Functional Programming in Javascript
Functional Programming in Javascript
gain an advanced understanding of the mathematics behind functional programming
About the Book
Note: This is not an Introductory book in JavaScript. The reader must have at least a couple of years of JavaScript experience. Please read the Sample pdf to get an idea about the content of the book, also browse some of the JsFiddles here :
- https://github.com/dimitris-papadimitriou-chr/FunctionalJsWithCategories
Paperback is now available in Amazon Functional Programming in JavaScript
One of the main reasons for this book is to transfer in the community of object-oriented developers some of the ideas and advancements happening to the functional community side and the mathematical foundations behind them.
Book Description
This book goes beyond the introductory ideas of functional programming, while progressively building on practical examples in a comprehensive manner. Each example is accompanied by online autonomous JS fiddle JavaScript code [https://jsfiddle.net/user/functionalCategories/fiddles/], which you can run fork and modify, in order to deepen your understanding of each section.
By the end of this book, you will have a deep understanding of the ideas behind functional JavaScript that will allow you to program in a functional style with confidence. Also, you will have an overview of how famous functional libraries like Ramda, Folktale, Sanctuary, etc. have implemented the different functional concepts.
What you will learn:
- Go beyond the Array.map by understanding how to generalize the idea of map to Functors like Maybe, Either and Promises, etc.
- Go beyond the idea of Array.reduce by understanding the concepts of fold and catamorphism over data structures.
- Learn how to combine functional ideas in order to solve practical problems.
- Use Monads like Maybe, Either, IO, Continuations, and Promises to chain computations.
- Get a deep understanding of recursive methods and learn how to define recursive methods on algebraic data structures.
About the Author
Table of Contents
-
Contents
-
About this book coding conventions 8
-
Type Safety 8
-
Fantasy land 10
- 1.1 Categories ... 13
- 1.2 Essential Lambda calculus with Js ... 15
- 1.3 SKI combinators ... 16
-
2 Basic Concepts
- 2.1 Basic Type Theory -[Optional] ... 19
- 2.2 Why Types are important ... 19
- 2.3 Variable Types ... 20
- 2.4 Function types ... 20
- 2.4.1 Functions with a single argument ... 20
- 2.4.2 Functions with multiple arguments ... 21
- 2.5 Generic Types ... 21
-
3 More Functional Concepts
- 3.1 Object literal notion ... 22
-
Important points 22
- 3.2 Pure functions and Side effects ... 23
- 3.3 Mutability ... 24
- 3.4 Immutability with Object literals ... 25
-
4 The Pillars
- 4.1 Monoids ... 27
- 4.2 Function composition as a monoid ... 30
- 4.3 Decorator Design pattern - Functional Perspective ... 31
- 4.4 Adapter Design pattern - Functional Perspective ... 33
- 4.5 Folding monoids ... 33
- 4.6 folding functions under composition ... 35
- 4.7 Composing monoids ... 36
- 4.8 Products of Monoids ... 39
- 4.9 Predicate monoidal Composition ... 40
- 4.10 Specification Pattern - Functional Perspective ... 42
- 4.11 Monoid homomorphisms and Parallelism ... 44
- 4.12 Parallelism using Web Workers ... 47
- 4.13 Higher-order functions ... 50
- 4.14 Strategy Design pattern - Functional Perspective ... 50
- 4.15 Currying and partial application ... 52
-
5 Algebraic Data Types
- 5.1 The product structure: ... 57
- 5.1.1 Universal Construction ... 58
- 5.1.2 Introduction / Elimination ... 59
- 5.2 The co-product (aka Union) structure: ... 60
- 5.2.1 Introduction / Elimination ... 63
- 5.3 Extending Union Types ... 64
- 5.3.1 Adding Pattern Matching extensions to Union Types ... 64
- 5.3.2 Rewriting Union Type methods with match ... 65
- 5.4 One ... 66
- 5.5 Recursive Algebraic Types ... 67
- 5.5.1 Rewriting map with match ... 68
- 5.5.2 On the value of the symbolic representation ... 69
- 5.5.3 Adding Pattern Matching extension to native array ... 70
-
6 Functors
- 6.1 The Identity Functor ... 75
- 6.2 Commutative Diagrams ... 77
- 6.3 The Functor Laws ... 78
- 6.4 Decorator design pattern - Functor ... 81
- 6.5 Pattern Matching ... 82
- 6.6 Pattern match - Compositions ... 83
- 6.7 Pattern matching - Inheritance ... 84
- 6.7.1 Pattern matching in functional libraries ... 87
- 6.8 Id Functor on the Fly ... 87
- 6.9 The Basic Functor Mechanics ... 88
- 6.10 IO Functor, a Lazy Id Functor ... 89
- 6.10.1 Lazy as Functor ... 90
- 6.10.2 IO Functor ... 91
- 6.11 Reader Functor ... 92
- 6.12 Maybe Functor ... 94
-
Dealing with null - Null object Design pattern 94
- 6.13 The Null Object Design pattern ... 95
- 6.14 The Functional equivalent - Maybe as Functor ... 96
- 6.15 Pattern matching ... 97
- 6.16 Refactoring the imperative example using Maybe ... 97
- 6.17 Maybe Functor Example ... 98
- 6.18 Maybe -React.js with Folktale.js [Optional] ... 100
- 6.19 Either ... 102
- 6.20 The Imperative equivalent to Either ... 104
- 6.21 Either -Sanctuary.js ... 105
- 6.22 Either -Folktale.js ... 107
- 6.23 Either Functor Example ... 108
- 6.24 Either Functor Example- Imperative Equivalent ... 109
- 6.25 Either Functor Example - Sanctuary.js ... 109
- 6.26 Either -React.js with Folktale.js [Optional] ... 110
- 6.27 Generalizing Either - biMap / mapLeft ... 111
- 6.28 Promise as Functor ... 112
- 6.29 The Promise - functor laws ... 114
- 6.30 Promise Functor Example ... 115
- 6.31 Maybe Functor Example ... 116
- 6.32 Composing Functors ... 118
- 6.33 Transformer Types ... 119
- 6.34 Promise-Maybe Composition Example ... 120
- 6.35 Transformer operators ... 121
- 6.36 Transformer Adapters (aka monad transformers) ... 121
- 6.37 Promise-Either Composition Example ... 122
- 6.38 Promise-Either -React.js with Folktale.js [Optional] ... 124
- 6.39 Try- Using Either for exception handling ... 125
- 6.40 Try Type Refactoring Example ... 128
- 6.41 Functors from Algebraic Data Types ... 129
- 6.42 Applicative Functor ... 132
- 6.43 Reader Applicative Functor ... 133
- 6.44 Composing Applicatives ... 135
-
7 Natural Transformations
- 7.1.1 Natural Transformation Between Maybe and Either ... 139
-
8 Monads
- 8.1 The Identity Monad ... 142
- 8.2 The Array Monad ... 143
- 8.3 Monad laws for Identity Monad ... 144
- 8.4 Monads -Kleisli Composition ... 145
- 8.5 Monad laws following Kleisli formulation ... 146
- 8.6 Maybe Monad ... 147
- 8.7 Maybe Monad Example ... 149
- 8.8 Either Monad ... 151
- 8.9 Either Monad Example ... 152
- 8.10 Promise as monad ... 153
- 8.11 Promise monad example ... 154
- 8.12 Fluture.js ... 155
- 8.13 Maybe-Promise monad combination ... 157
- 8.14 Either-Promise monad combination ... 158
- 8.15 Either-Promise monad Example-React.js with Folktale.js ... 159
- 8.16 Validation type ... 161
- 8.17 State Monad ... 161
- 8.18 Traversing with State ... 164
- 8.19 Reader Monad ... 166
- 8.20 IO monad ... 168
- 8.21 Writer Monad ... 169
- 8.22 Traversing with Writer ... 170
-
9 Catamorphisms Again
- 9.1 A brief mentioning of F-algebras ... 172
- 9.2 Catamorphisms ... 173
- 9.3 Initial algebra ... 176
- 9.3.1 F-Algebras Homomorhisms ... 176
- 9.4 Catamorphisms for Trees ... 178
- 9.5 Reversing a Tree ... 179
- 9.6 Catamorphisms with the Visitor Design pattern ... 180
- 9.6.1 F-Coalgebra ... 181
- 9.7 A brief mentioning of Anamorhisms ... 181
- 9.7.1 Corecursion ... 182
- 9.7.2 JavaScript Generators ... 183
- 9.7.3 A brief mentioning of Hylomorphisms ... 184
- 9.7.4 Hylomorhism example: Mergesort ... 186
- 9.8 Fold relation with Cata ... 187
-
10 Traversable
- 10.1 Traversable Array with Either applicative for validation ... 190
- 10.2 Traversable Algebraic data structures ... 191
- 10.3 Identity Functor Traversable ... 192
- 10.4 Traversing with The Promise - Parallel ... 193
- 10.5 Applicative Reader Isomorphism with the Interpreter Design pattern ... 194
- 10.5.1 A Catamorphism implementation ... 196
- 10.5.2 Object Oriented Interpreter Pattern implementation ... 196
- 10.6 Composing Traversables ... 197
- 10.7 Foldable ... 198
- 10.7.1 FoldMap ... 199
- 10.7.2 Filterable structures ... 201
- 10.8 Fold and FoldMap Derivation from Catamorphism ... 201
- 10.9 Traverse Derivation from Catamorphism ... 203
- 10.9.1 Mixins ... 203
- 10.9.2 Composing Foldables ... 204
- 10.9.3 Iterators ... 205
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11 Comonads
- 11.1 The Identity Comonad ... 207
- 11.2 Co-Monad laws for Identity Co-Monad ... 208
- 11.3 Co-Kleisli Composition ... 209
- 11.3.1 Co-Monad laws following Co-Kleisli formulation ... 210
- 11.4 Store Comonad ... 210
- 11.5 Lazy ... 211
- 11.6 Pair Comonad ... 212
- 11.7 Spatial Comonad and the Game of Life ... 215
- 11.8 Stream Comonad ... 218
- 11.9 Tree Comonad ... 219
- 11.9.1 Tree annotation example ... 220
-
12 F-Algebras
- 12.1 F-Algebras Homomorhisms ... 226
- 12.2 Initial Algebras ... 228
-
13 F -Coalgebra
- 13.1 Catmorphisms ... 230
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