[Haskell-cafe] monad . comonad = id
miguelimo38 at yandex.ru
Fri May 8 07:54:37 EDT 2009
Seems like I was wrong. It does satisfy comonad laws. Sorry.
However, the "duality" of monads and comonads isn't that simple. A comonad is actually a monad itself, but in different category. It has nothing
to do with inverse functions etc.
Jan Christiansen wrote on 08.05.2009 14:47:
> I have a question regarding the connection between monads and comonads.
> I always thought of the comonad operations as being the inverse
> operations of the corresponding monad functions. As I do not know the
> underlying theory I thought I simply ask the masters.
> Is there a formal verification for this intuition? That is, are there
> always corresponding instances for monad and comonad such that the
> following laws are satisfied?
> extract . return == id
> join . duplicate == id
> If this is the case I would like to know what the corresponding monad
> for the following comond could be. This comonad treats lists as pointed
> sets where the first element is focused.
> instance Comonad  where
> extract = head
> duplicate xs = init (zipWith (++) (tails xs) (inits xs))
> Obviously we can define return x = [x]. But I do not know how to define
> Cheers, Jan
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