For some monads the "wrap" gets awfully metaphorical (for State it's a function that produces the value and updated state, for Const there is no value, etc) but

For some monads the "wrap" gets awfully metaphorical (for State it's a function that produces the value and updated state, for Const there is no value, etc) but I don't think that's actually a problem, just a thing to be aware of. There is certainly no expectation that you can actually get your hands on the thing. A bigger issue is that you're missing a piece. If you can "wrap" values and "wrap" functions such that they operate on wrapped values, you (probably) have a functor. To be a monad you also need to have the ability to turn multiple layers of wrapping into one layer of wrapping. For lists, that's "flatten". I said "probably" above because there are rules these pieces need to follow to behave well. They're pretty simple but I don't think we need to dig into them at this level of discussion.