2 ms·

I'm not sure what I said that you are disagreeing with, but it's not clear to me that "monad" is strictly an adjective like "red". My understanding is that a m

I'm not sure what I said that you are disagreeing with, but it's not clear to me that "monad" is strictly an adjective like "red". My understanding is that a monad is a data type paired with a properly implemented bind and return (proper in the sense of obeying the monadic laws)... much like a monoid is a tuple with a binary operation and an identity element, a monad is a triple of bind, return, and the data structure. In a practical sense, I find myself saying "this behaves like a monad" rather than "this is a monad" or "this is monadic" (although that last one is an adjective like you say). Once you recognize the that something behaves monadically, you are free to write the plumbing (bind and return) and use the abstraction if you wish. Then again, I'm not a mathematician by any stretch of the imagination, and it's entirely possible I just completely missed the point you were trying to make. Just throwing out my thoughts.

jrockway 17y ago
I think we are saying the same thing. A monad is not a "nuclear waste container" or a "spacesuit". Nuclear waste containers and spacesuits could be monads. But "a implies b" does not mean "b implies a", and that's where people get confused. Anyway, I think what I am trying to say is that the problem is a grammar issue, rather than a programming issue or a mathematical issue. Monads are easy to grasp in terms of math or programming. They are apparently quite difficult to explain, however.
tel 17y ago
A list (for instance) is not a monad. A list plus appropriately defined unit_list and bind_list together form a tuple which is a monad. That's the 'is a' sense of monads. When you refer to a list itself, it's easier to think of it as having the adjective "monaded" since unit and bind are defined even if you don't usually carry them around with you. A list is a monad/has the properties of a monad because the appropriate definitions of unit and bind both can exist and are written.
- eru 17y ago
  And there are at least two sensible ways to make lists a Monad.
  - tel 17y ago
    Which just reinforces the fact that a monad is the collection of (<container>, bind, unit).

jrockway 17y ago

I think we are saying the same thing. A monad is not a "nuclear waste container" or a "spacesuit". Nuclear waste containers and spacesuits could be monads. But "a implies b" does not mean "b implies a", and that's where people get confused. Anyway, I think what I am trying to say is that the problem is a grammar issue, rather than a programming issue or a mathematical issue. Monads are easy to grasp in terms of math or programming. They are apparently quite difficult to explain, however.

tel 17y ago

A list (for instance) is not a monad. A list plus appropriately defined unit_list and bind_list together form a tuple which is a monad. That's the 'is a' sense of monads. When you refer to a list itself, it's easier to think of it as having the adjective "monaded" since unit and bind are defined even if you don't usually carry them around with you. A list is a monad/has the properties of a monad because the appropriate definitions of unit and bind both can exist and are written.

eru 17y ago
And there are at least two sensible ways to make lists a Monad.
- tel 17y ago
  Which just reinforces the fact that a monad is the collection of (<container>, bind, unit).