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