I quite belatedly realized that you come from Category Theory, so most of my sibling reply is probably old news to you. Sorry!
The most charitable response would be "yes", but it really depends on how you model your domain. Most instances of monads in software are at the type level, not at the value level, and "function" doesn't usually make sense at the type level.
The example I gave of a monad over posets does arise in the semantics of logic programming, but I haven't seen explicit recognition of monads in that area. Not that I've looked that hard, yet.
The most charitable response would be "yes", but it really depends on how you model your domain. Most instances of monads in software are at the type level, not at the value level, and "function" doesn't usually make sense at the type level.
The example I gave of a monad over posets does arise in the semantics of logic programming, but I haven't seen explicit recognition of monads in that area. Not that I've looked that hard, yet.