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mapM_ needs work
It should not be defined on top of mapM as that requires O(n) stack space.
It should also require an Applicative constraint, not a Monad.
You mean sequenceA_ ? Or do you mean going away from base's legacy API and providing only one set of function compatible to the most common denominator between Applicative and Monad (i.e. Applicative, since Monad implies Applicative now a day)?
hmm Looks like I need to spend more time reading your blog posts: http://neilmitchell.blogspot.ch/2015/09/making-sequencemapm-for-io-take-o1-stack.html
Should probably also be in Foldable not Mappable. And should Foldable should be a superclass of Mappable. And should Mappable just be Traversable.