{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE ExistentialQuantification #-}
{- |
Processes that use only the current and past data.
Essentially this is a data type for the 'Synthesizer.State.Signal.crochetL' function.
-}
{-
ToDo:
Causal process usually depend on the sample rate,
so we need a phantom type parameter of T for the rate.

Include ST monad for mutable arrays,
this can be useful for delay lines.
On the other hand, couldn't we also use the StorableVector.Cursor data structure
and avoid the ST monad here?
-}
module Synthesizer.Causal.Process (
   T(Cons),
   fromStateMaybe,
   fromState,
   fromSimpleModifier,
   fromInitializedModifier,

   id,
   map,
   first,
   second,
   compose,
   split,
   fanout,
   loop,

{-
   We don't re-export these identifiers
   because people could abuse them for other Arrows.

   (>>>), (***), (&&&),
   (Arrow.^<<), (Arrow.^>>), (Arrow.<<^), (Arrow.>>^),
-}

   apply,
   applyFst,
   applySnd,
   applySameType,
   applyConst,
   apply2,
   apply3,
   applyStorableChunk,

   feed,
   feedFst,
   feedSnd,
   feedGenericFst,
   feedGenericSnd,
   feedConstFst,
   feedConstSnd,

   crochetL,
   mapAccumL,
   scanL,
   scanL1,
   zipWith,
   consInit,
   chainControlled,
   replicateControlled,
   feedback,
   feedbackControlled,

   -- for testing
   applyFst',
   applySnd',
   ) where

import qualified Synthesizer.State.Signal as Sig
import qualified Synthesizer.Generic.Signal as SigG
import qualified Synthesizer.Causal.Class as Class
import qualified Synthesizer.Causal.Utility as ArrowUtil

import qualified Synthesizer.Plain.Modifier as Modifier

import qualified Data.StorableVector as SV

import Foreign.Storable (Storable, )

import qualified Control.Category as Cat
import Control.Arrow
          (Arrow(..), returnA, (<<<), (>>>), (^>>), ArrowLoop(..),
           Kleisli(Kleisli), runKleisli, )
import Control.Monad.Trans.State
          (State, runState,
           StateT(StateT), runStateT, )
import Control.Monad (liftM, )
import Control.Applicative (Applicative, liftA2, pure, (<*>), )

import Data.Tuple.HT (mapSnd, )

import qualified Algebra.Field as Field
import qualified Algebra.Ring as Ring
import qualified Algebra.Additive as Additive

import qualified Prelude as P
import Prelude hiding (id, map, zipWith, )



-- | Cf. StreamFusion  'Synthesizer.State.Signal.T'
data T a b =
   forall s. -- Seq s =>
      Cons !(a -> StateT s Maybe b)  -- compute next value
           !s                        -- initial state



{-# INLINE fromStateMaybe #-}
fromStateMaybe :: (a -> StateT s Maybe b) -> s -> T a b
fromStateMaybe :: forall a s b. (a -> StateT s Maybe b) -> s -> T a b
fromStateMaybe = forall a b s. (a -> StateT s Maybe b) -> s -> T a b
Cons

{-# INLINE fromState #-}
fromState :: (a -> State s b) -> s -> T a b
fromState :: forall a s b. (a -> State s b) -> s -> T a b
fromState a -> State s b
f =
   forall a s b. (a -> StateT s Maybe b) -> s -> T a b
fromStateMaybe (\a
x -> forall s (m :: * -> *) a. (s -> m (a, s)) -> StateT s m a
StateT (forall a. a -> Maybe a
Just forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall s a. State s a -> s -> (a, s)
runState (a -> State s b
f a
x)))

{-# INLINE fromSimpleModifier #-}
fromSimpleModifier ::
   Modifier.Simple s ctrl a b -> T (ctrl,a) b
fromSimpleModifier :: forall s ctrl a b. Simple s ctrl a b -> T (ctrl, a) b
fromSimpleModifier (Modifier.Simple s
s ctrl -> a -> State s b
f) =
   forall a s b. (a -> State s b) -> s -> T a b
fromState (forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry ctrl -> a -> State s b
f) s
s

{-# INLINE fromInitializedModifier #-}
fromInitializedModifier ::
   Modifier.Initialized s init ctrl a b -> init -> T (ctrl,a) b
fromInitializedModifier :: forall s init ctrl a b.
Initialized s init ctrl a b -> init -> T (ctrl, a) b
fromInitializedModifier (Modifier.Initialized init -> s
initF ctrl -> a -> State s b
f) init
initS =
   forall a s b. (a -> State s b) -> s -> T a b
fromState (forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry ctrl -> a -> State s b
f) (init -> s
initF init
initS)


{-
It's almost a Kleisli Arrow,
but the hidden type of the state disturbs.
-}
instance Cat.Category T where
   {-# INLINE id #-}
   {-# INLINE (.) #-}

   id :: forall a. T a a
id  = forall a s b. (a -> State s b) -> s -> T a b
fromState forall (m :: * -> *) a. Monad m => a -> m a
return ()
   . :: forall b c a. T b c -> T a b -> T a c
(.) = forall a b c. (a -> b -> c) -> b -> a -> c
flip forall a b c. T a b -> T b c -> T a c
compose

instance Arrow T where
   {-# INLINE arr #-}
   {-# INLINE first #-}
   {-# INLINE second #-}
   {-# INLINE (***) #-}
   {-# INLINE (&&&) #-}

   arr :: forall b c. (b -> c) -> T b c
arr    = forall b c. (b -> c) -> T b c
map
   first :: forall b c d. T b c -> T (b, d) (c, d)
first  = forall a0 a1 b0 b1.
(forall s.
 Kleisli (StateT s Maybe) a0 a1 -> Kleisli (StateT s Maybe) b0 b1)
-> T a0 a1 -> T b0 b1
liftKleisli forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (b, d) (c, d)
first
   second :: forall b c d. T b c -> T (d, b) (d, c)
second = forall a0 a1 b0 b1.
(forall s.
 Kleisli (StateT s Maybe) a0 a1 -> Kleisli (StateT s Maybe) b0 b1)
-> T a0 a1 -> T b0 b1
liftKleisli forall (a :: * -> * -> *) b c d.
Arrow a =>
a b c -> a (d, b) (d, c)
second
   *** :: forall b c b' c'. T b c -> T b' c' -> T (b, b') (c, c')
(***)  = forall b c b' c'. T b c -> T b' c' -> T (b, b') (c, c')
split
   &&& :: forall b c c'. T b c -> T b c' -> T b (c, c')
(&&&)  = forall b c c'. T b c -> T b c' -> T b (c, c')
fanout

{-
I think we cannot define an ArrowApply instance,
because we must extract the initial state somehow
from the inner (T a b) which is not possible.

instance ArrowApply T where
--   app = Cons (runKleisli undefined) ()
   app = first (arr (flip Cons () . runKleisli)) >>> app
-}


instance ArrowLoop T where
   {-# INLINE loop #-}
   loop :: forall b d c. T (b, d) (c, d) -> T b c
loop = forall a0 a1 b0 b1.
(forall s.
 Kleisli (StateT s Maybe) a0 a1 -> Kleisli (StateT s Maybe) b0 b1)
-> T a0 a1 -> T b0 b1
liftKleisli forall (a :: * -> * -> *) b d c.
ArrowLoop a =>
a (b, d) (c, d) -> a b c
loop


type instance Class.ProcessOf Sig.T = T

instance Class.C T where
   type SignalOf T = Sig.T
   toSignal :: forall a. T () a -> SignalOf T a
toSignal = forall a b c. (a -> b -> c) -> b -> a -> c
flip forall a b. T a b -> a -> T b
applyConst ()
   fromSignal :: forall b a. SignalOf T b -> T a b
fromSignal SignalOf T b
sig = forall a b. a -> b -> a
const () forall (a :: * -> * -> *) b c d.
Arrow a =>
(b -> c) -> a c d -> a b d
^>> forall (sig :: * -> *) a. Read sig a => sig a -> T () a
feed SignalOf T b
sig


instance Functor (T a) where
   fmap :: forall a b. (a -> b) -> T a a -> T a b
fmap = forall (arrow :: * -> * -> *) b c a.
Arrow arrow =>
(b -> c) -> arrow a b -> arrow a c
ArrowUtil.map

instance Applicative (T a) where
   pure :: forall a. a -> T a a
pure = forall (arrow :: * -> * -> *) b a. Arrow arrow => b -> arrow a b
ArrowUtil.pure
   <*> :: forall a b. T a (a -> b) -> T a a -> T a b
(<*>) = forall (arrow :: * -> * -> *) a b c.
Arrow arrow =>
arrow a (b -> c) -> arrow a b -> arrow a c
ArrowUtil.apply


instance (Additive.C b) => Additive.C (T a b) where
   zero :: T a b
zero = forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a. C a => a
Additive.zero
   negate :: T a b -> T a b
negate = forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a. C a => a -> a
Additive.negate
   + :: T a b -> T a b -> T a b
(+) = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 forall a. C a => a -> a -> a
(Additive.+)
   (-) = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 forall a. C a => a -> a -> a
(Additive.-)

instance (Ring.C b) => Ring.C (T a b) where
   one :: T a b
one = forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a. C a => a
Ring.one
   * :: T a b -> T a b -> T a b
(*) = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 forall a. C a => a -> a -> a
(Ring.*)
   T a b
x^ :: T a b -> Integer -> T a b
^Integer
n = forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (forall a. C a => a -> Integer -> a
Ring.^ Integer
n) T a b
x
   fromInteger :: Integer -> T a b
fromInteger = forall (f :: * -> *) a. Applicative f => a -> f a
pure forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. C a => Integer -> a
Ring.fromInteger

instance (Field.C b) => Field.C (T a b) where
   / :: T a b -> T a b -> T a b
(/) = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 forall a. C a => a -> a -> a
(Field./)
   recip :: T a b -> T a b
recip = forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a. C a => a -> a
Field.recip
   fromRational' :: Rational -> T a b
fromRational' = forall (f :: * -> *) a. Applicative f => a -> f a
pure forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. C a => Rational -> a
Field.fromRational'


instance (P.Num b) => P.Num (T a b) where
   + :: T a b -> T a b -> T a b
(+) = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 forall a. Num a => a -> a -> a
(P.+)
   (-) = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 forall a. Num a => a -> a -> a
(P.-)
   * :: T a b -> T a b -> T a b
(*) = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 forall a. Num a => a -> a -> a
(P.*)
   negate :: T a b -> T a b
negate = forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a. Num a => a -> a
P.negate
   abs :: T a b -> T a b
abs = forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a. Num a => a -> a
P.abs
   signum :: T a b -> T a b
signum = forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap forall a. Num a => a -> a
P.signum
   fromInteger :: Integer -> T a b
fromInteger = forall (f :: * -> *) a. Applicative f => a -> f a
pure forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Num a => Integer -> a
P.fromInteger

instance (P.Fractional b) => P.Fractional (T a b) where
   / :: T a b -> T a b -> T a b
(/) = forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 forall a. Fractional a => a -> a -> a
(P./)
   fromRational :: Rational -> T a b
fromRational = forall (f :: * -> *) a. Applicative f => a -> f a
pure forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Fractional a => Rational -> a
P.fromRational



{-# INLINE extendStateFstT #-}
extendStateFstT :: Monad m => StateT s m a -> StateT (t,s) m a
extendStateFstT :: forall (m :: * -> *) s a t.
Monad m =>
StateT s m a -> StateT (t, s) m a
extendStateFstT StateT s m a
st =
   forall s (m :: * -> *) a. (s -> m (a, s)) -> StateT s m a
StateT (\(t
t0,s
s0) -> forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM (forall b c a. (b -> c) -> (a, b) -> (a, c)
mapSnd (\s
s1 -> (t
t0,s
s1))) (forall s (m :: * -> *) a. StateT s m a -> s -> m (a, s)
runStateT StateT s m a
st s
s0))

{-# INLINE extendStateSndT #-}
extendStateSndT :: Monad m => StateT s m a -> StateT (s,t) m a
extendStateSndT :: forall (m :: * -> *) s a t.
Monad m =>
StateT s m a -> StateT (s, t) m a
extendStateSndT StateT s m a
st =
   forall s (m :: * -> *) a. (s -> m (a, s)) -> StateT s m a
StateT (\(s
s0,t
t0) -> forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM (forall b c a. (b -> c) -> (a, b) -> (a, c)
mapSnd (\s
s1 -> (s
s1,t
t0))) (forall s (m :: * -> *) a. StateT s m a -> s -> m (a, s)
runStateT StateT s m a
st s
s0))


{-# INLINE liftKleisli #-}
liftKleisli ::
   (forall s.
    Kleisli (StateT s Maybe) a0 a1 ->
    Kleisli (StateT s Maybe) b0 b1) ->
   T a0 a1 -> T b0 b1
liftKleisli :: forall a0 a1 b0 b1.
(forall s.
 Kleisli (StateT s Maybe) a0 a1 -> Kleisli (StateT s Maybe) b0 b1)
-> T a0 a1 -> T b0 b1
liftKleisli forall s.
Kleisli (StateT s Maybe) a0 a1 -> Kleisli (StateT s Maybe) b0 b1
op (Cons a0 -> StateT s Maybe a1
f s
s) =
   forall a b s. (a -> StateT s Maybe b) -> s -> T a b
Cons (forall (m :: * -> *) a b. Kleisli m a b -> a -> m b
runKleisli forall a b. (a -> b) -> a -> b
$ forall s.
Kleisli (StateT s Maybe) a0 a1 -> Kleisli (StateT s Maybe) b0 b1
op forall a b. (a -> b) -> a -> b
$ forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
Kleisli a0 -> StateT s Maybe a1
f) s
s

{-# INLINE liftKleisli2 #-}
liftKleisli2 ::
   (forall s.
      Kleisli (StateT s Maybe) a0 a1 ->
      Kleisli (StateT s Maybe) b0 b1 ->
      Kleisli (StateT s Maybe) c0 c1) ->
   T a0 a1 -> T b0 b1 -> T c0 c1
liftKleisli2 :: forall a0 a1 b0 b1 c0 c1.
(forall s.
 Kleisli (StateT s Maybe) a0 a1
 -> Kleisli (StateT s Maybe) b0 b1
 -> Kleisli (StateT s Maybe) c0 c1)
-> T a0 a1 -> T b0 b1 -> T c0 c1
liftKleisli2 forall s.
Kleisli (StateT s Maybe) a0 a1
-> Kleisli (StateT s Maybe) b0 b1 -> Kleisli (StateT s Maybe) c0 c1
op (Cons a0 -> StateT s Maybe a1
f s
s) (Cons b0 -> StateT s Maybe b1
g s
t) =
   forall a b s. (a -> StateT s Maybe b) -> s -> T a b
Cons
      (forall (m :: * -> *) a b. Kleisli m a b -> a -> m b
runKleisli
         (forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
Kleisli (forall (m :: * -> *) s a t.
Monad m =>
StateT s m a -> StateT (s, t) m a
extendStateSndT forall b c a. (b -> c) -> (a -> b) -> a -> c
. a0 -> StateT s Maybe a1
f) forall s.
Kleisli (StateT s Maybe) a0 a1
-> Kleisli (StateT s Maybe) b0 b1 -> Kleisli (StateT s Maybe) c0 c1
`op`
          forall (m :: * -> *) a b. (a -> m b) -> Kleisli m a b
Kleisli (forall (m :: * -> *) s a t.
Monad m =>
StateT s m a -> StateT (t, s) m a
extendStateFstT forall b c a. (b -> c) -> (a -> b) -> a -> c
. b0 -> StateT s Maybe b1
g)))
      (s
s,s
t)


{-# INLINE id #-}
id :: T a a
id :: forall a. T a a
id = forall (a :: * -> * -> *) b. Arrow a => a b b
returnA

{-# INLINE map #-}
map :: (a -> b) -> T a b
map :: forall b c. (b -> c) -> T b c
map a -> b
f = forall a s b. (a -> State s b) -> s -> T a b
fromState (forall (m :: * -> *) a. Monad m => a -> m a
return forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> b
f) ()

{-# INLINE compose #-}
compose :: T a b -> T b c -> T a c
compose :: forall a b c. T a b -> T b c -> T a c
compose = forall a0 a1 b0 b1 c0 c1.
(forall s.
 Kleisli (StateT s Maybe) a0 a1
 -> Kleisli (StateT s Maybe) b0 b1
 -> Kleisli (StateT s Maybe) c0 c1)
-> T a0 a1 -> T b0 b1 -> T c0 c1
liftKleisli2 forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
Category cat =>
cat a b -> cat b c -> cat a c
(>>>)

{-# INLINE split #-}
split :: T a b -> T c d -> T (a,c) (b,d)
split :: forall b c b' c'. T b c -> T b' c' -> T (b, b') (c, c')
split = forall a0 a1 b0 b1 c0 c1.
(forall s.
 Kleisli (StateT s Maybe) a0 a1
 -> Kleisli (StateT s Maybe) b0 b1
 -> Kleisli (StateT s Maybe) c0 c1)
-> T a0 a1 -> T b0 b1 -> T c0 c1
liftKleisli2 forall (a :: * -> * -> *) b c b' c'.
Arrow a =>
a b c -> a b' c' -> a (b, b') (c, c')
(***)

{-# INLINE fanout #-}
fanout :: T a b -> T a c -> T a (b,c)
fanout :: forall b c c'. T b c -> T b c' -> T b (c, c')
fanout = forall a0 a1 b0 b1 c0 c1.
(forall s.
 Kleisli (StateT s Maybe) a0 a1
 -> Kleisli (StateT s Maybe) b0 b1
 -> Kleisli (StateT s Maybe) c0 c1)
-> T a0 a1 -> T b0 b1 -> T c0 c1
liftKleisli2 forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
(&&&)


{-# INLINE runViewL #-}
runViewL :: (SigG.Read sig a) =>
   sig a ->
   (forall s. StateT s Maybe a -> s -> x) ->
   x
runViewL :: forall (sig :: * -> *) a x.
Read sig a =>
sig a -> (forall s. StateT s Maybe a -> s -> x) -> x
runViewL sig a
sig forall s. StateT s Maybe a -> s -> x
cont =
   forall (sig :: * -> *) y x.
Read sig y =>
sig y -> (forall s. (s -> Maybe (y, s)) -> s -> x) -> x
SigG.runViewL sig a
sig (\s -> Maybe (a, s)
f s
s -> forall s. StateT s Maybe a -> s -> x
cont (forall s (m :: * -> *) a. (s -> m (a, s)) -> StateT s m a
StateT s -> Maybe (a, s)
f) s
s)


{-# INLINE apply #-}
apply :: (SigG.Transform sig a, SigG.Transform sig b) =>
   T a b -> sig a -> sig b
apply :: forall (sig :: * -> *) a b.
(Transform sig a, Transform sig b) =>
T a b -> sig a -> sig b
apply (Cons a -> StateT s Maybe b
f s
s) =
   forall (sig :: * -> *) y0 y1 s.
(Transform0 sig, Storage (sig y0), Storage (sig y1)) =>
(y0 -> s -> Maybe (y1, s)) -> s -> sig y0 -> sig y1
SigG.crochetL (forall s (m :: * -> *) a. StateT s m a -> s -> m (a, s)
runStateT forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> StateT s Maybe b
f) s
s

{-# INLINE applySameType #-}
applySameType :: (SigG.Transform sig a) =>
   T a a -> sig a -> sig a
applySameType :: forall (sig :: * -> *) a.
Transform sig a =>
T a a -> sig a -> sig a
applySameType (Cons a -> StateT s Maybe a
f s
s) =
   forall (sig :: * -> *) y0 y1 s.
(Transform0 sig, Storage (sig y0), Storage (sig y1)) =>
(y0 -> s -> Maybe (y1, s)) -> s -> sig y0 -> sig y1
SigG.crochetL (forall s (m :: * -> *) a. StateT s m a -> s -> m (a, s)
runStateT forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> StateT s Maybe a
f) s
s


{- |
I think this function does too much.
Better use 'feedFst' and (>>>).
-}
{-# INLINE applyFst #-}
applyFst, applyFst' :: (SigG.Read sig a) =>
   T (a,b) c -> sig a -> T b c
applyFst :: forall (sig :: * -> *) a b c.
Read sig a =>
T (a, b) c -> sig a -> T b c
applyFst T (a, b) c
c sig a
as =
   T (a, b) c
c forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
<<< forall (sig :: * -> *) a b. Read sig a => sig a -> T b (a, b)
feedFst sig a
as

applyFst' :: forall (sig :: * -> *) a b c.
Read sig a =>
T (a, b) c -> sig a -> T b c
applyFst' (Cons (a, b) -> StateT s Maybe c
f s
s) sig a
as =
   forall (sig :: * -> *) a x.
Read sig a =>
sig a -> (forall s. StateT s Maybe a -> s -> x) -> x
runViewL sig a
as (\StateT s Maybe a
getNext s
r ->
   forall a b s. (a -> StateT s Maybe b) -> s -> T a b
Cons (\b
b ->
           do a
a <- forall (m :: * -> *) s a t.
Monad m =>
StateT s m a -> StateT (t, s) m a
extendStateFstT StateT s Maybe a
getNext
              forall (m :: * -> *) s a t.
Monad m =>
StateT s m a -> StateT (s, t) m a
extendStateSndT ((a, b) -> StateT s Maybe c
f (a
a,b
b)))
        (s
s,s
r))

{- |
I think this function does too much.
Better use 'feedSnd' and (>>>).
-}
{-# INLINE applySnd #-}
applySnd, applySnd' :: (SigG.Read sig b) =>
   T (a,b) c -> sig b -> T a c
applySnd :: forall (sig :: * -> *) b a c.
Read sig b =>
T (a, b) c -> sig b -> T a c
applySnd T (a, b) c
c sig b
as =
   T (a, b) c
c forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
<<< forall (sig :: * -> *) a b. Read sig a => sig a -> T b (b, a)
feedSnd sig b
as

applySnd' :: forall (sig :: * -> *) b a c.
Read sig b =>
T (a, b) c -> sig b -> T a c
applySnd' (Cons (a, b) -> StateT s Maybe c
f s
s) sig b
bs =
   forall (sig :: * -> *) a x.
Read sig a =>
sig a -> (forall s. StateT s Maybe a -> s -> x) -> x
runViewL sig b
bs (\StateT s Maybe b
getNext s
r ->
   forall a b s. (a -> StateT s Maybe b) -> s -> T a b
Cons (\a
a ->
           do b
b <- forall (m :: * -> *) s a t.
Monad m =>
StateT s m a -> StateT (t, s) m a
extendStateFstT StateT s Maybe b
getNext
              forall (m :: * -> *) s a t.
Monad m =>
StateT s m a -> StateT (s, t) m a
extendStateSndT ((a, b) -> StateT s Maybe c
f (a
a,b
b)))
        (s
s,s
r))

{- |
applyConst c x == apply c (repeat x)
-}
{-# INLINE applyConst #-}
applyConst :: T a b -> a -> Sig.T b
applyConst :: forall a b. T a b -> a -> T b
applyConst (Cons a -> StateT s Maybe b
f s
s) a
a =
   forall acc y. (acc -> Maybe (y, acc)) -> acc -> T y
Sig.unfoldR (forall s (m :: * -> *) a. StateT s m a -> s -> m (a, s)
runStateT (a -> StateT s Maybe b
f a
a)) s
s

{-
Can be easily done by converting the result of applyConst to generic signal
{-# INLINE applyConstGeneric #-}
applyConstGeneric :: SigG.LazySize -> T a b -> a -> sig b
applyConstGeneric size (Cons f s) a =
   SigG.unfoldR size (runStateT (f a)) s
-}


{-# INLINE apply2 #-}
apply2 ::
   (SigG.Read sig a, SigG.Transform sig b, SigG.Transform sig c) =>
   T (a,b) c -> sig a -> sig b -> sig c
apply2 :: forall (sig :: * -> *) a b c.
(Read sig a, Transform sig b, Transform sig c) =>
T (a, b) c -> sig a -> sig b -> sig c
apply2 T (a, b) c
f sig a
x sig b
y =
   forall (sig :: * -> *) a b.
(Transform sig a, Transform sig b) =>
T a b -> sig a -> sig b
apply (forall (sig :: * -> *) a b c.
Read sig a =>
T (a, b) c -> sig a -> T b c
applyFst T (a, b) c
f sig a
x) sig b
y

{-# INLINE apply3 #-}
apply3 ::
   (SigG.Read sig a, SigG.Read sig b, SigG.Transform sig c, SigG.Transform sig d) =>
   T (a,b,c) d -> sig a -> sig b -> sig c -> sig d
apply3 :: forall (sig :: * -> *) a b c d.
(Read sig a, Read sig b, Transform sig c, Transform sig d) =>
T (a, b, c) d -> sig a -> sig b -> sig c -> sig d
apply3 T (a, b, c) d
f sig a
x sig b
y sig c
z =
   forall (sig :: * -> *) a b c.
(Read sig a, Transform sig b, Transform sig c) =>
T (a, b) c -> sig a -> sig b -> sig c
apply2 (forall (sig :: * -> *) a b c.
Read sig a =>
T (a, b) c -> sig a -> T b c
applyFst ((\(a
a,(b
b,c
c)) -> (a
a,b
b,c
c)) forall (a :: * -> * -> *) b c d.
Arrow a =>
(b -> c) -> a c d -> a b d
^>> T (a, b, c) d
f) sig a
x) sig b
y sig c
z


{-
A generalized version could be of type

Transform sig a b => Causal.T a b -> Causal.T (sig a) (sig b)

but we cannot implement that,
since crochetL does not return the final state.
-}
applyStorableChunk ::
   (Storable a, Storable b) =>
   T a b -> T (SV.Vector a) (SV.Vector b)
applyStorableChunk :: forall a b.
(Storable a, Storable b) =>
T a b -> T (Vector a) (Vector b)
applyStorableChunk (Cons a -> StateT s Maybe b
next s
start) = forall a b s. (a -> StateT s Maybe b) -> s -> T a b
Cons
   (\Vector a
a -> forall s (m :: * -> *) a. (s -> m (a, s)) -> StateT s m a
StateT forall a b. (a -> b) -> a -> b
$ \Maybe s
ms ->
      forall a b c. (a -> b -> c) -> b -> a -> c
flip forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Maybe s
ms forall a b. (a -> b) -> a -> b
$ \s
s ->
         forall x y acc.
(Storable x, Storable y) =>
(x -> acc -> Maybe (y, acc))
-> acc -> Vector x -> (Vector y, Maybe acc)
SV.crochetLResult (forall s (m :: * -> *) a. StateT s m a -> s -> m (a, s)
runStateT forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> StateT s Maybe b
next) s
s Vector a
a)
   (forall a. a -> Maybe a
Just s
start)


{-# INLINE feed #-}
feed :: (SigG.Read sig a) =>
   sig a -> T () a
feed :: forall (sig :: * -> *) a. Read sig a => sig a -> T () a
feed sig a
proc =
   forall (sig :: * -> *) a x.
Read sig a =>
sig a -> (forall s. StateT s Maybe a -> s -> x) -> x
runViewL sig a
proc (\StateT s Maybe a
getNext ->
      forall a s b. (a -> StateT s Maybe b) -> s -> T a b
fromStateMaybe (forall a b. a -> b -> a
const StateT s Maybe a
getNext))

{-# INLINE feedFst #-}
feedFst :: (SigG.Read sig a) =>
   sig a -> T b (a,b)
feedFst :: forall (sig :: * -> *) a b. Read sig a => sig a -> T b (a, b)
feedFst sig a
proc =
   forall (sig :: * -> *) a x.
Read sig a =>
sig a -> (forall s. StateT s Maybe a -> s -> x) -> x
runViewL sig a
proc (\StateT s Maybe a
getNext ->
      forall a s b. (a -> StateT s Maybe b) -> s -> T a b
fromStateMaybe (\b
b -> forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (forall a b c. (a -> b -> c) -> b -> a -> c
flip (,) b
b) StateT s Maybe a
getNext))

{-# INLINE feedSnd #-}
feedSnd :: (SigG.Read sig a) =>
   sig a -> T b (b,a)
feedSnd :: forall (sig :: * -> *) a b. Read sig a => sig a -> T b (b, a)
feedSnd sig a
proc =
   forall (sig :: * -> *) a x.
Read sig a =>
sig a -> (forall s. StateT s Maybe a -> s -> x) -> x
runViewL sig a
proc (\StateT s Maybe a
getNext ->
      forall a s b. (a -> StateT s Maybe b) -> s -> T a b
fromStateMaybe (\b
b -> forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap ((,) b
b) StateT s Maybe a
getNext))

{-# INLINE feedConstFst #-}
feedConstFst :: a -> T b (a,b)
feedConstFst :: forall a b. a -> T b (a, b)
feedConstFst a
a = forall b c. (b -> c) -> T b c
map (\b
b -> (a
a,b
b))

{-# INLINE feedConstSnd #-}
feedConstSnd :: a -> T b (b,a)
feedConstSnd :: forall a b. a -> T b (b, a)
feedConstSnd a
a = forall b c. (b -> c) -> T b c
map (\b
b -> (b
b,a
a))

{-# INLINE feedGenericFst #-}
feedGenericFst :: (SigG.Read sig a) =>
   sig a -> T b (a,b)
feedGenericFst :: forall (sig :: * -> *) a b. Read sig a => sig a -> T b (a, b)
feedGenericFst =
   forall (sig :: * -> *) a b. Read sig a => sig a -> T b (a, b)
feedFst forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> T y
SigG.toState

{-# INLINE feedGenericSnd #-}
feedGenericSnd :: (SigG.Read sig a) =>
   sig a -> T b (b,a)
feedGenericSnd :: forall (sig :: * -> *) a b. Read sig a => sig a -> T b (b, a)
feedGenericSnd =
   forall (sig :: * -> *) a b. Read sig a => sig a -> T b (b, a)
feedSnd forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (sig :: * -> *) y.
(Read0 sig, Storage (sig y)) =>
sig y -> T y
SigG.toState



-- * list like functions

{-# INLINE crochetL #-}
crochetL :: (x -> acc -> Maybe (y, acc)) -> acc -> T x y
crochetL :: forall x acc y. (x -> acc -> Maybe (y, acc)) -> acc -> T x y
crochetL x -> acc -> Maybe (y, acc)
f acc
s = forall a s b. (a -> StateT s Maybe b) -> s -> T a b
fromStateMaybe (forall s (m :: * -> *) a. (s -> m (a, s)) -> StateT s m a
StateT forall b c a. (b -> c) -> (a -> b) -> a -> c
. x -> acc -> Maybe (y, acc)
f) acc
s

{-# INLINE mapAccumL #-}
mapAccumL :: (x -> acc -> (y, acc)) -> acc -> T x y
mapAccumL :: forall x acc y. (x -> acc -> (y, acc)) -> acc -> T x y
mapAccumL x -> acc -> (y, acc)
next = forall x acc y. (x -> acc -> Maybe (y, acc)) -> acc -> T x y
crochetL (\x
a acc
s -> forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$ x -> acc -> (y, acc)
next x
a acc
s)

{-# INLINE scanL #-}
scanL :: (acc -> x -> acc) -> acc -> T x acc
scanL :: forall acc x. (acc -> x -> acc) -> acc -> T x acc
scanL acc -> x -> acc
f = forall x acc y. (x -> acc -> (y, acc)) -> acc -> T x y
mapAccumL (\x
x acc
acc -> (acc
acc, acc -> x -> acc
f acc
acc x
x))

{-# INLINE scanL1 #-}
scanL1 :: (x -> x -> x) -> T x x
scanL1 :: forall x. (x -> x -> x) -> T x x
scanL1 x -> x -> x
f =
   forall x acc y. (x -> acc -> (y, acc)) -> acc -> T x y
mapAccumL (\x
x Maybe x
acc -> (x
x, forall a. a -> Maybe a
Just forall a b. (a -> b) -> a -> b
$ forall b a. b -> (a -> b) -> Maybe a -> b
maybe x
x (forall a b c. (a -> b -> c) -> b -> a -> c
flip x -> x -> x
f x
x) Maybe x
acc)) forall a. Maybe a
Nothing

{-# INLINE zipWith #-}
zipWith :: (SigG.Read sig a) =>
   (a -> b -> c) -> sig a -> T b c
zipWith :: forall (sig :: * -> *) a b c.
Read sig a =>
(a -> b -> c) -> sig a -> T b c
zipWith a -> b -> c
f = forall (sig :: * -> *) a b c.
Read sig a =>
T (a, b) c -> sig a -> T b c
applyFst (forall b c. (b -> c) -> T b c
map (forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry a -> b -> c
f))

{- |
Prepend an element to a signal,
but keep the signal length,
i.e. drop the last element.
-}
{-# INLINE consInit #-}
consInit :: x -> T x x
consInit :: forall x. x -> T x x
consInit = forall x acc y. (x -> acc -> (y, acc)) -> acc -> T x y
mapAccumL (\x
x x
acc -> (x
acc, x
x))



{-# INLINE chainControlled #-}
chainControlled :: [T (c,x) x] -> T (c,x) x
chainControlled :: forall c x. [T (c, x) x] -> T (c, x) x
chainControlled = forall (arrow :: * -> * -> *) c x.
Arrow arrow =>
[arrow (c, x) x] -> arrow (c, x) x
Class.chainControlled

{- |
If @T@ would be the function type @->@
then @replicateControlled 3 f@ computes
@\(c,x) -> f(c, f(c, f(c, x)))@.
-}
{-# INLINE replicateControlled #-}
replicateControlled :: Int -> T (c,x) x -> T (c,x) x
replicateControlled :: forall c x. Int -> T (c, x) x -> T (c, x) x
replicateControlled = forall (arrow :: * -> * -> *) c x.
Arrow arrow =>
Int -> arrow (c, x) x -> arrow (c, x) x
Class.replicateControlled


{-# INLINE feedback #-}
feedback :: T (a,c) b -> T b c -> T a b
feedback :: forall a c b. T (a, c) b -> T b c -> T a b
feedback T (a, c) b
forth T b c
back =
   forall (a :: * -> * -> *) b d c.
ArrowLoop a =>
a (b, d) (c, d) -> a b c
loop (T (a, c) b
forth forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
Category cat =>
cat a b -> cat b c -> cat a c
>>>  forall a. T a a
id forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
&&& T b c
back)

{-# INLINE feedbackControlled #-}
feedbackControlled :: T ((ctrl,a),c) b -> T (ctrl,b) c -> T (ctrl,a) b
feedbackControlled :: forall ctrl a c b.
T ((ctrl, a), c) b -> T (ctrl, b) c -> T (ctrl, a) b
feedbackControlled T ((ctrl, a), c) b
forth T (ctrl, b) c
back =
   forall (a :: * -> * -> *) b d c.
ArrowLoop a =>
a (b, d) (c, d) -> a b c
loop (forall b c. (b -> c) -> T b c
map (forall a b. (a, b) -> a
fstforall b c a. (b -> c) -> (a -> b) -> a -> c
.forall a b. (a, b) -> a
fst) forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
&&& T ((ctrl, a), c) b
forth  forall {k} (cat :: k -> k -> *) (a :: k) (b :: k) (c :: k).
Category cat =>
cat a b -> cat b c -> cat a c
>>>  forall b c. (b -> c) -> T b c
map forall a b. (a, b) -> b
snd forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
&&& T (ctrl, b) c
back)

{-
{-# INLINE feedbackControlled #-}
feedbackControlled :: T (ctrl, (a,c)) b -> T (ctrl,b) c -> T (ctrl,a) b
feedbackControlled forth back =
   loop ((\((ctrl,a),c) -> (ctrl, (a,c)))  ^>>
         map fst &&& forth  >>>
         map snd &&& back)
-}