Somewhat. A monad allows for representing an effectful program as a data structure, but it's not very "introspectable" by itself (which is what this article is advocating). For example, you can pass a monad around, but you can't tell what it will do. All you can really do with a monad is execute it and find out (similar to how a regular function is "opaque" - you can run it with various inputs but can't know ahead of time what it plans to do with them).

However, if you were to use "free monads", you get closer to what the author is talking about. Free monads are a special implementation of monad that don't actually _run_ any effects - they just build up a data benign structure that can be interpreted later (possibly as an effect).

To do defunctionalization, you don't need monads though - you just need to define data that represents operations. Monads can just provide convenient syntax to do this while looking like a sequential program.

Insofar as everything is related to monads, yes ;)

In fact you don't need to use monads at all here. I've used this pattern on merely applicative non-monadic initial algebras before; in fact, the article's "arithmetic expressions" example isn't what I would call "monadic", because it doesn't readily admit Bind as currently phrased.

Worse, the "writeSmallOddToFile" example isn't even generic at all, so I don't think there's a reasonable sense in which it could even be said to be functorial.