Algebraic Structures Tutorials

A catalog of tutorials written on algebraic structures. Feel free to do a PR/raise an issue if you know of any stellar tutorials on it.

Monoids

Monoid Est Ton Oid (2016)

A neat tutorial that introduces how monoids can be used to make code with reduce/fold operation cleaner.

Comonads, Monoids, and Trees (2015)

Monoid: Themes and Variations (Functional Pearl) (2012)

Brent Yorgey

Haskell Monoids and Their Uses (2009)

Dan Piponi

Free Monoids and Free Monads, Free of Category Theory (2017)

Ziyang Liu

Monoidal transducers are monoidal homomorphisms (2014)

Oleksandr Manzyuk

Monads

A good tutorial that first introduces group theory and algebraic structures before delving into the details on monads. This way, a somewhat natural progression can be seen on how the ideas got motivated and emerged into Category Theory. The part about duals and natural transformations are well written.

You Could Have Invented Monads! (And Maybe You Already Have.) (2006)

Dan Piponi

What is Monad? (2019)

Turtles Turtles Turtles

From monoids to monads (2008)

Dan Piponi

Translation from Haskell to JavaScript of selected portions of the best introduction to monads I’ve ever read (2011)

James Coglan

Monads for Javascript Developers (2020)

Paul Shen

Functors, Applicatives, and Monads in Pictures (2013)

Aditya Bargava’s visual introduction to functional programming concepts

Monads Demystified (2015)

Josh Haberman

Monads as Graphs (2019)

Neil Mitchell

If monads are the solution, what is the problem? (2018)

Dan Ghica

A nice article that outlines how monads can be used both at the meta-language level and object-language level. Also, addresses how Moggi’s framework was adapted to Haskell and the nuances of evaluation strategies Haskell has when adopting monads along with lazy evaluation.