This seems pretty good; the only thing on my mental checklist of "common monad discussion failures" is only a half-point off, because I'd suggest for:
"A monad is a type that wraps an object of another type. There is no direct way to get that ‘inside’ object. Instead you ask the monad to act on it for you."
that you want to add some emphasis that the monad interface itself provides no way to reach in and get the innards out, but that does not prevent specific implementations of the monad interface from providing ways of getting the insides. Obviously, Maybe X lets you get the value out if there is one, for instance. This can at least be inferred from the rest of the content in the post, since it uses types that can clearly be extracted from. It is not a requirement of implementing the monad interface on a particular type/class/whatever that there be no way to reach inside and manipulate the contents.
But otherwise pretty good.
(I think this was commonly screwed up in Haskell discussions because the IO monad looms so large, and does have that characteristic where you can never simply extract the inside, give or take unsafe calls. People who end up coming away from these discussions with the impression that the monads literally never let you extract the values come away with the question "What's the use of such a thing then?", to which the correct answer is indeed, yes, that's pretty useless. However, specific implementations always have some way of getting values out, be it via IO in the case of IO, direct querying in the case of List/Maybe/Option/Either, or other fancy things in the fancier implementations like STM. Controlling the extraction is generally how they implement their guarantees, if any, like for IO and STM.)
"A monad is a type that wraps an object of another type. There is no direct way to get that ‘inside’ object. Instead you ask the monad to act on it for you."
that you want to add some emphasis that the monad interface itself provides no way to reach in and get the innards out, but that does not prevent specific implementations of the monad interface from providing ways of getting the insides. Obviously, Maybe X lets you get the value out if there is one, for instance. This can at least be inferred from the rest of the content in the post, since it uses types that can clearly be extracted from. It is not a requirement of implementing the monad interface on a particular type/class/whatever that there be no way to reach inside and manipulate the contents.
But otherwise pretty good.
(I think this was commonly screwed up in Haskell discussions because the IO monad looms so large, and does have that characteristic where you can never simply extract the inside, give or take unsafe calls. People who end up coming away from these discussions with the impression that the monads literally never let you extract the values come away with the question "What's the use of such a thing then?", to which the correct answer is indeed, yes, that's pretty useless. However, specific implementations always have some way of getting values out, be it via IO in the case of IO, direct querying in the case of List/Maybe/Option/Either, or other fancy things in the fancier implementations like STM. Controlling the extraction is generally how they implement their guarantees, if any, like for IO and STM.)