Off the top of my head, I can't think of anything about sequence or sequenceA to justify their existence as class methods from the standpoint of practical programming. I could imagine they might be helpful to beginners who may find it easier to think about a container full of actions than about a container full of elements and a function that can be applied to them to get actions. But it's also not clear to me that removing methods is very valuable unless either:

1. We get down to just one method, which can be good for performance with non-regular types, or

2. We end up with a class that works with GND/DerivingVia, such as

  class (Foldable t, Functor t) => Traversable t where
    mapTraverse :: Applicative f => (t b -> r) -> (a -> f b) -> t a -> f r

The one-method bonus can generally be worked around with auxiliary classes in the rare cases where it comes up, so I wouldn't worry about that too much here.

On Sat, Nov 7, 2020, 9:47 PM Carter Schonwald <carter.schonwald@gmail.com> wrote:
Yeah, mapM is semantically different from traverse.  So dropping mapm seems ill advised.  

@david: is there an analogue for sequence?

On Sat, Nov 7, 2020 at 5:15 PM David Feuer <david.feuer@gmail.com> wrote:
In light of this example, I oppose the proposal.

On Sat, Nov 7, 2020, 5:04 PM David Feuer <david.feuer@gmail.com> wrote:
I don't know about measurements or anything. There are certainly *implementation strategies* for mapM that don't translate well to traverse. Imagine a queue, for example. One way to write mapM is this:

mapM f = go empty
  where
    go !acc xs = case uncons xs of
       Just (x, xs') -> do
         y <- f x
         go (acc `snoc` y)
       Nothing -> pure acc

There's no way to do anything operationally equivalent with just Applicative.

Is this a good way to write it? Well, that presumably depends on the queue and on the Monad, but I'd give it a good "possibly".

On Sat, Nov 7, 2020, 3:42 PM A S <masaeedu@gmail.com> wrote:
> Personally I would love to know of some kind of reasoning regarding these things, as I'm not aware of any! (efficiency of Applicative vs Monad based functions)

I agree. I'd be very interested in seeing an example (contrived or otherwise) of a specific Monad which is necessarily more efficient to `mapM` over some arbitrarily selected Traversable container than to `traverse`. That would be a good first step I think.

On Sat, Nov 7, 2020 at 3:29 PM Georgi Lyubenov <godzbanebane@gmail.com> wrote:
Hi!

Regarding the "there can be no instance for which mapM is more efficient than traverse":
There have been issues with Applicative functions leaking memory where Monad ones aren't in Polysemy - some of these have been fixed, but it's not clear that there are none left.
There is also this claim in parser-combinators:

> Due to the nature of the Applicative and Alternative abstractions, they are prone to memory leaks and not as efficient as their monadic counterparts. Although all the combinators we provide in this module are perfectly expressible in terms of Applicative and Alternative, please prefer Control.Monad.Combinators instead when possible.

I have not verified it, but it is a bit worrying.

Personally I would love to know of some kind of reasoning regarding these things, as I'm not aware of any! (efficiency of Applicative vs Monad based functions)


======
Georgi
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