D’oh, that’s what I get for writing untested code in an email.

Neutral doesn’t seem necessary since we have “null” in Foldable. I was thinking more along these lines:

instance (Alternative f, Foldable f) => Alternative (LeftBiased f) where

  empty = LeftBiased empty

  LeftBiased a <|> LeftBiased b = LeftBiased (if null a then b else a)

Under the assumption that “null empty” always holds. I think using the Alternative constraint for just “empty” makes sense because LeftBiased and RightBiased should only differ from the wrapped type in the implementation of (<|>), but it still seems a little iffy somehow.

To make the wrapping slightly less painful, another good bikeshed colour would be Pre/Post. (Dunno what you’d call “Unbiased” in that case, though.)

On a related note, I recall there was some discussion a while back about making a Monoid instance for Map where mappend is “unionWith mappend” instead of the left-biased “union”. These wrappers could also be used for that sort of thing, and it’d be nice to have a single standard for them with all the different use cases fleshed out.

On Sat, May 6, 2017 at 4:19 PM, MarLinn <monkleyon@gmail.com> wrote:

On 2017-05-07 00:23, Jon Purdy wrote:

I’ve wanted this before as well. Maybe we should throw a newtype at it?

newtype LeftBiased a = LeftBiased [a]

instance Alternative (LeftBiased a) where

  empty = []

  [] <|> b = b

  a <|> _ = a

newtype RightBiased a = RightBiased [a]

instance Alternative (RightBiased a) where

  empty = []

  a <|> [] = a

  _ <|> b = b

You forgot the fun wrapping and unwrapping. But no matter. Let's generalize!

	class Neutral a where
	    neutral :: a
	    isNeutral :: a -> Bool

	instance Neutral a => Alternative (LeftBiased  a) where
	    empty = LeftBiased neutral
	    (LeftBiased  a) <|> (LeftBiased  b) = LeftBiased  $ if isNeutral a then b else a

	instance Neutral a => Alternative (RightBiased a) where
	    empty = RightBiased neutral
	    (RightBiased a) <|> (RightBiased b) = RightBiased $ if isNeutral b then a else b

Why?

	type AllRight e a = LeftBiased  (Either e a)
	type AnyRight e a = RightBiased (Either e a)

	instance Neutral a => Neutral (AllRight e a) where
	    neutral = Right $ LeftBiased  neutral
	    isNeutral = fmap isRight

	instance Neutral e => Neutral (AnyRight e a) where
	    neutral = Left  $ RightBiased neutral
	    isNeutral = fmap isLeft

Is this a bit silly? Yes. My actual goal is to show that these concepts are bigger than they might appear, and how painful all those wrappers are. This is to advertise my language extension from my separate thread. And also because it's silly fun. Mostly that.

newtype Unbiased a = Unbiased (Maybe a)

instance (Monoid m) => Alternative (Unbiased m) where

  empty = Nothing

  Just a <|> Just b = Just (a <> b)

  _ <|> Just b = Just b

  Just a <|> _ = Just a

  _ <|> _ = Nothing

Mh, that's just liftA2 (<>) a b <|> a <|> b in terms of the regular instance. Now that is easy to generalize – just don't use it for lists.

Cheers,
MarLinn

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