[Haskell-cafe] Applicative functors with branch/choice ?

[Евгений Пермяков]

Let assume, that some computation takes argument and produces value 
Either a b. This computation may be represented in for different forms

====
computePure :: a -> Either b c

computeMonad :: a -> m (Either b c)

computeApplicative :: app a -> app (Either b c)

computeArrow :: arr a (Either b c)
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And now, having result, we need to execute several actions, making a 
choice, what actions to perform for Left and Right tags of Either. Pure 
function and monads are easy, as there is way to pattern-match on value 
and take actions depending on result. There is an extension to Arrow 
class that do the job -- ArrowChoice. However, I cannot find any way to 
make choice for Applicative. It seems that both Applicative and 
Alternative are not suited for it.

So, it seems for me, that Applicative API should be extended with 
typeclass for making choice what actions to execute depending on result 
of some test (pattern matching). Is there any reasonable definition of 
such typeclass or clear explanation, why such typeclass is unneeded?

The possible extension may look somehow like this:

class Applicative a => Branching a where
  branch :: a (Either b c) -> (a b -> a d) -> (a c -> a d) -> a d