Control.Arrow.Mix

We try to mix effects of two completely unrelated arrows a and b, where b is considered pure, and a — impure. Probably the most common use case would be a = Kleisli IO. We perform all the pure calculations first, and do the impure ones later.

Usage example:

newtype Test input output = Test {runTest :: (Kleisli IO :+ Kleisli (State String)) input output}
    deriving (Category, Arrow, ArrowChoice, ArrowLoop)

runStateMorphism :: s -> Kleisli (State s) :~> (->)
runStateMorphism s al i_input = evalState (runKleisli al i_input) s
execTest :: Test input output -> input -> IO output
execTest t = runKleisli $ unMix $ alMap (const $ runStateMorphism "") $ runTest t

rd = Test {runTest = liftImpure $ Kleisli $ const getLine}
wr = Test {runTest = liftImpure $ Kleisli putStrLn}
gt = Test {runTest = liftPure $ Kleisli $ const get}
pt = Test {runTest = liftPure $ Kleisli put}

test =
    proc () ->
        do line <- rd -< ()  -- effect from IO
           pt -< line        -- effect from State
           line' <- gt -< () -- effect from State
           wr -< line'       -- effect from IO

Documentation

liftImpure :: (ArrowChoice a, ArrowLoop a, Arrow b) => a input output -> (a :+ b) input output

We can lift impure arrows

liftPure :: (Arrow a, Arrow b) => b input output -> (a :+ b) input output

Pure arrows can be lifted too

unMix :: Arrow a => (a :+ (->)) :~> a

We need some way to extract the real computation from this :+; fortunately, if we manage to reduce the pure arrow to a function (using alongMap), we can reduce the type a :+ (->) to a.

unMix' :: Arrow a => (a :+ a) :~> a

If, for some reason, the pure arrow is, in fact, as impure as the impure one, we still can extract the real computation.

type :+ a b = Mix a :$~ b

a :+ b is an arrow incapsulating both a and b effects. It's functorial (and even monadic) in b.

module Control.Arrow.Mix.Category

module Control.Arrow.Mix.Utilities