Conversion between Automaton and StateArrow

StateAutoConversion.hs

{-# LANGUAGE GADTs #-}

module StateAutoConversion(fromAutomaton, toAutomaton, StateResult(StateResult)) where

import Prelude hiding (id, (.))

import Control.Category
import Control.Arrow

import Control.Arrow.Transformer
import Control.Arrow.Operations
import Control.Arrow.Transformer.State
import Control.Arrow.Transformer.Automaton

data StateResult a b c where
  StateResult :: StateArrow s a b c -> s -> StateResult a b c

fromAutomaton :: (ArrowApply a) => Automaton a b c -> StateResult a b c
fromAutomaton f = StateResult s f
  where s = StateArrow $ rejig ^>> app
        rejig ~(x, Automaton a) = (a, x)

toAutomaton :: (ArrowLoop a) => StateResult a b c -> Automaton a b c
toAutomaton (StateResult sa b) = loop (lift (runState sa) . second (delay b))