I'm just wondering if there is a short term for something that is both a monad and a monad. I did some searches, and I know these structures exist , but I did not find a name for them.
Such a creature, under certain conditions, is sometimes called the "Hopf monad" or "bimonade" ( http://ncatlab.org/nlab/show/Hopf+monad ).
However, this also requires the fulfillment of a number of axioms regarding distributive properties, and I have not seen it arise in the programming context in any particular way.
As far as I know, the term for definition does not exist, because the monad command does not provide anything: you can always return to enter or extract to exit.
return
extract
As types for enforcing certain restrictions, an overly permissive restriction will not be used. Since no one would use it (except for identity), no one probably bothered to name it.