Downloaded 17 times
![$를 이용한 함수 application
($) :: (a -> b) -> a -> b
f $ x = f x
> map ($ 3) [(4+), (10*), (^2), sqrt]
[7.0,30.0,9.0,1.7320508075688772]
($): 함수 f와 인자 a를 받아 f a를 호출함](https://image.slidesharecdn.com/haskell2-160521064250/75/2-3-2048.jpg)
![Type synonym
• type String = [Char]
• type Pos = (Int, Int)
origin :: Pos
origin = (0, 0)
left :: Pos -> Pos
left (x, y) = (x-1, y)](https://image.slidesharecdn.com/haskell2-160521064250/75/2-4-2048.jpg)
![Type synonym
• Can be nested
• type Trans = Pos -> Pos
• Can't be recursive
• type Tree = (Int, [Tree])](https://image.slidesharecdn.com/haskell2-160521064250/75/2-6-2048.jpg)
![Algebraic Data Type
data Answer = Yes | No | Unknown
answers :: [Answer]
answers = [Yes, No, Unknown]
flip :: Answer -> Answer
flip Yes = No
flip No = Yes
flip Unknown = Unknown](https://image.slidesharecdn.com/haskell2-160521064250/75/2-8-2048.jpg)
![재귀 타입 (Binary Tree)
flatten :: Tree a -> [a]
flatten (Leaf x) = [x]
flatten (Node l x r) = flatten l
++ [x]
++ flatten r](https://image.slidesharecdn.com/haskell2-160521064250/75/2-18-2048.jpg)
![getLine
getLine :: IO String
getLine = do x <- getChar
if x == 'n' then
return []
else
do xs <- getLine
return (x:xs)](https://image.slidesharecdn.com/haskell2-160521064250/75/2-35-2048.jpg)
![putStr/putStrLn
putStr :: String -> IO ()
putStr [] = return ()
putStr (x:xs) = do putChar x
putStr xs
putStrLn :: String -> IO ()
putStrLn = do putStr xs
putChar 'n'](https://image.slidesharecdn.com/haskell2-160521064250/75/2-36-2048.jpg)
![Maybe
• 함수의 리턴값이 보장되어 있지 않을 때 사용
> import Data.List
> :t elemIndex
elemIndex :: Eq a => a -> [a] -> Maybe Int
> elemIndex ‘b’ "abc"
Just 1
> elemIndex ‘z’ "abc"
Nothing](https://image.slidesharecdn.com/haskell2-160521064250/75/2-37-2048.jpg)
![Maybe
safediv :: Int -> Int -> Maybe Int
safediv _ 0 = Nothing
safediv m n = Just (m `div` n)
safehead :: [a] -> Maybe a
safehead [] = Nothing
safehead xs = Just (head xs)
data Maybe a = Nothing | Just a](https://image.slidesharecdn.com/haskell2-160521064250/75/2-39-2048.jpg)
![Higher Order
data RoseTree a = RLeaf a
| RNode [RoseTree a]
data BinTree = BLeaf a
| BNode (Pair (BinTree a))
data Pair a = MkPair a a](https://image.slidesharecdn.com/haskell2-160521064250/75/2-40-2048.jpg)
![Higher Order
data RoseTree a = RLeaf a
| RNode ([] (RoseTree a))
data BinTree = BLeaf a
| BNode (Pair (BinTree a))
— [] :: * -> * The list constructor
Syntactic Sugar를 제거하면?](https://image.slidesharecdn.com/haskell2-160521064250/75/2-41-2048.jpg)
![Higher Order
data Tree k a = Leaf a
| Node (k (Tree k a))
data RoseTree a = Tree [] a
data BinTree = Tree Pair a
data AnnTree = Tree AnnPair a
data Pair a = P a a
data AnnPair a = AP String a a
변화하는 부분을 인자로 추출하면?
• ‘a’는 type (a :: *)
• ‘k’는 type constructor (k :: * -> *)](https://image.slidesharecdn.com/haskell2-160521064250/75/2-42-2048.jpg)
![리스트에 대한 Functor
> import Data.Char
> fmap (+1) [1,2,3]
[2,3,4]
> fmap toUpper "qwertyuiop"
"QWERTYUIOP"](https://image.slidesharecdn.com/haskell2-160521064250/75/2-45-2048.jpg)
![콘텍스트로 이해하는
Functor
• [] functor
• 콘텍스트는 리스트
• (->) functor
• 첫 번째 인자가 a인 함수가 콘텍스트 (read-only 환
경)
• IO functor
• 사이드 이펙트가 가능한 computation이 콘텍스트](https://image.slidesharecdn.com/haskell2-160521064250/75/2-59-2048.jpg)
![Monoid 예제
• +, 0은 Monoid
• *, 1은 Monoid
• (++)과 []은 Monoid](https://image.slidesharecdn.com/haskell2-160521064250/75/2-62-2048.jpg)
![Monoid
> import Data.Monoid
> [1,2,3] `mappend` [4,5,6]
[1,2,3,4,5,6]
> [1,2,3] `mappend` mempty
[1,2,3]
> mempty `mappend` [1,2,3]
[1,2,3]](https://image.slidesharecdn.com/haskell2-160521064250/75/2-63-2048.jpg)
![합수 합성의 예
> (take 2 . filter (>=3) . map length) ["a", "ab", "abc",
"abcd", "abcde"]
[3,4]
> map (negate . abs) [5, -3, -6, 7, -3, 2, -19, 24]
[-5,-3,-6,-7,-3,-2,-19,-24]](https://image.slidesharecdn.com/haskell2-160521064250/75/2-75-2048.jpg)
![[SICP] 4.4 Logic Programming : 논리로 프로그램 짜기](https://cdn.slidesharecdn.com/ss_thumbnails/4-4-090608224521-phpapp02-thumbnail.jpg?width=640&height=640&fit=bounds)
하스켈 프로그래밍 입문 2
- 1. 하스켈 프로그래밍 입문 2 하스켈학교 2016년 5월 21일 서광열
- 2. 함수 합성 (.): 두함수를 인자로 받아 두 함수의 합성 함수를 리턴 함 (.) :: (b -> c) -> (a -> b) -> (a -> c) f . g = x -> f (g x) odd :: Int -> Bool odd = not . even
- 3. $를 이용한 함수application ($) :: (a -> b) -> a -> b f $ x = f x > map ($ 3) [(4+), (10*), (^2), sqrt] [7.0,30.0,9.0,1.7320508075688772] ($): 함수 f와 인자 a를 받아 f a를 호출함
- 4. Type synonym • typeString = [Char] • type Pos = (Int, Int) origin :: Pos origin = (0, 0) left :: Pos -> Pos left (x, y) = (x-1, y)
- 5. Type synonym • typePair a = (a, a) mult :: Pair Int -> Int mult (m, n) = m *n copy :: a -> Pair a copy x = (x, x)
- 6. Type synonym • Canbe nested • type Trans = Pos -> Pos • Can't be recursive • type Tree = (Int, [Tree])
- 7.
- 8. Algebraic Data Type dataAnswer = Yes | No | Unknown answers :: [Answer] answers = [Yes, No, Unknown] flip :: Answer -> Answer flip Yes = No flip No = Yes flip Unknown = Unknown
- 9. Algebraic Data Type dataShape = Circle Float | Rect Float Float square :: Float -> Shape square n = Rect n n area :: Shape -> Float area (Circle r) = pi * r^2 area (Rect x y) = x * y Circle :: Float -> Shape Rect :: Float -> Float -> Shape
- 10. 재귀 타입 (Succ) dataNat = Zero | Succ Nat Zero -- 0 Succ Zero -- 1 Succ (Succ Zero) -- 2 Succ (Succ (Succ Zero)) -- 3
- 11. 재귀 타입 (Succ) nat2int:: Nat -> Int nat2int Zero = 0 nat2int (Succ n) = 1 + nat2int n int2nat :: Int -> Nat int2nat 0 = Zero int2nat n = Succ (int2nat (n-1))
- 12. 재귀 타입 (Succ) --converting to and from integers add :: Nat -> Nat -> Nat add m n = int2nat (nat2int m + nat2int n) -- using recursion add Zero n = n add (Succ m) n = Succ (add m n)
- 13. 재귀 타입 (Succ) add(Succ (Succ Zero)) (Succ Zero) = Succ (add (Succ Zero) (Succ Zero) = Succ (Succ (add Zero (Succ Zero)) = Succ (Succ (Succ Zero))
- 14. 재귀 타입(Expr) data Expr= Val Int | Add Expr Expr | Mul Expr Expr -- 1 + (2 * 3) Add (Val 1) (Mul (Val 2) (Val 3))
- 15. 재귀 타입 (Expr) size:: Expr -> Int size (Val n) = 1 size (Add x y) = size x + size y size (Mul x y) = size x + size y eval :: Expr -> Int eval (Var n) = n eval (Add x y) = eval x + eval y eval (Mul x y) = eval x * eval y
- 16. 재귀 타입 (BinaryTree) data Tree a = Leaf a | Node (Tree a) a (Tree a) t: Tree Int t = Node (Node (Leaf 1) 3 (Leaf 4)) 5 (Node (Leaf 6) 7 (Leaf 9))
- 17. 재귀 타입 (BinaryTree) occurs :: Eq a => a -> Tree a -> Bool occurs x (Leaf y) = x == y occurs x (Node l y r) = x == y || occurs x l || occurs x r
- 18. 재귀 타입 (BinaryTree) flatten :: Tree a -> [a] flatten (Leaf x) = [x] flatten (Node l x r) = flatten l ++ [x] ++ flatten r
- 19. Algebraic Data Type요약 종류 예제 Enumeration data Season = Summer | Winter | Autumn | Spring Product data Pair = Pair Int Int Sum data Shape = Circle Float | Rect Float Float Polymorphic & Recursive data Tree a = Leaf a | Node (Tree a) a (Tree a)
- 20. Record data Person =Person { firstName :: String , lastName :: String , age :: Int } • 각 필드에 이름을 부여 • 필드 이름은 해당 필드 값을 꺼내는 getter 함수가 됨
- 21. Record 생성 및getter > :t Person Person :: String -> String -> Int -> Person > :t firstName firstName :: Person -> String > :t lastName lastName :: Person -> String > :t age age :: Person -> Int
- 22. Record > let p= Person { firstName = "Kwang", lastName = "Seo", age = 20 } > firstName p "Kwang" > age p 20
- 23. Record 패턴 매칭 fullName:: Person -> String fullName (Person {firstName = fn, lastName = ln}) = fn ++ " " ++ ln
- 24. deriving • Show, Eq등의 타입 클래스 인스턴스를 자동으로 생성 data Expr = Const Int | Add Expr Expr deriving (Eq, Show)
- 25. 타입 클래스 class Eqa where (==) :: a -> a -> Bool
- 26. 타입 클래스 data Expr= Const Int | Add Expr Expr instance Eq Expr where (Const _) == (Add _) = False (Add _) == (Const _) = False (Const i) == (Const i') = i == i' (Add x y) == (Add x' y') == x == x' && y == y'
- 27. 타입 클래스 class Eqa where (==), (/=) :: a -> a -> Bool x/=y = not (x==y) x==y = not (x/=y) (==)와 (/=) 중 하나만 구현해도 됨
- 28. 타입 클래스와 C#/Java인 터페이스 비교 C#/Java 하스켈 Class - Interface Type class Interface member Type-class member Interface implementation Type-class instance
- 29. 타입 클래스의 특징 •구현을 따로 지정 • 구현 타입에 대한 명시적 지정 • 여러 개의 레퍼런스 (binary method) • 결과 값에 대한 레퍼런스 (static method) • 멤버에 대한 디폴트 구현 • 여러 개의 타입 인자
- 30. 타입 클래스 메소드의종 류 > :t show (Show a) => a -> String > :t read (Read a) => String -> a > :t (==) (Eq a) => a -> a -> Bool • instance: show • static: read • binary: (==)
- 31.
- 32. IO • pure expression과impure action을 구분 • IO a • 액션을 수행하고 a 타입을 리턴 • 예) IO Char, IO ()
- 33. 간단한 액션 • getChar:: IO Char • 키보드에서 문자 하나를 읽어 리턴함 • putChar :: Char -> IO () • putChar c는 화면에 문자 c를 출력함 • return :: a -> IO a • return v는 아무런 액션을 하지 않고 v를 리턴함
- 34. do 표기법 do 표기법을이용해 여러 개의 액션을 하나의 액션으로 만들 수 있음 act :: IO (Char, Char) act = do x <- getChar getChar y <- getChar return (x, y)
- 35. getLine getLine :: IOString getLine = do x <- getChar if x == 'n' then return [] else do xs <- getLine return (x:xs)
- 36. putStr/putStrLn putStr :: String-> IO () putStr [] = return () putStr (x:xs) = do putChar x putStr xs putStrLn :: String -> IO () putStrLn = do putStr xs putChar 'n'
- 37. Maybe • 함수의 리턴값이보장되어 있지 않을 때 사용 > import Data.List > :t elemIndex elemIndex :: Eq a => a -> [a] -> Maybe Int > elemIndex ‘b’ "abc" Just 1 > elemIndex ‘z’ "abc" Nothing
- 38. Maybe의 콘텍스트 • Just1과 1 • Just "Hello"와 "Hello" • Just ‘a’와 ‘a’ • Nothing과 에러
- 39. Maybe safediv :: Int-> Int -> Maybe Int safediv _ 0 = Nothing safediv m n = Just (m `div` n) safehead :: [a] -> Maybe a safehead [] = Nothing safehead xs = Just (head xs) data Maybe a = Nothing | Just a
- 40. Higher Order data RoseTreea = RLeaf a | RNode [RoseTree a] data BinTree = BLeaf a | BNode (Pair (BinTree a)) data Pair a = MkPair a a
- 41. Higher Order data RoseTreea = RLeaf a | RNode ([] (RoseTree a)) data BinTree = BLeaf a | BNode (Pair (BinTree a)) — [] :: * -> * The list constructor Syntactic Sugar를 제거하면?
- 42. Higher Order data Treek a = Leaf a | Node (k (Tree k a)) data RoseTree a = Tree [] a data BinTree = Tree Pair a data AnnTree = Tree AnnPair a data Pair a = P a a data AnnPair a = AP String a a 변화하는 부분을 인자로 추출하면? • ‘a’는 type (a :: *) • ‘k’는 type constructor (k :: * -> *)
- 43. Higher Order • Maybea • Type • Kind : * • Maybe • Type Constructor • Kind : * -> *
- 44. Functor class Functor fwhere fmap :: (a -> b) -> f a -> f b
- 45. 리스트에 대한 Functor >import Data.Char > fmap (+1) [1,2,3] [2,3,4] > fmap toUpper "qwertyuiop" "QWERTYUIOP"
- 46. Maybe에 대한 Functor >fmap (+1) (Just 1) Just 2
- 47. Maybe에 대한 Functor instanceFunctor Maybe where fmap _ Nothing = Nothing fmap f (Just a) = Just (f a)
- 48. Identity에 대한 Functor newtypeIdentity a = Identity a
- 49. 튜플에 대한 Functor instanceMyFunctor ((,) a) where {- ... -}
- 50. (리뷰) 튜플의 생성 •두 개 인자를 받아 두 인자로 구성된 튜플을 리턴 • (,) :: a -> b -> (a, b)
- 51. 튜플의 partial application >:type (,) ‘X’ True (,) ‘X’ True :: (Char, Bool) > :type (,) ‘X’ (,) ‘X" :: (Char, b)
- 52. 튜플과 타입 시그너처 •(,)를 prefix로 함수로 사용할 수 있음 • (,)를 type constructor로 사용할 수 있음 foo :: b -> (,) Char b foo b = (,) ‘X’ b foo :: b -> (Char, b)
- 53. 튜플에 대한 Functor instanceFunctor ((,) a) where fmap f (a, b) = (a, f b)
- 54. 함수에 대한 Functor instanceFunctor ((->) a) where fmap f g = x -> f (g x)
- 55. IO에 대한 Functor >fmap (++"!") getLine hi "hi!"
- 56. IO에 대한 Functor readFile"/etc/passwd" (length . lines) `fmap` readFile "/etc/passwd"
- 57. Functor 법칙 • Identity함수는 결과에 영향이 없어야 함 • fmap id === id • 두 함수의 합성을 매핑하는 것과 각 함수의 매핑을 합성하는 것이 같아야 함 • fmap (g . h) = (fmap g) . (fmap h)
- 58. 리프팅(lifting) 관점에서 본 Functor classFunctor f where fmap :: (a -> b) -> f a -> f b class Functor f where fmap :: (a -> b) -> (f a -> f b)
- 59. 콘텍스트로 이해하는 Functor • []functor • 콘텍스트는 리스트 • (->) functor • 첫 번째 인자가 a인 함수가 콘텍스트 (read-only 환 경) • IO functor • 사이드 이펙트가 가능한 computation이 콘텍스트
- 60. Applicative Functor > (*)<$> Just 2 <*> Just 8 Just 16
- 61. Monoid Monoid는 다음 성질을만족시키는 함수 •이다 1. Set(S)는 바이너리 함수 • 에 대해 닫혀 있음 • ∀ a,b ∈ S: a•b ∈ S 2. 바이너리 함수는 associative • ∀ a,b,c ∈ S: (a•b)•c = a•(b•c) 3. e는 identity element • ∃ e∈S: ∀ a∈S: e•a = a•e = a
- 62. Monoid 예제 • +,0은 Monoid • *, 1은 Monoid • (++)과 []은 Monoid
- 63. Monoid > import Data.Monoid >[1,2,3] `mappend` [4,5,6] [1,2,3,4,5,6] > [1,2,3] `mappend` mempty [1,2,3] > mempty `mappend` [1,2,3] [1,2,3]
- 64. Maybe 다시 보기 •Maybe a 타입의 값아 a -> Maybe b인 함수가 있으면 Maybe b를 어떻게 얻을 수 있을까? • bind 함수 • (>>=) :: (Monad m) => ma -> (a -> m b) -> m b
- 65. bind의 필요성 f ::Int -> Maybe Int f n = Just (n+1) > f 1 Just 2 > f (Just 1) ERROR!
- 66. bind (>>=) > :t(>>=) (>>=) :: Monad m => m a -> (a -> m b) -> m b > Just 1 >>= f Just 2
- 67. Monad 타입 클래스 classMonad m where return :: a -> m a (>>=) :: m a -> (a -> m b) -> m b
- 68. >> 함수 > print"foo" >>= _ -> print "bar" "foo" "bar" > print "foo" >> print "bar" "foo" "bar" main = do print "foo" print "bar"
- 69. bind 함수와 do표기법 main = do putStrLn "Enter name:" name <- getLine putStrLn ("Hi " ++ name) main = putStrLn "Enter name:" >> getLine >>= putStrLn.("Hi " ++)
- 70. 모나드 법칙 1. leftidentity • return a >>= f ≡ f a 2. Right Identity • m >>= return ≡ m 3. Associativity • (m >>= f) >>= g ≡ m >>= (x -> f x >>= g)
- 71. do 표기법으로 보는모나드 법칙
- 72.
- 73. 함수 합성 • f:: A -> B • g :: B -> C • g . f :: A -> C
- 74. 함수 합성의 법칙 1.(f . g) . h = f . (g . h) 2. f . id = f 3. id . f = f
- 75. 합수 합성의 예 >(take 2 . filter (>=3) . map length) ["a", "ab", "abc", "abcd", "abcde"] [3,4] > map (negate . abs) [5, -3, -6, 7, -3, 2, -19, 24] [-5,-3,-6,-7,-3,-2,-19,-24]
- 76. 카테고리 법칙 1. (f .g) . h = f . (g . h) 2. f . id = f 3. id . f = f class Category cat where id :: cat a a (.) :: cat b c -> cat a b -> cat a c instance Category (->) where id x = x (f . g) x = f (g x)
- 77.
- 78. Maybe 함수의 합성 •f :: A -> Maybe B • g :: B -> Maybe C • g .f • ERROR!
- 79. Maybe 함수의 합성 (<=<):: (b -> Maybe c) -> (a -> Maybe b) -> (a -> Maybe c) (f <=< g) x = case g x of Just y -> f y Nothing -> Nothing return :: (a -> Maybe a) return = Just
- 80. 함수 합성과의 비교 id:: (a -> a) return :: (a -> Maybe a) (.) :: (b -> c) -> (a -> b) -> (a -> c) (<=<) :: (b -> Maybe c) -> (a -> Maybe b) -> (a -> Maybe c) (f . g) x = f (g x) (f <=< g) x = f =<< (g x)
- 81. Reader 함수의 합성 •f :: A -> (R -> B) • g :: B -> (R -> C) • g . f • ERROR!
- 82. Reader 함수의 합성 (<=<):: (b -> (r -> c)) -> (a -> (r -> b)) -> (a -> (r -> c)) (f <=< g) x = r -> f ((g x) r) r return :: a -> (r -> a) return a = r -> a
- 83. 함수 합성과의 비교 id:: (a -> a) return :: (a -> (r-> a)) (.) :: (b -> c) -> (a -> b) -> (a -> c) (<=<) :: (b -> (r -> c)) -> (a -> (r -> b)) -> (a -> (r -> c)) (f . g) x = f (g x) (f <=< g) x = r -> f ((g x) r) r
- 84. Kleisli 카테고리 newtype Kleislim a b = Kleisli { runKleisli :: a -> m b } instance Monad m => Category (Kleisli m) where id = Kleisli return (Kleisli f) . (Kleisli g) = Kleisli (f <=< g)
- 85. Kleisli 카테고리와 Monad classMonad m where (>>=) :: m a -> (a -> m b) -> m b return :: a -> m a • (a >>= f) = (f <=< id) a • (f <=< g) x = f =<< (g x)
- 86. Kleisli 카테고리로 보는모 나드 법칙 카테고리 법칙 1. left identity • return >=> g ≡ g 2. Right Identity • f >=> return ≡ f 3. Associativity • (f >=> g) >=> h ≡ f >=> (g >=> h) (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c 모나드 법칙 1. left identity • m >>= return = m 2. Right Identity • return x >>= f = f x 3. Associativity • m >>= (y -> g y >>= f) = (m >>= g) >>= f
- 87. 모나드의 종류 • Maybe •Either • IO • Reader • Writer • State • Continuation • Parser • Pipe • …
- 88. Monad의 함의 사이드 이펙트가있는 함수에 조합성을 주기 위한 구조 Functional Programming Compositional Programming
- 89. 숙제 • CIS 194Homework 4,5,7,8번을 풉니다 • http://www.seas.upenn.edu/~cis194/lectures.html
- 90. 참고 자료 1. Slidesof Programming in Haskell • http://www.cs.nott.ac.uk/~pszgmh/book.html 2. Learn You a Haskell for Great Good! • http://learnyouahaskell.com/chapters 3. A Gentle Introduction to Haskell 98 • https://www.haskell.org/tutorial/haskell-98-tutorial.pdf 4. Slides of Functional systems in Haskell (Stanford CS240h Spring 2014) • http://www.scs.stanford.edu/14sp-cs240h/slides/ 5. Slides of Introduction to Haskell (University of Virginia CS 1501 Lectures Spring 2013) • http://shuklan.com/haskell/index.html