Ross Paterson
Many computations ignore their input value. You can recognize them by their type: [...]
Inspection of types is not allowed with GHC's constraint-based type checker, which rules out things like this.
Too bad. Would it be possible to get rid of "-< ()"?
## returnA
We don't need it anymore, and it has quite a stupid definition. Get rid of it in favor of 'id'.
It would be reasonable to redefine returnA = id
Yes, that would be a good start. For many applications using 'id' instead of 'arr id' gives a huge performance boost. In my particular case (I'm doing wire-based FRP (WFRP)) I often start with a complex "sum" network of categorical computations: c1 . c2 <|> c3 . c4 . (c5 <|> c6) <|> c7 The distinguishing feature of WFRP, what makes it so fast, is that you can get rid of complexity by recognizing 'id' and 'empty' when they pop up. The component computations can "morph" into them over time, for example for 3 is identity-like for three seconds and then switches to 'empty'. You can recognize and discard entire subnetworks quickly.
## Operators
I often need to mix regular arguments with computation arguments in banana notation:
let f c = f' x y c z (| f (comp -< v) |)
This wouldn't be legal if f was defined inside the proc. If the arguments come from outside the proc, you could write (permuting the arguments)
(| (f x y z) (comp -< v) |)
If they're defined inside the proc, you'd have something like
(| f (comp -< v) |) x y z
Of course, and that's the inconvenient part. You have to write wrapper functions. It would be nice, if the bananas would consider unparenthesized expressions as regular arguments.
## PreArrow
All sensible arrows form a family of functors:
instance (Arrow a) => Functor (a b) where fmap f = (arr f .)
But they do more: Every arrow is a profunctor as defined in the 'profunctors' package:
instance (Arrow a) => Profunctor a where lmap f = (. arr f) rmap = fmap
That's just what you called PreArrow,
Not so: every arrow has lmap and rmap, but not everything that has an lmap also has an rmap.
I see. You want to get rid of 'arr' altogether. On one hand that is desirable. On the other hand for arrows lmap and rmap are equivalent. You can define 'arr' given 'lmap': arr f = lmap f id From that you can define fmap. This leads to the conclusion that as soon as the arrow notation does more than simple composition you need a functor anyway.
## Applicative
One of the main bottlenecks of arrows is the heavy tuple handling, but most (if not all) arrows form a family of applicative functors. I noticed a huge speedup by moving from arrow style to applicative style where possible:
liftA2 (+) (lmap f c) (fmap g d)
is often much faster than:
arr (uncurry (+)) . (c . arr f &&& arr g . d)
Besides being more readable it sometimes improved the performance of my code by an order of magnitude. So perhaps check to see if the category forms an applicative functor. If it does, you can get along without Arrow entirely.
In fact I propose to generalize all the Arrow* classes to Category* classes.
That sounds reasonable. It's convenient to use simpler classes instead of Arrow where possible, but it's not always possible.
The idea is this: If there are both Arrow and Applicative instances (can you check this?), the arrow notation could use applicative combinators instead of arrowic ones where possible: proc x' -> do f <- comp1 -< x' x <- comp2 -< x' comp3 -< f x If this is possible, arrow notation would likely rewrite it to comp3 . ((\f x -> f x) <$> comp1 <*> comp2) and, as a nice bonus, recognize that \f x -> f x is really just id and optimize the fmap away: comp3 . (comp1 <*> comp2) The pattern is: A computation composed of subcomputations where each of them takes the same arrow variable as input. The corresponding arrow version is unnecessarily expensive because of the tuple wrapping and unwrapping, comp3 . arr (\(f, x) -> f x) . comp1 &&& comp2 whereas the applicative version is really straightforward and fast. Greets, Ertugrul -- Not to be or to be and (not to be or to be and (not to be or to be and (not to be or to be and ... that is the list monad.