I know, I know, the world does not need yet another introduction to monads (or yet another article complaining that world does not need yet another introduction to monads). So you’ll be glad to know this isn’t one of those, in the sense that it’s not new
Syntax extension for Monads in Ocaml Jacques Carette, Lydia E. van Dijk and Oleg Kiselyov This Camlp4 extension provides some syntactic sugar to beautify monadic expressions. Example: A simple but realistic example of the use of a list monad looks like this bind [1; 2; 3] (fun a -> bind [3; 4; 5] (fun b -> return (a + b))) where we assume the appropriate definitions of the functions "bind" and "return". With the help of "pa_monad" this can be written as perform a <-- [1; 2; 3]; b <-- [3; 4; 5]; return (a + b) which is much clearer and thus easier to understand and maintain. By the way, the expression evaluates to [4; 5; 6; 5; 6; 7; 6; 7; 8] the sum of each pair of values of the input list
Collection of links to monad implementations in various languages. Due to recent discussions here on LtU and on the Haskell mailing lists I've compiled a list of links to implementations of monads in various languages. If you know of any that aren't listed here, please submit them in a comment. * Clean * Haskell * Java * Joy * OCaml * Perl * Prolog * Python * Ruby * Scheme
Generalising Monoids The word 'monad' is derived from the word 'monoid'. The explanation usually given is that there is an analogy between monoids and monads. On the surface, this seems a bit unlikely. The join operation in a monad is supposed to correspond to the binary operator in the monoid, but join is a completely different kind of thing, certainly not a binary operator in any usual sense. I'm going to make this analogy precise so that it's clear that both monoids and monads are examples of the same construction. In fact, I'm going to write some Haskell code to define monoids and monads in almost exactly the same way. I was surprised to find I could do this because instances of Haskell's Monoid and Monad aren't even the same kind of thing (where I'm using 'kind' in its technical sense). But it can be done.
In denotational semantics and functional programming, the terms monad morphism, monad layering, monad constructor, and monad transformer have by now accumulated 20 years of twisted history. The exchange between Eric Kidd and sigfpe about the probability monad prompted me to investigate this history
S. Goncharov, L. Schröder, and T. Mossakowski. Mathematical Foundations of Computer Science, volume 4162 of Lecture Notes in Computer Science, page 447-458. Springer; Berlin; http://www.springer.de, (2006)
D. Walter, L. Schröder, and T. Mossakowski. Algebra and Coalgebra in Computer Science, volume 3629 of Lecture Notes in Computer Science, page 424-438. Springer; Berlin; http://www.springer.de, (2005)
L. Schröder, and T. Mossakowski. Fundamental Approaches to Software Engineering (FASE 2003), volume 2621 of Lecture Notes in Computer Science, page 261--277. Springer; Berlin; http://www.springer.de, (2003)