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![Список
-- Список на АТД:
data List a = Empty | Cons a (List a)
myList1 = Cons 1 (Cons 2 (Cons 3 Empty))
-- Списки в Haskell:
myList1 = [1, 2, 3]
myList2 = 1 : 2 : 3 : []
myList3 = 1 : [2, 3]
http://learnyouahaskell.com/zippers](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-9-2048.jpg)
![Zipper для списка
data Zipper a = Zip [a] a [a]
toLeft (Zip xs a (y:ys)) = Zip (a:xs) y ys
toRight (Zip (x:xs) a ys) = Zip xs x (a:ys)
extract (Zip _ a _) = a
http://learnyouahaskell.com/zippers](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-10-2048.jpg)
![Zipper для списка
zipper = Zip [] 0 [1..10]
> toLeft zipper
Zip [0] 1 [2, 3, 4, 5, 6, 7, 8, 9, 10]
> extract (toLeft (toLeft zipper))
2](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-11-2048.jpg)
![Zip [2, 1, 0] 3 [4..10]
Текущий элемент
Сохраненный Контекст](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-12-2048.jpg)
![data Tree a = Empty | Node a (Tree a) (Tree a)
data Direction = L | R
modify :: (a -> a) -> Tree a -> [Direction] -> Tree a
Дерево
1
2
5 3
1
2
50 30](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-13-2048.jpg)
![data Tree a = Empty | Node a (Tree a) (Tree a)
data Direction = L | R
modify :: (a -> a) -> Tree a -> [Direction] -> Tree a
newTree1 = modify (*10) myTree [R, L]
newTree2 = modify (*10) newTree1 [R, R]
Изменение дерева
1
2
50 30](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-14-2048.jpg)
![data Tree a = Empty | Node a (Tree a) (Tree a)
data NodeCtx a = LCtx a (Tree a)
| RCtx a (Tree a)
data TreeZipper a = TZ (Tree a) [NodeCtx a]
extract (TZ (Node a _ _) _) = a
Zipper для дерева](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-15-2048.jpg)
![2
35 RCtx 1
> goRight zipper
TZ (Node 2 (Node 5 Empty Empty)
(Node 3 Empty Empty))
[RCtx 1 Empty]
1
2
35
tree = Node 1
Empty
(Node 2
(Node 5 Empty Empty)
(Node 3 Empty Empty))
zipper = TZ tree []](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-17-2048.jpg)
![fromZipper :: TreeZipper a -> Tree a
fromZipper (TZ cur []) = cur
fromZipper z = fromZipper (goUp z)
Сборка дерева
RCtx 1
LCtx 2 3
5
1
2
35](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-18-2048.jpg)
![data TreeDir = U | L | R
modify :: (a -> a) -> TreeZipper a -> [TreeDir] -> TreeZipper a
modify f (TZ (Node a l r) ctxs) [] = TZ (Node (f a) l r) ctxs
modify f z (L:dirs) = modify f (goLeft z) dirs
modify f z (R:dirs) = modify f (goRight z) dirs
modify f z (U:dirs) = modify f (goUp z) dirs
Изменение дерева](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-19-2048.jpg)
![tree = Node 1
Empty
(Node 2
(Node 5 Empty Empty)
(Node 3 Empty Empty))
zipper = TZ tree []
newZipper1 = modify (*10) zipper [R, L]
newZipper2 = modify (*10) newZipper1 [U, R]
newTree = fromZipper newZipper
Изменение дерева 1
2
5 3
1
2
50 30](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-20-2048.jpg)
![“Жизнь” без идиом
type Cell = (Int, Int)
type Grid = [Cell]
step :: Grid -> Grid
step p = let
next all [] = []
next all cur@((aX, aY) : alives) =
[(x, y) | x <- lim aX, y <- lim aY, length (neighbours8 (x, y) all) == 3]
++ (next all alives)
alive all cell = length (neighbours8 cell all) `elem` [2,3]
in L.nub $ filter (alive p) p ++ (next p p)](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-22-2048.jpg)
![“Жизнь” без идиом
type Cell = (Int, Int)
type Grid = [Cell]
step :: Grid -> Grid
step p = let
next all [] = []
next all cur@((aX, aY) : alives) =
[(x, y) | x <- lim aX, y <- lim aY, length (neighbours8 (x, y) all) == 3]
++ (next all alives)
alive all cell = length (neighbours8 cell all) `elem` [2,3]
in L.nub $ filter (alive p) p ++ (next p p)
这是什么？](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-23-2048.jpg)
![“Жизнь” на монадах
type Cell = (Int, Int)
type Grid = [Cell]
step :: Grid -> Grid
step cells = do
(newCell, n) <- frequencies $ concatMap neighbours cells
guard $ (n == 3) || (n == 2 && newCell `elem` cells)
return newCell
http://rhnh.net/2012/01/02/conway's-game-of-life-in-haskell](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-24-2048.jpg)
![“Жизнь” на комонадах и зипперах
data Universe a = Universe [a] a [a]
data Cell = Dead | Alive
newtype Grid = Grid (Universe (Universe Cell))
rule :: Grid Cell -> Cell
rule grid
| nc == 2 = extract grid
| nc == 3 = Alive
| otherwise = Dead
where nc = length $ filter (==Alive) (neighbours grid)
next grid = grid =>> rule
http://habrahabr.ru/post/225473/](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-25-2048.jpg)
![Правило вывода
type Segment = (Float, Float)
type Segments = [(Float, Float)]
cantorRule :: Segment -> Segments
cantorRule (x1, x2) = let
len = x2 - x1
oneThird = len / 3.0
in [(x1, x1 + oneThird), (x2 - oneThird, x2)]](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-27-2048.jpg)
![Фрактал - список списков
cantorGen :: Segments -> Segments
cantorGen segs = concatMap cantorRule segs
fractal :: [Segments]
fractal = iterate cantorGen [(0.0, 0.9)]
> take 2 fractal
[ [(0.0,0.9)], [(0.0,0.3),(0.6,0.9)] ]](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-28-2048.jpg)
![data Layer a = Layer a
comonadCantorRule :: Layer Segments -> Segments
comonadCantorRule layer = cantorGen (extract layer)
comonadCantorGen :: Layer Segments -> Layer Segments
comonadCantorGen layer = layer =>> comonadCantorRule
> take 2 $ iterate comonadCantorGen cantorLayer
[ Layer [(0.0,9.0)], Layer [(0.0,3.0),(6.0,9.0)] ]
Фрактал - список слоев](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-29-2048.jpg)
![Зипперы - это комонады
http://habrahabr.ru/post/225473/
data Universe a = Universe [a] a [a]
left, right :: Universe a -> Universe a
left (Universe (a:as) x bs) = Universe as a (x:bs)
right (Universe as x (b:bs)) = Universe (x:as) b bs
extract :: Universe a -> a
extract (Universe _ x _) = x
duplicate :: Universe a -> Universe (Universe a)
duplicate u = Universe (tail $ iterate left u) u (tail $ iterate right u)](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-35-2048.jpg)
![Зиппер зипперов чисел
universe = Universe [-1, -2..] 0 [1, 2..]
universeOfUniverses = duplicate universe
http://habrahabr.ru/post/225473/](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-36-2048.jpg)
![1
2
35
> goLeft (goRight zipper)
TZ (Node 5 Empty Empty)
[ LCtx 2 (Node 3 Empty Empty)
, RCtx 1 Empty]
RCtx 1
LCtx 2 3
5](https://image.slidesharecdn.com/random-150324111149-conversion-gate01/75/slide-37-2048.jpg)
Uploaded byAlexander Granin
Идиоматичный функциональный код
Документ охватывает основные концепции функционального программирования и объектно-ориентированного программирования, включая идиомы, паттерны и примеры кода на Haskell. В нем рассматриваются такие темы, как иммутабельность, чистые функции, зипперы и комонады. Также обсуждаются отличия между ооп-паттернами и фп-идиомами, а также приводятся примеры реализации различных подходов к алгоритмам, таким как игра 'Жизнь' и построение фрактала Кантора.
Идиоматичный функциональный код
- 1.
- 2. Изменяемое состояние Присваивание Сторонние эффекты Методы,функции Циклы Базовые типы Иммутабельность Декларация Чистые функции Функции, лямбды Рекурсия Базовые типы Императивное программирование Функциональное программирование
- 3. Класс = поля+ методы Объект класса Наследование, ассоциация Функторы, делегаты Интерфейсы ООП-паттерны Модуль = типы + функции Значение АТД Комбинаторы, композиция Лямбды, ФВП, продолжения Обобщение типов ??? Объектно - ориентированное программирование Функциональное программирование
- 4. Класс = поля+ методы Объект класса Наследование, ассоциация Функторы, делегаты Интерфейсы ООП-паттерны Модуль = типы + функции Значение АТД Комбинаторы, композиция Лямбды, ФВП, продолжения Обобщение типов Функциональные идиомы Объектно - ориентированное программирование Функциональное программирование
- 5. Функциональные идиомы ● Foldable,Traversable ● Functors ● Applicative Functors ● Monoids ● Monads ● ... ● Existential types ● Lenses ● Zippers ● Comonads ● GATDs ● ...
- 6. Функциональные идиомы ● Foldable,Traversable ● Functors ● Applicative Functors ● Monoids ● Monads ● Existential types ● Lenses ● Zippers ● Comonads ● GATDs В чем разница между понятиями “ООП-паттерн” и “ФП-идиома”?
- 7. ООП-паттерн vs Идиома Паттерн:подход “снаружи”. Несколько классов связываются в единую систему с обобщающими интерфейсами. Идиома: подход “изнутри”. Идиома структурирует данные, обобщает и пополняет их свойства.
- 8.
- 9. Список -- Список наАТД: data List a = Empty | Cons a (List a) myList1 = Cons 1 (Cons 2 (Cons 3 Empty)) -- Списки в Haskell: myList1 = [1, 2, 3] myList2 = 1 : 2 : 3 : [] myList3 = 1 : [2, 3] http://learnyouahaskell.com/zippers
- 10. Zipper для списка dataZipper a = Zip [a] a [a] toLeft (Zip xs a (y:ys)) = Zip (a:xs) y ys toRight (Zip (x:xs) a ys) = Zip xs x (a:ys) extract (Zip _ a _) = a http://learnyouahaskell.com/zippers
- 11. Zipper для списка zipper= Zip [] 0 [1..10] > toLeft zipper Zip [0] 1 [2, 3, 4, 5, 6, 7, 8, 9, 10] > extract (toLeft (toLeft zipper)) 2
- 12. Zip [2, 1,0] 3 [4..10] Текущий элемент Сохраненный Контекст
- 13. data Tree a= Empty | Node a (Tree a) (Tree a) data Direction = L | R modify :: (a -> a) -> Tree a -> [Direction] -> Tree a Дерево 1 2 5 3 1 2 50 30
- 14. data Tree a= Empty | Node a (Tree a) (Tree a) data Direction = L | R modify :: (a -> a) -> Tree a -> [Direction] -> Tree a newTree1 = modify (*10) myTree [R, L] newTree2 = modify (*10) newTree1 [R, R] Изменение дерева 1 2 50 30
- 15. data Tree a= Empty | Node a (Tree a) (Tree a) data NodeCtx a = LCtx a (Tree a) | RCtx a (Tree a) data TreeZipper a = TZ (Tree a) [NodeCtx a] extract (TZ (Node a _ _) _) = a Zipper для дерева
- 16. goLeft :: TreeZippera -> TreeZipper a goLeft (TZ (Node a l r) ctxs) = (TZ l (LCtx a r : ctxs)) goRight :: TreeZipper a -> TreeZipper a goRight (TZ (Node a l r) ctxs) = (TZ r (RCtx a l : ctxs)) goUp :: TreeZipper a -> TreeZipper a goUp = ... Zipper для дерева
- 17. 2 35 RCtx 1 >goRight zipper TZ (Node 2 (Node 5 Empty Empty) (Node 3 Empty Empty)) [RCtx 1 Empty] 1 2 35 tree = Node 1 Empty (Node 2 (Node 5 Empty Empty) (Node 3 Empty Empty)) zipper = TZ tree []
- 18. fromZipper :: TreeZippera -> Tree a fromZipper (TZ cur []) = cur fromZipper z = fromZipper (goUp z) Сборка дерева RCtx 1 LCtx 2 3 5 1 2 35
- 19. data TreeDir =U | L | R modify :: (a -> a) -> TreeZipper a -> [TreeDir] -> TreeZipper a modify f (TZ (Node a l r) ctxs) [] = TZ (Node (f a) l r) ctxs modify f z (L:dirs) = modify f (goLeft z) dirs modify f z (R:dirs) = modify f (goRight z) dirs modify f z (U:dirs) = modify f (goUp z) dirs Изменение дерева
- 20. tree = Node1 Empty (Node 2 (Node 5 Empty Empty) (Node 3 Empty Empty)) zipper = TZ tree [] newZipper1 = modify (*10) zipper [R, L] newZipper2 = modify (*10) newZipper1 [U, R] newTree = fromZipper newZipper Изменение дерева 1 2 5 3 1 2 50 30
- 21.
- 22. “Жизнь” без идиом typeCell = (Int, Int) type Grid = [Cell] step :: Grid -> Grid step p = let next all [] = [] next all cur@((aX, aY) : alives) = [(x, y) | x <- lim aX, y <- lim aY, length (neighbours8 (x, y) all) == 3] ++ (next all alives) alive all cell = length (neighbours8 cell all) `elem` [2,3] in L.nub $ filter (alive p) p ++ (next p p)
- 23. “Жизнь” без идиом typeCell = (Int, Int) type Grid = [Cell] step :: Grid -> Grid step p = let next all [] = [] next all cur@((aX, aY) : alives) = [(x, y) | x <- lim aX, y <- lim aY, length (neighbours8 (x, y) all) == 3] ++ (next all alives) alive all cell = length (neighbours8 cell all) `elem` [2,3] in L.nub $ filter (alive p) p ++ (next p p) 这是什么？
- 24. “Жизнь” на монадах typeCell = (Int, Int) type Grid = [Cell] step :: Grid -> Grid step cells = do (newCell, n) <- frequencies $ concatMap neighbours cells guard $ (n == 3) || (n == 2 && newCell `elem` cells) return newCell http://rhnh.net/2012/01/02/conway's-game-of-life-in-haskell
- 25. “Жизнь” на комонадахи зипперах data Universe a = Universe [a] a [a] data Cell = Dead | Alive newtype Grid = Grid (Universe (Universe Cell)) rule :: Grid Cell -> Cell rule grid | nc == 2 = extract grid | nc == 3 = Alive | otherwise = Dead where nc = length $ filter (==Alive) (neighbours grid) next grid = grid =>> rule http://habrahabr.ru/post/225473/
- 26. Множество Кантора накомонадах
- 27. Правило вывода type Segment= (Float, Float) type Segments = [(Float, Float)] cantorRule :: Segment -> Segments cantorRule (x1, x2) = let len = x2 - x1 oneThird = len / 3.0 in [(x1, x1 + oneThird), (x2 - oneThird, x2)]
- 28. Фрактал - списоксписков cantorGen :: Segments -> Segments cantorGen segs = concatMap cantorRule segs fractal :: [Segments] fractal = iterate cantorGen [(0.0, 0.9)] > take 2 fractal [ [(0.0,0.9)], [(0.0,0.3),(0.6,0.9)] ]
- 29. data Layer a= Layer a comonadCantorRule :: Layer Segments -> Segments comonadCantorRule layer = cantorGen (extract layer) comonadCantorGen :: Layer Segments -> Layer Segments comonadCantorGen layer = layer =>> comonadCantorRule > take 2 $ iterate comonadCantorGen cantorLayer [ Layer [(0.0,9.0)], Layer [(0.0,3.0),(6.0,9.0)] ] Фрактал - список слоев
- 30. Определение комонады class Functorw => Comonad w where extract :: w a -> a duplicate :: w a -> w (w a) extend :: (w a -> b) -> w a -> w b extend f = fmap f . duplicate duplicate = extend id (=>>) :: Comonad w => w a -> (w a -> b) -> w b cx =>> rule = extend rule cx
- 31. Простейшая комонада Layer dataLayer a = Layer a instance Functor Layer where fmap f (Layer a) = Layer (f a) instance Comonad Layer where duplicate (Layer a) = Layer (Layer a) -- w a -> w (w a) extract (Layer a) = a -- w a -> a
- 32. Layer Segments Layer Segments Layer duplicate = Layer Segments Segmentsextract= duplicate :: w a -> w (w a) extract :: w a -> a
- 33. = Layer Segments Layer comonadRule = Layer Segments Layer Segments =>>comonadRule = =>> :: w a -> (w a -> b) -> w b comonadRule :: (w a -> b) Layer Segments Layer = fmap comonadRule =
- 34. Спасибо за внимание! АлександрГранин graninas@gmail.com
- 35. Зипперы - этокомонады http://habrahabr.ru/post/225473/ data Universe a = Universe [a] a [a] left, right :: Universe a -> Universe a left (Universe (a:as) x bs) = Universe as a (x:bs) right (Universe as x (b:bs)) = Universe (x:as) b bs extract :: Universe a -> a extract (Universe _ x _) = x duplicate :: Universe a -> Universe (Universe a) duplicate u = Universe (tail $ iterate left u) u (tail $ iterate right u)
- 36. Зиппер зипперов чисел universe= Universe [-1, -2..] 0 [1, 2..] universeOfUniverses = duplicate universe http://habrahabr.ru/post/225473/
- 37. 1 2 35 > goLeft (goRightzipper) TZ (Node 5 Empty Empty) [ LCtx 2 (Node 3 Empty Empty) , RCtx 1 Empty] RCtx 1 LCtx 2 3 5