Awesome Recursion Schemes
A curation of useful resources for learning about and using recursion schemes.
Recursion schemes are simple, composable combinators, that automate the process of traversing and recursing through nested data structures.
Contents
Introductions
- 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.
Articles
- 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.
Hylomorphisms in the Wild
Articles by Bartosz Milewski about solving small, practical problems by applying a hylomorphism.
- Stalking a Hylomorphism in the Wild - Advent of Code 2017, Domino challenge
- Open Seasons on Hylomorphisms - Advent of Code 2018, String comparison challenge
Papers
- 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.