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#66Alternative and MonadPlus instances for ContT

jpath

The laws seem to check out and Codensity from kan-extensions has them as well.

Codensity is the same as ContT but with a universally qualified return type, so you can not do things like callCC:

newtype Codensity m a = Codensity { runCodensity :: forall b . (a -> m b) -> m b }

This is what these instances would look like:

instance (Monad m, Alternative m) => Alternative (ContT r m) where
  empty = lift empty
  ContT mx <|> ContT my = ContT $ \cont -> mx cont <|> my cont
instance (Monad m, Alternative m) => MonadPlus (ContT r m)

• jpathSat Jan 26 18:21:07 UTC 2019
  • description updated
• jpathSat Jan 26 18:36:35 UTC 2019

  Ok, actually I this does not honour the right identity of mzero, i.e: m >> mzero = mzero. E.g:

  >>> (`runContT` pure) $ ContT $ \_ -> pure () :: Maybe ()
  Just ()

  Alternative does not have that law though, so that would still be possible. But if you do not want a type that is both a Monad and an Alternative but not a MonadPlus I would understand that.

  Another question would be whether empty should be lift empty or ContT $ \_ -> empty. The former at least satisfies the left identity of mzero, but the latter does not require a Monad constraint on m.

• jpathSat Jan 26 18:37:02 UTC 2019
  • description updated
• jpathSat Jan 26 18:39:11 UTC 2019

  That should have been

  >>> (`runContT` pure) $ (ContT $ \_ -> pure ()) >> mzero :: Maybe ()
  Just ()

• jpathSat Jan 26 18:51:28 UTC 2019
  • status set to closed

  Closing this issue, as I think these instances are not well behaved enough. Even for Alternative I would expect fa *> mzero = mzero, even if it is not stated in the laws.