SIMON THOMPSON LEARNING FUNCTIONAL PROGRAMMING

Transcription

1 SIMON THOMPSON LEARNING FUNCTIONAL PROGRAMMING

2 The essence of functional programming Beginning to learn functional programming Resources, advice and bottlenecks

3 THE ESSENCE OF FUNCTIONAL PROGRAMMING

4 LISP Miranda Elm Erlang Idris F# Haskell Elixir Scala OCaml

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6 higher-order functions pattern matching types data lambdas recursion

7 higher-order functions pattern matching types data lambdas recursion

8 reactive lenses higher-order functions dependent types DSLs lazy pattern matching types data monoids types, types, types, lambdas monads recursion immutability effects

9 fun

10 Model the world as data + Functions over the data + Functions as data

11 And when I say function I mean in the mathematical sense, taking inputs to outputs, and doing nothing else!

12 The approach underlies lots of examples,

13 The approach underlies lots of examples, libraries, laziness, monads, lenses

14 Rock-Paper-Scissors

15 Original image:

16 We choose what to play, depending on the history of all your moves. Original image:

17 data Move = Rock Paper Scissors We choose what to play, depending on the history of all your moves. beat :: [Move] -> Move beat [] = Rock beat (x:xs) = case x of Rock -> Scissors Paper -> Rock Scissors -> Paper Original image:

18 Parsers

19 text parse tree remaining text

20 text parse tree remaining text

21 Side-effects

22 store before input result store after

23 Delay/force streams

24 Original image:

25 cons(x,xs) -> fun() -> {X,Xs} end. head(l) -> case (L()) of {H,_} -> H end. tail(l) -> case (L()) of {_,T} -> T end. Original image:

26 -define(cons(x,xs), -> fun() fun() -> {X,Xs} -> {X,Xs} end. end). head(l) -> case (L()) of {H,_} -> H end. tail(l) -> case (L()) of {_,T} -> T end. Original image:

27 github.com/simonjohnthompson/streams github.com/simonjohnthompson/interaction

28 type

29 Functions give us expressivity + Types help to constrain that + Give a language for modelling

30 BEGINNING FUNCTIONAL PROGRAMMING

31 lambdas higher-order functions types data

32 higher-order functions pattern matching types data lambdas recursion

33 Pick any language Start with the concrete before going to complex abstractions.

34 PATTERN MATCHING

35 type Point = (Float,Float) data Shape = Circle Point Float Rectangle Point Float Float area :: Shape -> Float area (Circle _ r) = pi*r*r area (Rectangle _ h w) = h*w

36 type Point = (Float,Float) data Shape = Circle Point Float Rectangle Point Float Float area :: Shape -> Float -type area (Circle point() _:: r) {float(),float()}. = pi*r*r area (Rectangle _ h w) = h*w -type shape() :: {circle,point(),float()} {rectangle,point(),float(),float()}. -spec area(shape()) -> float(). area({circle,_,r}) -> math:pi()*r*r; area({rectangle,h,w}) -> H*W.

37 type Point = (Float,Float) data Shape = Circle Point Float Rectangle Point Float Float area :: Shape -> Float area (Circle _ r) = pi*r*r area (Rectangle _ h w) = h*w -type point() :: {float(),float()}. -type shape() :: {circle,point(),float()} {rectangle,point(),float(),float()}. -spec area(shape()) -> float(). area({circle,_,r}) -> math:pi()*r*r; area({rectangle,h,w}) -> H*W.

38 PATTERN MATCHING!

39 area :: Shape -> Float area (Circle _ r) = pi*r*r area (Rectangle _ h w) = h*w

40 area :: Shape -> Float area (Circle _ r) = pi*r*r area (Rectangle _ h w) = h*w Link to something more familiar

41 area :: Shape -> Float area (Circle _ r) = pi*r*r area (Rectangle _ h w) = h*w area shape = if is_circle shape then pi*(radius shape)*(radius shape) else height shape * width shape is_circle :: Shape -> Bool is_circle (Circle ) = True is_circle _ = False radius, height, width :: Shape -> Float radius (Circle _ r) = r height (Rectangle _ h _) = h width (Rectangle w) = w

42 area :: Shape -> Float area (Circle _ r) = pi*r*r area (Rectangle _ h w) = h*w area shape = if is_circle shape then pi*(radius shape)*(radius shape) else height shape * width shape is_circle :: Shape -> Bool is_circle (Circle ) = True is_circle _ = False radius, height, width :: Shape -> Float radius (Circle _ r) = r height (Rectangle _ h _) = h width (Rectangle w) = w

43 RECURSION

44 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs

45 The nub of a list is the list with all duplicates removed. nub([]) -> []; nub([x Xs]) -> [X nub(remove(x,xs))]. remove(_,[]) -> []; remove(x,[x Xs]) -> remove(x,xs); remove(x,[y Xs]) -> [Y remove(x,xs)].

46 The nub of a list is the list with all duplicates removed. nub([]) -> []; nub([x Xs]) -> [X nub(remove(x,xs))]. remove(_,[]) -> []; remove(x,[x Xs]) -> remove(x,xs); remove(x,[y Xs]) -> [Y remove(x,xs)].

47 RECURSION!

48 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Generate all the answers? nub [] = [] nub [1] = nub (1:[]) = 1 : nub [] = [1] nub [2,1] = nub (2:[1]) = 2 : nub [1] = [2,1] nub [1,2,1] = nub (1:[2,1]) = nub [2,1] = [2,1]

49 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Generate all the answers? nub [] = [] nub [1] = nub (1:[]) = 1 : nub [] = [1] nub [2,1] = nub (2:[1]) = 2 : nub [1] = [2,1] nub [1,2,1] = nub (1:[2,1]) = nub [2,1] = [2,1]

50 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Generate all the answers? nub [] = [] nub [1] = nub (1:[]) = 1 : nub [] = [1] nub [2,1] = nub (2:[1]) = 2 : nub [1] = [2,1] nub [1,2,1] = nub (1:[2,1]) = nub [2,1] = [2,1]

51 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Generate all the answers? nub [] = [] nub [1] = nub (1:[]) = 1 : nub [] = [1] nub [2,1] = nub (2:[1]) = 2 : nub [1] = [2,1] nub [1,2,1] = nub (1:[2,1]) = nub [2,1] = [2,1]

52 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Rewrite work top down nub [1,2,1] = nub (1:[2,1]) = nub [2,1] = nub (2:[1]) = 2 : nub [1] = 2 : nub (1:[]) = 2 : 1 : nub [] = 2 : 1 : [] = 2 :[1] = [2,1]

53 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Rewrite work top down nub [1,2,1] = nub (1:[2,1]) = nub [2,1] = nub (2:[1]) = 2 : nub [1] = 2 : nub (1:[]) = 2 : 1 : nub [] = 2 : 1 : [] = 2 :[1] = [2,1]

54 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Rewrite work top down nub [1,2,1] = nub (1:[2,1]) = nub [2,1] = nub (2:[1]) = 2 : nub [1] = 2 : nub (1:[]) = 2 : 1 : nub [] = 2 : 1 : [] = 2 :[1] = [2,1]

55 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Rewrite work top down nub [1,2,1] = nub (1:[2,1]) = nub [2,1] = nub (2:[1]) = 2 : nub [1] = 2 : nub (1:[]) = 2 : 1 : nub [] = 2 : 1 : [] = 2 :[1] = [2,1]

56 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Rewrite work top down nub [1,2,1] = nub (1:[2,1]) = nub [2,1] = nub (2:[1]) = 2 : nub [1] = 2 : nub (1:[]) = 2 : 1 : nub [] = 2 : 1 : [] = 2 :[1] = [2,1]

57 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Rewrite work top down nub [1,2,1] = nub (1:[2,1]) = nub [2,1] = nub (2:[1]) = 2 : nub [1] = 2 : nub (1:[]) = 2 : 1 : nub [] = 2 : 1 : [] = 2 :[1] = [2,1]

58 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Rewrite work top down nub [1,2,1] = nub (1:[2,1]) = nub [2,1] = nub (2:[1]) = 2 : nub [1] = 2 : nub (1:[]) = 2 : 1 : nub [] = 2 : 1 : [] = 2 :[1] = [2,1]

59 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Rewrite work top down nub [1,2,1] = nub (1:[2,1]) = nub [2,1] = nub (2:[1]) = 2 : nub [1] = 2 : nub (1:[]) = 2 : 1 : nub [] = 2 : 1 : [] = 2 :[1] = [2,1]

60 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Rewrite work top down nub [1,2,1] = nub (1:[2,1]) = nub [2,1] = nub (2:[1]) = 2 : nub [1] = 2 : nub (1:[]) = 2 : 1 : nub [] = 2 : 1 : [] = 2 :[1] = [2,1]

61 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Rewrite work top down nub [1,2,1] = nub (1:[2,1]) = nub [2,1] = nub (2:[1]) = 2 : nub [1] = 2 : nub (1:[]) = 2 : 1 : nub [] = 2 : 1 : [] = 2 :[1] = [2,1]

62 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Accept the template: the lists get shorter foo [] = foo (x:xs) = x foo xs

63 The nub of a list is the list with all duplicates removed. nub :: Eq a => [a] -> [a] nub [] = [] nub(x:xs) = if elem x xs then nub xs else x : nub xs Accept the template: the lists get shorter foo [] = foo (x:xs) = x foo xs and look at some examples nub [1,2] = [1,2] nub [2,1,2] = [1,2]

64 How to get started (with recursion)? Examples, examples, examples. From simple five finger exercises, to a favourite small library.

65 RESOURCES

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73 Online Wiki-books, MOOCs, video channels, try-xxx, tutorials

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76 Working together XXX-bridge, code clubs, meet-ups, reading groups

77 AND THEN

78 Pick any language Start with the concrete before going to complex abstractions.

79 Choosing a language LISP Elm Idris F# Miranda Haskell Elixir Erlang OCaml Scala

80 Find a project Reimplement something Try something new Join an Open Source project

81 Systems

82 Abstraction This board belongs to Newcastle University PhD student Tom Fisher, who is doing research in homological algebra. Thanks to Christian Perfect for the photo. whatsonmyblackboard.wordpress.com

83 Enjoy! Type-driven development Functional Concurrency Systems programming in ML

84 SIMON THOMPSON LEARNING FUNCTIONAL PROGRAMMING