4 ms·
It does given a Functor definition. Typically in Category Theoretic presentations Monad is defined as a functor T along with mu and nu, operations that are (a -
by tel 11y ago
It does given a Functor definition. Typically in Category Theoretic presentations Monad is defined as a functor T along with mu and nu, operations that are (a -> T a) and (T (T a) -> T a), 'unit' and 'join'.
The rules for Monad are perfectly well-stated in terms of join—perhaps even better stated if you're one to like Category Theoretic diagram chasing.
- AdieuToLogic 11y agoAgain, you are quite right. I did not present the other ways to define a conforming Monad and may have mistakenly implied that the unit/flatMap form is "the" way to make one. For completeness, the forms I am aware of are (in no particular order): * unit and flatMap * unit and compose * unit, map, and join The valid form which you reference being a model of the last one. AFAIK, for any container 'T' to be able to satisfy the Monad laws, at least one of the aforementioned three combinators must exist for the container.
- dllthomas 11y ago"Compose" being Kleisli composition?
- dragonwriter 11y ago> AFAIK, for any container 'T' to be able to satisfy the Monad laws, at least one of the aforementioned three combinators must exist for the container. All three of them must, actually, since if one of them exists, all of them do (and you can define the other two in terms of the one you know.)