Re: [containers] Proposal: Add traverseKeys, traverseKeysWith, traverseKeysMonotonic to Data.Map

Hi, On Tue, Mar 11, 2014 at 9:38 PM, Edward Kmett wrote:

What does it mean to talk about a monotonic function with Applicative side-effects (a -> f b) in this setting?

I'm not able to determine how laws for such a beast work.

Would a definition like the below help? A function (m :: a -> f b) is monotonic iff for all finite (xs :: [a]), the following two expressions are equivalent: isMonotonic <$> traverse (\x -> (x,) <$> m x) xs True <$ traverse (\x -> (x,) <$> m x) xs where isMonotonic :: (Ord a, Ord b) => [(a, b)] -> Bool isMonotonic xs = and $ zipWith (<=) sorted (drop 1 sorted) where sorted = sortBy (compare `on` fst) xs -- Takano Akio