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<h1 id="awesome-recursion-schemes-awesome">Awesome Recursion Schemes <a
href="https://github.com/sindresorhus/awesome"><img
src="https://cdn.rawgit.com/sindresorhus/awesome/d7305f38d29fed78fa85652e3a63e154dd8e8829/media/badge.svg"
alt="Awesome" /></a></h1>
<blockquote>
<p>A curation of useful resources for learning about and using recursion
schemes.</p>
</blockquote>
<p>Recursion schemes are simple, composable combinators, that automate
the process of traversing and recursing through nested data
structures.</p>
<h2 id="contents">Contents</h2>
<ul>
<li><a href="#introductions">Introductions</a></li>
<li><a href="#articles">Articles</a></li>
<li><a href="#papers">Papers</a></li>
<li><a href="#presentations">Presentations</a></li>
<li><a href="#cheat-sheets">Cheat Sheets</a></li>
<li><a href="#podcasts">Podcasts</a></li>
<li><a href="#implementations">Implementations</a></li>
</ul>
<h2 id="introductions">Introductions</h2>
<ul>
<li><a href="https://github.com/passy/awesome-recursion-schemes">Awesome
Recursion Schemes</a> - A curation of useful resources for learning
about and using recursion schemes.</li>
<li><a href="https://jtobin.io/practical-recursion-schemes">Practical
Recursion Schemes</a> - Introduction to pattern functors, fix points,
anamorphisms, catamorphisms, paramorphisms and hylomorphisms, requiring
very little prior knowledge.</li>
<li><a
href="http://blog.sumtypeofway.com/an-introduction-to-recursion-schemes/">An
Introduction to Recursion Schemes</a> - Three-part series in which you
discover recursion schemes from scratch and implement a small subset of
Edward Kmett’s library.</li>
<li><a
href="https://www.schoolofhaskell.com/user/bartosz/understanding-algebras">Understanding
Algebras</a> - Bartosz Milewski explains F-algebras and shows how to use
them in the context of catamorphisms.</li>
<li><a
href="https://medium.com/@JosephJnk/recursion-schemes-in-javascript-and-flow-with-static-land-recursision-schemes-97cf10599fb7">Recursion
Schemes in JavaScript and Flow</a> - Series introducing recursion
schemes and related concepts in JavaScript, aimed at developers with a
minimal functional programming background.</li>
</ul>
<h2 id="articles">Articles</h2>
<ul>
<li><a
href="http://comonad.com/reader/2009/recursion-schemes/">Recursion
Schemes: A Field Guide (Redux)</a> - List of various recursion schemes
with code samples.</li>
<li><a href="https://wiki.haskell.org/Catamorphisms">Catamorphisms</a> -
Definition on the Haskell Wiki.</li>
<li><a
href="https://www.schoolofhaskell.com/user/edwardk/recursion-schemes/catamorphisms">Catamorphisms</a>
- Short definition with code on School of Haskell by Edward Kmett.</li>
<li><a href="https://jtobin.io/rotating-squares">Rotating Squares</a> -
Using a hylomorphism to rotate a quadtree by Jared Tobin.</li>
<li><a
href="http://blog.sumtypeofway.com/recursion-schemes-part-v/">Recursion
Schemes, Part V: Hello, Hylomorphisms</a></li>
<li><a href="https://jtobin.io/promorphisms-pre-post">Promorphisms, Pre
and Post</a> - Practical examples of pre- and postpromorphisms by Jared
Tobin.</li>
<li><a href="https://jtobin.io/time-traveling-recursion">Time Traveling
Recursion Schemes</a> - Exploring histo and futu by example by Jared
Tobin.</li>
<li><a
href="http://blog.sumtypeofway.com/recursion-schemes-part-iv-time-is-of-the-essence/">Recursion
Schemes, Part IV: Time is of the Essence</a> - Practical article about
histomorphism and the futumorphism.</li>
<li><a
href="https://github.com/sellout/recursion-scheme-talk/blob/master/cheat%20sheet.pdf">Cheat
Sheet</a> - Map of various recursion schemes and their duals.</li>
<li><a
href="http://logji.blogspot.co.uk/2012/02/correcting-visitor-pattern.html">Correcting
the Visitor pattern</a> - Showing that the Visitor pattern implements an
f-algebra for use with a catamorphism (in Java).</li>
<li><a href="https://free.cofree.io/2017/11/13/recursion/">Recursion
Schemes in Scala</a> - Introduces the fixpoint combinator, anamorphism,
catamorphism, hylomorphism, paramorphism, apomorphism, histomorphism,
dynamorphism and futumorphism.</li>
<li><a
href="https://duplode.github.io/posts/whats-in-a-fold.html">What’s in a
Fold: The Basic Catamorphism in recursion-schemes</a> - Introduces
catamorphism as a generalization of fold.</li>
</ul>
<h3 id="hylomorphisms-in-the-wild">Hylomorphisms in the Wild</h3>
<p>Articles by Bartosz Milewski about solving small, practical problems
by applying a hylomorphism.</p>
<ul>
<li><a
href="https://bartoszmilewski.com/2017/12/29/stalking-a-hylomorphism-in-the-wild/">Stalking
a Hylomorphism in the Wild</a> - Advent of Code 2017, Domino
challenge</li>
<li><a
href="https://bartoszmilewski.com/2018/12/20/open-season-on-hylomorphisms/">Open
Seasons on Hylomorphisms</a> - Advent of Code 2018, String comparison
challenge</li>
</ul>
<h2 id="papers">Papers</h2>
<ul>
<li><a
href="http://maartenfokkinga.github.io/utwente/mmf91m.pdf">Functional
Programming with Bananas, Lenses, Envelopes and Barbed Wire, 1991,
Meijer et al.</a> - The original paper most of this is based on.</li>
<li><a
href="http://www.cs.ox.ac.uk/ralf.hinze/publications/Sorting.pdf">A
Duality of Sorts, 2013, Hinze et al.</a> - Shows that many basic sorting
algorithms exist as a pair, and that these pairs arise naturally out of
the duality between folds and unfolds.</li>
<li><a
href="http://www.cs.ox.ac.uk/people/daniel.james/sorting/sorting.pdf">Sorting
with Bialgebras and Distributive Laws, 2012, Hinze et al.</a> - Shows
how paramorphisms and apomorphisms can be used for more efficient
implementations of sorting algorithms.</li>
<li><a
href="http://research.microsoft.com/en-us/um/people/simonpj/Papers/hmap/hmap.ps">Scrap
your boilerplate: a practical design pattern for generic programming,
2003, SPJ et al.</a> - Design pattern for writing programs that traverse
data structures built from rich mutually-recursive data types.</li>
</ul>
<h2 id="presentations">Presentations</h2>
<ul>
<li><a href="http://www.timphilipwilliams.com/slides.html">Slidedecks by
Tim Philip Williams</a> - “Recursion Schemes by Example” and “Exotic
Tools for Exotic Trades” provide concise definitions as well as
practical examples of many recursion schemes.</li>
<li><a href="https://www.youtube.com/watch?v=9EGYSb9vov8">Unifying
Structured Recursion Schemes</a> - 12 min presentation by Ralf Hinze,
Nicolas Wu, and Jeremy Gibbons.</li>
<li><a href="https://www.youtube.com/watch?v=Zw9KeP3OzpU">Recursion
Schemes</a> - Presented by Tim Williams at the London Haskell
meetup.</li>
<li><a href="https://www.youtube.com/watch?v=PK4SOaAGVfg">F-algebras or:
How I Learned to Stop Worrying and Love the Type System</a> - Presented
by Anthony Burzillo at the NYC Haskell User’s Group.</li>
<li><a href="https://www.youtube.com/watch?v=i5A2Amfcir8">A Gentle
Introduction to Recursion Schemes</a> - Presented by Jean Remi
Desjardins at Lambdaconf 2016.</li>
<li><a
href="https://github.com/sellout/recursion-scheme-talk">recursion-scheme-talk</a>
- Collection of slide decks about recursion schemes.</li>
<li><a href="https://www.youtube.com/watch?v=5Kr7IykGMzU">Bracer:
Transforming Real-World Languages with Coproducts and Recursion
Schemes</a> - High-level talk about structuring programs with coproducts
and recursion schemes by Patrick Thomson.</li>
<li><a href="https://www.youtube.com/watch?v=24UoRaoKLjM">Recursion:
Where Functional Programming Hits Bottom</a> - Introduction to recursive
fix point data structures and recursion schemes in Haskell and Scala by
Greg Pfeil.</li>
<li><a href="https://www.youtube.com/watch?v=-98fR9VmLbQ">Programming
with algebras</a> - Bartosz Milewski’s article in talk form, presented
at LambdaCon.</li>
<li><a
href="https://www.youtube.com/watch?v=XZ9nPZbaYfE&amp;t=3s">Peeling the
Banana: Recursion Schemes from First Principles</a> - Zainab Ali’s
Introductory talk presented at LambdaWorld.</li>
</ul>
<h2 id="cheat-sheets">Cheat Sheets</h2>
<ul>
<li><a
href="https://ipfs.io/ipfs/QmTppu1VDAQWsdiyVSZX6qb8PErdpwzNP2oKfEhcgaBvWR/guide-to-morphisms.pdf">The
Hitchhiker’s Guide to Morphisms</a> - Overview of different morphisms
including a printable PDF.</li>
</ul>
<h2 id="podcasts">Podcasts</h2>
<ul>
<li><a href="http://www.magicreadalong.com/">Magic Read Along</a> -
Casual discussions about category theory that often bring up recursion
schemes, including <a
href="http://www.magicreadalong.com/episode/33">episode 33</a> which
talks about Histomorphisms and Futumorphisms.</li>
<li><a href="https://scala.love/">Scala Love</a> - Podcast about Scala
that brings up recursion schemes in <a
href="https://scala.love/happy-valentin/">the second episode</a>.</li>
<li><a href="https://www.haskellcast.com/">The Haskell Cast</a> -
Recursion schemes come up in <a
href="https://www.haskellcast.com/episode/013-john-wiegley-on-categories-and-compilers">Episode
13 with John Wiegley</a>.</li>
</ul>
<h2 id="implementations">Implementations</h2>
<ul>
<li><a
href="https://github.com/ekmett/recursion-schemes/">recursion-schemes</a>
for Haskell - The canonical implementation by Edward Kmett.</li>
<li><a href="https://github.com/slamdata/matryoshka">Matryoshka</a> for
Scala using Scalaz - Generalized folds, unfolds, and traversals for
fixed point data structures.</li>
<li><a href="https://github.com/andyscott/droste">andyscott/droste</a>
for Scala using Cats - Generalized folds, unfolds, and traversals for
fixed point data structures.</li>
<li><a
href="https://github.com/vmchale/recursion_schemes/">recursion_schemes</a>
for Idris, based off Edward Kmett’s Haskell library.</li>
<li><a
href="https://github.com/slamdata/purescript-matryoshka">purescript-matryoshka</a>
for PureScript - Work-in-process port of matryoshka.</li>
<li><a href="https://github.com/vmchale/recursion">recursion</a> for ATS
- Demonstration of recursion schemes in ATS.</li>
<li><a href="https://github.com/sellout/dada">dada</a> for Dhall - a
library for recursion schemes in Dhall.</li>
<li><a
href="https://github.com/JosephJNK/static-land-recursion-schemes">static-land-recursion-schemes</a>
for JavaScript/Flow - Schemes for data structures written in the style
of <a
href="https://github.com/gcanti/flow-static-land">flow-static-land</a>.</li>
<li><a href="https://github.com/aedans/Katalyst">Katalyst</a> for Kotlin
- a re-envisioning based off Matryoshka using lightweight higher kinded
polymorphism.</li>
</ul>
<h2 id="license">License</h2>
<p>This content is licensed under <a
href="https://creativecommons.org/publicdomain/zero/1.0/">CC0</a>.</p>
<p><a
href="https://github.com/passy/awesome-recursion-schemes">recursionschemes.md
Github</a></p>