F# for Fun and Profit
  • Introduction
  • Getting started
    • Contents of the book
    • "Why use F#?" in one page
    • Installing and using F#
    • F# syntax in 60 seconds
    • Learning F#
    • Troubleshooting F#
    • Low-risk ways to use F# at work
      • Twenty six low-risk ways to use F# at work
      • Using F# for development and devops scripts
      • Using F# for testing
      • Using F# for database related tasks
      • Other interesting ways of using F# at work
  • Why use F#?
    • The "Why use F#?" Series
      • Introduction to the 'Why use F#' series
      • F# syntax in 60 seconds
      • Comparing F# with C#: A simple sum
      • Comparing F# with C#: Sorting
      • Comparing F# with C#: Downloading a web page
      • Four Key Concepts
      • Conciseness
      • Type inference
      • Low overhead type definitions
      • Using functions to extract boilerplate code
      • Using functions as building blocks
      • Pattern matching for conciseness
      • Convenience
      • Out-of-the-box behavior for types
      • Functions as interfaces
      • Partial Application
      • Active patterns
      • Correctness
      • Immutability
      • Exhaustive pattern matching
      • Using the type system to ensure correct code
      • Worked example: Designing for correctness
      • Concurrency
      • Asynchronous programming
      • Messages and Agents
      • Functional Reactive Programming
      • Completeness
      • Seamless interoperation with .NET libraries
      • Anything C# can do...
      • Why use F#: Conclusion
  • Thinking Functionally
    • The "Thinking Functionally" Series
      • Thinking Functionally: Introduction
      • Mathematical functions
      • Function Values and Simple Values
      • How types work with functions
      • Currying
      • Partial application
      • Function associativity and composition
      • Defining functions
      • Function signatures
      • Organizing functions
      • Attaching functions to types
      • Worked example: A stack based calculator
  • Understanding F# ###
    • The "Expressions and syntax" Series
      • Expressions and syntax: Introduction
      • Expressions vs. statements
      • Overview of F# expressions
      • Binding with let, use, and do
      • F# syntax: indentation and verbosity
      • Parameter and value naming conventions
      • Control flow expressions
      • Exceptions
      • Match expressions
      • Formatted text using printf
      • Worked example: Parsing command line arguments
      • Worked example: Roman numerals
    • The "Understanding F# types" Series
      • Understanding F# types: Introduction
      • Overview of types in F#
      • Type abbreviations
      • Tuples
      • Records
      • Discriminated Unions
      • The Option type
      • Enum types
      • Built-in .NET types
      • Units of measure
      • Understanding type inference
    • Choosing between collection functions
    • The "Object-oriented programming in F#" Series
      • Object-oriented programming in F#: Introduction
      • Classes
      • Inheritance and abstract classes
      • Interfaces
      • Object expressions
    • The "Computation Expressions" Series
      • Computation expressions: Introduction
      • Understanding continuations
      • Introducing 'bind'
      • Computation expressions and wrapper types
      • More on wrapper types
      • Implementing a builder: Zero and Yield
      • Implementing a builder: Combine
      • Implementing a builder: Delay and Run
      • Implementing a builder: Overloading
      • Implementing a builder: Adding laziness
      • Implementing a builder: The rest of the standard methods
    • Organizing modules in a project
    • The "Dependency cycles" Series
      • Cyclic dependencies are evil
      • Refactoring to remove cyclic dependencies
      • Cycles and modularity in the wild
    • The "Porting from C#" Series
      • Porting from C# to F#: Introduction
      • Getting started with direct porting
  • Functional Design ###
    • The "Designing with types" Series
      • Designing with types: Introduction
      • Single case union types
      • Making illegal states unrepresentable
      • Discovering new concepts
      • Making state explicit
      • Constrained strings
      • Non-string types
      • Designing with types: Conclusion
    • Algebraic type sizes and domain modelling
    • Thirteen ways of looking at a turtle
      • Thirteen ways of looking at a turtle (part 2)
      • Thirteen ways of looking at a turtle - addendum
  • Functional Patterns ###
    • How to design and code a complete program
    • A functional approach to error handling (Railway oriented programming)
      • Railway oriented programming: Carbonated edition
    • The "Understanding monoids" Series
      • Monoids without tears
      • Monoids in practice
      • Working with non-monoids
    • The "Understanding Parser Combinators" Series
      • Understanding Parser Combinators
      • Building a useful set of parser combinators
      • Improving the parser library
      • Writing a JSON parser from scratch
    • The "Handling State" Series
      • Dr Frankenfunctor and the Monadster
      • Completing the body of the Monadster
      • Refactoring the Monadster
    • The "Map and Bind and Apply, Oh my!" Series
      • Understanding map and apply
      • Understanding bind
      • Using the core functions in practice
      • Understanding traverse and sequence
      • Using map, apply, bind and sequence in practice
      • Reinventing the Reader monad
      • Map and Bind and Apply, a summary
    • The "Recursive types and folds" Series
      • Introduction to recursive types
      • Catamorphism examples
      • Introducing Folds
      • Understanding Folds
      • Generic recursive types
      • Trees in the real world
    • The "A functional approach to authorization" Series
      • A functional approach to authorization
      • Constraining capabilities based on identity and role
      • Using types as access tokens
  • Testing
    • An introduction to property-based testing
    • Choosing properties for property-based testing
  • Examples and Walkthroughs
    • Worked example: Designing for correctness
    • Worked example: A stack based calculator
    • Worked example: Parsing command line arguments
    • Worked example: Roman numerals
    • Commentary on 'Roman Numerals Kata with Commentary'
    • Calculator Walkthrough: Part 1
      • Calculator Walkthrough: Part 2
      • Calculator Walkthrough: Part 3
      • Calculator Walkthrough: Part 4
    • Enterprise Tic-Tac-Toe
      • Enterprise Tic-Tac-Toe, part 2
    • Writing a JSON parser from scratch
  • Other
    • Ten reasons not to use a statically typed functional programming language
    • Why I won't be writing a monad tutorial
    • Is your programming language unreasonable?
    • We don't need no stinking UML diagrams
    • Introvert and extrovert programming languages
    • Swapping type-safety for high performance using compiler directives
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  1. Functional Patterns ###

The "Understanding monoids" Series

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Last updated 5 years ago

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In this series, we'll look at a very common "pattern" known as a monoid.

Monoids are not really a design pattern; more an approach to working with many different types of values in a common way. In fact, once you understand monoids, you will start seeing them everywhere!

  • . A mostly mathless discussion of a common functional pattern.

  • . Monoids without tears - Part 2.

  • . Monoids without tears - Part 3.

Monoids without tears
Monoids in practice
Working with non-monoids