Total functions embed into partial ones, which is why we have a partiality monad. The opposite arrow doesn't exist, which is why we don't have a totality monad.
Now lazy and eager are properly adjectives that govern beta reduction, that is, the interaction between a function and its argument.
The short of it is that neither an eager nor a lazy monad makes any sense.
(Heh, I'm totally citing this in the monads class I teach as proof of why unpacking monads starting from functors is a win.)
Now lazy and eager are properly adjectives that govern beta reduction, that is, the interaction between a function and its argument.
The short of it is that neither an eager nor a lazy monad makes any sense.
(Heh, I'm totally citing this in the monads class I teach as proof of why unpacking monads starting from functors is a win.)