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 "Recursive types and folds" Series

PreviousMap and Bind and Apply, a summaryNextIntroduction to recursive types

Last updated 5 years ago

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In this series, we'll look at recursive types and how to use them, and on the way, we'll look at catamorphisms, tail recursion, the difference between left and right folds, and more.

  • . Don't fear the catamorphism....

  • . Applying the rules to other domains.

  • . Threading state through a recursive data structure.

  • . Recursion vs. iteration.

  • . Implementing a domain in three ways.

  • . Examples using databases, JSON and error handling.

Introduction to recursive types
Catamorphism examples
Introducing Folds
Understanding Folds
Generic recursive types
Trees in the real world