On 01/11/13 11:42, Nathan van Doorn wrote:
Proposal: add the following laws to the documentation of Control.Applicative.Alternative:
* empty <*> a = empty * f <*> empty = empty
These laws correspond to the laws given in MonadPlus- if you take mzero = empty and ap = (<*>), the ones in MonadPlus imply these- and I don't think this proposal should be too controversial.
As far as I can see, the documentation for MonadPlus does not specify these laws anywhere [1,2]. Consider the IO monad. These laws claim that launchMissiles *> fail "empty" = fail "empty" This is clearly *not* true. -- If we add laws, I think we should first consider the much more reasonable monoid laws identity empty <|> a = a a <|> empty = a associativity: (a <|> b) <|> c = a <|> (b <|> c) In the MonadPlus world, the controversial part is the choice between left distribution (f <|> g) <*> a = (f <*> a) <|> (g <*> a) or left catch pure a <|> b = pure a Your proposal would be left zero empty <*> a = empty right zero f <*> empty = empty And as mentioned above, right zero is problematic. The fmap version should be okay though map zero f <$> empty = empty Twan [1] http://hackage.haskell.org/package/base-4.6.0.1/docs/Control-Monad.html#t:Mo... [2] http://www.haskell.org/haskellwiki/MonadPlus