Provide Arrow lift functions for Control.Arrow

It is currently difficult to build complex datastructures by combining arrows, because there are no lift functions defined on Arrow. These can be built easily from the class functions:

liftArrow :: Arrow a => (c -> d) -> a b c -> a b d
liftArrow = (^>>)
liftArrow2 :: Arrow a => (c -> c' -> d) -> a b c -> a b c' -> a b d
liftArrow2 f a1 a2 = arr (\a -> (a, a)) >>> (a1 *** a2) >>> arr (\(a, b) -> f a b)
liftArrow3 :: Arrow a => (c -> c' -> c'' -> d) -> a b c -> a b c' -> a b c'' -> a b d
liftArrow3 f a1 a2 a3 = arr (\a -> (a, (a, a))) >>> (a1 *** a2 *** a3) >>> arr (\(a, (b, c)) -> f a b c)
liftArrow4 :: Arrow a => (c -> c' -> c'' -> c''' -> d) -> a b c -> a b c' -> a b c'' -> a b c''' -> a b d
liftArrow4 f a1 a2 a3 a4 = arr (\a -> (a, (a, (a, a)))) >>> (a1 *** a2 *** a3 *** a4) >>> arr (\(a, (b, (c, d))) -> f a b c d)
liftArrow5 :: Arrow a => (c -> c' -> c'' -> c''' -> c'''' -> d) -> a b c -> a b c' -> a b c'' -> a b c''' -> a b d
liftArrow5 f a1 a2 a3 a4 a5 = arr (\a -> (a, (a, (a, (a, a))))) >>> (a1 *** a2 *** a3 *** a4 *** a5) >>> arr (\(a, (b, (c, (d, e)))) -> f a b c d e)

I suggest these be added to Control.Arrow.

elliott suggested (on #haskell on Freenode) that something like arr2 = arr . uncurry could be defined as a building block, from which the lift functions could be defined.

Trac metadata

Trac field	Value
Version	7.2.1
Type	FeatureRequest
TypeOfFailure	OtherFailure
Priority	normal
Resolution	Unresolved
Component	libraries/base
Test case
Differential revisions
BlockedBy
Related
Blocking
CC
Operating system
Architecture