haskell - Can a monad be a comonad? -


i know monad is. think have correctly wrapped mind around comonad is. (or rather, 1 is seems simple enough; tricky part comprehending what's useful this...)

my question is: can monad and comonad?

i foresee 2 possible answers:

  • yes, common , useful.
  • no, such different jobs there no reason want both.

so, it?

yes. turning comments answer:

newtype identity = identity {runidenity :: a} deriving functor instance monad identity   return = identity   join = runidentity instance comonad identity   coreturn = runidentity   cojoin = identity

reader , writer exact duals, shown by

class comonoid m   comempty :: (m,a) ->   comappend :: m -> (m,m) --every haskell type comonoid --that because cccs boring!  instance monoid => monad ((,) a)   return x = (mempty,x)   join (a,(b,x)) = (a <> b, x) instance comonoid => comonad ((,) a)   coreturn = comempty   cojoin = associate . first comappend  instance comonoid => monad ((->) a)   return = flip (curry comempty)   join f = uncurry f . comappend instance monoid => comonad ((->) a)    coreturn f = f mempty   cojoin f b = f (a <> b)

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