mix-arrows-1.0: Mixing effects of one arrow into another one

Control.Arrow.Mix

Description

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
```

Synopsis

# Documentation

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

We can lift impure arrows

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

Pure arrows can be lifted too

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

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) :~> aSource

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 :\$~ bSource

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