I’ve been playing around with an Arrow concept, which to my knowledge is original. I’ve decided to call this a FactoryArrow:

newtype FactoryArrow m n a b = FactoryArrow { runFactory :: m (Kleisli n a b) }

Where m and n are Monads. m is a single-pass initialization monad, while n is a multiple-pass working monad. The arrow supports all of the standard accessory arrow typeclasses, including ArrowLoop if n implements MonadFix, and ArrowApply if m and n are the same.

This arrow simply captures a two-phase initialize-and-run design pattern.

To the best of my imagination, there cannot be a corresponding useful FactoryMonad. I would be extremely interested if anyone can contradict me on that point.

My current interest is in using the FactoryArrow as a replacement for the mealy-style arrows by using IORefs (or potentially even STM transaction variables) to store automaton states instead of unevaluated thunks.

The corresponding implementation as of the time of this writing.

2 thoughts on “FactoryArrow

  1. Any Arrow wrapped in an Applicative gives another arrow

    newtype ApArrow f (~>) a b = ApArrow { runApArrow :: f (a ~> b) }

    Since every Monad is also an Applicative functor, your FactoryArrow m n = ApArrow m (Kleisli n)

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