Except this “simple” metaphor isn’t too useful. For monads like IO and State, “monad as a container” is a stretch. And some don’t fit at all — the list monad often is imagined as a computational context with nondeterminism, not simply a container.
I don't really understand your point of view. Especially the list monad is literally a list. The shape of bind for the list monad is [a] -> (a -> [b]) -> [b]. If that's not a container, I don't know what is. The fact that it can be used to solve problems where the list represents a non-deterministic result is really secondary. I mean, I suppose you can think of it as being different, but it seems a lot more complicated in my mind.
I think some "containers" a definitely hard to envision. A partially applied function is also a monad (i.e. it's trivial to write a meaningful bind for it). It may be hard to think of a partially applied function as "containing" the applied parameters, but I still think that's easier than any other way of envisioning it. But maybe it's a matter of horses for courses.
I think some "containers" a definitely hard to envision. A partially applied function is also a monad (i.e. it's trivial to write a meaningful bind for it). It may be hard to think of a partially applied function as "containing" the applied parameters, but I still think that's easier than any other way of envisioning it. But maybe it's a matter of horses for courses.