. Monday, June 13, 2011 20

21. Haskell [ ]
e.g. []
[1, 2, 3]
(:)
e.g. [1] => 1 : []
[1, 2, 3] => 1 : 2 : 3 : []
Monday, June 13, 2011 21

22. (:) LISP
cons
cons Haskell
cons :: a -> [a] -> [a] --
cons x [] = [x] --
cons x1 (x2:xs) = x1 : (cons x2 xs)
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23. cons :: a -> [a] -> [a] --
cons x [] = [x] --
cons x1 (x2:xs) = x1 : (cons x2 xs)
// C++
template <typename a>
std::list<a>
cons(a const& x, std::list<a> const& xs);
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24. cons :: a -> [a] -> [a] --
cons x [] = [x] --
cons x1 (x2:xs) = x1 : (cons x2 xs)
e.g. cons 0 [1,2,3,4]
=> x1 0, x2 1, xs [2,3,4]
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25. (Int)
sum
sum :: [Int] -> Int
sum [] = 0
sum (n:ns) = n + (sum ns)
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26. cons sum
cons :: a -> [a] -> [a]
cons x [] = [x]
cons x1 (x2:xs) = x1 : (cons x2 xs)
sum :: [Int] -> Int
sum [] = 0
sum (n:ns) = n + (sum ns)
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27. cons x [] = [x]
sum [] = 0
cons x1 (x2:xs) = x1 : (cons x2 xs)
sum (n :ns) = n + (sum ns)
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28. (Int)
product
product :: [Int] -> Int
product [] = 1
product (n:ns) = n * product ns
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29. cons x [] = [x]
sum [] = 0
product [] = 1
cons x1 (x2:xs) = x1 : (cons x2 xs)
sum (n :ns) = n + (sum ns)
product (n :ns) = n * (product ns)
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30. (Bool)
allTrue
allTrue :: [Bool] -> Bool
allTrue [] = True
allTrue (b:bs) = b && allTrue ns
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31. (Bool)
anyTrue
anyTrue :: [Bool] -> Bool
anyTrue [] = False
anyTrue (b:bs) = b || anyTrue ns
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32. cons x [] = [x]
sum [] = 0
product [] = 1
allTrue [] = True
anyTrue [] = False
cons x1 (x2:xs) = x1 : (cons x2 xs)
sum (n :ns) = n + (sum ns)
product (n :ns) = n * (product ns)
allTrue (b :bs) = b && (allTrue bs)
anyTrue (b :bs) = b || (anyTrue bs)
Monday, June 13, 2011 32

33. cons x [] = [x]
sum [] = 0
product [] = 1
allTrue [] = True
anyTrue [] = False
cons x1 (x2:xs) = x1 : (cons x2 xs)
sum (n :ns) = n + (sum ns)
product (n :ns) = n * (product ns)
allTrue (b :bs) = b && (allTrue bs)
anyTrue (b :bs) = b || (anyTrue bs)
Monday, June 13, 2011 32

34. reduce :: (a -> [a] -> a) -> a -> [a] -> a
reduce f x0 [] = x0
reduce f x0 (x1:xs) = f x1 (reduce f x0 xs)
sum = reduce (+) 0
product = reduce (*) 1
allTrue = reduce (&&) True
anyTrue = reduce (||) False
Monday, June 13, 2011 33

35. reduce :: (a -> [a] -> a) -> a -> [a] -> a
reduce f x0 [] = x0
reduce f x0 (x1:xs) = f x1 (reduce f x0 xs)
sum = reduce (+) 0
product = reduce (*) 1
allTrue = reduce (&&) True
anyTrue = reduce (||) False
Monday, June 13, 2011 33

36. reduce :: (a -> [a] -> a) -> a -> [a] -> a
reduce f x0 [] = x0
reduce f x0 (x1:xs) = f x1 (reduce f x0 xs)
sum = reduce (+) 0
product = reduce (*) 1
allTrue = reduce (&&) True
anyTrue = reduce (||) False
Monday, June 13, 2011 33

37. reduce :: (a -> [a] -> a) -> a -> [a] -> a
reduce f x0 [] = x0
reduce f x0 (x1:xs) = f x1 (reduce f x0 xs)
sum = reduce (+) 0
product = reduce (*) 1
allTrue = reduce (&&) True
anyTrue = reduce (||) False
Monday, June 13, 2011 33

38. cons reduce
append :: [a] -> [a] -> [a]
append xs ys = reduce (:) ys xs
append [1,2] [3,4]
-> reduce (:) [3,4] [1,2]
-> reduce (:) [3,4] (1:2:[])
-> 1 : (reduce (:) [3,4] (2:[]))
-> 1 : 2 : (reduce (:) [3,4] [])
-> 1 : 2 : [3,4]
-> [1,2,3,4]
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39. Monday, June 13, 2011 35

40. Monday, June 13, 2011 36

41. Monday, June 13, 2011 37

42. Functions
as Building Blocks
for constructing programs
http://www.flickr.com/photos/stevendepolo/5597111652
Monday, June 13, 2011 38

43. Functions as Glue
for bonding functions
http://www.flickr.com/photos/pseudoego/5417919481
Monday, June 13, 2011 39

44. Monday, June 13, 2011 40

45. -- Haskell
reduce (+) 0 [1..10]
// C++
int ns[] = {1,2,3,4,5,6,7,8,9,10};
std::accumulate(ns, ns + 10, 0, &std::plus<int>);
# Ruby
[*1..10].inject(0, :+)
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46. Monday, June 13, 2011 42

47. Lazy Evaluation
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48. Monday, June 13, 2011 44

49. Monday, June 13, 2011 45

50. http://www.sampou.org/haskell/article/whyfp.html
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51. http://www.infoq.com/interviews/john-hughes-fp
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52. http://weblog.raganwald.com/2007/03/why-why-functional-programming-matters.html
Monday, June 13, 2011 48

53. language evaluation pureness
Haskell lazy pure
Concurrent Clean lazy pure
OCaml strict impure
F# strict impure
Scheme strict impure
Monday, June 13, 2011 49

54. language evaluation pureness
Haskell lazy pure
Concurrent Clean lazy pure
OCaml strict impure
F# strict impure
Scheme strict impure
Monday, June 13, 2011 50

55. Monday, June 13, 2011 51

56. Monday, 1
2010 3 June 13, 2011 52

57. Functional Programming
Monday, June 13, 2011 53

58. A lot of programming
languages
available for
functional programming
http://www.flickr.com/photos/32712959@N07/3222623206
Monday, June 13, 2011 54

59. Monday, June 13, 2011 55

60. High-order Functions
Monday, June 13, 2011 56

61. Functions
as Building Blocks
for constructing programs
http://www.flickr.com/photos/stevendepolo/5597111652
Monday, June 13, 2011 57

62. Functions as Glue
for bonding functions
http://www.flickr.com/photos/pseudoego/5417919481
Monday, June 13, 2011 58

63. Lazy Evaluation
Monday, June 13, 2011 59

64. Monday, June 13, 2011 60