Awesome Recursion Schemes

A curation of useful resources for learning about and using recursion schemes.

Practical Recursion Schemes

Introduction to pattern functors, fix points, anamorphisms, catamorphisms, paramorphisms and hylomorphisms, requiring very little prior knowledge.

An Introduction to Recursion Schemes

Three-part series in which you discover recursion schemes from scratch and implement a small subset of Edward Kmett's library.

Understanding Algebras

Bartosz Milewski explains F-algebras and shows how to use them in the context of catamorphisms.

Recursion Schemes in JavaScript and Flow

Series introducing recursion schemes and related concepts in JavaScript, aimed at developers with a minimal functional programming background.

Recursion Schemes: A Field Guide (Redux)

List of various recursion schemes with code samples.

Catamorphisms

Definition on the Haskell Wiki.

Catamorphisms

Short definition with code on School of Haskell by Edward Kmett.

Rotating Squares

Using a hylomorphism to rotate a quadtree by Jared Tobin.

Recursion Schemes, Part V: Hello, Hylomorphisms

Promorphisms, Pre and Post

Practical examples of pre- and postpromorphisms by Jared Tobin.

Time Traveling Recursion Schemes

Exploring histo and futu by example by Jared Tobin.

Recursion Schemes, Part IV: Time is of the Essence

Practical article about histomorphism and the futumorphism.

Cheat Sheet

Map of various recursion schemes and their duals.

Correcting the Visitor pattern

Showing that the Visitor pattern implements an f-algebra for use with a catamorphism (in Java).

Recursion Schemes in Scala

Introduces the fixpoint combinator, anamorphism, catamorphism, hylomorphism, paramorphism, apomorphism, histomorphism, dynamorphism and futumorphism.

What's in a Fold: The Basic Catamorphism in recursion-schemes

Introduces catamorphism as a generalization of fold.

Stalking a Hylomorphism in the Wild

Advent of Code 2017, Domino challenge

Open Seasons on Hylomorphisms

Advent of Code 2018, String comparison challenge

Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire, 1991, Meijer et al.

The original paper most of this is based on.

A Duality of Sorts, 2013, Hinze et al.

Shows that many basic sorting algorithms exist as a pair, and that these pairs arise naturally out of the duality between folds and unfolds.

Sorting with Bialgebras and Distributive Laws, 2012, Hinze et al.

Shows how paramorphisms and apomorphisms can be used for more efficient implementations of sorting algorithms.

Scrap your boilerplate: a practical design pattern for generic programming, 2003, SPJ et al.

Design pattern for writing programs that traverse data structures built from rich mutually-recursive data types.

Slidedecks by Tim Philip Williams

"Recursion Schemes by Example" and "Exotic Tools for Exotic Trades" provide concise definitions as well as practical examples of many recursion schemes.

Unifying Structured Recursion Schemes

12 min presentation by Ralf Hinze, Nicolas Wu, and Jeremy Gibbons.

Recursion Schemes

Presented by Tim Williams at the London Haskell meetup.

F-algebras or: How I Learned to Stop Worrying and Love the Type System

Presented by Anthony Burzillo at the NYC Haskell User's Group.

A Gentle Introduction to Recursion Schemes

Presented by Jean Remi Desjardins at Lambdaconf 2016.

Cheat Sheet

Map of various recursion schemes and their duals.

Bracer: Transforming Real-World Languages with Coproducts and Recursion Schemes

High-level talk about structuring programs with coproducts and recursion schemes by Patrick Thomson.

Recursion: Where Functional Programming Hits Bottom

Introduction to recursive fix point data structures and recursion schemes in Haskell and Scala by Greg Pfeil.

Programming with algebras

Bartosz Milewski's article in talk form, presented at LambdaCon.

Peeling the Banana: Recursion Schemes from First Principles

Zainab Ali's Introductory talk presented at LambdaWorld.

The Hitchhiker's Guide to Morphisms

Overview of different morphisms including a printable PDF.

Magic Read Along

Casual discussions about category theory that often bring up recursion schemes, including episode 33 which talks about Histomorphisms and Futumorphisms.

Scala Love

Podcast about Scala that brings up recursion schemes in the second episode.

The Haskell Cast

Recursion schemes come up in Episode 13 with John Wiegley.

recursion-schemes

for Haskell - The canonical implementation by Edward Kmett.

Matryoshka

for Scala using Scalaz - Generalized folds, unfolds, and traversals for fixed point data structures.

andyscott/droste

for Scala using Cats - Generalized folds, unfolds, and traversals for fixed point data structures.

recursion_schemes

for Idris, based off Edward Kmett's Haskell library.

purescript-matryoshka

for PureScript - Work-in-process port of matryoshka.

recursion

for ATS - Demonstration of recursion schemes in ATS.

dada

for Dhall - a library for recursion schemes in Dhall.

static-land-recursion-schemes

for JavaScript/Flow - Schemes for data structures written in the style of flow-static-land.

Katalyst

for Kotlin - a re-envisioning based off Matryoshka using lightweight higher kinded polymorphism.