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 input = evalState (runKleisli al input) s
execTest :: Test input output -> input -> IO output
execTest t = runKleisli $ unPlus $ alMap (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

module Control.Arrow.Mix.Category

data (a :+ b) input output

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

Instances

Arrow a => AlFunctor (:+ a)

Arrow a => AlMonad (:+ a)

(Arrow a, Arrow b) => Arrow (:+ a b)

(Arrow a, ArrowChoice b) => ArrowChoice (:+ a b)

(Arrow a, ArrowLoop b) => ArrowLoop (:+ a b)

(Arrow a, Arrow b) => Category (:+ a b)

liftImpure :: (ArrowChoice a, ArrowLoop a, Arrow b) => a :~> (a :+ b)

We can lift impure arrows

liftPure :: (Arrow a, Arrow b) => b :~> (a :+ b)

Pure arrows can be lifted too

unPlus :: 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 alMap), we can reduce the type a :+ (->) to a.

unPlus' :: 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.

plusTwist :: (Arrow a, AlFunctor f, Arrow c) => (a :+ f c) :~> f (a :+ c)

(:+) is right commutative-associative: a :+ (b :+ c) and b :+ (a :+ c) can be reduced to one another with plusTwist function

plusAssoc :: (Arrow a, Arrow b, Arrow c) => (a :+ (b :+ c)) :~> ((a :+ b) :+ c)

(:+) is also associative

plusCommute :: (Arrow a, ArrowChoice b, ArrowLoop b) => (a :+ b) :~> (b :+ a)

this function is experimental - no idea about how this would interact with other arrow combinators and functions defined in this module