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|
{-# LANGUAGE CPP #-}
{-# LANGUAGE FlexibleInstances #-}
-----------------------------------------------------------------------------
-- |
-- Module : Control.Arrow.Transformer.Automaton
-- Copyright : (c) Ross Paterson 2003
-- License : BSD-style (see the LICENSE file in the distribution)
--
-- Maintainer : R.Paterson@city.ac.uk
-- Stability : experimental
-- Portability : non-portable (multi-parameter type classes)
--
-- Simple Mealy-style automata.
module Control.Arrow.Transformer.Automaton(
Automaton(Automaton), runAutomaton,
) where
import Control.Arrow.Internals
import Control.Arrow.Operations
import Control.Arrow.Transformer
import Control.Applicative
import Control.Arrow
import Control.Category
import Data.Monoid
#if (MIN_VERSION_base(4,9,0)) && !(MIN_VERSION_base(4,11,0))
import Data.Semigroup
#endif
import Data.Stream
import Prelude hiding (id,(.))
-- | An arrow type comprising Mealy-style automata, each step of which is
-- is a computation in the original arrow type.
newtype Automaton a b c = Automaton (a b (c, Automaton a b c))
instance Arrow a => ArrowTransformer Automaton a where
lift f = c
where
c = Automaton (f &&& arr (const c))
instance Arrow a => Category (Automaton a) where
id = lift id
Automaton f . Automaton g =
Automaton (arr (\((z, cf), cg) -> (z, cf . cg)) . first f . g)
instance Arrow a => Arrow (Automaton a) where
arr f = lift (arr f)
first (Automaton f) =
Automaton (first f >>>
arr (\((x', c), y) -> ((x', y), first c)))
second (Automaton f) =
Automaton (second f >>>
arr (\(x, (y', c)) -> ((x, y'), second c)))
Automaton f1 *** Automaton f2 =
Automaton ((f1 *** f2) >>>
arr (\((x', c1), (y', c2)) -> ((x', y'), c1 *** c2)))
Automaton f1 &&& Automaton f2 =
Automaton ((f1 &&& f2) >>>
arr (\((x1, c1), (x2, c2)) -> ((x1, x2), c1 &&& c2)))
instance ArrowChoice a => ArrowChoice (Automaton a) where
left (Automaton f) = left_f
where
left_f = Automaton (left f >>> arr combine)
combine (Left (y, cf)) = (Left y, left cf)
combine (Right z) = (Right z, left_f)
right (Automaton f) = right_f
where
right_f = Automaton (right f >>> arr combine)
combine (Left z) = (Left z, right_f)
combine (Right (y, cf)) = (Right y, right cf)
Automaton f1 +++ Automaton f2 =
Automaton ((f1 +++ f2) >>> arr combine)
where
combine (Left (x, c)) = (Left x, c +++ Automaton f2)
combine (Right (x, c)) = (Right x, Automaton f1 +++ c)
Automaton f1 ||| Automaton f2 =
Automaton ((f1 +++ f2) >>> arr combine)
where
combine (Left (x, c)) = (x, c ||| Automaton f2)
combine (Right (x, c)) = (x, Automaton f1 ||| c)
instance ArrowZero a => ArrowZero (Automaton a) where
zeroArrow = Automaton zeroArrow
instance ArrowPlus a => ArrowPlus (Automaton a) where
Automaton f <+> Automaton g = Automaton (f <+> g)
-- Circuit combinators
instance ArrowLoop a => ArrowLoop (Automaton a) where
loop (Automaton f) =
Automaton (loop (f >>>
arr (\((x, y), cf) -> ((x, loop cf), y))))
instance ArrowLoop a => ArrowCircuit (Automaton a) where
delay x = Automaton (arr (\x' -> (x, delay x')))
-- Other instances
instance Arrow a => Functor (Automaton a b) where
fmap f g = g >>> arr f
instance Arrow a => Applicative (Automaton a b) where
pure x = arr (const x)
f <*> g = f &&& g >>> arr (uncurry id)
instance ArrowPlus a => Alternative (Automaton a b) where
empty = zeroArrow
f <|> g = f <+> g
#if MIN_VERSION_base(4,9,0)
instance ArrowPlus a => Semigroup (Automaton a b c) where
(<>) = (<+>)
#endif
instance ArrowPlus a => Monoid (Automaton a b c) where
mempty = zeroArrow
#if !(MIN_VERSION_base(4,11,0))
mappend = (<+>)
#endif
-- runAutomaton (Automaton f) = proc (e, Cons x xs) -> do
-- (y, c) <- f <- (e, x)
-- ys <- runAutomaton c -<< (e, xs)
-- returnA -< Cons y ys
-- | Encapsulating an automaton by running it on a stream of inputs,
-- obtaining a stream of outputs.
--
-- Typical usage in arrow notation:
--
-- > proc p -> do
-- > ...
-- > ys <- (|runAutomaton (\x -> ...)|) xs
--
-- Here @xs@ refers to the input stream and @x@ to individual
-- elements of that stream. @ys@ is bound to the output stream.
runAutomaton :: (ArrowLoop a, ArrowApply a) =>
Automaton a (e,b) c -> a (e,Stream b) (Stream c)
runAutomaton (Automaton f) =
arr (\(e, Cons x xs) -> ((e, x), (e, xs))) >>>
first f >>>
arr (\((y, c), (e, xs)) -> (y, (runAutomaton c, (e, xs)))) >>>
second app >>>
arr (uncurry Cons)
instance (ArrowLoop a, ArrowApply a) => ArrowAddStream (Automaton a) a where
liftStream = lift
elimStream = runAutomaton
-- other promotions
instance ArrowWriter w a => ArrowWriter w (Automaton a) where
write = lift write
newWriter (Automaton f) =
Automaton (newWriter f >>>
arr (\((c, f'), w) -> ((c, w), newWriter f')))
instance ArrowError r a => ArrowError r (Automaton a) where
raise = lift raise
tryInUnless f0@(Automaton f) s0@(Automaton s) h0@(Automaton h) =
Automaton (tryInUnless f sA hA)
where
sA = arr (\(b,(c,f')) -> ((b,c),f')) >>> first s >>>
arr (\((d,s'),f') -> (d, tryInUnless f' s' h0))
hA = h >>> arr (\(d,h') -> (d, tryInUnless f0 s0 h'))
newError (Automaton f) = Automaton (newError f >>> arr h)
where
h (Left ex) = (Left ex, newError (Automaton f))
h (Right (c, f')) = (Right c, newError f')
instance ArrowReader r a => ArrowReader r (Automaton a) where
readState = lift readState
newReader (Automaton f) =
Automaton (newReader f >>> second (arr newReader))
instance ArrowState s a => ArrowState s (Automaton a) where
fetch = lift fetch
store = lift store
-- encapsulations
instance ArrowAddWriter w a a' =>
ArrowAddWriter w (Automaton a) (Automaton a') where
liftWriter (Automaton f) =
Automaton (liftWriter f >>>
arr (\(c, f') -> (c, liftWriter f')))
elimWriter (Automaton f) =
Automaton (elimWriter f >>>
arr (\((c, f'), w) -> ((c, w), elimWriter f')))
instance ArrowAddReader r a a' =>
ArrowAddReader r (Automaton a) (Automaton a') where
liftReader (Automaton f) =
Automaton (liftReader f >>>
arr (\(c, f') -> (c, liftReader f')))
elimReader (Automaton f) =
Automaton (elimReader f >>> second (arr elimReader))
instance ArrowAddState r a a' =>
ArrowAddState r (Automaton a) (Automaton a') where
liftState (Automaton f) =
Automaton (liftState f >>>
arr (\(c, f') -> (c, liftState f')))
elimState (Automaton f) =
Automaton (elimState f >>>
arr (\((c, f'), s) -> ((c, s), elimState f')))
|
