Book Image

Learning Functional Programming in Go

By : Lex Sheehan
Book Image

Learning Functional Programming in Go

By: Lex Sheehan

Overview of this book

Lex Sheehan begins slowly, using easy-to-understand illustrations and working Go code to teach core functional programming (FP) principles such as referential transparency, laziness, recursion, currying, and chaining continuations. This book is a tutorial for programmers looking to learn FP and apply it to write better code. Lex guides readers from basic techniques to advanced topics in a logical, concise, and clear progression. The book is divided into four modules. The first module explains the functional style of programming: pure functional programming, manipulating collections, and using higher-order functions. In the second module, you will learn design patterns that you can use to build FP-style applications. In the next module, you will learn FP techniques that you can use to improve your API signatures, increase performance, and build better cloud-native applications. The last module covers Category Theory, Functors, Monoids, Monads, Type classes and Generics. By the end of the book, you will be adept at building applications the FP way.
Table of Contents (21 chapters)
Title Page
Credits
About the Author
Acknowledgments
About the Reviewer
www.PacktPub.com
Customer Feedback
Preface
Index

Homomorphism


Here's a Venn diagram depicting how the different categories of homomorphisms relate to one another:

Abbreviation

Description

Mono

Set of monomorphisms (injective)

Epi

Set of epimorphism (surjective)

Iso

Set of isomorphisms (bijective)

Auto

Set of automorphisms (bijective and endomorphic)

 

A homomorphism is a correspondence between set A (the domain) and set B (the codomain or range), so that each object in A determines a unique object in B and each object in B has an arrow/function/morphism pointing to it from A.

If operations, for example, addition and multiplication, are defined for A and B, it is required that they correspond. That is, a * b must correspond to f(a) * f(b).

Homomorphisms preserve correspondence

Correspondence must be as follows:

  • Single-valued: The morphism must at least be a partial function
  • Surjective: Each a in A has at least one f(a) in B

Homomorphism is a way to compare two groups for structural similarities. It's a function between two groups that preserve their structure...