Distributitivity of MonadPlus instance for Maybe

[DavidHarrison]

The tests brings up the following example:

x = Just (false)
y = Just (true)
x >>= f = Nothing
y >>= f = Just ("")

in the distributivity law for MonadPlus:

((x <|> y) >>= f) == ((x >>= f) <|> (y >>= f))

which evaluates to:

Nothing == Just ("")

[DavidHarrison]

Also brought up by the tests is:

x = Just ("")
mempty <> x = Nothing

for the left identity law of Monoid:

mempty <> x == x

If I understand correctly, (<>) and (<|>) are the same for Maybe.

[paf31]

mempty should be Just mempty for Maybe. Is it not?

Sent from my iPhone

On Jul 5, 2015, at 6:31 PM, David Harrison notifications@github.com wrote:

Also brought up by the tests is:

x = Just ("") mempty <> x = Nothing for the left identity law of monoid:

mempty <> x == x If I understand correctly, (<>) and (<|>) are the same for Maybe.

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[DavidHarrison]

purescript-maybe defines Monoid as:

instance monoidMaybe :: (Semigroup a) => Monoid (Maybe a) where
  mempty = Nothing

Changing that would resolve the issue for monoids, though I'm not sure how it works with McBride's view of the instance, the current behavior for the First wrapper in Haskell, which has the monoid instance:

instance Monoid (First a) where
        mempty = First Nothing
        First Nothing `mappend` r = r
        l `mappend` _             = l

For the MonadPlus instance, Haskell has the same behaviour. It seems that MonadPlus for Maybe and IO do not satisfy Left Distribution, but instead Left Catch.

[hdgarrood]

If we had mempty = Just mempty, then we'd need a stronger constraint of Monoid a for the Monoid (Maybe a) instance. That's not necessarily a problem but I would like to have some way of making a Semigroup (which is not a Monoid) into a Monoid by adding an extra element to act as the identity.

[hdgarrood]

Also: shall we add tests from purescript-quickcheck-laws to the tests of libraries like purescript-maybe, so that we don't get caught out by things like these again?

[garyb]

We can't do that without introducing circular dependencies. @paf31 and I have argued a bit over that in the past, as to me, devDependencies aren't real dependencies, but you do need a slight hack of having to delete purescript-maybe from bower_components after bower installing.

Alternatively you need a separate test project inside this project, with its own bower.json, but then it's a hassle to keep things up to date between both sets of dependencies, etc. It's probably less bad now we're using npm scripts to do build stuff, but I dunno.

[hdgarrood]

aww yeah: purescript/purescript-maybe#13

[garyb]

Looks like we fixed this at some point, I think by changing (<|>).