mix-arrows-0.1: 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 :: Mix (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 \$ arrCancelUnitFst \$ unMix \$ alongMap (runStateMorphism "") \$ runTest \$ first 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

data Mix a b input output Source

`Mix a b` is an arrow incapsulating both `a` and `b` effects. It's functorial in `b`.

Instances

 AlongMap (Mix a) (Arrow a, Arrow b) => Arrow (Mix a b) (Arrow a, ArrowChoice b) => ArrowChoice (Mix a b) (Arrow a, ArrowLoop b) => ArrowLoop (Mix a b) (Arrow a, Arrow b) => Category (Mix a b)

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

We can lift impure arrows

liftPure :: (Arrow a, Arrow b) => b :~> Mix a bSource

Pure arrows can be lifted too

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

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

unMix' :: Arrow a => Mix 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.