A list is a monad

I used to struggle with understanding the "receipe" metaphor for monads when it comes to lists. But a list (or, really any collection) as a monad can be thought of as the "discrete nondeterminism monad".

Meaning that every collection is a set of possible inputs to the computation that is provided as the argument to a `flatMap` operation. Each `flatMap`, by definition, returns a new collection of possible outputs for each of the inputs, and each of those collections gets concatenated. Every item in the final output collection represents the result of following some path through the computations, selecting a single item at each step. Importantly, the type of the output of each `flatMap` operation can differ from the input.

You can imagine extending this by assigning probabilities, or making the domain continuous (I think...). These extensions would still be monads, just without being simple collections.

It's kind of like how multiplication over whole numbers is repeated addition, but that metaphor becomes less useful for other domains of numbers.