{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TypeFamilies #-}
{-# OPTIONS -fplugin=AsyncRattus.Plugin #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE CPP #-}


-- | Programming with signals.

module AsyncRattus.Signal
  ( map
  , mkInputSig
  , getInputSig
  , filterMap
  , filterMapAwait
  , filter
  , filterAwait
  , trigger
  , triggerAwait
  , mapAwait
  , switch
  , switchS
  , switchAwait
  , interleave
  , mkSig
  , mkBoxSig
  , current
  , future
  , const
  , scan
  , scanAwait
  , scanMap
  , Sig(..)
  , zipWith
  , zipWith3
  , zip
  , cond
  , integral
  , derivative
  )

where

import AsyncRattus
import AsyncRattus.Channels
import Prelude hiding (map, const, zipWith, zipWith3, zip, filter)
import Data.VectorSpace
import Data.Ratio ((%))

infixr 5 :::

-- | @Sig a@ is a stream of values of type @a@.
data Sig a = !a ::: !(O (Sig a))

instance Producer (Sig a) a where
  getCurrent :: Sig a -> Maybe' a
getCurrent Sig a
p = a -> Maybe' a
forall a. a -> Maybe' a
Just' (Sig a -> a
forall a. Sig a -> a
current Sig a
p)
  getNext :: forall b. Sig a -> (forall q. Producer q a => O q -> b) -> b
getNext Sig a
p forall q. Producer q a => O q -> b
cb = O (Sig a) -> b
forall q. Producer q a => O q -> b
cb (Sig a -> O (Sig a)
forall a. Sig a -> O (Sig a)
future Sig a
p)

newtype SigMaybe a = SigMaybe (Sig (Maybe' a))

instance Producer (SigMaybe a) a where
  getCurrent :: SigMaybe a -> Maybe' a
getCurrent (SigMaybe Sig (Maybe' a)
p) = Sig (Maybe' a) -> Maybe' a
forall a. Sig a -> a
current Sig (Maybe' a)
p
  getNext :: forall b. SigMaybe a -> (forall q. Producer q a => O q -> b) -> b
getNext (SigMaybe Sig (Maybe' a)
p) forall q. Producer q a => O q -> b
cb = O (SigMaybe a) -> b
forall q. Producer q a => O q -> b
cb (SigMaybe a -> O (SigMaybe a)
forall a. a -> O a
delay (Sig (Maybe' a) -> SigMaybe a
forall a. Sig (Maybe' a) -> SigMaybe a
SigMaybe (O (Sig (Maybe' a)) -> Sig (Maybe' a)
forall a. O a -> a
adv (Sig (Maybe' a) -> O (Sig (Maybe' a))
forall a. Sig a -> O (Sig a)
future Sig (Maybe' a)
p))))

-- | Get the current value of a signal.
current :: Sig a -> a
current :: forall a. Sig a -> a
current (a
x ::: O (Sig a)
_) = a
x


-- | Get the future the signal.
future :: Sig a -> O (Sig a)
future :: forall a. Sig a -> O (Sig a)
future (a
_ ::: O (Sig a)
xs) = O (Sig a)
xs

-- | Apply a function to the value of a signal.
map :: Box (a -> b) -> Sig a -> Sig b
map :: forall a b. Box (a -> b) -> Sig a -> Sig b
map Box (a -> b)
f (a
x ::: O (Sig a)
xs) = Box (a -> b) -> a -> b
forall a. Box a -> a
unbox Box (a -> b)
f a
x b -> O (Sig b) -> Sig b
forall a. a -> O (Sig a) -> Sig a
::: Sig b -> O (Sig b)
forall a. a -> O a
delay (Box (a -> b) -> Sig a -> Sig b
forall a b. Box (a -> b) -> Sig a -> Sig b
map Box (a -> b)
f (O (Sig a) -> Sig a
forall a. O a -> a
adv O (Sig a)
xs))

-- | Variant of 'getInput' that returns a signal instead of a boxed
-- delayed computation.
getInputSig :: IO (Box (O (Sig a)) :* (a -> IO ()))
getInputSig :: forall a. IO (Box (O (Sig a)) :* (a -> IO ()))
getInputSig = do (Box (O a)
s :* a -> IO ()
cb) <- IO (Box (O a) :* (a -> IO ()))
forall a. IO (Box (O a) :* (a -> IO ()))
getInput
                 (Box (O (Sig a)) :* (a -> IO ()))
-> IO (Box (O (Sig a)) :* (a -> IO ()))
forall a. a -> IO a
forall (m :: * -> *) a. Monad m => a -> m a
return (Box (O a) -> Box (O (Sig a))
forall a. Box (O a) -> Box (O (Sig a))
mkBoxSig Box (O a)
s Box (O (Sig a)) -> (a -> IO ()) -> Box (O (Sig a)) :* (a -> IO ())
forall a b. a -> b -> a :* b
:* a -> IO ()
cb)

-- | Turn a producer into a signal. This is a variant of 'mkInput'
-- that returns a signal instead of a boxed delayed computation.
mkInputSig :: Producer p a => p -> IO (Box (O (Sig a)))
mkInputSig :: forall p a. Producer p a => p -> IO (Box (O (Sig a)))
mkInputSig p
p = Box (O a) -> Box (O (Sig a))
forall a. Box (O a) -> Box (O (Sig a))
mkBoxSig (Box (O a) -> Box (O (Sig a)))
-> IO (Box (O a)) -> IO (Box (O (Sig a)))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> p -> IO (Box (O a))
forall p a. Producer p a => p -> IO (Box (O a))
mkInput p
p


-- | This function is essentially the composition of 'filter' with
-- 'map'. The signal produced by @filterMap f s@ has the value @v@
-- whenever @s@ has the value @u@ such that @unbox f u = Just' v@.
filterMap :: Box (a -> Maybe' b) -> Sig a -> IO (Box (O (Sig b)))
filterMap :: forall a b. Box (a -> Maybe' b) -> Sig a -> IO (Box (O (Sig b)))
filterMap Box (a -> Maybe' b)
f Sig a
s = SigMaybe b -> IO (Box (O (Sig b)))
forall p a. Producer p a => p -> IO (Box (O (Sig a)))
mkInputSig (Sig (Maybe' b) -> SigMaybe b
forall a. Sig (Maybe' a) -> SigMaybe a
SigMaybe (Box (a -> Maybe' b) -> Sig a -> Sig (Maybe' b)
forall a b. Box (a -> b) -> Sig a -> Sig b
map Box (a -> Maybe' b)
f Sig a
s))

-- | This function is similar to 'filterMap' but takes a delayed
-- signal (type @O (Sig a)@) as an argument instead of a signal (@Sig
-- a@).
filterMapAwait :: Box (a -> Maybe' b) -> O (Sig a) -> IO (Box (O (Sig b)))
filterMapAwait :: forall a b.
Box (a -> Maybe' b) -> O (Sig a) -> IO (Box (O (Sig b)))
filterMapAwait Box (a -> Maybe' b)
f O (Sig a)
s = O (SigMaybe b) -> IO (Box (O (Sig b)))
forall p a. Producer p a => p -> IO (Box (O (Sig a)))
mkInputSig (SigMaybe b -> O (SigMaybe b)
forall a. a -> O a
delay (Sig (Maybe' b) -> SigMaybe b
forall a. Sig (Maybe' a) -> SigMaybe a
SigMaybe (Box (a -> Maybe' b) -> Sig a -> Sig (Maybe' b)
forall a b. Box (a -> b) -> Sig a -> Sig b
map Box (a -> Maybe' b)
f (O (Sig a) -> Sig a
forall a. O a -> a
adv O (Sig a)
s))))

-- | Filter the given signal using a predicate. The signal produced by
-- @filter p s@ contains only values from @s@ that satisfy the
-- predicate @p@.
filter :: Box (a -> Bool) -> Sig a -> IO (Box (O (Sig a)))
filter :: forall a. Box (a -> Bool) -> Sig a -> IO (Box (O (Sig a)))
filter Box (a -> Bool)
p = Box (a -> Maybe' a) -> Sig a -> IO (Box (O (Sig a)))
forall a b. Box (a -> Maybe' b) -> Sig a -> IO (Box (O (Sig b)))
filterMap ((a -> Maybe' a) -> Box (a -> Maybe' a)
forall a. a -> Box a
box (\ a
x -> if Box (a -> Bool) -> a -> Bool
forall a. Box a -> a
unbox Box (a -> Bool)
p a
x then a -> Maybe' a
forall a. a -> Maybe' a
Just' a
x else Maybe' a
forall a. Maybe' a
Nothing'))

-- | This function is similar to 'filter' but takes a delayed signal
-- (type @O (Sig a)@) as an argument instead of a signal (@Sig a@).
filterAwait :: Box (a -> Bool) -> O (Sig a) -> IO (Box (O (Sig a)))
filterAwait :: forall a. Box (a -> Bool) -> O (Sig a) -> IO (Box (O (Sig a)))
filterAwait Box (a -> Bool)
p = Box (a -> Maybe' a) -> O (Sig a) -> IO (Box (O (Sig a)))
forall a b.
Box (a -> Maybe' b) -> O (Sig a) -> IO (Box (O (Sig b)))
filterMapAwait ((a -> Maybe' a) -> Box (a -> Maybe' a)
forall a. a -> Box a
box (\ a
x -> if Box (a -> Bool) -> a -> Bool
forall a. Box a -> a
unbox Box (a -> Bool)
p a
x then a -> Maybe' a
forall a. a -> Maybe' a
Just' a
x else Maybe' a
forall a. Maybe' a
Nothing'))


-- | This function is a variant of 'zipWith'. Whereas @zipWith f xs
-- ys@ produces a new value whenever @xs@ or @ys@ produce a new value,
-- @trigger f xs ys@ only produces a new value when xs produces a new
-- value.
--
-- Example:
--
-- >                      xs:  1 2 3     2
-- >                      ys:  1     0 5 2
-- >
-- > zipWith (box (+)) xs ys:  2 3 4 3 8 4
-- > trigger (box (+)) xy ys:  2     3 8 4

trigger :: (Stable a, Stable b) => Box (a -> b -> c) -> Sig a -> Sig b -> IO (Box (Sig c))
trigger :: forall a b c.
(Stable a, Stable b) =>
Box (a -> b -> c) -> Sig a -> Sig b -> IO (Box (Sig c))
trigger Box (a -> b -> c)
f (a
a ::: O (Sig a)
as) bs :: Sig b
bs@(b
b:::O (Sig b)
_) = do Box (O (Sig c))
s <- Box (a -> b -> c) -> O (Sig a) -> Sig b -> IO (Box (O (Sig c)))
forall b a c.
Stable b =>
Box (a -> b -> c) -> O (Sig a) -> Sig b -> IO (Box (O (Sig c)))
triggerAwait Box (a -> b -> c)
f O (Sig a)
as Sig b
bs
                                     Box (Sig c) -> IO (Box (Sig c))
forall a. a -> IO a
forall (m :: * -> *) a. Monad m => a -> m a
return (Sig c -> Box (Sig c)
forall a. a -> Box a
box (Box (a -> b -> c) -> a -> b -> c
forall a. Box a -> a
unbox Box (a -> b -> c)
f a
a b
b c -> O (Sig c) -> Sig c
forall a. a -> O (Sig a) -> Sig a
::: Box (O (Sig c)) -> O (Sig c)
forall a. Box a -> a
unbox Box (O (Sig c))
s))
-- | This function is similar to 'trigger' but takes a delayed signal
-- (type @O (Sig a)@) as an argument instead of a signal (@Sig a@).
triggerAwait :: Stable b => Box (a -> b -> c) -> O (Sig a) -> Sig b -> IO (Box (O (Sig c)))
triggerAwait :: forall b a c.
Stable b =>
Box (a -> b -> c) -> O (Sig a) -> Sig b -> IO (Box (O (Sig c)))
triggerAwait Box (a -> b -> c)
f O (Sig a)
as Sig b
bs = Box (O c) -> Box (O (Sig c))
forall a. Box (O a) -> Box (O (Sig a))
mkBoxSig (Box (O c) -> Box (O (Sig c)))
-> IO (Box (O c)) -> IO (Box (O (Sig c)))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> O (SigMaybe c) -> IO (Box (O c))
forall p a. Producer p a => p -> IO (Box (O a))
mkInput ((Sig (Maybe' c) -> SigMaybe c)
-> Box (Sig (Maybe' c) -> SigMaybe c)
forall a. a -> Box a
box Sig (Maybe' c) -> SigMaybe c
forall a. Sig (Maybe' a) -> SigMaybe a
SigMaybe Box (Sig (Maybe' c) -> SigMaybe c)
-> O (Sig (Maybe' c)) -> O (SigMaybe c)
forall a b. Box (a -> b) -> O a -> O b
`mapO` (Box (a -> b -> c) -> O (Sig a) -> Sig b -> O (Sig (Maybe' c))
forall b a c.
Stable b =>
Box (a -> b -> c) -> O (Sig a) -> Sig b -> O (Sig (Maybe' c))
trig Box (a -> b -> c)
f O (Sig a)
as Sig b
bs)) where
  trig :: Stable b => Box (a -> b -> c) -> O (Sig a) -> Sig b -> O (Sig (Maybe' c))
  trig :: forall b a c.
Stable b =>
Box (a -> b -> c) -> O (Sig a) -> Sig b -> O (Sig (Maybe' c))
trig Box (a -> b -> c)
f O (Sig a)
as (b
b ::: O (Sig b)
bs) =
    Sig (Maybe' c) -> O (Sig (Maybe' c))
forall a. a -> O a
delay (case O (Sig a) -> O (Sig b) -> Select (Sig a) (Sig b)
forall a b. O a -> O b -> Select a b
select O (Sig a)
as O (Sig b)
bs of
            Fst (a
a' ::: O (Sig a)
as') O (Sig b)
bs' -> c -> Maybe' c
forall a. a -> Maybe' a
Just' (Box (a -> b -> c) -> a -> b -> c
forall a. Box a -> a
unbox Box (a -> b -> c)
f a
a' b
b) Maybe' c -> O (Sig (Maybe' c)) -> Sig (Maybe' c)
forall a. a -> O (Sig a) -> Sig a
::: Box (a -> b -> c) -> O (Sig a) -> Sig b -> O (Sig (Maybe' c))
forall b a c.
Stable b =>
Box (a -> b -> c) -> O (Sig a) -> Sig b -> O (Sig (Maybe' c))
trig Box (a -> b -> c)
f O (Sig a)
as' (b
b b -> O (Sig b) -> Sig b
forall a. a -> O (Sig a) -> Sig a
::: O (Sig b)
bs')
            Snd O (Sig a)
as' Sig b
bs' -> Maybe' c
forall a. Maybe' a
Nothing' Maybe' c -> O (Sig (Maybe' c)) -> Sig (Maybe' c)
forall a. a -> O (Sig a) -> Sig a
::: Box (a -> b -> c) -> O (Sig a) -> Sig b -> O (Sig (Maybe' c))
forall b a c.
Stable b =>
Box (a -> b -> c) -> O (Sig a) -> Sig b -> O (Sig (Maybe' c))
trig Box (a -> b -> c)
f O (Sig a)
as' Sig b
bs'
            Both (a
a' ::: O (Sig a)
as') (b
b' ::: O (Sig b)
bs') -> c -> Maybe' c
forall a. a -> Maybe' a
Just' (Box (a -> b -> c) -> a -> b -> c
forall a. Box a -> a
unbox Box (a -> b -> c)
f a
a' b
b') Maybe' c -> O (Sig (Maybe' c)) -> Sig (Maybe' c)
forall a. a -> O (Sig a) -> Sig a
::: Box (a -> b -> c) -> O (Sig a) -> Sig b -> O (Sig (Maybe' c))
forall b a c.
Stable b =>
Box (a -> b -> c) -> O (Sig a) -> Sig b -> O (Sig (Maybe' c))
trig Box (a -> b -> c)
f O (Sig a)
as' (b
b' b -> O (Sig b) -> Sig b
forall a. a -> O (Sig a) -> Sig a
::: O (Sig b)
bs')
          )

-- | A version of @map@ for delayed signals.
mapAwait :: Box (a -> b) -> O (Sig a) -> O (Sig b)
mapAwait :: forall a b. Box (a -> b) -> O (Sig a) -> O (Sig b)
mapAwait Box (a -> b)
f O (Sig a)
d = Sig b -> O (Sig b)
forall a. a -> O a
delay (Box (a -> b) -> Sig a -> Sig b
forall a b. Box (a -> b) -> Sig a -> Sig b
map Box (a -> b)
f (O (Sig a) -> Sig a
forall a. O a -> a
adv O (Sig a)
d))

-- | Turns a boxed delayed computation into a delayed signal.
mkSig :: Box (O a) -> O (Sig a)
mkSig :: forall a. Box (O a) -> O (Sig a)
mkSig Box (O a)
b = Sig a -> O (Sig a)
forall a. a -> O a
delay (O a -> a
forall a. O a -> a
adv (Box (O a) -> O a
forall a. Box a -> a
unbox Box (O a)
b) a -> O (Sig a) -> Sig a
forall a. a -> O (Sig a) -> Sig a
::: Box (O a) -> O (Sig a)
forall a. Box (O a) -> O (Sig a)
mkSig Box (O a)
b)

-- | Variant of 'mkSig' that returns a boxed delayed signal
mkBoxSig :: Box (O a) -> Box (O (Sig a))
mkBoxSig :: forall a. Box (O a) -> Box (O (Sig a))
mkBoxSig Box (O a)
b = O (Sig a) -> Box (O (Sig a))
forall a. a -> Box a
box (Box (O a) -> O (Sig a)
forall a. Box (O a) -> O (Sig a)
mkSig Box (O a)
b)


-- | Construct a constant signal that never updates.
const :: a -> Sig a
const :: forall a. a -> Sig a
const a
x = a
x a -> O (Sig a) -> Sig a
forall a. a -> O (Sig a) -> Sig a
::: O (Sig a)
forall a. O a
never

-- | Similar to Haskell's 'scanl'.
--
-- > scan (box f) x (v1 ::: v2 ::: v3 ::: ... ) == (x `f` v1) ::: ((x `f` v1) `f` v2) ::: ...
--
-- Note: Unlike 'scanl', 'scan' starts with @x `f` v1@, not @x@.

scan :: (Stable b) => Box(b -> a -> b) -> b -> Sig a -> Sig b
scan :: forall b a. Stable b => Box (b -> a -> b) -> b -> Sig a -> Sig b
scan Box (b -> a -> b)
f b
acc (a
a ::: O (Sig a)
as) = b
acc' b -> O (Sig b) -> Sig b
forall a. a -> O (Sig a) -> Sig a
::: Sig b -> O (Sig b)
forall a. a -> O a
delay (Box (b -> a -> b) -> b -> Sig a -> Sig b
forall b a. Stable b => Box (b -> a -> b) -> b -> Sig a -> Sig b
scan Box (b -> a -> b)
f b
acc' (O (Sig a) -> Sig a
forall a. O a -> a
adv O (Sig a)
as))
  where acc' :: b
acc' = Box (b -> a -> b) -> b -> a -> b
forall a. Box a -> a
unbox Box (b -> a -> b)
f b
acc a
a

-- | Like 'scan', but uses a delayed signal.
scanAwait :: (Stable b) => Box (b -> a -> b) -> b -> O (Sig a) -> Sig b
scanAwait :: forall b a.
Stable b =>
Box (b -> a -> b) -> b -> O (Sig a) -> Sig b
scanAwait Box (b -> a -> b)
f b
acc O (Sig a)
as = b
acc b -> O (Sig b) -> Sig b
forall a. a -> O (Sig a) -> Sig a
::: Sig b -> O (Sig b)
forall a. a -> O a
delay (Box (b -> a -> b) -> b -> Sig a -> Sig b
forall b a. Stable b => Box (b -> a -> b) -> b -> Sig a -> Sig b
scan Box (b -> a -> b)
f b
acc (O (Sig a) -> Sig a
forall a. O a -> a
adv O (Sig a)
as))

-- | 'scanMap' is a composition of 'map' and 'scan':
--
-- > scanMap f g x === map g . scan f x
scanMap :: (Stable b) => Box (b -> a -> b) -> Box (b -> c) -> b -> Sig a -> Sig c
scanMap :: forall b a c.
Stable b =>
Box (b -> a -> b) -> Box (b -> c) -> b -> Sig a -> Sig c
scanMap Box (b -> a -> b)
f Box (b -> c)
p b
acc (a
a ::: O (Sig a)
as) =  Box (b -> c) -> b -> c
forall a. Box a -> a
unbox Box (b -> c)
p b
acc' c -> O (Sig c) -> Sig c
forall a. a -> O (Sig a) -> Sig a
::: Sig c -> O (Sig c)
forall a. a -> O a
delay (Box (b -> a -> b) -> Box (b -> c) -> b -> Sig a -> Sig c
forall b a c.
Stable b =>
Box (b -> a -> b) -> Box (b -> c) -> b -> Sig a -> Sig c
scanMap Box (b -> a -> b)
f Box (b -> c)
p b
acc' (O (Sig a) -> Sig a
forall a. O a -> a
adv O (Sig a)
as))
  where acc' :: b
acc' = Box (b -> a -> b) -> b -> a -> b
forall a. Box a -> a
unbox Box (b -> a -> b)
f b
acc a
a

-- | This function allows to switch from one signal to another one
-- dynamically. The signal defined by @switch xs ys@ first behaves
-- like @xs@, but as soon as @ys@ produces a new value, @switch xs ys@
-- behaves like @ys@.
--
-- Example:
--
-- >           xs: 1 2 3 4 5   6 7 8   9
-- >           ys:         1 2   3 4 5 6
-- >
-- > switch xs ys: 1 2 3 1 2 4   3 4 5 6
switch :: Sig a -> O (Sig a) -> Sig a
switch :: forall a. Sig a -> O (Sig a) -> Sig a
switch (a
x ::: O (Sig a)
xs) O (Sig a)
d = a
x a -> O (Sig a) -> Sig a
forall a. a -> O (Sig a) -> Sig a
::: Sig a -> O (Sig a)
forall a. a -> O a
delay (case O (Sig a) -> O (Sig a) -> Select (Sig a) (Sig a)
forall a b. O a -> O b -> Select a b
select O (Sig a)
xs O (Sig a)
d of
                                     Fst   Sig a
xs'  O (Sig a)
d'  -> Sig a -> O (Sig a) -> Sig a
forall a. Sig a -> O (Sig a) -> Sig a
switch Sig a
xs' O (Sig a)
d'
                                     Snd   O (Sig a)
_    Sig a
d'  -> Sig a
d'
                                     Both  Sig a
_    Sig a
d'  -> Sig a
d')

-- | This function is similar to 'switch', but the (future) second
-- signal may depend on the last value of the first signal.
switchS :: Stable a => Sig a -> O (a -> Sig a) -> Sig a
switchS :: forall a. Stable a => Sig a -> O (a -> Sig a) -> Sig a
switchS (a
x ::: O (Sig a)
xs) O (a -> Sig a)
d = a
x a -> O (Sig a) -> Sig a
forall a. a -> O (Sig a) -> Sig a
::: Sig a -> O (Sig a)
forall a. a -> O a
delay (case O (Sig a) -> O (a -> Sig a) -> Select (Sig a) (a -> Sig a)
forall a b. O a -> O b -> Select a b
select O (Sig a)
xs O (a -> Sig a)
d of
                                     Fst   Sig a
xs'  O (a -> Sig a)
d'  -> Sig a -> O (a -> Sig a) -> Sig a
forall a. Stable a => Sig a -> O (a -> Sig a) -> Sig a
switchS Sig a
xs' O (a -> Sig a)
d'
                                     Snd   O (Sig a)
_    a -> Sig a
f  -> a -> Sig a
f a
x
                                     Both  Sig a
_    a -> Sig a
f  -> a -> Sig a
f a
x)

-- | This function is similar to 'switch' but works on delayed signals
-- instead of signals.
switchAwait :: O (Sig a) -> O (Sig a) -> O (Sig a)
switchAwait :: forall a. O (Sig a) -> O (Sig a) -> O (Sig a)
switchAwait O (Sig a)
xs O (Sig a)
ys = Sig a -> O (Sig a)
forall a. a -> O a
delay (case O (Sig a) -> O (Sig a) -> Select (Sig a) (Sig a)
forall a b. O a -> O b -> Select a b
select O (Sig a)
xs O (Sig a)
ys of
                                  Fst  Sig a
xs'  O (Sig a)
d'  -> Sig a -> O (Sig a) -> Sig a
forall a. Sig a -> O (Sig a) -> Sig a
switch Sig a
xs' O (Sig a)
d'
                                  Snd  O (Sig a)
_    Sig a
d'  -> Sig a
d'
                                  Both Sig a
_    Sig a
d'  -> Sig a
d')

-- | This function interleaves two signals producing a new value @v@
-- whenever either input stream produces a new value @v@. In case the
-- input signals produce a new value simultaneously, the function
-- argument is used break ties, i.e. to compute the new output value based
-- on the two new input values
--
-- Example:
--
-- >                         xs: 1 3   5 3 1 3
-- >                         ys:   0 2   4
-- >
-- > interleave (box (+)) xs ys: 1 3 2 5 7 1 3
interleave :: Box (a -> a -> a) -> O (Sig a) -> O (Sig a) -> O (Sig a)
interleave :: forall a. Box (a -> a -> a) -> O (Sig a) -> O (Sig a) -> O (Sig a)
interleave Box (a -> a -> a)
f O (Sig a)
xs O (Sig a)
ys = Sig a -> O (Sig a)
forall a. a -> O a
delay (case O (Sig a) -> O (Sig a) -> Select (Sig a) (Sig a)
forall a b. O a -> O b -> Select a b
select O (Sig a)
xs O (Sig a)
ys of
                              Fst (a
x ::: O (Sig a)
xs') O (Sig a)
ys' -> a
x a -> O (Sig a) -> Sig a
forall a. a -> O (Sig a) -> Sig a
::: Box (a -> a -> a) -> O (Sig a) -> O (Sig a) -> O (Sig a)
forall a. Box (a -> a -> a) -> O (Sig a) -> O (Sig a) -> O (Sig a)
interleave Box (a -> a -> a)
f O (Sig a)
xs' O (Sig a)
ys'
                              Snd O (Sig a)
xs' (a
y ::: O (Sig a)
ys') -> a
y a -> O (Sig a) -> Sig a
forall a. a -> O (Sig a) -> Sig a
::: Box (a -> a -> a) -> O (Sig a) -> O (Sig a) -> O (Sig a)
forall a. Box (a -> a -> a) -> O (Sig a) -> O (Sig a) -> O (Sig a)
interleave Box (a -> a -> a)
f O (Sig a)
xs' O (Sig a)
ys'
                              Both (a
x ::: O (Sig a)
xs') (a
y ::: O (Sig a)
ys') -> Box (a -> a -> a) -> a -> a -> a
forall a. Box a -> a
unbox Box (a -> a -> a)
f a
x a
y a -> O (Sig a) -> Sig a
forall a. a -> O (Sig a) -> Sig a
::: Box (a -> a -> a) -> O (Sig a) -> O (Sig a) -> O (Sig a)
forall a. Box (a -> a -> a) -> O (Sig a) -> O (Sig a) -> O (Sig a)
interleave Box (a -> a -> a)
f O (Sig a)
xs' O (Sig a)
ys')


-- | This function is a variant of combines the values of two signals
-- using the function argument. @zipWith f xs ys@ produces a new value
-- @unbox f x y@ whenever @xs@ or @ys@ produce a new value, where @x@
-- and @y@ are the current values of @xs@ and @ys@, respectively.
--
-- Example:
--
-- >                      xs:  1 2 3     2
-- >                      ys:  1     0 5 2
-- >
-- > zipWith (box (+)) xs ys:  2 3 4 3 8 4

zipWith :: (Stable a, Stable b) => Box(a -> b -> c) -> Sig a -> Sig b -> Sig c
zipWith :: forall a b c.
(Stable a, Stable b) =>
Box (a -> b -> c) -> Sig a -> Sig b -> Sig c
zipWith Box (a -> b -> c)
f (a
a ::: O (Sig a)
as) (b
b ::: O (Sig b)
bs) = Box (a -> b -> c) -> a -> b -> c
forall a. Box a -> a
unbox Box (a -> b -> c)
f a
a b
b c -> O (Sig c) -> Sig c
forall a. a -> O (Sig a) -> Sig a
::: Sig c -> O (Sig c)
forall a. a -> O a
delay (
    case O (Sig a) -> O (Sig b) -> Select (Sig a) (Sig b)
forall a b. O a -> O b -> Select a b
select O (Sig a)
as O (Sig b)
bs of
      Fst Sig a
as' O (Sig b)
lbs -> Box (a -> b -> c) -> Sig a -> Sig b -> Sig c
forall a b c.
(Stable a, Stable b) =>
Box (a -> b -> c) -> Sig a -> Sig b -> Sig c
zipWith Box (a -> b -> c)
f Sig a
as' (b
b b -> O (Sig b) -> Sig b
forall a. a -> O (Sig a) -> Sig a
::: O (Sig b)
lbs)
      Snd O (Sig a)
las Sig b
bs' -> Box (a -> b -> c) -> Sig a -> Sig b -> Sig c
forall a b c.
(Stable a, Stable b) =>
Box (a -> b -> c) -> Sig a -> Sig b -> Sig c
zipWith Box (a -> b -> c)
f (a
a a -> O (Sig a) -> Sig a
forall a. a -> O (Sig a) -> Sig a
::: O (Sig a)
las) Sig b
bs'
      Both Sig a
as' Sig b
bs' -> Box (a -> b -> c) -> Sig a -> Sig b -> Sig c
forall a b c.
(Stable a, Stable b) =>
Box (a -> b -> c) -> Sig a -> Sig b -> Sig c
zipWith Box (a -> b -> c)
f Sig a
as' Sig b
bs'
  )

-- | Variant of 'zipWith' with three signals.
zipWith3 :: forall a b c d. (Stable a, Stable b, Stable c) => Box(a -> b -> c -> d) -> Sig a -> Sig b -> Sig c -> Sig d
zipWith3 :: forall a b c d.
(Stable a, Stable b, Stable c) =>
Box (a -> b -> c -> d) -> Sig a -> Sig b -> Sig c -> Sig d
zipWith3 Box (a -> b -> c -> d)
f Sig a
as Sig b
bs Sig c
cs = Box (Box (c -> d) -> c -> d)
-> Sig (Box (c -> d)) -> Sig c -> Sig d
forall a b c.
(Stable a, Stable b) =>
Box (a -> b -> c) -> Sig a -> Sig b -> Sig c
zipWith ((Box (c -> d) -> c -> d) -> Box (Box (c -> d) -> c -> d)
forall a. a -> Box a
box (\Box (c -> d)
f c
x -> Box (c -> d) -> c -> d
forall a. Box a -> a
unbox Box (c -> d)
f c
x)) Sig (Box (c -> d))
cds Sig c
cs
  where cds :: Sig (Box (c -> d))
        cds :: Sig (Box (c -> d))
cds = Box (a -> b -> Box (c -> d))
-> Sig a -> Sig b -> Sig (Box (c -> d))
forall a b c.
(Stable a, Stable b) =>
Box (a -> b -> c) -> Sig a -> Sig b -> Sig c
zipWith ((a -> b -> Box (c -> d)) -> Box (a -> b -> Box (c -> d))
forall a. a -> Box a
box (\a
a b
b -> (c -> d) -> Box (c -> d)
forall a. a -> Box a
box (\ c
c -> Box (a -> b -> c -> d) -> a -> b -> c -> d
forall a. Box a -> a
unbox Box (a -> b -> c -> d)
f a
a b
b c
c))) Sig a
as Sig b
bs

-- | If-then-else lifted to signals. @cond bs xs ys@ produces a stream
-- whose value is taken from @xs@ whenever @bs@ is true and from @ys@
-- otherwise.
cond :: Stable a => Sig Bool -> Sig a -> Sig a -> Sig a
cond :: forall a. Stable a => Sig Bool -> Sig a -> Sig a -> Sig a
cond = Box (Bool -> a -> a -> a) -> Sig Bool -> Sig a -> Sig a -> Sig a
forall a b c d.
(Stable a, Stable b, Stable c) =>
Box (a -> b -> c -> d) -> Sig a -> Sig b -> Sig c -> Sig d
zipWith3 ((Bool -> a -> a -> a) -> Box (Bool -> a -> a -> a)
forall a. a -> Box a
box (\Bool
b a
x a
y -> if Bool
b then a
x else a
y))


-- | This is a special case of 'zipWith' using the tupling
-- function. That is,
--
-- > zip = zipWith (box (:*))
zip :: (Stable a, Stable b) => Sig a -> Sig b -> Sig (a:*b)
zip :: forall a b. (Stable a, Stable b) => Sig a -> Sig b -> Sig (a :* b)
zip = Box (a -> b -> a :* b) -> Sig a -> Sig b -> Sig (a :* b)
forall a b c.
(Stable a, Stable b) =>
Box (a -> b -> c) -> Sig a -> Sig b -> Sig c
zipWith ((a -> b -> a :* b) -> Box (a -> b -> a :* b)
forall a. a -> Box a
box a -> b -> a :* b
forall a b. a -> b -> a :* b
(:*))

-- | Sampling interval (in microseconds) for the 'integral' and
-- 'derivative' functions.

dt :: Int
dt :: Int
dt = Int
20000

-- | @integral x xs@ computes the integral of the signal @xs@ with the
-- constant @x@. For example, if @xs@ is the velocity of an object,
-- the signal @integral 0 xs@ describes the distance travelled by that
-- object.
integral :: forall a v . (VectorSpace v a, Eq v, Fractional a, Stable v, Stable a)
  => v -> Sig v -> Sig v
integral :: forall a v.
(VectorSpace v a, Eq v, Fractional a, Stable v, Stable a) =>
v -> Sig v -> Sig v
integral = v -> Sig v -> Sig v
int 
  where int :: v -> Sig v -> Sig v
int v
cur (v
x ::: O (Sig v)
xs)
          | v
x v -> v -> Bool
forall a. Eq a => a -> a -> Bool
== v
forall v a. VectorSpace v a => v
zeroVector = v
cur v -> O (Sig v) -> Sig v
forall a. a -> O (Sig a) -> Sig a
::: Sig v -> O (Sig v)
forall a. a -> O a
delay (v -> Sig v -> Sig v
int v
cur (O (Sig v) -> Sig v
forall a. O a -> a
adv O (Sig v)
xs))
          | Bool
otherwise = v
cur v -> O (Sig v) -> Sig v
forall a. a -> O (Sig a) -> Sig a
::: Sig v -> O (Sig v)
forall a. a -> O a
delay (
              case O (Sig v) -> O () -> Select (Sig v) ()
forall a b. O a -> O b -> Select a b
select O (Sig v)
xs (Box (O ()) -> O ()
forall a. Box a -> a
unbox (Int -> Box (O ())
timer Int
dt)) of
                Fst Sig v
xs' O ()
_ -> v -> Sig v -> Sig v
int v
cur Sig v
xs'
                Snd O (Sig v)
xs' () -> v -> Sig v -> Sig v
int (a
dtf a -> v -> v
forall v a. VectorSpace v a => a -> v -> v
*^ (v
cur v -> v -> v
forall v a. VectorSpace v a => v -> v -> v
^+^ v
x)) (v
x v -> O (Sig v) -> Sig v
forall a. a -> O (Sig a) -> Sig a
::: O (Sig v)
xs')
                Both (v
x' ::: O (Sig v)
xs') () ->  v -> Sig v -> Sig v
int (a
dtf a -> v -> v
forall v a. VectorSpace v a => a -> v -> v
*^ (v
cur v -> v -> v
forall v a. VectorSpace v a => v -> v -> v
^+^ v
x')) (v
x'v -> O (Sig v) -> Sig v
forall a. a -> O (Sig a) -> Sig a
::: O (Sig v)
xs'))
         -- sampling interval in seconds
        dtf :: a
        dtf :: a
dtf = Rational -> a
forall a. Fractional a => Rational -> a
fromRational (Int -> Integer
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
dt Integer -> Integer -> Rational
forall a. Integral a => a -> a -> Ratio a
% Integer
1000000)
                
-- | Compute the derivative of a signal. For example, if @xs@ is the
-- velocity of an object, the signal @derivative xs@ describes the
-- acceleration travelled by that object.
derivative :: forall a v . (VectorSpace v a, Eq v, Fractional a, Stable v, Stable a)
  => Sig v -> Sig v
derivative :: forall a v.
(VectorSpace v a, Eq v, Fractional a, Stable v, Stable a) =>
Sig v -> Sig v
derivative Sig v
xs = v -> v -> Sig v -> Sig v
der v
forall v a. VectorSpace v a => v
zeroVector (Sig v -> v
forall a. Sig a -> a
current Sig v
xs) Sig v
xs where
  -- inverse sampling interval in seconds
  dtf :: a
  dtf :: a
dtf = Int -> a
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
dt a -> a -> a
forall a. Num a => a -> a -> a
* a
0.000001

  der :: v -> v -> Sig v -> Sig v
  der :: v -> v -> Sig v -> Sig v
der v
d v
last (v
x:::O (Sig v)
xs)
    | v
d v -> v -> Bool
forall a. Eq a => a -> a -> Bool
== v
forall v a. VectorSpace v a => v
zeroVector = v
forall v a. VectorSpace v a => v
zeroVector v -> O (Sig v) -> Sig v
forall a. a -> O (Sig a) -> Sig a
::: Sig v -> O (Sig v)
forall a. a -> O a
delay
                        (let v
x' ::: O (Sig v)
xs' = O (Sig v) -> Sig v
forall a. O a -> a
adv O (Sig v)
xs
                         in v -> v -> Sig v -> Sig v
der ((v
x' v -> v -> v
forall v a. VectorSpace v a => v -> v -> v
^-^ v
x) v -> a -> v
forall v a. VectorSpace v a => v -> a -> v
^/ a
dtf) v
x (v
x' v -> O (Sig v) -> Sig v
forall a. a -> O (Sig a) -> Sig a
::: O (Sig v)
xs'))
    | Bool
otherwise = v
d v -> O (Sig v) -> Sig v
forall a. a -> O (Sig a) -> Sig a
::: Sig v -> O (Sig v)
forall a. a -> O a
delay (
        case O (Sig v) -> O () -> Select (Sig v) ()
forall a b. O a -> O b -> Select a b
select O (Sig v)
xs (Box (O ()) -> O ()
forall a. Box a -> a
unbox (Int -> Box (O ())
timer Int
dt)) of
          Fst Sig v
xs' O ()
_ -> v -> v -> Sig v -> Sig v
der v
d v
last Sig v
xs'
          Snd O (Sig v)
xs' () -> v -> v -> Sig v -> Sig v
der ((v
x v -> v -> v
forall v a. VectorSpace v a => v -> v -> v
^-^ v
last) v -> a -> v
forall v a. VectorSpace v a => v -> a -> v
^/ a
dtf) v
x (v
x v -> O (Sig v) -> Sig v
forall a. a -> O (Sig a) -> Sig a
::: O (Sig v)
xs')
          Both (v
x' ::: O (Sig v)
xs') () ->  v -> v -> Sig v -> Sig v
der ((v
x' v -> v -> v
forall v a. VectorSpace v a => v -> v -> v
^-^ v
last) v -> a -> v
forall v a. VectorSpace v a => v -> a -> v
^/ a
dtf) v
x' (v
x' v -> O (Sig v) -> Sig v
forall a. a -> O (Sig a) -> Sig a
::: O (Sig v)
xs'))

-- Prevent functions from being inlined too early for the rewrite
-- rules to fire.

{-# NOINLINE [1] map #-}
{-# NOINLINE [1] const #-}
{-# NOINLINE [1] scan #-}
{-# NOINLINE [1] scanMap #-}
{-# NOINLINE [1] zip #-}


{-# RULES

  "const/map" forall (f :: Stable b => Box (a -> b))  x.
    map f (const x) = let x' = unbox f x in const x' ;

  "map/map" forall f g xs.
    map f (map g xs) = map (box (unbox f . unbox g)) xs ;

  "map/scan" forall f p acc as.
    map p (scan f acc as) = scanMap f p acc as ;

  "zip/map" forall xs ys f.
    map f (zip xs ys) = let f' = unbox f in zipWith (box (\ x y -> f' (x :* y))) xs ys;

  "scan/scan" forall f g b c as.
    scan g c (scan f b as) =
      let f' = unbox f; g' = unbox g in
      scanMap (box (\ (b:*c) a -> let b' = f' b a in (b':* g' c b'))) (box snd') (b:*c) as ;

  "scan/scanMap" forall f g p b c as.
    scan g c (scanMap f p b as) =
      let f' = unbox f; g' = unbox g; p' = unbox p in
      scanMap (box (\ (b:*c) a -> let b' = f' (p' b) a in (b':* g' c b'))) (box snd') (b:*c) as ;

#-}