Lection 5

Каррирование

(+) 9 5
-- 14
sum x y = (+) x y
sum = (+)
-- :t (+)
(+) :: Num a => a -> a -> a-- ДМ, вывод типов правоассоциативен
(+) :: Num a => a -> (a -> a)> (+) (9 5)
?> ((+) 9) 5
?

Каррирование

> let sumWith9 = (+) 9
> :t sumWith9
sumWith9 :: Integer -> Integer
> sumWith9 5
14
> sumWith9 90
99
> let res = sumWith9 42
51
> :t res
res :: Integer

ФВП

> let doItAgain f x = f (f x)
> doItAgain sumWith9 3
21
zipWith' :: (a -> b -> c) -> [a] -> [b] -> [c]
?
> zipWith (+) [1, 2, 3, 4] [4, 3, 2, 1]
[5, 5, 5, 5]
> zipWith (++) ["CSKA", "Zenith"] ["champion", "champion"]

ФВП

flip' :: (a -> b -> c) -> b -> a -> c
flip' f y x = f x y
> flip' zip [1,2,3,4,5] "hello"
[('h',1),('e',2),('l',3),('l',4),('o',5)]
> zipWith (flip' div) [2,2..] [10,8,6,4,2]
[5,4,3,2,1]

map

map :: (a -> b) -> [a] -> [b]
map _ [] = []
map f (x:xs) = f x : map f xs
> map (+3) [1,5,3,1,6]
[4,8,6,4,9]
> map (++ "!") ["BIFF", "BANG", "POW"]
["BIFF!","BANG!","POW!"]
> map (replicate 3) [3..6]
[[3,3,3],[4,4,4],[5,5,5],[6,6,6]]
> map (map (^2)) [[1,2],[3,4,5,6],[7,8]]
[[1,4],[9,16,25,36],[49,64]]
> map fst [(1,2),(3,5),(6,3),(2,6),(2,5)]
[1,3,6,2,2]

filter

filter :: (a -> Bool) -> [a] -> [a]
filter _ [] = []
filter p (x:xs)
  | p x = x : filter p xs
  | otherwise = filter p xs
> filter (>3) [1,5,3,2,1,6,4,3,2,1]
[5,6,4]
> filter (==3) [1,2,3,4,5]
[3]

filter

> filter even [1..10]
[2,4,6,8,10]
> let notNull x = not (null x) in filter notNull [[1,2,3],[],
  [3,4,5],[2,2],[],[],[]]
[[1,2,3],[3,4,5],[2,2]]
> filter (`elem` ['a'..'z']) "u LaUgH aT mE BeCaUsE I aM
  diFfeRent"
"uagameasadifeent"
> filter (`elem` ['A'..'Z']) "i lauGh At You BecAuse u r aLL the
  Same"
"GAYBALLS"

λ-выражения

square x = x * x
oddsSquares = filter (\x -> odd x) (map square [1..100])
oddsSquares = filter (\x -> odd x) (map (\x->x*x) [1..100])
square = \x → x * x
flip' :: (a -> b -> c) -> b -> a -> c
flip' f = \x y -> f y x

Показать список

map (\(x,y) -> show x ++ "). " ++ y) (zip [1..]
  ["Трус", "Балбес", "Бывалый"])

calcDistance (x,y) (a,b) = sqrt (w^2 + h^2)
  where (w,h) = (x-a, b-y)
points = [(1,1),(5,3),(2,5),(7,4),(5,5),(3,2),(0,4)]

sort [] = []
sort ((x,o):xs) =
  let
    smallerSorted = sort (filter (\(y,o) -> y <= x) xs)
    biggerSorted = sort (filter (\(y,o) -> y > x) xs)
  in smallerSorted ++ [(x,o)] ++ biggerSorted

nearest3 dest =
  take 3 (sort (map (\p -> (calcDistance p dest, p)) points))
> nearest3 (2,2)

var metroStations = [{lat: 52.234, lng: 30.482, name:
  'Kashirskaya'},..]
  , calcDistance = (point, station) => {
    station.dist = 180 * arctan ... // distance algorythm (mutable)
    return station;
  };

nearest3 = point => metroStations
  .map(function(m) {return calcDistance(point, m);})
  .sort(function(a,b) {return a.dist > b .dist;})
  .slice(0,3)
  .filter(function(m) {return m.dist < 2000;})

nearest3({lattitude: 52.0, longitude: 31.0})

Применение функций

putStrLn (show (1 + 1))

Применение функций

> :t ($)
($) :: (a -> b) -> a -> b
f $ x = f x
f (g (z x)) === f $ g $ z x правоассоцитивноputStrLn (show $ 1 + 1)
putStrLn $ show (1 + 1)
putStrLn $ show $ 1 + 1

$ .

> :t (.)
(.) :: (b -> c) -> (a -> b) -> a -> c
f . g = \x -> f (g x)(putStrLn . show) (1 + 1)
putStrLn . show $ 1 + 1

Применение функций

nearest3 dest =
  filter (\(dist, p) -> dist < 2)
  $ take 3
  $ sort
  $ map (\p -> (calcDistance p dest, p)) points
-- No more LISP!
nearest3 dest =
  filter (\(dist, p) -> dist < 2)
    (take 3 (sort (map (\p -> (calcDistance p dest, p)) points)))
> sum 9 (sum 6 (sum 3 1))
> sum 9 $ sum 6 $ sum 3 1

Композиция функций

> map (\xs -> negate (sum (tail xs))) [[1..5],[3..6],[1..7]]
[-14,-15,-27]
> map (negate . sum . tail) [[1..5],[3..6],[1..7]]
[-14,-15,-27]

Композиция функций

nearest3 dest = take 3 . sort . map (\p ->
  (calcDistance p dest, p))
main = do
putStr . show $ nearest3 (2,2) points
{-
main = do
putStrLn . show $ nearest3 (2,2) points
-}

mapM

main = do
mapM putStrLn ["adf\taff","dfaf\tsf","asdf\tf","asddf\tf"]
> main
adf   aff
dfaf  sf
asdf  f
asddf f
[(),(),(),()]
main = do
  mapM putStrLn ["adf\taff","dfaf\tsf","asdf\tf","asddf\tf"]
  return ()
main = do
  mapM_ putStrLn ["adf\taff","dfaf\tsf","asdf\tf","asddf\tf"]

Task

Числа Фиббоначе, бесконечный список

[1, 1, 2, 3, 5, 8, 13, ...]

KP

Список треугольных чисел

Список пирамидальных чисел

n-е треугольное число tn равно количеству одинаковых монет, из которых можно построить равносторонний треугольник, на каждой стороне которого укладывается n монет.

n-е пирамидальное число pn равно количеству одинаковых шаров, из которых можно построить пирамиду с треугольным основанием, на каждой стороне которой укладывается n шаров