ConnectJS Functional Programming Basics in ES6

Transcript

1. Functional Programming Basics in ES6 Jeremy Fairbank jeremyfairbank.com @elpapapollo
2. Hi, I’m Jeremy jfairbank @elpapapollo pushagency.io blog.jeremyfairbank.com simplybuilt.com
3. What is a function?
4. What is a function?
5. What is a function? Relation that pairs each element in the domain with exactly one element in the range. Domain Range
6. What is a function?
7. What is a function?
8. What is a function?
9. What is a function? Domain
10. What is a function? Domain Range
11. Unique mapping from input to output! Domain Range
12. Ugh, math?
13. Alonzo Church
14. Alonzo Church • Church-Turing Thesis • Lambda Calculus • Represent computation in terms of “function abstraction and application using variable binding and substitution.”
15. λ-Calculus Represent computation in terms of “function abstraction and application using variable binding and substitution.”
16. Represent computation in terms of “function abstraction and application using variable binding and substitution.” λ-Calculus
17. Represent computation in terms of “function abstraction and application using variable binding and substitution.” λ-Calculus Bind “x” to function => parameters
18. Represent computation in terms of “function abstraction and application using variable binding and substitution.” λ-Calculus Substitution => apply arguments
19. λ-Calculus Functions are anonymous.
20. Functions are anonymous. λ-Calculus
21. Functions are anonymous. λ-Calculus X
22. Functions are anonymous. λ-Calculus Functions are expressions and units of computation.
23. λ-Calculus Functions are single input.
24. Functions are single input. λ-Calculus
25. Functions are single input. λ-Calculus
26. Functions are single input. λ-Calculus Break down into smaller pieces — currying!
27. That’s nice. What about functional programming?
28. λ-Calculus shows the power of functional computation. Functional programming brings it to life in computer science!
29. What is Functional Programming?
30. – 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?
31. TL;DR Programming without assignment statements.
32. Key Concepts • Declarative (vs. Imperative) • First Class Functions • Referential Transparency and Purity • Recursion • Immutability • Partial Application and Currying • Composition
33. Thar be ES6 ahead!
34. 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']
35. 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']
36. 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']
37. 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; };
38. 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); }
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'] function print(a) { var args = [].slice.call(arguments, 1); console.log.apply(console, [a].concat(args)); }
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'] var _ref = ['foo', 'bar', 'baz']; var x = _ref[0]; var y = _ref.slice(1); console.log(x); console.log(y);
41. Declarative vs. Imperative
42. 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
43. 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]
44. 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]
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. 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
49. Declarative function doubleNumber(n) { return n * 2; } function doubleNumbers(numbers) { return numbers.map(doubleNumber); } doubleNumbers([1, 2, 3]); // [2, 4, 6]
50. First Class Functions Functions are expressions/values.
51. 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); // ''
52. 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); // ''
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 as arguments
56. 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); }
57. 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); }
58. First Class Functions Functions as return values
59. 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
60. Closures
61. Closures • Allow functions to reference other scopes • “Close over” variables in higher scopes • Critical to functional programming paradigms like partial application
62. Closures // New function “closes” over x function additionFactory(x) { return (y) => x + y; } const add1 = additionFactory(1); add1(2); // 3
63. // New function “closes” over x function additionFactory(x) { return (y) => x + y; } const add1 = additionFactory(1); add1(2); // 3 Closures Same x
64. 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'
65. 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'
66. 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
67. 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'
68. 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'
69. 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'
70. 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'
71. Referential Transparency
72. 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
73. 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;
74. 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;
75. 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;
76. Referential Transparency let counter = 0; function addToCounter(n) { counter++; return n + counter; } // Not referentially transparent let value1 = addToCounter(1) + addToCounter(1); // 5 let value2 = 2 + 3; // Not the same value every call!
77. Idempotency
78. Idempotency • Special case of referential transparency • Multiple function applications produce the same result as one application
79. 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
80. 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
81. 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
82. Purity
83. Purity • “Strict referential transparency” • No side effects • No global/shared state • No impure arguments • No I/O
84. 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(' '); }
85. 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); }
86. 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
87. 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
88. 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
89. 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
90. Recursion
91. 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
92. Recursion: Factorial
93. Recursion: Factorial function factorial(n) { let result = 1; while (n > 1) { result *= n--; } return result; } Imperative
94. 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
95. Recursion: Factorial function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); }
96. Recursion: Factorial function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); } Base case
97. Recursion: Factorial function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); } Recursive call
98. Recursion: Factorial
99. Recursion: Factorial factorial(4);
100. Recursion: Factorial factorial(4); 4 * factorial(3);
101. Recursion: Factorial factorial(4); 4 * factorial(3); 4 * 3 * factorial(2);
102. Recursion: Factorial factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1);
103. Recursion: Factorial factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1;
104. Recursion: Factorial factorial(4); 4 * factorial(3); 4 * 3 * factorial(2); 4 * 3 * 2 * factorial(1); 4 * 3 * 2 * 1; 4 * 3 * 2;
105. 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;
106. 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;
107. What about recursion performance?
108. Recursion Performance let value = factorial(100000); console.log(value); // ???
109. Recursion Performance let value = factorial(100000); console.log(value); // ??? RangeError: Maximum call stack size exceeded
110. Recursion: Factorial function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); }
111. Recursion: Factorial function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); }
112. 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;
113. 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
114. 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
115. 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
116. 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
117. 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
118. 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
119. 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
120. 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
121. 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
122. 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
123. Tail call optimization to the rescue!
124. Tail Call Optimization
125. 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!)
126. Tail Call Optimization Unoptimizable function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); }
127. Tail Call Optimization Unoptimizable function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); } 1
128. Tail Call Optimization Unoptimizable function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); } 1 2
129. Tail Call Optimization Unoptimizable function factorial(n) { if (n < 2) { return 1; } return n * factorial(n - 1); } 1 3 2
130. Optimize Factorial function factorial(n, accum = 1) { if (n < 2) { return accum; } return factorial(n - 1, n * accum); }
131. Optimize Factorial function factorial(n, accum = 1) { if (n < 2) { return accum; } return factorial(n - 1, n * accum); } Current value accumulator
132. Optimize Factorial function factorial(n, accum = 1) { if (n < 2) { return accum; } return factorial(n - 1, n * accum); } Return the accumulator for base case
133. Optimize Factorial function factorial(n, accum = 1) { if (n < 2) { return accum; } return factorial(n - 1, n * accum); } Move calculation inside the call
134. Optimize Factorial function factorial(n, accum = 1) { if (n < 2) { return accum; } return factorial(n - 1, n * accum); } 1
135. Optimize Factorial function factorial(n, accum = 1) { if (n < 2) { return accum; } return factorial(n - 1, n * accum); } 1 2
136. Optimize Factorial function factorial(n, accum = 1) { if (n < 2) { return accum; } return factorial(n - 1, n * accum); } 1 3 2
137. And now? let value = factorial(100000); console.log(value); // Infinity
138. Factorial TCO factorial(4 /*, 1 */); factorial(3, 4); factorial(2, 12); factorial(1, 24); 24;
139. Factorial TCO factorial(4 /*, 1 */); factorial(3, 4); factorial(2, 12); factorial(1, 24); 24; <main> Stack
140. Factorial TCO <main> factorial(4, 1) Stack factorial(4 /*, 1 */); factorial(3, 4); factorial(2, 12); factorial(1, 24); 24;
141. Factorial TCO <main> factorial(3, 4) Stack factorial(4 /*, 1 */); factorial(3, 4); factorial(2, 12); factorial(1, 24); 24;
142. Factorial TCO <main> factorial(2, 12) Stack factorial(4 /*, 1 */); factorial(3, 4); factorial(2, 12); factorial(1, 24); 24;
143. Factorial TCO <main> factorial(1, 24) Stack factorial(4 /*, 1 */); factorial(3, 4); factorial(2, 12); factorial(1, 24); 24;
144. Factorial TCO <main> Stack factorial(4 /*, 1 */); factorial(3, 4); factorial(2, 12); factorial(1, 24); 24;
145. Recursion: Fibonacci
146. Recursion: Fibonacci
147. Recursion: Fibonacci Base cases
148. Recursion: Fibonacci Recurrence
149. Recursion: Fibonacci function fibonacci(n) { if (n < 2) { return n; } return fibonacci(n - 1) + fibonacci(n - 2); }
150. Recursion: Fibonacci function fibonacci(n) { if (n < 2) { return n; } return fibonacci(n - 1) + fibonacci(n - 2); } Base Cases
151. Recursion: Fibonacci function fibonacci(n) { if (n < 2) { return n; } return fibonacci(n - 1) + fibonacci(n - 2); } Recurrence
152. 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); }
153. Performance Revisited fibonacci(1); // 0 ms
154. Performance Revisited fibonacci(1); // 0 ms fibonacci(5); // 0 ms
155. Performance Revisited fibonacci(1); // 0 ms fibonacci(5); // 0 ms fibonacci(20); // 0 ms
156. Performance Revisited fibonacci(1); // 0 ms fibonacci(5); // 0 ms fibonacci(20); // 0 ms fibonacci(30); // 13 ms
157. Performance Revisited fibonacci(1); // 0 ms fibonacci(5); // 0 ms fibonacci(20); // 0 ms fibonacci(30); // 13 ms fibonacci(35); // 131 ms
158. 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
159. 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!
160. 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
161. Exponential Growth Runtime (ms) 0 4500 9000 13500 18000 Nth number of Fibonacci Sequence 0 10 20 30 40 50
162. Recursive Call Tree
163. Recursive Call Tree Computing some of the same values several times!
164. Recursive Call Tree Computing some of the same values several times! fibonacci(4) x 2
165. Recursive Call Tree Computing some of the same values several times! fibonacci(4) x 2 fibonacci(3) x 3
166. Recursive Call Tree Computing some of the same values several times! fibonacci(4) x 2 fibonacci(3) x 3 fibonacci(2) x 5
167. 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
168. TCO and Dynamic Programming
169. 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
170. Fibonacci TCO function fibonacci(n, current = 0, next = 1) { if (n === 0) { return current; } return fibonacci(n - 1, next, current + next); }
171. Fibonacci TCO function fibonacci(n, current = 0, next = 1) { if (n === 0) { return current; } return fibonacci(n - 1, next, current + next); } Two accumulators
172. 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
173. 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
174. 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;
175. 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
176. 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
177. Partial Application
178. 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
179. 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
180. 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
181. 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
182. 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
183. Partial Application function partial(fn, ...args) { return (...otherArgs) => { return fn(...args, ...otherArgs); }; }
184. Partial Application function partial(fn, ...args) { return (...otherArgs) => { return fn(...args, ...otherArgs); }; } Applied arguments
185. Partial Application function partial(fn, ...args) { return (...otherArgs) => { return fn(...args, ...otherArgs); }; } Return new closure
186. Partial Application function partial(fn, ...args) { return (...otherArgs) => { return fn(...args, ...otherArgs); }; } Remaining arguments
187. Partial Application function partial(fn, ...args) { return (...otherArgs) => { return fn(...args, ...otherArgs); }; } Call original function with all arguments
188. Partial Application: Why? • Build up functions from smaller pieces • Remove duplication • Generalize function abstraction (i.e. no additionFactory type functions)
189. 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]
190. Currying
191. 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?)
192. 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
193. 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
194. 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
195. 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
196. 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
197. 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
198. Currying function curry(fn, len = fn.length) { return (...args) => { if (args.length >= len) { return fn(...args); } return curry( partial(fn, ...args), len - args.length ); }; }
199. 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!
200. 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)
201. 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
202. 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
203. 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
204. 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
205. 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]
206. Function Composition
207. Function Composition
208. Function Composition • Compose functions together to form new functions • Pipe function output to next function • Helps enforce modularity/ SOC by keeping functions small
209. 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
210. 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
211. 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
212. 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)); }
213. 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)); }
214. 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)); }
215. 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)); }
216. 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)); }
217. </fp-basics>
218. But why Functional Programming?
219. Why FP • Concise, elegant solutions to problems • Modularity and composition • Eliminate data races with immutability • Unit tests are simpler — no checking for state changes
220. • Prof. Frisby’s Mostly Adequate…
 (github.com/MostlyAdequate/mostly-adequate-guide) • Babel (babeljs.io) • Lodash (lodash.com) • Ramda (ramdajs.com) • Clojurescript (github.com/clojure/clojurescript) • Immutable.js (github.com/facebook/immutable-js) • React (facebook.github.io/react/) • Redux (redux.js.org)
221. Thanks! jfairbank @elpapapollo blog.jeremyfairbank.com Code samples (some ES5 too) github.com/jfairbank/functional-javascript