![37
-- sortString [“ba”, “ab”, “cd”] == [“ab”, “ba”, “cd”]
sortString :: [String] -> [String]
sortString [] = []
sortString (p:xs) =
(sortString lesser) ++ [p] ++ (sortString greater)
where
lesser = filter (< p) xs
greater = filter (>= p) xs
Code
duplication](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-37-320.jpg)
![38
-- sortInteger [1, 3, 2] == [1, 2, 3]
sortInteger :: [Integer] -> [Integer]
sortInteger [] = []
sortInteger (p:xs) =
(sortInteger lesser) ++ [p] ++ (sortInteger greater)
where
lesser = filter (< p) xs
greater = filter (>= p) xs
Code
duplication](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-38-320.jpg)
![41
Generalized
sort :: Ord a => [a] -> [a]
sort [] = []
sort (p:xs) = (sort lesser) ++ [p] ++ (sort greater)
where
lesser = filter (< p) xs
greater = filter (>= p) xs](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-41-320.jpg)
![47
Mapping
over the
value in a
context
repA :: Int -> List Char -- repA 3 == aaa
asciiNumber :: Char -> Int -- asciiNumber ‘a’ == 97
composed :: Int -> List Int -- composed 2 == [97, 97]
composed x = fmap asciiNumber (repA x)
fmap :: (a -> b)
—> List a —> List b](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-47-320.jpg)
![48
Lifting a
function in
a context
length :: String -> Int -- length “example” == 7
-- listLength [“example”, “test”] == [7, 4]
listLength :: List String -> List Int
listLength = fmap length
fmap :: (a -> b)
—> List a —> List b](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-48-320.jpg)
![49
Abstracting
over f map
-- fproduct [1, 2, 3] ((+) 1) == [(1,2), (2, 3), (3, 4)]
fproduct :: List a -> (a -> b) -> List (a, b)
fproduct list f = fmap (a -> (a, f a)) list](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-49-320.jpg)
![56
Functor for
List
instance Functor List where
fmap :: (a -> b) -> List a -> List b
fmap f [] = []
fmap f (x:xs) = f x : fmap f xs](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-56-320.jpg)
![61
When
functor is
not enough
head :: List Int -> Maybe Int
head [] = Nothing
head (x:xs) = Just x
-- fiveDivBy 2 == Just 2.5
-- fiveDivBy 0 == Nothing
fiveDivBy :: Int -> Maybe Int
fiveDivBy 0 = Nothing
fiveDivBy x = Just (5 / x)](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-61-320.jpg)
![65
When
functor is
not enough
composed :: List Int -> Maybe Maybe Int
composed list = fmap fiveDivBy (head list)
-- composed [1, 2] == Just (Just 5)
-- composed [] == Nothing
-- composed [0, 3] == Just (Nothing)](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-65-320.jpg)
![66
When
functor is
not enough
composed :: List Int -> Maybe Int
composed list = flatten (fmap fiveDivBy (head list))
-- composed [1, 2] == Just 5
-- composed [] == Nothing
-- composed [0, 3] == Nothing](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-66-320.jpg)
![71
Composing
with Monads
head :: List Int -> Maybe Int
head [] = Nothing
head (x: xs) = Just x
fiveDivBy :: Int -> Maybe Int
fiveDivBy 0 = Nothing
fiveDivBy x = Just (5 / x)](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-71-320.jpg)
![74
Composing
with Monads
composed :: List Int -> Maybe Int
composed list = (head list) >>= fiveDivBy
-- composed [1, 2] == Just 5
-- composed [] == Nothing
-- composed [0, 3] == Nothing](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-74-320.jpg)
![86
Kleisli
examples
head :: [a] -> Maybe a
head [] = Nothing
head (x:xs) = Just x
fiveDivBy :: Double -> Maybe Double
fiveDivBy 0 = Nothing
fiveDivBy x = Just (5 / x)](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-86-320.jpg)
![87
Kleisli
examples
composed :: [Double] -> Maybe Double
composed = head >=> fiveDivBy](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-87-320.jpg)
![88
Kleisli
examples
composed :: [Double] -> Maybe Double
composed = head >=> fiveDivBy
-- composed [1.0, 2.0, 3.0] == Just 5.0
-- composed [0.0, 1.0, 2.0] == Nothing
-- composed [] == Nothing](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-88-320.jpg)
![89
Kleisli
examples
composed :: [Double] -> Maybe Double
composed list = case head list of
Just x -> fiveDivBy x
Nothing -> Nothing](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-89-320.jpg)
![91
Kleisli
examples
composed :: [Double] -> Maybe String
composed = head >=> fiveDivBy >=> another](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-91-320.jpg)
![92
Kleisli
examples
composed :: [Double] -> Maybe String
composed list = case head list of
Just x -> case fiveDivBy x of
Just y -> another y
Nothing -> Nothing
Nothing -> Nothing](https://image.slidesharecdn.com/fp-from-fundamentals-180321123930/85/Functional-programming-from-its-fundamentals-92-320.jpg)
Functional programming from its fundamentals
- 1. 1 Functional programming f rom its fundamentals
- 2. 2
- 3. 3 Beauvais Cathedral Height of Ulm minister 161.5m Height of Beauvais Cathedral 48m
- 4. 4 Whoami I am Software engineer at OpenValue Co-organizer of FP Ams Working at ING Bank
- 5. 5 The goal of today
- 6. 6 Content Fundamentals of functional programming LJ Why do we need functional programming Common constructs from the fundamentals
- 8. 8 A function is a mapping between a domain and a codomain. The only effect of a function is computing the result Programming with mathematical functions
- 9. 9 Properties of a function Totality A function must yield a value for every possible input Purity A function’s only effect must be the computation of its return value Determinism A function must yield the same result for the same input
- 10. 10 Expressions can be replaced with their values without changing the meaning of the program Referential transparency
- 11. Integer x = 1 new Pair<Integer, Integer>(x, x) new Pair<Integer, Integer>(1, 1)
- 12. public Integer random() { … } Integer x = random(); new Pair<Integer, Integer>(x, x) public Integer random() { … } new Pair<Integer, Integer>(random(), random())
- 13. 13 Creates a new function from two other functions where the second function will be called with the result of evaluating the first function Function composition
- 14. 14 Function composition public static Integer length(String s) { return s.length(); } public static Integer plus2(Integer x) { return x + 2; } public static Integer lengthPlus2(String s) { return plus2(length(s)); }
- 15. 15 Function composition public static <IN, MID, OUT> Function<IN, OUT> compose(Function<IN, MID> fst, Function<MID, OUT> snd) { return (x -> snd.apply(fst.apply(x))); }
- 17. 17
- 18. 18 (.) :: (b -> c) -> (a -> b) -> (a -> c) (.) g f = a -> g (f a) Function composition
- 19. 19 length :: String -> Int plus2 :: Int -> Int lengthPlus2 :: String -> Int -- lengthPlus2 "Hello Crowd!" -- 14 lengthPlus2 = plus2 . length Function composition
- 20. 20 String -> Int Int -> Int Function composition
- 22. 22 Why do we need functional programming
- 23. 23 Why do we need functional programming Concurrency & Parallelism Easier to reason aboutReducing cognitive load
- 24. 24 public class Class1 { public String head(List<String> list) { if (list.size() <= 0) { return null; } return list.get(0); } } Example 1
- 25. 25 public class Class2 { public Integer program(List<String> list) { // can produce null pointer if list is empty return head(list).length(); } } Example 1
- 26. 26 public class Class1 { public Optional<String> head(List<String> list) { if (list.size() <= 0) { return Optional.empty(); } return Optional.of(list.get(0)); } } Example 2
- 27. 27 public class Class2 { public Optional<Integer> program(List<String> list) { if (head(list).isPresent()) { return Optional.of(head(list).get().length()); } else { return Optional.empty(); } } } Example 2
- 28. 28 Common constructs f rom the fundamentals
- 29. 29 Translating a function that takes multiple arguments into evaluating a sequence of functions, each with a single argument. Currying
- 30. 30 (+) :: Int -> Int -> Int -- (+) 2 3 == 5 Currying
- 31. 31 (+) :: Int -> (Int -> Int) -- (+) 2 3 == 5 Currying
- 32. 32 doSomething :: String -> Int -> Double -> Int -> Int -- doSomething “test” 1 1.0 5 == 9 Currying
- 33. 33 doSomething :: String -> (Int -> (Double -> (Int -> Int))) -- doSomething “test” 1 1.0 5 == 9 Currying
- 34. 34 (+) :: Int -> (Int -> Int) plus2 :: Int -> Int plus2 = (+) 2 -- plus2 5 == 7 Currying
- 35. 35 A tool to perform ad-hoc polymorphism in a functional programming language Type classes
- 36. 36 public class Class1 { public Optional<String> head(List<String> list) { if (list.size() <= 0) { return Optional.empty(); } return Optional.of(list.get(0)); } } Polymorphism in life
- 37. 37 -- sortString [“ba”, “ab”, “cd”] == [“ab”, “ba”, “cd”] sortString :: [String] -> [String] sortString [] = [] sortString (p:xs) = (sortString lesser) ++ [p] ++ (sortString greater) where lesser = filter (< p) xs greater = filter (>= p) xs Code duplication
- 38. 38 -- sortInteger [1, 3, 2] == [1, 2, 3] sortInteger :: [Integer] -> [Integer] sortInteger [] = [] sortInteger (p:xs) = (sortInteger lesser) ++ [p] ++ (sortInteger greater) where lesser = filter (< p) xs greater = filter (>= p) xs Code duplication
- 39. 39 class Ord a where (<) :: a -> a -> Bool (<=) :: a -> a -> Bool (==) :: a -> a -> Bool (/=) :: a -> a -> Bool (>) :: a -> a -> Bool (>=) :: a -> a -> Bool Ord typeclass
- 40. 40 instance Ord Integer where (<) a b = … (<=) a b = … (==) a b = … (/=) a b = … (>) a b = … (>=) a b = … Ord instance for Integer
- 41. 41 Generalized sort :: Ord a => [a] -> [a] sort [] = [] sort (p:xs) = (sort lesser) ++ [p] ++ (sort greater) where lesser = filter (< p) xs greater = filter (>= p) xs
- 43. 43 Abstract over type constructors that can be mapped over Functor
- 44. 44 repA :: Int -> List Char -- repA 3 == aaa asciiNumber :: Char -> Int -- asciiNumber ‘a’ == 97 When function composition doesn't f it
- 45. 45 Int -> List Char Char -> Int When function composition doesn't f it
- 46. 46 Mapping over the value in a context fmap :: (a -> b) —> List a —> List b
- 47. 47 Mapping over the value in a context repA :: Int -> List Char -- repA 3 == aaa asciiNumber :: Char -> Int -- asciiNumber ‘a’ == 97 composed :: Int -> List Int -- composed 2 == [97, 97] composed x = fmap asciiNumber (repA x) fmap :: (a -> b) —> List a —> List b
- 48. 48 Lifting a function in a context length :: String -> Int -- length “example” == 7 -- listLength [“example”, “test”] == [7, 4] listLength :: List String -> List Int listLength = fmap length fmap :: (a -> b) —> List a —> List b
- 49. 49 Abstracting over f map -- fproduct [1, 2, 3] ((+) 1) == [(1,2), (2, 3), (3, 4)] fproduct :: List a -> (a -> b) -> List (a, b) fproduct list f = fmap (a -> (a, f a)) list
- 50. 50 Abstracting over f map -- fproduct (Just 5) ((+) 1) == Just (5, 6) fproduct :: Maybe a -> (a -> b) -> Maybe (a, b) fproduct ma f = fmap (a -> (a, f a)) ma
- 51. 51 Abstracting over f map fproduct :: IO a -> (a -> b) -> IO (a, b) fproduct ma f = fmap (a -> (a, f a)) ma
- 52. 52 Code duplication fproduct :: List a -> (a -> b) -> List (a, b) fproduct ma f = fmap (a -> (a, f a)) ma fproduct :: Maybe a -> (a -> b) -> Maybe (a, b) fproduct ma f = fmap (a -> (a, f a)) ma fproduct :: IO a -> (a -> b) -> IO (a, b) fproduct ma f = fmap (a -> (a, f a)) ma
- 53. 53 Functor typeclass class Functor f where fmap :: (a -> b) -> f a -> f b
- 55. 55 Functor for optionality instance Functor Maybe where fmap :: (a -> b) -> Maybe a -> Maybe b fmap f (Just x) = Just $ f x fmap f Nothing = Nothing
- 56. 56 Functor for List instance Functor List where fmap :: (a -> b) -> List a -> List b fmap f [] = [] fmap f (x:xs) = f x : fmap f xs
- 57. 57 Generalizing f product function fproduct :: Functor f => f a -> (a -> b) -> f (a, b) fproduct ma f = fmap (a -> (a, f a)) ma
- 59. 59 Transforming values in context Functor typeclass allows polymorphism Recap ƽ
- 60. 60 Combine computations that depend on each other Monad
- 61. 61 When functor is not enough head :: List Int -> Maybe Int head [] = Nothing head (x:xs) = Just x -- fiveDivBy 2 == Just 2.5 -- fiveDivBy 0 == Nothing fiveDivBy :: Int -> Maybe Int fiveDivBy 0 = Nothing fiveDivBy x = Just (5 / x)
- 62. 62 Map over f with g resulting in context List Int -> Maybe Int Int -> Maybe Int
- 63. 63 When functor is not enough composed list = fmap fiveDivBy (head list)
- 64. 64 When functor is not enough composed :: List Int -> Maybe Maybe Int composed list = fmap fiveDivBy (head list)
- 65. 65 When functor is not enough composed :: List Int -> Maybe Maybe Int composed list = fmap fiveDivBy (head list) -- composed [1, 2] == Just (Just 5) -- composed [] == Nothing -- composed [0, 3] == Just (Nothing)
- 66. 66 When functor is not enough composed :: List Int -> Maybe Int composed list = flatten (fmap fiveDivBy (head list)) -- composed [1, 2] == Just 5 -- composed [] == Nothing -- composed [0, 3] == Nothing
- 67. 67 The Monad typeclass class Monad m where return :: a -> m a fmap :: (a -> b) -> m a -> m b flatten :: m (m a) -> m a
- 68. 68 The Monad typeclass class Monad m where return :: a -> m a (>>=) :: m a -> (a -> m b) -> m b
- 69. 69 The Monad typeclass class Monad m where return :: a -> m a fmap :: (a -> b) -> m a -> m b flatten :: m (m a) -> m a (>>=) :: m a -> (a -> m b) -> m b (>>=) ma f = flatten (fmap f ma)
- 70. 70 The Monad typeclass instance Monad Maybe where return :: a -> Maybe a return x = Just x fmap :: (a -> b) -> Maybe a -> Maybe b fmap f (Just x) = Just (f x) fmap f Nothing = Nothing flatten :: Maybe (Maybe a) -> Maybe a flatten (Just (Just x)) = Just x flatten _ = Nothing
- 71. 71 Composing with Monads head :: List Int -> Maybe Int head [] = Nothing head (x: xs) = Just x fiveDivBy :: Int -> Maybe Int fiveDivBy 0 = Nothing fiveDivBy x = Just (5 / x)
- 72. 72 Composing with Monads List Int -> Maybe Int Int -> Maybe Int Head fiveDivBy
- 73. 73 Composing with Monads composed :: List Int -> Maybe Int composed list = flatten (fmap fiveDivBy (head list))
- 74. 74 Composing with Monads composed :: List Int -> Maybe Int composed list = (head list) >>= fiveDivBy -- composed [1, 2] == Just 5 -- composed [] == Nothing -- composed [0, 3] == Nothing
- 75. 75 Abstracting function composition with effects List Int -> Maybe Int Int -> Maybe Int Head fiveDivBy
- 76. 76 Abstracting function composition with effects a -> Maybe b b -> Maybe c f g
- 77. 77 Abstracting function composition with effects a -> List b b -> List c f g
- 78. 78 Abstracting function composition with effects a -> IO b b -> IO c f g
- 79. 79 Abstracting function composition with effects listComposition :: (a -> List b) -> (b -> List c) -> (a -> List c) listComposition f g = a -> (f a) >>= g
- 80. 80 Abstracting function composition with effects maybeComposition :: (a -> Maybe b) -> (b -> Maybe c) -> (a -> Maybe c) maybeComposition f g = a -> (f a) >>= g
- 81. 81 Abstracting function composition with effects ioComposition :: (a -> IO b) -> (b -> IO c) -> (a -> IO c) ioComposition f g = a -> (f a) >>= g
- 82. 82 listComposition :: (a -> List b) -> (b -> List c) -> (a -> List c) listComposition f g = a -> (f a) >>= g maybeComposition :: (a -> Maybe b) -> (b -> Maybe c) -> (a -> Maybe c) maybeComposition f g = a -> (f a) >>= g ioComposition :: (a -> IO b) -> (b -> IO c) -> (a -> IO c) ioComposition f g = a -> (f a) >>= g
- 83. 83 listComposition :: (a -> List b) -> (b -> List c) -> (a -> List c) listComposition f g = a -> (f a) >>= g maybeComposition :: (a -> Maybe b) -> (b -> Maybe c) -> (a -> Maybe c) maybeComposition f g = a -> (f a) >>= g ioComposition :: (a -> IO b) -> (b -> IO c) -> (a -> IO c) ioComposition f g = a -> (f a) >>= g
- 84. 84 listComposition :: (a -> m b) -> (b -> m c) -> (a -> m c) listComposition f g = a -> (f a) >>= g maybeComposition :: (a -> m b) -> (b -> m c) -> (a -> m c) maybeComposition f g = a -> (f a) >>= g ioComposition :: (a -> m b) -> (b -> m c) -> (a -> m c) ioComposition f g = a -> (f a) >>= g
- 85. 85 Kleisli composition (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> (a -> m c) (>=>) f g = a -> (f a) >>= g
- 86. 86 Kleisli examples head :: [a] -> Maybe a head [] = Nothing head (x:xs) = Just x fiveDivBy :: Double -> Maybe Double fiveDivBy 0 = Nothing fiveDivBy x = Just (5 / x)
- 87. 87 Kleisli examples composed :: [Double] -> Maybe Double composed = head >=> fiveDivBy
- 88. 88 Kleisli examples composed :: [Double] -> Maybe Double composed = head >=> fiveDivBy -- composed [1.0, 2.0, 3.0] == Just 5.0 -- composed [0.0, 1.0, 2.0] == Nothing -- composed [] == Nothing
- 89. 89 Kleisli examples composed :: [Double] -> Maybe Double composed list = case head list of Just x -> fiveDivBy x Nothing -> Nothing
- 90. 90 Kleisli examples another :: Double -> Maybe String
- 91. 91 Kleisli examples composed :: [Double] -> Maybe String composed = head >=> fiveDivBy >=> another
- 92. 92 Kleisli examples composed :: [Double] -> Maybe String composed list = case head list of Just x -> case fiveDivBy x of Just y -> another y Nothing -> Nothing Nothing -> Nothing
- 93. 93 Monad allows sequencing of computations Monad typeclass for abstracting over monads Recap ƽKleisli composition as function composition with embellished types
- 94. 94 Beauty of functional programming Function composition doesn’t fit all requirements anymore We start with function composition Beautiful abstractions to fit the new requirements