Discussion: traversing roots and leaves
My proposal to move liftA2 into the Applicative class should help get fmaps out of internal nodes in traverse implementations. But there are still two trouble spots: 1. The smaller trouble spot is at the root, when dealing with newtype wrappers. For example, the simplest way to write traverse for Data.Sequence.Seq would be instance Traversable Seq where traverse f (Seq xs) = Seq <$> traverse f xs The extra fmap may not be free. Today, the only fix is to manually inline the definition of the underlying traversal and manually fuse the fmaps. It works, but it's gross! We could work around this easily using an extra Traversable method: mapTraversed :: Applicative f => (t b -> r) -> (a -> f b) -> t a -> f r but that wouldn't help with the larger problem below. 2. Leaves are really painful. Data structures that store at most one element per leaf make obvious traversals expensive. For example, in Data.Map, the obvious implementation would be instance Traversable (Map k) where traverse _ Tip = pure Tip traverse f (Bin s k v l r) = liftA3 (Bin s k) (f v) (traverse f l) (traverse f r) The trouble is that we would generate a slew of `pure Tip`s that we'd then have to combine. For instance, (Bin 1 k v Tip Tip) would give liftA3 (Bin 1 k) (f v) (pure Tip) (pure Tip) Today we work around this by looking ahead at the children of the element we're considering, so we get fmap (\v' -> Bin 1 k v' Tip Tip) (f v) instead, which is still pretty lousy but better. It makes me rather sad to have to write disgustingly ugly Traversable instances just to avoid silly performance issues like this. Does anyone have an idea for fixing (2), and ideally simultaneously taking care of (1)? Thanks, David Feuer
On 2017-01-19 02:57 PM, David Feuer wrote:
2. Leaves are really painful. Data structures that store at most one element per leaf make obvious traversals expensive. For example, in Data.Map, the obvious implementation would be
instance Traversable (Map k) where traverse _ Tip = pure Tip traverse f (Bin s k v l r) = liftA3 (Bin s k) (f v) (traverse f l) (traverse f r)
The trouble is that we would generate a slew of `pure Tip`s that we'd then have to combine. For instance, (Bin 1 k v Tip Tip) would give liftA3 (Bin 1 k) (f v) (pure Tip) (pure Tip)
It makes me rather sad to have to write disgustingly ugly Traversable instances just to avoid silly performance issues like this. Does anyone have an idea for fixing (2), and ideally simultaneously taking care of (1)?
I can't offer any immediate fix, but my impression of problem (2) is that it's for compiler to solve. I doesn't seem right that you should be manually enumerating all the simple cases close to the tips and inlining them explicitly. Since traverse is forcing the entire spine of the Map, there is not issue with the change in strictness. The compiler should in principle be smart enough to enumerate all possible node shapes and expand the function definitions for each of them. It would be similar to loop unrolling in some ways. Since this kind of transformation would probably be expensive at compile-time and would increase the generated code size, it should likely require a command-line option (-O2) or a pragma to activate. In short, the solution to problem #2 is to log a GHC proposal and get the burden off your shoulders.
No, I don't think so. The trouble is that GHC can't assume the Applicative
instance is valid. Optimizing this requires knowledge of things like
liftA3 f (pure x) m (pure y) = (\m' -> f x m' y) <$> m
GHC can only discover such facts when enough inlining and/or specialization
happen. Also, figuring out how close you should get to the leaves before
trying to coalesce actions may be a judgement call in some cases.
On Jan 23, 2017 3:01 PM, "Mario Blažević"
On 2017-01-19 02:57 PM, David Feuer wrote:
2. Leaves are really painful. Data structures that store at most one element per leaf make obvious traversals expensive. For example, in Data.Map, the obvious implementation would be
instance Traversable (Map k) where traverse _ Tip = pure Tip traverse f (Bin s k v l r) = liftA3 (Bin s k) (f v) (traverse f l) (traverse f r)
The trouble is that we would generate a slew of `pure Tip`s that we'd then have to combine. For instance, (Bin 1 k v Tip Tip) would give liftA3 (Bin 1 k) (f v) (pure Tip) (pure Tip)
It makes me rather sad to have to write disgustingly ugly Traversable instances just to avoid silly performance issues like this. Does anyone have an idea for fixing (2), and ideally simultaneously taking care of (1)?
I can't offer any immediate fix, but my impression of problem (2) is that it's for compiler to solve. I doesn't seem right that you should be manually enumerating all the simple cases close to the tips and inlining them explicitly.
Since traverse is forcing the entire spine of the Map, there is not issue with the change in strictness. The compiler should in principle be smart enough to enumerate all possible node shapes and expand the function definitions for each of them. It would be similar to loop unrolling in some ways.
Since this kind of transformation would probably be expensive at compile-time and would increase the generated code size, it should likely require a command-line option (-O2) or a pragma to activate.
In short, the solution to problem #2 is to log a GHC proposal and get the burden off your shoulders.
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participants (2)
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David Feuer -
Mario Blažević