Converting Monad notation to Arrow notation

Question

I\'m trying to understand arrow notation, in particularly how it works with Monads. With Monads I can define the following:

f = (*2)
g = Just 5 >>= (return         


        

Answer 1

First we need an arrow with the same semantics as the Maybe monad. We could define it from scratch, but the easiest way is to wrap the Maybe monad into Kleisli:

type MaybeArrow = Kleisli Maybe

Then we'll also need a way how to run this monad to extract the result:

runMaybeArrow :: MaybeArrow () a -> Maybe a
runMaybeArrow = flip runKleisli ()

Also it'll be handy to have a way how to create a constant arrow from a given value (which just ignores its input):

val :: (Arrow a) => c -> a b c
val = arr . const

And finally, we get:

g' = runMaybeArrow (val 5 >>> arr f)