[Haskell-cafe] monad . comonad = id
jac at informatik.uni-kiel.de
Fri May 8 07:44:51 EDT 2009
On 08.05.2009, at 13:14, Miguel Mitrofanov wrote:
>> 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.
> That's not true.
I thought there is some kind of duality between monads and comonads in
category theory. Does this "only" refer to the types of the functions
or am I totally wrong here?
>> 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))
> First of all, this is NOT a comonad. The term "comonad" doesn't
> refer just to instances of Comonad class, it refers to instances
> that satisfy several laws.
I am aware of this. I thought it does satisfy all the laws. Which one
have I missed?
> Secondly, "" is a monad, and there is an instance of Monad class
> for it. It's working; don't fix it.
I am also aware of this. Perhaps I should have used a data type like
data Pointed a = Pointed a [a]
but in this case a corresponding duplicate implementation is more
I am very sorry if have asked a stupid question.
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