CodeStock: Functional Programming Basics in JavaScript

Transcript

1. Functional Programming Basics in JavaScript 2:40 PM / Ballroom A
2. Functional Programming Basics in JavaScript Jeremy Fairbank @elpapapollo
3. Understand, apply, and create basic functional programming tenets and constructs in JavaScript.
4. Hi, I’m Jeremy jfairbank @elpapapollo pushagency.io blog.jeremyfairbank.com simplybuilt.com
5. What is a function?
6. What is a function?
7. What is a function? Relation that pairs each element in the domain with exactly one element in the range. Domain Range
8. What is a function?
9. What is a function?
10. What is a function?
11. What is a function? Domain
12. What is a function? Domain Range
13. Unique mapping from input to output! Domain Range
14. Ugh, math?
15. Alonzo Church
16. Alonzo Church • Church-Turing Thesis • Lambda Calculus • Represent computation in terms of “function abstraction and application using variable binding and substitution.”
17. λ-Calculus Represent computation in terms of “function abstraction and application using variable binding and substitution.”
18. Represent computation in terms of “function abstraction and application using variable binding and substitution.” λ-Calculus
19. Represent computation in terms of “function abstraction and application using variable binding and substitution.” λ-Calculus Bind “x” to function => parameters
20. Represent computation in terms of “function abstraction and application using variable binding and substitution.” λ-Calculus Substitution => apply arguments
21. λ-Calculus Functions are anonymous.
22. Functions are anonymous. λ-Calculus
23. Functions are anonymous. λ-Calculus X
24. Functions are anonymous. λ-Calculus Functions are expressions and units of computation.
25. λ-Calculus Functions are single input.
26. Functions are single input. λ-Calculus
27. Functions are single input. λ-Calculus
28. Functions are single input. λ-Calculus Break down into smaller pieces — currying!
29. That’s nice. What about functional programming?
30. λ-Calculus shows the power of functional computation. Functional programming brings it to life in computer science!
31. What is Functional Programming?
32. – Wikipedia “In computer science, functional programming is a programming paradigm — a style of building the structure and elements of computer programs — that treats computation as the evaluation of mathematical functions and avoids changing- state and mutable data. It is a declarative programming paradigm, which means programming is done with expressions.” What is Functional Programming?
33. TL;DR Programming without assignment statements.
34. Key Concepts • Declarative (vs. Imperative) • First Class Functions • Referential Transparency and Purity • Recursion • Immutability • Partial Application and Currying • Composition
35. Thar be ES2015 ahead!
36. const greeting = 'hello'; let n = 42; n = 5; const add = (x, y) => x + y; const printAndReturn = (string) => { console.log(string); return string; }; function greet(g = 'Hi') { console.log(g); } function print(a, ...args) { console.log(a, ...args); } const [x, ...y] = ['foo', 'bar', 'baz']; console.log(x); // foo console.log(y); // ['bar', 'baz']
37. var greeting = 'hello'; const greeting = 'hello'; let n = 42; n = 5; const add = (x, y) => x + y; const printAndReturn = (string) => { console.log(string); return string; }; function greet(g = 'Hi') { console.log(g); } function print(a, ...args) { console.log(a, ...args); } const [x, ...y] = ['foo', 'bar', 'baz']; console.log(x); // foo console.log(y); // ['bar', 'baz']
38. var n = 42; n = 5; const greeting = 'hello'; let n = 42; n = 5; const add = (x, y) => x + y; const printAndReturn = (string) => { console.log(string); return string; }; function greet(g = 'Hi') { console.log(g); } function print(a, ...args) { console.log(a, ...args); } const [x, ...y] = ['foo', 'bar', 'baz']; console.log(x); // foo console.log(y); // ['bar', 'baz']
39. const greeting = 'hello'; let n = 42; n = 5; const add = (x, y) => x + y; const printAndReturn = (string) => { console.log(string); return string; }; function greet(g = 'Hi') { console.log(g); } function print(a, ...args) { console.log(a, ...args); } const [x, ...y] = ['foo', 'bar', 'baz']; console.log(x); // foo console.log(y); // ['bar', 'baz'] var add = function(x, y) { return x + y; }; var printAndReturn = function(string) { console.log(string); return string; };
40. const greeting = 'hello'; let n = 42; n = 5; const add = (x, y) => x + y; const printAndReturn = (string) => { console.log(string); return string; }; function greet(g = 'Hi') { console.log(g); } function print(a, ...args) { console.log(a, ...args); } const [x, ...y] = ['foo', 'bar', 'baz']; console.log(x); // foo console.log(y); // ['bar', 'baz'] function greet() { var g = arguments[0] === undefined ? 'Hi' : arguments[0]; console.log(g); }
41. const greeting = 'hello'; let n = 42; n = 5; const add = (x, y) => x + y; const printAndReturn = (string) => { console.log(string); return string; }; function greet(g = 'Hi') { console.log(g); } function print(a, ...args) { console.log(a, ...args); } const [x, ...y] = ['foo', 'bar', 'baz']; console.log(x); // foo console.log(y); // ['bar', 'baz'] function print(a) { var args = [].slice.call(arguments, 1); console.log.apply(console, [a],concat(args)); }
42. const greeting = 'hello'; let n = 42; n = 5; const add = (x, y) => x + y; const printAndReturn = (string) => { console.log(string); return string; }; function greet(g = 'Hi') { console.log(g); } function print(a, ...args) { console.log(a, ...args); } const [x, ...y] = ['foo', 'bar', 'baz']; console.log(x); // foo console.log(y); // ['bar', 'baz'] var _ref = ['foo', 'bar', 'baz']; var x = _ref[0]; var y = _ref.slice(1); console.log(x); console.log(y);
43. Declarative vs. Imperative
44. Imperative • Most familiar style of programming • Telling the computer how to accomplish a task • Algorithms are a series of steps • Mutable data usually involved • C, C++, Java
45. Imperative function doubleNumbers(numbers) { const doubled = []; const l = numbers.length; for (let i = 0; i < l; i++) { let doubledNumber = numbers[i] * 2; doubled.push(doubledNumber); } return doubled; } doubleNumbers([1, 2, 3]); // [2, 4, 6]
46. Imperative function doubleNumbers(numbers) { const doubled = []; const l = numbers.length; for (let i = 0; i < l; i++) { let doubledNumber = numbers[i] * 2; doubled.push(doubledNumber); } return doubled; } doubleNumbers([1, 2, 3]); // [2, 4, 6]
47. Imperative function doubleNumbers(numbers) { const doubled = []; const l = numbers.length; for (let i = 0; i < l; i++) { let doubledNumber = numbers[i] * 2; doubled.push(doubledNumber); } return doubled; } doubleNumbers([1, 2, 3]); // [2, 4, 6]
48. Imperative function doubleNumbers(numbers) { const doubled = []; const l = numbers.length; for (let i = 0; i < l; i++) { let doubledNumber = numbers[i] * 2; doubled.push(doubledNumber); } return doubled; } doubleNumbers([1, 2, 3]); // [2, 4, 6]
49. Imperative function doubleNumbers(numbers) { const doubled = []; const l = numbers.length; for (let i = 0; i < l; i++) { let doubledNumber = numbers[i] * 2; doubled.push(doubledNumber); } return doubled; } doubleNumbers([1, 2, 3]); // [2, 4, 6]
50. Declarative • Typically associated with functional programming • Telling the computer what you want, not how to get it • Algorithms are compositions of functions • Immutable data (or minimal side effects) preferred • SQL, HTML, Haskell, DSLs
51. Declarative function doubleNumber(n) { return n * 2; } function doubleNumbers(numbers) { return numbers.map(doubleNumber); } doubleNumbers([1, 2, 3]); // [2, 4, 6]
52. First Class Functions Functions are expressions/values.
53. First Class Functions Functions are expressions/values. // Function declaration function add(x, y) { return x + y; } // Assign to a variable const addAlias = add; // Assign an anonymous function expression const multiply = (x, y) => x * y; // Functions have properties console.log(add.name); // 'add' console.log(addAlias.name); // 'add' console.log(multiply.name); // ''
54. First Class Functions Functions are expressions/values. // Function declaration function add(x, y) { return x + y; } // Assign to a variable const addAlias = add; // Assign an anonymous function expression const multiply = (x, y) => x * y; // Functions have properties console.log(add.name); // 'add' console.log(addAlias.name); // 'add' console.log(multiply.name); // ''
55. First Class Functions Functions are expressions/values. // Function declaration function add(x, y) { return x + y; } // Assign to a variable const addAlias = add; // Assign an anonymous function expression const multiply = (x, y) => x * y; // Functions have properties console.log(add.name); // 'add' console.log(addAlias.name); // 'add' console.log(multiply.name); // ''
56. First Class Functions Functions are expressions/values. // Function declaration function add(x, y) { return x + y; } // Assign to a variable const addAlias = add; // Assign an anonymous function expression const multiply = (x, y) => x * y; // Functions have properties console.log(add.name); // 'add' console.log(addAlias.name); // 'add' console.log(multiply.name); // ''
57. First Class Functions Functions as arguments
58. First Class Functions Functions as arguments // Passing in anonymous functions myEventLib.on('update', (data) => console.log(data)); function doubleNumber(n) { return n * 2; } // Earlier example, passing in named function function doubleNumbers(numbers) { return numbers.map(doubleNumber); }
59. First Class Functions Functions as arguments // Passing in anonymous functions myEventLib.on('update', (data) => console.log(data)); function doubleNumber(n) { return n * 2; } // Earlier example, passing in named function function doubleNumbers(numbers) { return numbers.map(doubleNumber); }
60. First Class Functions Functions as return values
61. First Class Functions Functions as return values // Return a new function that adds a number // to another function additionFactory(x) { return (y) => x + y; } const add1 = additionFactory(1); add1(2); // 3
62. First Class Functions Functions as return values // Return a new function that adds a number // to another function additionFactory(x) { return (y) => x + y; } const add1 = additionFactory(1); add1(2); // 3
63. First Class Functions Functions as return values // Return a new function that adds a number // to another function additionFactory(x) { return (y) => x + y; } const add1 = additionFactory(1); add1(2); // 3
64. Closures
65. Closures • Allow functions to reference other scopes • “Close over” variables in higher scopes • Critical to functional programming paradigms like partial application
66. Closures // New function “closes” over x function additionFactory(x) { return (y) => x + y; } const add1 = additionFactory(1); add1(2); // 3
67. // New function “closes” over x function additionFactory(x) { return (y) => x + y; } const add1 = additionFactory(1); add1(2); // 3 Closures Same x
68. Closures let myValue = 'foo'; function closure() { console.log(myValue); } function trickyClosure() { let myValue = 'bar'; console.log(myValue); } function anotherTrickyClosure() { myValue = 'hello world'; console.log(myValue); } closure(); // 'foo' trickyClosure(); // 'bar' closure(); // 'foo' anotherTrickyClosure(); // 'hello world' closure(); // 'hello world' trickyClosure(); // 'bar'
69. Closures let myValue = 'foo'; function closure() { console.log(myValue); } function trickyClosure() { let myValue = 'bar'; console.log(myValue); } function anotherTrickyClosure() { myValue = 'hello world'; console.log(myValue); } closure(); // 'foo' trickyClosure(); // 'bar' closure(); // 'foo' anotherTrickyClosure(); // 'hello world' closure(); // 'hello world' trickyClosure(); // 'bar'
70. let myValue = 'foo'; function closure() { console.log(myValue); } function trickyClosure() { let myValue = 'bar'; console.log(myValue); } function anotherTrickyClosure() { myValue = 'hello world'; console.log(myValue); } closure(); // 'foo' trickyClosure(); // 'bar' closure(); // 'foo' anotherTrickyClosure(); // 'hello world' closure(); // 'hello world' trickyClosure(); // 'bar' Closures
71. Closures let myValue = 'foo'; function closure() { console.log(myValue); } function trickyClosure() { let myValue = 'bar'; console.log(myValue); } function anotherTrickyClosure() { myValue = 'hello world'; console.log(myValue); } closure(); // 'foo' trickyClosure(); // 'bar' closure(); // 'foo' anotherTrickyClosure(); // 'hello world' closure(); // 'hello world' trickyClosure(); // 'bar'
72. Closures let myValue = 'foo'; // Becomes 'hello world' function closure() { console.log(myValue); } function trickyClosure() { let myValue = 'bar'; console.log(myValue); } function anotherTrickyClosure() { myValue = 'hello world'; console.log(myValue); } closure(); // 'foo' trickyClosure(); // 'bar' closure(); // 'foo' anotherTrickyClosure(); // 'hello world' closure(); // 'hello world' trickyClosure(); // 'bar'
73. Closures let myValue = 'foo'; // Now 'hello world' function closure() { console.log(myValue); } function trickyClosure() { let myValue = 'bar'; console.log(myValue); } function anotherTrickyClosure() { myValue = 'hello world'; console.log(myValue); } closure(); // 'foo' trickyClosure(); // 'bar' closure(); // 'foo' anotherTrickyClosure(); // 'hello world' closure(); // 'hello world' trickyClosure(); // 'bar'
74. Closures let myValue = 'foo'; // Now 'hello world' function closure() { console.log(myValue); } function trickyClosure() { let myValue = 'bar'; console.log(myValue); } function anotherTrickyClosure() { myValue = 'hello world'; console.log(myValue); } closure(); // 'foo' trickyClosure(); // 'bar' closure(); // 'foo' anotherTrickyClosure(); // 'hello world' closure(); // 'hello world' trickyClosure(); // 'bar'
75. Referential Transparency
76. Referential Transparency • Fuzzy term associated with purity • For a given input, a function always returns the same value • Replace function calls with return value • No dependency on state outside function
77. Referential Transparency function doubleNumber(n) { return n * 2; } function square(n) { return n * n; } function add6(n) { return n + 6; } // Reduces down to the same value let value1 = add6(square(doubleNumber(3))); // 42 let value2 = add6(square(6)); // 42 let value3 = add6(36); // 42 let value4 = 42; // Same value for every call let otherValue1 = doubleNumber(3) + doubleNumber(3) + doubleNumber(3) + doubleNumber(3); let otherValue2 = 6 + 6 + 6 + 6;
78. Referential Transparency function doubleNumber(n) { return n * 2; } function square(n) { return n * n; } function add6(n) { return n + 6; } // Reduces down to the same value let value1 = add6(square(doubleNumber(3))); // 42 let value2 = add6(square(6)); // 42 let value3 = add6(36); // 42 let value4 = 42; // Same value for every call let otherValue1 = doubleNumber(3) + doubleNumber(3) + doubleNumber(3) + doubleNumber(3); let otherValue2 = 6 + 6 + 6 + 6;
79. Referential Transparency function doubleNumber(n) { return n * 2; } function square(n) { return n * n; } function add6(n) { return n + 6; } // Reduces down to the same value let value1 = add6(square(doubleNumber(3))); // 42 let value2 = add6(square(6)); // 42 let value3 = add6(36); // 42 let value4 = 42; // Same value for every call let otherValue1 = doubleNumber(3) + doubleNumber(3) + doubleNumber(3) + doubleNumber(3); let otherValue2 = 6 + 6 + 6 + 6;
80. Referential Transparency let counter = 0; function addToCounter1(n) { counter++; return n + counter; } function addToCounter2(n) { let counter = 0; counter++; return n + counter; } // Not referentially transparent let value1 = addToCounter1(1) + addToCounter1(1); // 5 let value2 = 2 + 3; // Not the same value every call! // Referentially transparent let otherValue1 = addToCounter2(1) + addToCounter2(1); // 4 let otherValue2 = 2 + 2;
81. Referential Transparency let counter = 0; function addToCounter1(n) { counter++; return n + counter; } function addToCounter2(n) { let counter = 0; counter++; return n + counter; } // Not referentially transparent let value1 = addToCounter1(1) + addToCounter1(1); // 5 let value2 = 2 + 3; // Not the same value every call! // Referentially transparent let otherValue1 = addToCounter2(1) + addToCounter2(1); // 4 let otherValue2 = 2 + 2;
82. Referential Transparency let counter = 0; function addToCounter1(n) { counter++; return n + counter; } function addToCounter2(n) { let counter = 0; counter++; return n + counter; } // Not referentially transparent let value1 = addToCounter1(1) + addToCounter1(1); // 5 let value2 = 2 + 3; // Not the same value every call! // Referentially transparent let otherValue1 = addToCounter2(1) + addToCounter2(1); // 4 let otherValue2 = 2 + 2;
83. Idempotency
84. Idempotency • Special case of referential transparency • Multiple function applications produce the same result as one application
85. Idempotency let abs = Math.abs; function identity(x) { return x; } function add2(n) { return n + 2; } // Idempotent and referentially transparent abs(abs(abs(abs(-1)))) === abs(-1); identity(identity(identity(42))) === identity(42); // Not idempotent, but referentially transparent add2(add2(add2(1))) !== add2(1); // 7 !== 3
86. Idempotency let abs = Math.abs; function identity(x) { return x; } function add2(n) { return n + 2; } // Idempotent and referentially transparent abs(abs(abs(abs(-1)))) === abs(-1); identity(identity(identity(42))) === identity(42); // Not idempotent, but referentially transparent add2(add2(add2(1))) !== add2(1); // 7 !== 3
87. Idempotency let abs = Math.abs; function identity(x) { return x; } function add2(n) { return n + 2; } // Idempotent and referentially transparent abs(abs(abs(abs(-1)))) === abs(-1); identity(identity(identity(42))) === identity(42); // Not idempotent, but referentially transparent add2(add2(add2(1))) !== add2(1); // 7 !== 3
88. Purity
89. Purity • “Strict referential transparency” • No side effects • No global/shared state • No impure arguments • No I/O
90. Pure Functions function add(x, y) { return x + y; } function capitalize(string) { return string[0].toUpperCase() + string.slice(1).toLowerCase(); } function toTitleCase(string) { return string .split(/\s+/) .map(capitalize) .join(' '); }
91. Pure Functions function add(x, y) { return x + y; } function capitalize(string) { return string[0].toUpperCase() + string.slice(1).toLowerCase(); } function toTitleCase(string) { return string .split(/\s+/) .map(capitalize) .join(' '); }
92. Pure Functions function add(x, y) { return x + y; } function capitalize(string) { return string[0].toUpperCase() + string.slice(1).toLowerCase(); } function toTitleCase(string) { return string .split(/\s+/) .map(capitalize) .join(' '); }
93. Pure Functions function add(x, y) { return x + y; } function capitalize(string) { return string[0].toUpperCase() + string.slice(1).toLowerCase(); } function toTitleCase(string) { return string .split(/\s+/) .map(capitalize) .join(' '); }
94. Pure Functions function add(x, y) { return x + y; } function capitalize(string) { return string[0].toUpperCase() + string.slice(1).toLowerCase(); } function toTitleCase(string) { return string .split(/\s+/) .map(capitalize) .join(' '); } • No side effects. • String and number arguments are immutable.
95. Impure Functions let myName = 'Jeremy'; const myHobbies = ['programming', 'reading', 'playing guitar']; function getName() { return myName; } function printName(name) { console.log(name); } function add(x, y) { myName = 'Joe'; return x + y; } function hobbiesMapper(hobbies) { return (fn) => hobbies.map(fn); }
96. let myName = 'Jeremy'; const myHobbies = ['programming', 'reading', 'playing guitar']; function getName() { return myName; } function printName(name) { console.log(name); } function add(x, y) { myName = 'Joe'; return x + y; } function hobbiesMapper(hobbies) { return (fn) => hobbies.map(fn); } Impure Functions Accesses global state
97. let myName = 'Jeremy'; const myHobbies = ['programming', 'reading', 'playing guitar']; function getName() { return myName; } function printName(name) { console.log(name); } function add(x, y) { myName = 'Joe'; return x + y; } function hobbiesMapper(hobbies) { return (fn) => hobbies.map(fn); } Impure Functions Prints to stdout
98. let myName = 'Jeremy'; const myHobbies = ['programming', 'reading', 'playing guitar']; function getName() { return myName; } function printName(name) { console.log(name); } function add(x, y) { myName = 'Joe'; return x + y; } function hobbiesMapper(hobbies) { return (fn) => hobbies.map(fn); } Impure Functions Modifies global state
99. let myName = 'Jeremy'; const myHobbies = ['programming', 'reading', 'playing guitar']; function getName() { return myName; } function printName(name) { console.log(name); } function add(x, y) { myName = 'Joe'; return x + y; } function hobbiesMapper(hobbies) { return (fn) => hobbies.map(fn); } Impure Functions Array may mutate
100. Recursion
101. Recursion • Defining a solution to a problem in terms of itself • Solve the problem by solving smaller pieces • Similar to inductive proofs • In programming, a function that calls itself • In FP, imperative looping (e.g. with while or for) is practically nonexistent, so solve with recursion
102. Recursion: Factorial
103. Recursion: Factorial function factorial(n) { let result = 1; while (n > 1) { result *= n--; } return result; } Imperative
104. Recursion: Factorial function factorial(n) { let result = 1; while (n > 1) { result *= n--; } return result; } Imperative function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); } Recursive
105. Recursion: Factorial function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); }
106. Recursion: Factorial function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); } Base case
107. Recursion: Factorial function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); } Recursive call
108. Recursion: Factorial
109. Recursion: Factorial factorial(4);
110. Recursion: Factorial factorial(4); 4 * factorial(3);
111. Recursion: Factorial factorial(4); 4 * factorial(3); 4 * 3 * factorial(2);
112. Recursion: Factorial factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1);
113. Recursion: Factorial factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1;
114. Recursion: Factorial factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1; 4 * 3 * 2;
115. Recursion: Factorial factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1; 4 * 3 * 2; 4 * 6;
116. Recursion: Factorial factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1; 4 * 3 * 2; 4 * 6; 24;
117. What about recursion performance?
118. Recursion Performance let value = factorial(100000); console.log(value); // ???
119. Recursion Performance let value = factorial(100000); console.log(value); // ??? RangeError: Maximum call stack size exceeded
120. Recursion: Factorial function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); }
121. Recursion: Factorial function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); }
122. Recursion: Factorial factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1; 4 * 3 * 2; 4 * 6; 24;
123. Recursion: Factorial factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1; 4 * 3 * 2; 4 * 6; 24; <main> Stack
124. Recursion: Factorial factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1; 4 * 3 * 2; 4 * 6; 24; <main> factorial(4) Stack
125. Recursion: Factorial <main> factorial(4) factorial(3) factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1; 4 * 3 * 2; 4 * 6; 24; Stack
126. Recursion: Factorial <main> factorial(4) factorial(3) factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1; 4 * 3 * 2; 4 * 6; 24; factorial(2) Stack
127. Recursion: Factorial <main> factorial(4) factorial(3) factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1; 4 * 3 * 2; 4 * 6; 24; factorial(2) factorial(1) Stack
128. Recursion: Factorial <main> factorial(4) factorial(3) factorial(2) factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1; 4 * 3 * 2; 4 * 6; 24; Stack
129. Recursion: Factorial <main> factorial(4) factorial(3) factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1; 4 * 3 * 2; 4 * 6; 24; Stack
130. Recursion: Factorial <main> factorial(4) factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1; 4 * 3 * 2; 4 * 6; 24; Stack
131. Recursion: Factorial <main> factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1; 4 * 3 * 2; 4 * 6; 24; Stack
132. Recursion Performance let value = factorial(100000); console.log(value); // ??? 100,000 calls = 100,000 stack frames 1 stack frame ≈ 48b Max stack usage ≈ 1mb 100,000 × 48 / 1024 / 1024 = 4.58mb > 1mb
133. Tail call optimization to the rescue!
134. Tail Call Optimization
135. Tail Call Optimization • Optimize recursive functions to not exhaust max stack size • Replace stack frames instead of adding new ones • The last statement before returning must be recursive call • Typically rewrite function to include an accumulator that holds the current result • (Coming to JavaScript in ES2015!)
136. Tail Call Optimization Unoptimizable function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); }
137. Tail Call Optimization Unoptimizable function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); } 1
138. Tail Call Optimization Unoptimizable function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); } 1 2
139. Tail Call Optimization Unoptimizable function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); } 1 3 2
140. Optimize Factorial function factorial(n, accum = 1) { if (n < 2) { return accum; } return factorial(n - 1, n * accum); }
141. Optimize Factorial function factorial(n, accum = 1) { if (n < 2) { return accum; } return factorial(n - 1, n * accum); } Current value accumulator
142. Optimize Factorial function factorial(n, accum = 1) { if (n < 2) { return accum; } return factorial(n - 1, n * accum); } Return the accumulator for base case
143. Optimize Factorial function factorial(n, accum = 1) { if (n < 2) { return accum; } return factorial(n - 1, n * accum); } Move calculation inside the call
144. Optimize Factorial function factorial(n, accum = 1) { if (n < 2) { return accum; } return factorial(n - 1, n * accum); } 1
145. Optimize Factorial function factorial(n, accum = 1) { if (n < 2) { return accum; } return factorial(n - 1, n * accum); } 1 2
146. Optimize Factorial function factorial(n, accum = 1) { if (n < 2) { return accum; } return factorial(n - 1, n * accum); } 1 3 2
147. And now? let value = factorial(100000); console.log(value); // Infinity
148. Factorial TCO factorial(4 /*, 1 */); factorial(3, 4); factorial(2, 12); factorial(1, 24); 24;
149. Factorial TCO factorial(4 /*, 1 */); factorial(3, 4); factorial(2, 12); factorial(1, 24); 24; <main> Stack
150. Factorial TCO <main> factorial(4, 1) Stack factorial(4 /*, 1 */); factorial(3, 4); factorial(2, 12); factorial(1, 24); 24;
151. Factorial TCO <main> factorial(3, 4) Stack factorial(4 /*, 1 */); factorial(3, 4); factorial(2, 12); factorial(1, 24); 24;
152. Factorial TCO <main> factorial(2, 12) Stack factorial(4 /*, 1 */); factorial(3, 4); factorial(2, 12); factorial(1, 24); 24;
153. Factorial TCO <main> factorial(1, 24) Stack factorial(4 /*, 1 */); factorial(3, 4); factorial(2, 12); factorial(1, 24); 24;
154. Factorial TCO <main> Stack factorial(4 /*, 1 */); factorial(3, 4); factorial(2, 12); factorial(1, 24); 24;
155. Recursion: Fibonacci
156. Recursion: Fibonacci
157. Recursion: Fibonacci Base cases
158. Recursion: Fibonacci Recurrence
159. Recursion: Fibonacci function fibonacci(n) { if (n < 2) { return n; } return fibonacci(n - 1) + fibonacci(n - 2); }
160. Recursion: Fibonacci function fibonacci(n) { if (n < 2) { return n; } return fibonacci(n - 1) + fibonacci(n - 2); } Base Cases
161. Recursion: Fibonacci function fibonacci(n) { if (n < 2) { return n; } return fibonacci(n - 1) + fibonacci(n - 2); } Recurrence
162. Recursion: Fibonacci fib(0); // 0 fib(1); // 1 fib(2); // 1 fib(3); // 2 fib(4); // 3 fib(5); // 5 function fibonacci(n) { if (n < 2) { return n; } return fibonacci(n - 1) + fibonacci(n - 2); }
163. Performance Revisited fibonacci(1); // 0 ms
164. Performance Revisited fibonacci(1); // 0 ms fibonacci(5); // 0 ms
165. Performance Revisited fibonacci(1); // 0 ms fibonacci(5); // 0 ms fibonacci(20); // 0 ms
166. Performance Revisited fibonacci(1); // 0 ms fibonacci(5); // 0 ms fibonacci(20); // 0 ms fibonacci(30); // 13 ms
167. Performance Revisited fibonacci(1); // 0 ms fibonacci(5); // 0 ms fibonacci(20); // 0 ms fibonacci(30); // 13 ms fibonacci(35); // 131 ms
168. Performance Revisited fibonacci(1); // 0 ms fibonacci(5); // 0 ms fibonacci(20); // 0 ms fibonacci(30); // 13 ms fibonacci(35); // 131 ms fibonacci(40); // 1516 ms
169. Performance Revisited fibonacci(1); // 0 ms fibonacci(5); // 0 ms fibonacci(20); // 0 ms fibonacci(30); // 13 ms fibonacci(35); // 131 ms fibonacci(40); // 1516 ms fibonacci(45); // 16.6 seconds!
170. Performance Revisited fibonacci(1); // 0 ms fibonacci(5); // 0 ms fibonacci(20); // 0 ms fibonacci(30); // 13 ms fibonacci(35); // 131 ms fibonacci(40); // 1516 ms fibonacci(45); // 16.6 seconds! fibonacci(100); // Who knows how long
171. Exponential Growth Runtime (ms) 0 4500 9000 13500 18000 Nth number of Fibonacci Sequence 0 10 20 30 40 50
172. Recursive Call Tree
173. Recursive Call Tree Computing some of the same values several times!
174. Recursive Call Tree Computing some of the same values several times! fibonacci(4) x 2
175. Recursive Call Tree Computing some of the same values several times! fibonacci(4) x 2 fibonacci(3) x 3
176. Recursive Call Tree Computing some of the same values several times! fibonacci(4) x 2 fibonacci(3) x 3 fibonacci(2) x 5
177. Recursive Call Tree Computing some of the same values several times! fibonacci(4) x 2 fibonacci(3) x 3 fibonacci(2) x 5 fibonacci(1) x 3
178. TCO and Dynamic Programming
179. TCO and Dynamic Programming • Build up the result from the leaves of the tree • Avoids recalculating the same values • Make recursive calls in the reverse direction
180. Fibonacci TCO function fibonacci(n, current = 0, next = 1) { if (n === 0) { return current; } return fibonacci(n - 1, next, current + next); }
181. Fibonacci TCO function fibonacci(n, current = 0, next = 1) { if (n === 0) { return current; } return fibonacci(n - 1, next, current + next); } Two accumulators
182. Fibonacci TCO function fibonacci(n, current = 0, next = 1) { if (n === 0) { return current; } return fibonacci(n - 1, next, current + next); } Results for next call
183. Fibonacci TCO function fibonacci(n, current = 0, next = 1) { if (n === 0) { return current; } return fibonacci(n - 1, next, current + next); } Reach the end, so return whatever was built up
184. Fibonacci TCO fibonacci(6 /*, 0, 1 */); fibonacci(5, 1, 1); fibonacci(4, 1, 2); fibonacci(3, 2, 3); fibonacci(2, 3, 5); fibonacci(1, 5, 8); fibonacci(0, 8, 13); 8;
185. Fibonacci TCO fibonacci(6 /*, 0, 1 */); fibonacci(5, 1, 1); fibonacci(4, 1, 2); fibonacci(3, 2, 3); fibonacci(2, 3, 5); fibonacci(1, 5, 8); fibonacci(0, 8, 13); 8; Fibonacci sequence
186. Fibonacci Performance fibonacci(1); // 0 ms fibonacci(5); // 0 ms fibonacci(20); // 0 ms fibonacci(30); // 0 ms fibonacci(35); // 0 ms fibonacci(40); // 0 ms fibonacci(45); // 0 ms fibonacci(100); // 0 ms
187. Functional Arrays
188. Functional Arrays • Common operations like map can be implemented in FP • Enforce immutability by returning new array • No looping; use recursion!
189. Array#map Map values in array to other values in new array function map(fn, array) { if (array.length === 0) { return array; } const [head, ...tail] = array; return [fn(head), ...map(fn, tail)]; }
190. Array#map Map values in array to other values in new array function map(fn, array) { if (array.length === 0) { return array; } const [head, ...tail] = array; return [fn(head), ...map(fn, tail)]; } Function first; good for currying
191. Array#map Map values in array to other values in new array function map(fn, array) { if (array.length === 0) { return array; } const [head, ...tail] = array; return [fn(head), ...map(fn, tail)]; } Grab the first element and remaining elements
192. function map(fn, array) { if (array.length === 0) { return array; } const [head, ...tail] = array; return [fn(head), ...map(fn, tail)]; } Array#map Map values in array to other values in new array var head = array[0];
193. function map(fn, array) { if (array.length === 0) { return array; } const [head, ...tail] = array; return [fn(head), ...map(fn, tail)]; } Array#map Map values in array to other values in new array var tail = array.slice(1);
194. Array#map Map values in array to other values in new array function map(fn, array) { if (array.length === 0) { return array; } const [head, ...tail] = array; return [fn(head), ...map(fn, tail)]; } Return new array with altered head and mapped array of remaining elements
195. Array#map Map values in array to other values in new array function map(fn, array) { if (array.length === 0) { return array; } const [head, ...tail] = array; return [fn(head), ...map(fn, tail)]; } return [fn(head)].concat(map(fn, tail));
196. Array#map Map values in array to other values in new array function map(fn, array) { if (array.length === 0) { return array; } const [head, ...tail] = array; return [fn(head), ...map(fn, tail)]; } Base case: empty array.
197. Array#map Map values in array to other values in new array function square(n) { return n * n; } let numbers = [1, 2, 3]; let squaredNumbers = map(square, numbers); // [1, 4, 9];
198. Partial Application
199. Partial Application • Assign values to function parameters without evaluating the function (i.e. “prefill” argument values) • Produce a new function that takes in any remaining unassigned arguments
200. Partial Application // Before we would use this function additionFactory(x) { return (y) => x + y; } let add1 = additionFactory(1); add1(2); // 3 // Now we can write an add function // and use partial application function add(x, y) { return x + y; } // Partial application with native `bind` function add1 = add.bind(null, 1); add1(2); // 3 // Use a custom-written `partial` function add1 = partial(add, 1); add1(2); // 3
201. Partial Application // Before we would use this function additionFactory(x) { return (y) => x + y; } let add1 = additionFactory(1); add1(2); // 3 // Now we can write an add function // and use partial application function add(x, y) { return x + y; } // Partial application with native `bind` function add1 = add.bind(null, 1); add1(2); // 3 // Use a custom-written `partial` function add1 = partial(add, 1); add1(2); // 3
202. Partial Application // Before we would use this function additionFactory(x) { return (y) => x + y; } let add1 = additionFactory(1); add1(2); // 3 // Now we can write an add function // and use partial application function add(x, y) { return x + y; } // Partial application with native `bind` function add1 = add.bind(null, 1); add1(2); // 3 // Use a custom-written `partial` function add1 = partial(add, 1); add1(2); // 3
203. Partial Application // Before we would use this function additionFactory(x) { return (y) => x + y; } let add1 = additionFactory(1); add1(2); // 3 // Now we can write an add function // and use partial application function add(x, y) { return x + y; } // Partial application with native `bind` function add1 = add.bind(null, 1); add1(2); // 3 // Use a custom-written `partial` function add1 = partial(add, 1); add1(2); // 3
204. Partial Application function partial(fn, ...args) { return (...otherArgs) => { return fn(...args, ...otherArgs); }; }
205. Partial Application function partial(fn, ...args) { return (...otherArgs) => { return fn(...args, ...otherArgs); }; } Applied arguments
206. Partial Application function partial(fn, ...args) { return (...otherArgs) => { return fn(...args, ...otherArgs); }; } Return new closure
207. Partial Application function partial(fn, ...args) { return (...otherArgs) => { return fn(...args, ...otherArgs); }; } Remaining arguments
208. Partial Application function partial(fn, ...args) { return (...otherArgs) => { return fn(...args, ...otherArgs); }; } Call original function with all arguments
209. Partial Application: Why? • Build up functions from smaller pieces • Remove duplication • Generalize function abstraction (i.e. no additionFactory type functions)
210. Partial Application: Why? function multiply(x, y) { return x * y; } const doubleNumber = partial(multiply, 2); const numbers = [1, 2, 3]; const doubledNumbers = map(doubleNumber, numbers); console.log(doubledNumbers); // [2, 4, 6]
211. Currying
212. Currying • Similar to partial application • Bakes partial application into a function • Successive invocations of function with arguments returns a new function with those arguments assigned • Keep returning a new function until all arguments “filled,” and then invoke the actual function with all of those arguments (sounds recursive, huh?)
213. Currying const add = curry((x, y, z) => x + y + z); // All arguments supplied, normal invocation. add(1, 2, 3); // 6 // Supply arguments one at a time. Final argument // induces invocation. add(1)(2)(3); // 6 // Equivalent to previous example. let add1 = add(1); let add3 = add1(2); add3(3); // 6 // Supply more than one argument at a time. add(1, 2)(3); // 6 add(1)(2, 3); // 6
214. Currying const add = curry((x, y, z) => x + y + z); // All arguments supplied, normal invocation. add(1, 2, 3); // 6 // Supply arguments one at a time. Final argument // induces invocation. add(1)(2)(3); // 6 // Equivalent to previous example. let add1 = add(1); let add3 = add1(2); add3(3); // 6 // Supply more than one argument at a time. add(1, 2)(3); // 6 add(1)(2, 3); // 6
215. Currying const add = curry((x, y, z) => x + y + z); // All arguments supplied, normal invocation. add(1, 2, 3); // 6 // Supply arguments one at a time. Final argument // induces invocation. add(1)(2)(3); // 6 // Equivalent to previous example. let add1 = add(1); let add3 = add1(2); add3(3); // 6 // Supply more than one argument at a time. add(1, 2)(3); // 6 add(1)(2, 3); // 6
216. Currying const add = curry((x, y, z) => x + y + z); // All arguments supplied, normal invocation. add(1, 2, 3); // 6 // Supply arguments one at a time. Final argument // induces invocation. add(1)(2)(3); // 6 // Equivalent to previous example. let add1 = add(1); let add3 = add1(2); add3(3); // 6 // Supply more than one argument at a time. add(1, 2)(3); // 6 add(1)(2, 3); // 6
217. Currying const add = curry((x, y, z) => x + y + z); // All arguments supplied, normal invocation. add(1, 2, 3); // 6 // Supply arguments one at a time. Final argument // induces invocation. add(1)(2)(3); // 6 // Equivalent to previous example. let add1 = add(1); let add3 = add1(2); add3(3); // 6 // Supply more than one argument at a time. add(1, 2)(3); // 6 add(1)(2, 3); // 6
218. Currying const add = curry((x, y, z) => x + y + z); // All arguments supplied, normal invocation. add(1, 2, 3); // 6 // Supply arguments one at a time. Final argument // induces invocation. add(1)(2)(3); // 6 // Equivalent to previous example. let add1 = add(1); let add3 = add1(2); add3(3); // 6 // Supply more than one argument at a time. add(1, 2)(3); // 6 add(1)(2, 3); // 6
219. Currying function curry(fn, len = fn.length) { return (...args) => { if (args.length >= len) { return fn(...args); } return curry( partial(fn, ...args), len - args.length ); }; }
220. Currying function curry(fn, len = fn.length) { return (...args) => { if (args.length >= len) { return fn(...args); } return curry( partial(fn, ...args), len - args.length ); }; } Knowing arity is important!
221. Currying function curry(fn, len = fn.length) { return (...args) => { if (args.length >= len) { return fn(...args); } return curry( partial(fn, ...args), len - args.length ); }; } Arguments to apply (or invoke)
222. Currying function curry(fn, len = fn.length) { return (...args) => { if (args.length >= len) { return fn(...args); } return curry( partial(fn, ...args), len - args.length ); }; } Recursive call if not all arguments supplied
223. Currying function curry(fn, len = fn.length) { return (...args) => { if (args.length >= len) { return fn(...args); } return curry( partial(fn, ...args), len - args.length ); }; } Curry the partially applied function
224. Currying function curry(fn, len = fn.length) { return (...args) => { if (args.length >= len) { return fn(...args); } return curry( partial(fn, ...args), len - args.length ); }; } Arity decreases
225. Currying function curry(fn, len = fn.length) { return (...args) => { if (args.length >= len) { return fn(...args); } return curry( partial(fn, ...args), len - args.length ); }; } Base case: all arguments supplied
226. Currying: Why? let curriedMap = curry(map); let multiply = curry((x, y) => x * y); let doubleNumbers = curriedMap(multiply(2)); let numbers = [1, 2, 3]; console.log(doubleNumbers(numbers)); // [2, 4, 6]
227. Function Composition
228. Function Composition
229. Function Composition • Compose functions together to form new functions • Pipe function output to next function • Helps enforce modularity/ SOC by keeping functions small
230. Function Composition let multiply = curry((x, y) => x * y); let multiply2 = multiply(2); let multiply3 = multiply(3); let multiply6 = compose(multiply2, multiply3); 2 * 3 * 6 === multiply6(6); // 36 let add = curry((x, y) => x + y); let subtract = curry((y, x) => -y + x); let add5 = compose(add(6), add(1), subtract(2)); 3 - 2 + 6 + 1 === add5(3); // 8
231. Function Composition let multiply = curry((x, y) => x * y); let multiply2 = multiply(2); let multiply3 = multiply(3); let multiply6 = compose(multiply2, multiply3); 2 * 3 * 6 === multiply6(6); // 36 let add = curry((x, y) => x + y); let subtract = curry((y, x) => -y + x); let add5 = compose(add(6), add(1), subtract(2)); 3 - 2 + 6 + 1 === add5(3); // 8
232. Function Composition let multiply = curry((x, y) => x * y); let multiply2 = multiply(2); let multiply3 = multiply(3); let multiply6 = compose(multiply2, multiply3); 2 * 3 * 6 === multiply6(6); // 36 let add = curry((x, y) => x + y); let subtract = curry((y, x) => -y + x); let add5 = compose(add(6), add(1), subtract(2)); 3 - 2 + 6 + 1 === add5(3); // 8
233. Function Composition function compose(...fns) { return (...args) => { const result = fns.reduceRight((memo, fn) => { return [fn(...memo)]; }, args); return result[0]; }; } function compose(f, g) { return (...args) => f(g(...args)); }
234. Function Composition function compose(...fns) { return (...args) => { const result = fns.reduceRight((memo, fn) => { return [fn(...memo)]; }, args); return result[0]; }; } function compose(f, g) { return (...args) => f(g(...args)); }
235. Function Composition function compose(...fns) { return (...args) => { const result = fns.reduceRight((memo, fn) => { return [fn(...memo)]; }, args); return result[0]; }; } function compose(f, g) { return (...args) => f(g(...args)); }
236. Function Composition function compose(...fns) { return (...args) => { const result = fns.reduceRight((memo, fn) => { return [fn(...memo)]; }, args); return result[0]; }; } function compose(f, g) { return (...args) => f(g(...args)); }
237. Function Composition function compose(...fns) { return (...args) => { const result = fns.reduceRight((memo, fn) => { return [fn(...memo)]; }, args); return result[0]; }; } function compose(f, g) { return (...args) => f(g(...args)); }
238. </fp-basics>
239. But why Functional Programming?
240. Why FP • Concise, elegant solutions to problems • Modularity and composition • Eliminate data races with immutability • Unit tests are simpler — no checking for state changes
241. Extra Resources • Babel (babeljs.io) • Lodash (lodash.com) • Clojurescript (github.com/clojure/clojurescript) • Immutable.js (github.com/facebook/immutable-js) • React (facebook.github.io/react/)
242. Thanks! jfairbank @elpapapollo blog.jeremyfairbank.com Code samples (some ES5 too) github.com/jfairbank/functional-javascript