If you have an affinity for programming language theory (as I do), and wander around the internet searching for topics of interest, eventually you will run into references to monads. They’re neither trivial, nor as complex as the dearth of proper explanations of them might suggest.

In a nutshell, they are the PLT manifestation of a concept from category theory, and abstract away propagation of results and side effects, without actually performing side effects or leaving a pure-functional paradigm. Any attempt at description beyond that point tends to either

a) get terribly botched*, or

b) turn into a real category theory explanation, which most people don’t have the background to understand easily

and for those reasons I will refrain from attempting further explanation myself. I don’t have confidence in my own ability to explain in a non-interactive medium, and I certainly don’t have the mathematics background to formalize it.

The internet is littered with tutorials and explanations “in laymen’s terms” of what monads are, what they are for, why we care, etc. Every such tutorial I have started (at least a dozen, probably several more – all highly recommended) has either bored me to tears, struck me as completely inane, or simply confused me.

I had decided that I was simply going to have to learn abstract algebra and category theory in order to really get a handle on what they were, until a wonderful post appeared on LtU, linking to one of the earlier papers on monads. The paper, by Philip Wadler, gives not only a clear explanation of what a monad is, but also provides a strong motivation for looking for monads, an approachable description of how they are derived from a practical point of view for use in a type system, and a number of useful, nontrivial examples. Probably one of the most well-written academic papers I’ve read. You should be familiar with an ML-style type system and notation to understand the examples. Or you need be be good at picking up such things on the fly.

Monads for Functional Programming. Enjoy.

* The canonical example of a monad is for some reason the Maybe monad, though I don’t know why – it’s certainly a monad, but it’s actually not the most intuitive first example. Most of the monad explanations I found online immediately launch into using Maybe as an example of why monads aren’t hard. They’re not, but the example is usually provided far too early, without enough background, motivation, or explanation, making the reader simply feel like he or she is missing some greater complexity (which is true) which was already explained (which usually is not the case). Wadler’s example of a simple interpreter is much clearer.