diff --git a/CHANGELOG b/CHANGELOG --- a/CHANGELOG +++ b/CHANGELOG @@ -1,6 +1,15 @@ +2015-03-30 Ivan Perez + * src/FRP/Yampa/Task.hs: Adds Functor and Applicative instances, + for compatibility with base >= 4.8 (issue #7, pull request by + Ryan Scott). + * Yampa.cabal: version bump (0.9.6.1). + +2015-03-04 Ivan Perez + * src/: Coding style improvements. + 2014-08-29 Ivan Perez - * Yampa.cabal: version bump (0.9.6) + * Yampa.cabal: version bump (0.9.6). * src/: Adds a substantial amount of documentation. * src/FRP/Yampa.hs: Adds a new pause combinator. @@ -10,14 +19,14 @@ 2014-04-26 Ivan Perez - * Yampa.cabal: version bump (0.9.5) - * Adds CHANGELOG to cabal file + * Yampa.cabal: version bump (0.9.5). + * Adds CHANGELOG to cabal file. 2014-04-07 Ivan Perez * Yampa.cabal: new maintainer, version bump (0.9.4). - * src/: documentation is exposed so that Haddock can process it - * No interface changes + * src/: documentation is exposed so that Haddock can process it. + * No interface changes. Copyright (c) 2003, Henrik Nilsson, Antony Courtney and Yale University. All rights reserved. diff --git a/Yampa.cabal b/Yampa.cabal --- a/Yampa.cabal +++ b/Yampa.cabal @@ -1,5 +1,5 @@ name: Yampa -version: 0.9.6 +version: 0.9.6.1 cabal-version: >= 1.6 license: BSD3 license-file: LICENSE diff --git a/src/FRP/Yampa.hs b/src/FRP/Yampa.hs --- a/src/FRP/Yampa.hs +++ b/src/FRP/Yampa.hs @@ -148,3458 +148,3458 @@ Random(..), -- * Basic definitions - Time, -- [s] Both for time w.r.t. some reference and intervals. - DTime, -- [s] Sampling interval, always > 0. - SF, -- Signal Function. - Event(..), -- Events; conceptually similar to Maybe (but abstract). - --- Temporray! --- SF(..), sfTF', - --- Main instances - -- SF is an instance of Arrow and ArrowLoop. Method instances: - -- arr :: (a -> b) -> SF a b - -- (>>>) :: SF a b -> SF b c -> SF a c - -- (<<<) :: SF b c -> SF a b -> SF a c - -- first :: SF a b -> SF (a,c) (b,c) - -- second :: SF a b -> SF (c,a) (c,b) - -- (***) :: SF a b -> SF a' b' -> SF (a,a') (b,b') - -- (&&&) :: SF a b -> SF a b' -> SF a (b,b') - -- returnA :: SF a a - -- loop :: SF (a,c) (b,c) -> SF a b - - -- Event is an instance of Functor, Eq, and Ord. Some method instances: - -- fmap :: (a -> b) -> Event a -> Event b - -- (==) :: Event a -> Event a -> Bool - -- (<=) :: Event a -> Event a -> Bool - - -- ** Lifting - arrPrim, arrEPrim, -- For optimization - --- * Signal functions - --- ** Basic signal functions - identity, -- :: SF a a - constant, -- :: b -> SF a b - localTime, -- :: SF a Time - time, -- :: SF a Time, Other name for localTime. - --- ** Initialization - (-->), -- :: b -> SF a b -> SF a b, infixr 0 - (>--), -- :: a -> SF a b -> SF a b, infixr 0 - (-=>), -- :: (b -> b) -> SF a b -> SF a b infixr 0 - (>=-), -- :: (a -> a) -> SF a b -> SF a b infixr 0 - initially, -- :: a -> SF a a - --- ** Simple, stateful signal processing - sscan, -- :: (b -> a -> b) -> b -> SF a b - sscanPrim, -- :: (c -> a -> Maybe (c, b)) -> c -> b -> SF a b - --- * Events --- ** Basic event sources - never, -- :: SF a (Event b) - now, -- :: b -> SF a (Event b) - after, -- :: Time -> b -> SF a (Event b) - repeatedly, -- :: Time -> b -> SF a (Event b) - afterEach, -- :: [(Time,b)] -> SF a (Event b) - afterEachCat, -- :: [(Time,b)] -> SF a (Event [b]) - delayEvent, -- :: Time -> SF (Event a) (Event a) - delayEventCat, -- :: Time -> SF (Event a) (Event [a]) - edge, -- :: SF Bool (Event ()) - iEdge, -- :: Bool -> SF Bool (Event ()) - edgeTag, -- :: a -> SF Bool (Event a) - edgeJust, -- :: SF (Maybe a) (Event a) - edgeBy, -- :: (a -> a -> Maybe b) -> a -> SF a (Event b) - --- ** Stateful event suppression - notYet, -- :: SF (Event a) (Event a) - once, -- :: SF (Event a) (Event a) - takeEvents, -- :: Int -> SF (Event a) (Event a) - dropEvents, -- :: Int -> SF (Event a) (Event a) - --- ** Pointwise functions on events - noEvent, -- :: Event a - noEventFst, -- :: (Event a, b) -> (Event c, b) - noEventSnd, -- :: (a, Event b) -> (a, Event c) - event, -- :: a -> (b -> a) -> Event b -> a - fromEvent, -- :: Event a -> a - isEvent, -- :: Event a -> Bool - isNoEvent, -- :: Event a -> Bool - tag, -- :: Event a -> b -> Event b, infixl 8 - tagWith, -- :: b -> Event a -> Event b, - attach, -- :: Event a -> b -> Event (a, b), infixl 8 - lMerge, -- :: Event a -> Event a -> Event a, infixl 6 - rMerge, -- :: Event a -> Event a -> Event a, infixl 6 - merge, -- :: Event a -> Event a -> Event a, infixl 6 - mergeBy, -- :: (a -> a -> a) -> Event a -> Event a -> Event a - mapMerge, -- :: (a -> c) -> (b -> c) -> (a -> b -> c) - -- -> Event a -> Event b -> Event c - mergeEvents, -- :: [Event a] -> Event a - catEvents, -- :: [Event a] -> Event [a] - joinE, -- :: Event a -> Event b -> Event (a,b),infixl 7 - splitE, -- :: Event (a,b) -> (Event a, Event b) - filterE, -- :: (a -> Bool) -> Event a -> Event a - mapFilterE, -- :: (a -> Maybe b) -> Event a -> Event b - gate, -- :: Event a -> Bool -> Event a, infixl 8 - --- * Switching --- ** Basic switchers - switch, dSwitch, -- :: SF a (b, Event c) -> (c -> SF a b) -> SF a b - rSwitch, drSwitch, -- :: SF a b -> SF (a,Event (SF a b)) b - kSwitch, dkSwitch, -- :: SF a b - -- -> SF (a,b) (Event c) - -- -> (SF a b -> c -> SF a b) - -- -> SF a b - --- ** Parallel composition and switching --- *** Parallel composition and switching over collections with broadcasting - parB, -- :: Functor col => col (SF a b) -> SF a (col b) - pSwitchB,dpSwitchB, -- :: Functor col => - -- col (SF a b) - -- -> SF (a, col b) (Event c) - -- -> (col (SF a b) -> c -> SF a (col b)) - -- -> SF a (col b) - rpSwitchB,drpSwitchB,-- :: Functor col => - -- col (SF a b) - -- -> SF (a, Event (col (SF a b)->col (SF a b))) - -- (col b) - --- *** Parallel composition and switching over collections with general routing - par, -- Functor col => - -- (forall sf . (a -> col sf -> col (b, sf))) - -- -> col (SF b c) - -- -> SF a (col c) - pSwitch, dpSwitch, -- pSwitch :: Functor col => - -- (forall sf . (a -> col sf -> col (b, sf))) - -- -> col (SF b c) - -- -> SF (a, col c) (Event d) - -- -> (col (SF b c) -> d -> SF a (col c)) - -- -> SF a (col c) - rpSwitch,drpSwitch, -- Functor col => - -- (forall sf . (a -> col sf -> col (b, sf))) - -- -> col (SF b c) - -- -> SF (a, Event (col (SF b c) -> col (SF b c))) - -- (col c) - --- * Discrete to continuous-time signal functions --- ** Wave-form generation - old_hold, -- :: a -> SF (Event a) a - hold, -- :: a -> SF (Event a) a - dHold, -- :: a -> SF (Event a) a - trackAndHold, -- :: a -> SF (Maybe a) a - --- ** Accumulators - accum, -- :: a -> SF (Event (a -> a)) (Event a) - accumHold, -- :: a -> SF (Event (a -> a)) a - dAccumHold, -- :: a -> SF (Event (a -> a)) a - accumBy, -- :: (b -> a -> b) -> b -> SF (Event a) (Event b) - accumHoldBy, -- :: (b -> a -> b) -> b -> SF (Event a) b - dAccumHoldBy, -- :: (b -> a -> b) -> b -> SF (Event a) b - accumFilter, -- :: (c -> a -> (c, Maybe b)) -> c - -- -> SF (Event a) (Event b) - old_accum, -- :: a -> SF (Event (a -> a)) (Event a) - old_accumBy, -- :: (b -> a -> b) -> b -> SF (Event a) (Event b) - old_accumFilter, -- :: (c -> a -> (c, Maybe b)) -> c - --- * Delays --- ** Basic delays - pre, -- :: SF a a - iPre, -- :: a -> SF a a - old_pre, old_iPre, - --- ** Timed delays - delay, -- :: Time -> a -> SF a a - --- ** Variable delay - pause, -- :: b -> SF a b -> SF a Bool -> SF a b - --- * State keeping combinators - --- ** Loops with guaranteed well-defined feedback - loopPre, -- :: c -> SF (a,c) (b,c) -> SF a b - loopIntegral, -- :: VectorSpace c s => SF (a,c) (b,c) -> SF a b - --- ** Integration and differentiation - integral, -- :: VectorSpace a s => SF a a - - derivative, -- :: VectorSpace a s => SF a a -- Crude! - imIntegral, -- :: VectorSpace a s => a -> SF a a - - -- Temporarily hidden, but will eventually be made public. - -- iterFrom, -- :: (a -> a -> DTime -> b -> b) -> b -> SF a b - --- * Noise (random signal) sources and stochastic event sources - noise, -- :: noise :: (RandomGen g, Random b) => - -- g -> SF a b - noiseR, -- :: noise :: (RandomGen g, Random b) => - -- (b,b) -> g -> SF a b - occasionally, -- :: RandomGen g => g -> Time -> b -> SF a (Event b) - --- * Reactimation - reactimate, -- :: IO a - -- -> (Bool -> IO (DTime, Maybe a)) - -- -> (Bool -> b -> IO Bool) - -- -> SF a b - -- -> IO () - ReactHandle, - reactInit, -- IO a -- init - -- -> (ReactHandle a b -> Bool -> b -> IO Bool) -- actuate - -- -> SF a b - -- -> IO (ReactHandle a b) --- process a single input sample: - react, -- ReactHandle a b - -- -> (DTime,Maybe a) - -- -> IO Bool - --- * Embedding - --- (tentative: will be revisited) - embed, -- :: SF a b -> (a, [(DTime, Maybe a)]) -> [b] - embedSynch, -- :: SF a b -> (a, [(DTime, Maybe a)]) -> SF Double b - deltaEncode, -- :: Eq a => DTime -> [a] -> (a, [(DTime, Maybe a)]) - deltaEncodeBy, -- :: (a -> a -> Bool) -> DTime -> [a] - -- -> (a, [(DTime, Maybe a)]) - - -- * Auxiliary definitions - -- Reverse function composition and arrow plumbing aids - ( # ), -- :: (a -> b) -> (b -> c) -> (a -> c), infixl 9 - dup, -- :: a -> (a,a) - swap, -- :: (a,b) -> (b,a) - - -) where - -import Control.Monad (unless) -import System.Random (RandomGen(..), Random(..)) - -#if __GLASGOW_HASKELL__ >= 610 -import qualified Control.Category (Category(..)) -#else -#endif - -import Control.Arrow -import FRP.Yampa.Diagnostics -import FRP.Yampa.Miscellany (( # ), dup, swap) -import FRP.Yampa.Event -import FRP.Yampa.VectorSpace - -import Data.IORef - -infixr 0 -->, >--, -=>, >=- - ------------------------------------------------------------------------------- --- Basic type definitions with associated utilities ------------------------------------------------------------------------------- - --- The time type is really a bit boguous, since, as time passes, the minimal --- interval between two consecutive floating-point-represented time points --- increases. A better approach might be to pick a reasonable resolution --- and represent time and time intervals by Integer (giving the number of --- "ticks"). --- --- That might also improve the timing of time-based event sources. --- One might actually pick the overall resolution in reactimate, --- to be passed down, possibly in the form of a global parameter --- record, to all signal functions on initialization. (I think only --- switch would need to remember the record, since it is the only place --- where signal functions get started. So it wouldn't cost all that much. - - --- | Time is used both for time intervals (duration), and time w.r.t. some --- agreed reference point in time. - --- Conceptually, Time = R, i.e. time can be 0 -- or even negative. -type Time = Double -- [s] - - --- | DTime is the time type for lengths of sample intervals. Conceptually, --- DTime = R+ = { x in R | x > 0 }. Don't assume Time and DTime have the --- same representation. -type DTime = Double -- [s] - --- Representation of signal function in initial state. --- (Naming: "TF" stands for Transition Function.) - --- | Signal function that transforms a signal carrying values of some type 'a' --- into a signal carrying values of some type 'b'. You can think of it as --- (Signal a -> Signal b). A signal is, conceptually, a --- function from 'Time' to value. -data SF a b = SF {sfTF :: a -> Transition a b} - - --- Representation of signal function in "running" state. --- --- Possibly better design for Inv. --- Problem: tension between on the one hand making use of the --- invariant property, and on the other keeping track of how something --- has been constructed (SFCpAXA, in particular). --- Idea: Add a boolean field to SFCpAXA and SF' that classifies --- a signal function as being invarying. --- A function sfIsInv computes to True for SFArr, SFAcc (and SFSScan, --- possibly more), extracts the field in other cases. --- --- Motivation for using a function (Event a -> b) in SFArrE --- rather than (a -> Event b) or (a -> b) or even (Event a -> Event b). --- The result type should be just "b" as opposed to "Event b" for --- increased flexibility (e.g. matching "routing functions"). --- When the result type actually IS (Event b), and this fact is --- exploitable, we'll be in a context where is it clear that --- this is a fact, so we don't lose anything. --- Since the idea is that the function is only going to be applied --- when the there is an event, one could imagine the input type --- just "a". But that's not the type of function we're given, --- so it would have to be "massaged" a bit (precomposing with Event) --- to fit. This will gain nothing, and potentially we will lose if --- we actually need to recover the original function. --- In fact, we sometimes really need to recover the original function --- (e.g. currently in switch), and to do it correctly (also handling --- NoEvent), we'd have to work quite hard introducing further --- inefficiencies. --- Summary: Make use of what we are given and only wrap things up later --- when it is clear whatthe need is going to be, thus avoiding costly --- "unwrapping". - --- GADTs needed in particular for SFEP, but also e.g. SFSScan --- exploits them since there are more type vars than in the type con. --- But one could use existentials for those. - - -data SF' a b where - SFArr :: !(DTime -> a -> Transition a b) -> !(FunDesc a b) -> SF' a b - -- The b is intentionally unstrict as the initial output sometimes - -- is undefined (e.g. when defining pre). In any case, it isn't - -- necessarily used and should thus not be forced. - SFSScan :: !(DTime -> a -> Transition a b) - -> !(c -> a -> Maybe (c, b)) -> !c -> b - -> SF' a b - SFEP :: !(DTime -> Event a -> Transition (Event a) b) - -> !(c -> a -> (c, b, b)) -> !c -> b - -> SF' (Event a) b - SFCpAXA :: !(DTime -> a -> Transition a d) - -> !(FunDesc a b) -> !(SF' b c) -> !(FunDesc c d) - -> SF' a d - -- SFPair :: ... - SF' :: !(DTime -> a -> Transition a b) -> SF' a b - --- A transition is a pair of the next state (in the form of a signal --- function) and the output at the present time step. - -type Transition a b = (SF' a b, b) - - -sfTF' :: SF' a b -> (DTime -> a -> Transition a b) -sfTF' (SFArr tf _) = tf -sfTF' (SFSScan tf _ _ _) = tf -sfTF' (SFEP tf _ _ _) = tf -sfTF' (SFCpAXA tf _ _ _) = tf -sfTF' (SF' tf) = tf - - --- !!! 2005-06-30 --- Unclear why, but the isInv mechanism seems to do more --- harm than good. --- Disable completely and see what happens. -{- -sfIsInv :: SF' a b -> Bool --- sfIsInv _ = False -sfIsInv (SFArr _ _) = True --- sfIsInv (SFAcc _ _ _ _) = True -sfIsInv (SFEP _ _ _ _) = True --- sfIsInv (SFSScan ...) = True -sfIsInv (SFCpAXA _ inv _ _ _) = inv -sfIsInv (SF' _ inv) = inv --} - --- "Smart" constructors. The corresponding "raw" constructors should not --- be used directly for construction. - -sfArr :: FunDesc a b -> SF' a b -sfArr FDI = sfId -sfArr (FDC b) = sfConst b -sfArr (FDE f fne) = sfArrE f fne -sfArr (FDG f) = sfArrG f - - -sfId :: SF' a a -sfId = sf - where - sf = SFArr (\_ a -> (sf, a)) FDI - - -sfConst :: b -> SF' a b -sfConst b = sf - where - sf = SFArr (\_ _ -> (sf, b)) (FDC b) - - -sfNever :: SF' a (Event b) -sfNever = sfConst NoEvent - --- Assumption: fne = f NoEvent -sfArrE :: (Event a -> b) -> b -> SF' (Event a) b -sfArrE f fne = sf - where - sf = SFArr (\_ ea -> (sf, case ea of NoEvent -> fne ; _ -> f ea)) - (FDE f fne) - -sfArrG :: (a -> b) -> SF' a b -sfArrG f = sf - where - sf = SFArr (\_ a -> (sf, f a)) (FDG f) - - -sfSScan :: (c -> a -> Maybe (c, b)) -> c -> b -> SF' a b -sfSScan f c b = sf - where - sf = SFSScan tf f c b - tf _ a = case f c a of - Nothing -> (sf, b) - Just (c', b') -> (sfSScan f c' b', b') - -sscanPrim :: (c -> a -> Maybe (c, b)) -> c -> b -> SF a b -sscanPrim f c_init b_init = SF {sfTF = tf0} - where - tf0 a0 = case f c_init a0 of - Nothing -> (sfSScan f c_init b_init, b_init) - Just (c', b') -> (sfSScan f c' b', b') - - --- The event-processing function *could* accept the present NoEvent --- output as an extra state argument. That would facilitate composition --- of event-processing functions somewhat, but would presumably incur an --- extra cost for the more common and simple case of non-composed event --- processors. --- -sfEP :: (c -> a -> (c, b, b)) -> c -> b -> SF' (Event a) b -sfEP f c bne = sf - where - sf = SFEP (\_ ea -> case ea of - NoEvent -> (sf, bne) - Event a -> let - (c', b, bne') = f c a - in - (sfEP f c' bne', b)) - f - c - bne - - --- epPrim is used to define hold, accum, and other event-processing --- functions. -epPrim :: (c -> a -> (c, b, b)) -> c -> b -> SF (Event a) b -epPrim f c bne = SF {sfTF = tf0} - where - tf0 NoEvent = (sfEP f c bne, bne) - tf0 (Event a) = let - (c', b, bne') = f c a - in - (sfEP f c' bne', b) - - -{- --- !!! Maybe something like this? --- !!! But one problem is that the invarying marking would be lost --- !!! if the signal function is taken apart and re-constructed from --- !!! the function description and subordinate signal function in --- !!! cases like SFCpAXA. -sfMkInv :: SF a b -> SF a b -sfMkInv sf = SF {sfTF = ...} - - sfMkInvAux :: SF' a b -> SF' a b - sfMkInvAux sf@(SFArr _ _) = sf - -- sfMkInvAux sf@(SFAcc _ _ _ _) = sf - sfMkInvAux sf@(SFEP _ _ _ _) = sf - sfMkInvAux sf@(SFCpAXA tf inv fd1 sf2 fd3) - | inv = sf - | otherwise = SFCpAXA tf' True fd1 sf2 fd3 - where - tf' = \dt a -> let (sf', b) = tf dt a in (sfMkInvAux sf', b) - sfMkInvAux sf@(SF' tf inv) - | inv = sf - | otherwise = SF' tf' True - tf' = - --} - --- Motivation for event-processing function type --- (alternative would be function of type a->b plus ensuring that it --- only ever gets invoked on events): --- * Now we need to be consistent with other kinds of arrows. --- * We still want to be able to get hold of the original function. --- 2005-02-30: OK, for FDE, invarant is that the field of type b = --- f NoEvent. - -data FunDesc a b where - FDI :: FunDesc a a -- Identity function - FDC :: b -> FunDesc a b -- Constant function - FDE :: (Event a -> b) -> b -> FunDesc (Event a) b -- Event-processing fun - FDG :: (a -> b) -> FunDesc a b -- General function - -fdFun :: FunDesc a b -> (a -> b) -fdFun FDI = id -fdFun (FDC b) = const b -fdFun (FDE f _) = f -fdFun (FDG f) = f - -fdComp :: FunDesc a b -> FunDesc b c -> FunDesc a c -fdComp FDI fd2 = fd2 -fdComp fd1 FDI = fd1 -fdComp (FDC b) fd2 = FDC ((fdFun fd2) b) -fdComp _ (FDC c) = FDC c --- Hardly worth the effort? --- 2005-03-30: No, not only not worth the effort as the only thing saved --- would be an application of f2. Also wrong since current invariant does --- not imply that f1ne = NoEvent. Moreover, we cannot really adopt that --- invariant as it is not totally impossible for a user to create a function --- that breaks it. --- fdComp (FDE f1 f1ne) (FDE f2 f2ne) = --- FDE (f2 . f1) (vfyNoEvent (f1 NoEvent) f2ne) -fdComp (FDE f1 f1ne) fd2 = FDE (f2 . f1) (f2 f1ne) - where - f2 = fdFun fd2 -fdComp (FDG f1) (FDE f2 f2ne) = FDG f - where - f a = case f1 a of - NoEvent -> f2ne - f1a -> f2 f1a -fdComp (FDG f1) fd2 = FDG (fdFun fd2 . f1) - - -fdPar :: FunDesc a b -> FunDesc c d -> FunDesc (a,c) (b,d) -fdPar FDI FDI = FDI -fdPar FDI (FDC d) = FDG (\(~(a, _)) -> (a, d)) -fdPar FDI fd2 = FDG (\(~(a, c)) -> (a, (fdFun fd2) c)) -fdPar (FDC b) FDI = FDG (\(~(_, c)) -> (b, c)) -fdPar (FDC b) (FDC d) = FDC (b, d) -fdPar (FDC b) fd2 = FDG (\(~(_, c)) -> (b, (fdFun fd2) c)) -fdPar fd1 fd2 = FDG (\(~(a, c)) -> ((fdFun fd1) a, (fdFun fd2) c)) - - -fdFanOut :: FunDesc a b -> FunDesc a c -> FunDesc a (b,c) -fdFanOut FDI FDI = FDG dup -fdFanOut FDI (FDC c) = FDG (\a -> (a, c)) -fdFanOut FDI fd2 = FDG (\a -> (a, (fdFun fd2) a)) -fdFanOut (FDC b) FDI = FDG (\a -> (b, a)) -fdFanOut (FDC b) (FDC c) = FDC (b, c) -fdFanOut (FDC b) fd2 = FDG (\a -> (b, (fdFun fd2) a)) -fdFanOut (FDE f1 f1ne) (FDE f2 f2ne) = FDE f1f2 f1f2ne - where - f1f2 NoEvent = f1f2ne - f1f2 ea@(Event _) = (f1 ea, f2 ea) - - f1f2ne = (f1ne, f2ne) -fdFanOut fd1 fd2 = - FDG (\a -> ((fdFun fd1) a, (fdFun fd2) a)) - - --- Verifies that the first argument is NoEvent. Returns the value of the --- second argument that is the case. Raises an error otherwise. --- Used to check that functions on events do not map NoEvent to Event --- wherever that assumption is exploited. -vfyNoEv :: Event a -> b -> b -vfyNoEv NoEvent b = b -vfyNoEv _ _ = usrErr "AFRP" "vfyNoEv" "Assertion failed: Functions on events must not map NoEvent to Event." - - --- Freezes a "running" signal function, i.e., turns it into a continuation in --- the form of a plain signal function. -freeze :: SF' a b -> DTime -> SF a b -freeze sf dt = SF {sfTF = (sfTF' sf) dt} - - -freezeCol :: Functor col => col (SF' a b) -> DTime -> col (SF a b) -freezeCol sfs dt = fmap (flip freeze dt) sfs - - ------------------------------------------------------------------------------- --- Arrow instance and implementation ------------------------------------------------------------------------------- -#if __GLASGOW_HASKELL__ >= 610 -instance Control.Category.Category SF where - (.) = flip compPrim - id = SF $ \x -> (sfId,x) -#else -#endif - -instance Arrow SF where - arr = arrPrim - first = firstPrim - second = secondPrim - (***) = parSplitPrim - (&&&) = parFanOutPrim -#if __GLASGOW_HASKELL__ >= 610 -#else - (>>>) = compPrim -#endif - - --- Lifting. - --- | Lifts a pure function into a signal function (applied pointwise). -{-# NOINLINE arrPrim #-} -arrPrim :: (a -> b) -> SF a b -arrPrim f = SF {sfTF = \a -> (sfArrG f, f a)} - --- | Lifts a pure function into a signal function applied to events --- (applied pointwise). -{-# RULES "arrPrim/arrEPrim" arrPrim = arrEPrim #-} -arrEPrim :: (Event a -> b) -> SF (Event a) b -arrEPrim f = SF {sfTF = \a -> (sfArrE f (f NoEvent), f a)} - - --- Composition. --- The definition exploits the following identities: --- sf >>> identity = sf -- New --- identity >>> sf = sf -- New --- sf >>> constant c = constant c --- constant c >>> arr f = constant (f c) --- arr f >>> arr g = arr (g . f) --- --- !!! Notes/Questions: --- !!! How do we know that the optimizations terminate? --- !!! Probably by some kind of size argument on the SF tree. --- !!! E.g. (Hopefully) all compPrim optimizations are such that --- !!! the number of compose nodes decrease. --- !!! Should verify this! --- --- !!! There is a tension between using SFInv to signal to superior --- !!! signal functions that the subordinate signal function will not --- !!! change form, and using SFCpAXA to allow fusion in the context --- !!! of some suitable superior signal function. -compPrim :: SF a b -> SF b c -> SF a c -compPrim (SF {sfTF = tf10}) (SF {sfTF = tf20}) = SF {sfTF = tf0} - where - tf0 a0 = (cpXX sf1 sf2, c0) - where - (sf1, b0) = tf10 a0 - (sf2, c0) = tf20 b0 - --- The following defs are not local to compPrim because cpAXA needs to be --- called from parSplitPrim. --- Naming convention: cp where and is one of: --- X - arbitrary signal function --- A - arbitrary pure arrow --- C - constant arrow --- E - event-processing arrow --- G - arrow known not to be identity, constant (C) or --- event-processing (E). - -cpXX :: SF' a b -> SF' b c -> SF' a c -cpXX (SFArr _ fd1) sf2 = cpAX fd1 sf2 -cpXX sf1 (SFArr _ fd2) = cpXA sf1 fd2 -{- --- !!! 2005-07-07: Too strict. --- !!! But the question is if it is worth to define pre in terms of sscan ... --- !!! It is slower than the simplest possible pre, and the kind of coding --- !!! required to ensure that the laziness props of the second SF are --- !!! preserved might just slow things down further ... -cpXX (SFSScan _ f1 s1 b) (SFSScan _ f2 s2 c) = - sfSScan f (s1, b, s2, c) c - where - f (s1, b, s2, c) a = - case f1 s1 a of - Nothing -> - case f2 s2 b of - Nothing -> Nothing - Just (s2', c') -> Just ((s1, b, s2', c'), c') - Just (s1', b') -> - case f2 s2 b' of - Nothing -> Just ((s1', b', s2, c), c) - Just (s2', c') -> Just ((s1', b', s2', c'), c') --} --- !!! 2005-07-07: Indeed, this is a bit slower than the code above (14%). --- !!! But both are better than not composing (35% faster and 26% faster)! -cpXX (SFSScan _ f1 s1 b) (SFSScan _ f2 s2 c) = - sfSScan f (s1, b, s2, c) c - where - f (s1, b, s2, c) a = - let - (u, s1', b') = case f1 s1 a of - Nothing -> (True, s1, b) - Just (s1',b') -> (False, s1', b') - in - case f2 s2 b' of - Nothing | u -> Nothing - | otherwise -> Just ((s1', b', s2, c), c) - Just (s2', c') -> Just ((s1', b', s2', c'), c') -cpXX (SFSScan _ f1 s1 eb) (SFEP _ f2 s2 cne) = - sfSScan f (s1, eb, s2, cne) cne - where - f (s1, eb, s2, cne) a = - case f1 s1 a of - Nothing -> - case eb of - NoEvent -> Nothing - Event b -> - let (s2', c, cne') = f2 s2 b - in - Just ((s1, eb, s2', cne'), c) - Just (s1', eb') -> - case eb' of - NoEvent -> Just ((s1', eb', s2, cne), cne) - Event b -> - let (s2', c, cne') = f2 s2 b - in - Just ((s1', eb', s2', cne'), c) --- !!! 2005-07-09: This seems to yield only a VERY marginal speedup --- !!! without seq. With seq, substantial speedup! -cpXX (SFEP _ f1 s1 bne) (SFSScan _ f2 s2 c) = - sfSScan f (s1, bne, s2, c) c - where - f (s1, bne, s2, c) ea = - let (u, s1', b', bne') = case ea of - NoEvent -> (True, s1, bne, bne) - Event a -> - let (s1', b, bne') = f1 s1 a - in - (False, s1', b, bne') - in - case f2 s2 b' of - Nothing | u -> Nothing - | otherwise -> Just (seq s1' (s1', bne', s2, c), c) - Just (s2', c') -> Just (seq s1' (s1', bne', s2', c'), c') --- The function "f" is invoked whenever an event is to be processed. It then --- computes the output, the new state, and the new NoEvent output. --- However, when sequencing event processors, the ones in the latter --- part of the chain may not get invoked since previous ones may --- decide not to "fire". But a "new" NoEvent output still has to be --- produced, i.e. the old one retained. Since it cannot be computed by --- invoking the last event-processing function in the chain, it has to --- be remembered. Since the composite event-processing function remains --- constant/unchanged, the NoEvent output has to be part of the state. --- An alternarive would be to make the event-processing function take an --- extra argument. But that is likely to make the simple case more --- expensive. See note at sfEP. -cpXX (SFEP _ f1 s1 bne) (SFEP _ f2 s2 cne) = - sfEP f (s1, s2, cne) (vfyNoEv bne cne) - where - f (s1, s2, cne) a = - case f1 s1 a of - (s1', NoEvent, NoEvent) -> ((s1', s2, cne), cne, cne) - (s1', Event b, NoEvent) -> - let (s2', c, cne') = f2 s2 b in ((s1', s2', cne'), c, cne') - _ -> usrErr "AFRP" "cpXX" "Assertion failed: Functions on events must not map NoEvent to Event." --- !!! 2005-06-28: Why isn't SFCpAXA (FDC ...) checked for? --- !!! No invariant rules that out, and it would allow to drop the --- !!! event processor ... Does that happen elsewhere? -cpXX sf1@(SFEP _ _ _ _) (SFCpAXA _ (FDE f21 f21ne) sf22 fd23) = - cpXX (cpXE sf1 f21 f21ne) (cpXA sf22 fd23) --- f21 will (hopefully) be invoked less frequently if merged with the --- event processor. -cpXX sf1@(SFEP _ _ _ _) (SFCpAXA _ (FDG f21) sf22 fd23) = - cpXX (cpXG sf1 f21) (cpXA sf22 fd23) --- Only functions whose domain is known to be Event can be merged --- from the left with event processors. -cpXX (SFCpAXA _ fd11 sf12 (FDE f13 f13ne)) sf2@(SFEP _ _ _ _) = - cpXX (cpAX fd11 sf12) (cpEX f13 f13ne sf2) --- !!! Other cases to look out for: --- !!! any sf >>> SFCpAXA = SFCpAXA if first arr is const. --- !!! But the following will presumably not work due to type restrictions. --- !!! Need to reconstruct sf2 I think. --- cpXX sf1 sf2@(SFCpAXA _ _ (FDC b) sf22 fd23) = sf2 -cpXX (SFCpAXA _ fd11 sf12 fd13) (SFCpAXA _ fd21 sf22 fd23) = - -- Termination: The first argument to cpXX is no larger than - -- the current first argument, and the second is smaller. - cpAXA fd11 (cpXX (cpXA sf12 (fdComp fd13 fd21)) sf22) fd23 --- !!! 2005-06-27: The if below accounts for a significant slowdown. --- !!! One would really like a cheme where opts only take place --- !!! after a structural change ... --- cpXX sf1 sf2 = cpXXInv sf1 sf2 --- cpXX sf1 sf2 = cpXXAux sf1 sf2 -cpXX sf1 sf2 = SF' tf -- False - -- if sfIsInv sf1 && sfIsInv sf2 then cpXXInv sf1 sf2 else SF' tf False - where - tf dt a = (cpXX sf1' sf2', c) - where - (sf1', b) = (sfTF' sf1) dt a - (sf2', c) = (sfTF' sf2) dt b - - -{- -cpXXAux sf1@(SF' _ _) sf2@(SF' _ _) = SF' tf False - where - tf dt a = (cpXXAux sf1' sf2', c) - where - (sf1', b) = (sfTF' sf1) dt a - (sf2', c) = (sfTF' sf2) dt b -cpXXAux sf1 sf2 = SF' tf False - where - tf dt a = (cpXXAux sf1' sf2', c) - where - (sf1', b) = (sfTF' sf1) dt a - (sf2', c) = (sfTF' sf2) dt b --} - -{- -cpXXAux sf1 sf2 | unsimplifiable sf1 sf2 = SF' tf False - | otherwise = cpXX sf1 sf2 - where - tf dt a = (cpXXAux sf1' sf2', c) - where - (sf1', b) = (sfTF' sf1) dt a - (sf2', c) = (sfTF' sf2) dt b - - unsimplifiable sf1@(SF' _ _) sf2@(SF' _ _) = True - unsimplifiable sf1 sf2 = True --} - -{- --- wrong ... -cpXXAux sf1@(SF' _ False) sf2 = SF' tf False -cpXXAux sf1@(SFCpAXA _ False _ _ _) sf2 = SF' tf False -cpXXAux sf1 sf2@(SF' _ False) = SF' tf False -cpXXAux sf1 sf2@(SFCpAXA _ False _ _ _) = SF' tf False -cpXXAux sf1 sf2 = - if sfIsInv sf1 && sfIsInv sf2 then cpXXInv sf1 sf2 else SF' tf False - where - tf dt a = (cpXXAux sf1' sf2', c) - where - (sf1', b) = (sfTF' sf1) dt a - (sf2', c) = (sfTF' sf2) dt b --} - -{- -cpXXInv sf1 sf2 = SF' tf True - where - tf dt a = sf1 `seq` sf2 `seq` (cpXXInv sf1' sf2', c) - where - (sf1', b) = (sfTF' sf1) dt a - (sf2', c) = (sfTF' sf2) dt b --} - --- !!! No. We need local defs. Keep fd1 and fd2. Extract f1 and f2 --- !!! once and fo all. Get rid of FDI and FDC at the top level. --- !!! First local def. analyse sf2. SFArr, SFAcc etc. tf in --- !!! recursive case just make use of f1 and f3. --- !!! if sf2 is SFInv, that's delegated to a second local --- !!! recursive def. that does not analyse sf2. - -cpAXA :: FunDesc a b -> SF' b c -> FunDesc c d -> SF' a d --- Termination: cpAX/cpXA, via cpCX, cpEX etc. only call cpAXA if sf2 --- is SFCpAXA, and then on the embedded sf and hence on a smaller arg. -cpAXA FDI sf2 fd3 = cpXA sf2 fd3 -cpAXA fd1 sf2 FDI = cpAX fd1 sf2 -cpAXA (FDC b) sf2 fd3 = cpCXA b sf2 fd3 -cpAXA _ _ (FDC d) = sfConst d -cpAXA fd1 sf2 fd3 = - cpAXAAux fd1 (fdFun fd1) fd3 (fdFun fd3) sf2 - where - -- Really: cpAXAAux :: SF' b c -> SF' a d - -- Note: Event cases are not optimized (EXA etc.) - cpAXAAux :: FunDesc a b -> (a -> b) -> FunDesc c d -> (c -> d) - -> SF' b c -> SF' a d - cpAXAAux fd1 _ fd3 _ (SFArr _ fd2) = - sfArr (fdComp (fdComp fd1 fd2) fd3) - cpAXAAux fd1 _ fd3 _ sf2@(SFSScan _ _ _ _) = - cpAX fd1 (cpXA sf2 fd3) - cpAXAAux fd1 _ fd3 _ sf2@(SFEP _ _ _ _) = - cpAX fd1 (cpXA sf2 fd3) - cpAXAAux fd1 _ fd3 _ (SFCpAXA _ fd21 sf22 fd23) = - cpAXA (fdComp fd1 fd21) sf22 (fdComp fd23 fd3) - cpAXAAux fd1 f1 fd3 f3 sf2 = SFCpAXA tf fd1 sf2 fd3 -{- - if sfIsInv sf2 then - cpAXAInv fd1 f1 fd3 f3 sf2 - else - SFCpAXA tf False fd1 sf2 fd3 --} - where - tf dt a = (cpAXAAux fd1 f1 fd3 f3 sf2', f3 c) - where - (sf2', c) = (sfTF' sf2) dt (f1 a) - -{- - cpAXAInv fd1 f1 fd3 f3 sf2 = SFCpAXA tf True fd1 sf2 fd3 - where - tf dt a = sf2 `seq` (cpAXAInv fd1 f1 fd3 f3 sf2', f3 c) - where - (sf2', c) = (sfTF' sf2) dt (f1 a) --} - -cpAX :: FunDesc a b -> SF' b c -> SF' a c -cpAX FDI sf2 = sf2 -cpAX (FDC b) sf2 = cpCX b sf2 -cpAX (FDE f1 f1ne) sf2 = cpEX f1 f1ne sf2 -cpAX (FDG f1) sf2 = cpGX f1 sf2 - -cpXA :: SF' a b -> FunDesc b c -> SF' a c -cpXA sf1 FDI = sf1 -cpXA _ (FDC c) = sfConst c -cpXA sf1 (FDE f2 f2ne) = cpXE sf1 f2 f2ne -cpXA sf1 (FDG f2) = cpXG sf1 f2 - --- Don't forget that the remaining signal function, if it is --- SF', later could turn into something else, like SFId. -cpCX :: b -> SF' b c -> SF' a c -cpCX b (SFArr _ fd2) = sfConst ((fdFun fd2) b) --- 2005-07-01: If we were serious about the semantics of sscan being required --- to be independent of the sampling interval, I guess one could argue for a --- fixed-point computation here ... Or maybe not. --- cpCX b (SFSScan _ _ _ _) = sfConst -cpCX b (SFSScan _ f s c) = sfSScan (\s _ -> f s b) s c -cpCX b (SFEP _ _ _ cne) = sfConst (vfyNoEv b cne) -cpCX b (SFCpAXA _ fd21 sf22 fd23) = - cpCXA ((fdFun fd21) b) sf22 fd23 -cpCX b sf2 = SFCpAXA tf (FDC b) sf2 FDI -{- - if sfIsInv sf2 then - cpCXInv b sf2 - else - SFCpAXA tf False (FDC b) sf2 FDI --} - where - tf dt _ = (cpCX b sf2', c) - where - (sf2', c) = (sfTF' sf2) dt b - - -{- -cpCXInv b sf2 = SFCpAXA tf True (FDC b) sf2 FDI - where - tf dt _ = sf2 `seq` (cpCXInv b sf2', c) - where - (sf2', c) = (sfTF' sf2) dt b --} - - -cpCXA :: b -> SF' b c -> FunDesc c d -> SF' a d -cpCXA b sf2 FDI = cpCX b sf2 -cpCXA _ _ (FDC c) = sfConst c -cpCXA b sf2 fd3 = cpCXAAux (FDC b) b fd3 (fdFun fd3) sf2 - where - -- fd1 = FDC b - -- f3 = fdFun fd3 - - -- Really: SF' b c -> SF' a d - cpCXAAux :: FunDesc a b -> b -> FunDesc c d -> (c -> d) - -> SF' b c -> SF' a d - cpCXAAux _ b _ f3 (SFArr _ fd2) = sfConst (f3 ((fdFun fd2) b)) - cpCXAAux _ b _ f3 (SFSScan _ f s c) = sfSScan f' s (f3 c) - where - f' s _ = case f s b of - Nothing -> Nothing - Just (s', c') -> Just (s', f3 c') - cpCXAAux _ b _ f3 (SFEP _ _ _ cne) = sfConst (f3 (vfyNoEv b cne)) - cpCXAAux _ b fd3 _ (SFCpAXA _ fd21 sf22 fd23) = - cpCXA ((fdFun fd21) b) sf22 (fdComp fd23 fd3) - cpCXAAux fd1 b fd3 f3 sf2 = SFCpAXA tf fd1 sf2 fd3 -{- - if sfIsInv sf2 then - cpCXAInv fd1 b fd3 f3 sf2 - else - SFCpAXA tf False fd1 sf2 fd3 --} - where - tf dt _ = (cpCXAAux fd1 b fd3 f3 sf2', f3 c) - where - (sf2', c) = (sfTF' sf2) dt b - -{- - -- For some reason, seq on sf2' in tf is faster than making - -- cpCXAInv strict in sf2 by seq-ing on the top level (which would - -- be similar to pattern matching on sf2). - cpCXAInv fd1 b fd3 f3 sf2 = SFCpAXA tf True fd1 sf2 fd3 - where - tf dt _ = sf2 `seq` (cpCXAInv fd1 b fd3 f3 sf2', f3 c) - where - (sf2', c) = (sfTF' sf2) dt b --} - - -cpGX :: (a -> b) -> SF' b c -> SF' a c -cpGX f1 sf2 = cpGXAux (FDG f1) f1 sf2 - where - cpGXAux :: FunDesc a b -> (a -> b) -> SF' b c -> SF' a c - cpGXAux fd1 _ (SFArr _ fd2) = sfArr (fdComp fd1 fd2) - -- We actually do know that (fdComp (FDG f1) fd21) is going to - -- result in an FDG. So we *could* call a cpGXA here. But the - -- price is "inlining" of part of fdComp. - cpGXAux _ f1 (SFSScan _ f s c) = sfSScan (\s a -> f s (f1 a)) s c - -- We really shouldn't see an EP here, as that would mean - -- an arrow INTRODUCING events ... - cpGXAux fd1 _ (SFCpAXA _ fd21 sf22 fd23) = - cpAXA (fdComp fd1 fd21) sf22 fd23 - cpGXAux fd1 f1 sf2 = SFCpAXA tf fd1 sf2 FDI -{- - if sfIsInv sf2 then - cpGXInv fd1 f1 sf2 - else - SFCpAXA tf False fd1 sf2 FDI --} - where - tf dt a = (cpGXAux fd1 f1 sf2', c) - where - (sf2', c) = (sfTF' sf2) dt (f1 a) - -{- - cpGXInv fd1 f1 sf2 = SFCpAXA tf True fd1 sf2 FDI - where - tf dt a = sf2 `seq` (cpGXInv fd1 f1 sf2', c) - where - (sf2', c) = (sfTF' sf2) dt (f1 a) --} - - -cpXG :: SF' a b -> (b -> c) -> SF' a c -cpXG sf1 f2 = cpXGAux (FDG f2) f2 sf1 - where - -- Really: cpXGAux :: SF' a b -> SF' a c - cpXGAux :: FunDesc b c -> (b -> c) -> SF' a b -> SF' a c - cpXGAux fd2 _ (SFArr _ fd1) = sfArr (fdComp fd1 fd2) - cpXGAux _ f2 (SFSScan _ f s b) = sfSScan f' s (f2 b) - where - f' s a = case f s a of - Nothing -> Nothing - Just (s', b') -> Just (s', f2 b') - cpXGAux _ f2 (SFEP _ f1 s bne) = sfEP f s (f2 bne) - where - f s a = let (s', b, bne') = f1 s a in (s', f2 b, f2 bne') - cpXGAux fd2 _ (SFCpAXA _ fd11 sf12 fd22) = - cpAXA fd11 sf12 (fdComp fd22 fd2) - cpXGAux fd2 f2 sf1 = SFCpAXA tf FDI sf1 fd2 -{- - if sfIsInv sf1 then - cpXGInv fd2 f2 sf1 - else - SFCpAXA tf False FDI sf1 fd2 --} - where - tf dt a = (cpXGAux fd2 f2 sf1', f2 b) - where - (sf1', b) = (sfTF' sf1) dt a - -{- - cpXGInv fd2 f2 sf1 = SFCpAXA tf True FDI sf1 fd2 - where - tf dt a = (cpXGInv fd2 f2 sf1', f2 b) - where - (sf1', b) = (sfTF' sf1) dt a --} - -cpEX :: (Event a -> b) -> b -> SF' b c -> SF' (Event a) c -cpEX f1 f1ne sf2 = cpEXAux (FDE f1 f1ne) f1 f1ne sf2 - where - cpEXAux :: FunDesc (Event a) b -> (Event a -> b) -> b - -> SF' b c -> SF' (Event a) c - cpEXAux fd1 _ _ (SFArr _ fd2) = sfArr (fdComp fd1 fd2) - cpEXAux _ f1 _ (SFSScan _ f s c) = sfSScan (\s a -> f s (f1 a)) s c - -- We must not capture cne in the f closure since cne can change! - -- See cpXX the SFEP/SFEP case for a similar situation. However, - -- FDE represent a state-less signal function, so *its* NoEvent - -- value never changes. Hence we only need to verify that it is - -- NoEvent once. - cpEXAux _ f1 f1ne (SFEP _ f2 s cne) = - sfEP f (s, cne) (vfyNoEv f1ne cne) - where - f scne@(s, cne) a = - case (f1 (Event a)) of - NoEvent -> (scne, cne, cne) - Event b -> - let (s', c, cne') = f2 s b in ((s', cne'), c, cne') - cpEXAux fd1 _ _ (SFCpAXA _ fd21 sf22 fd23) = - cpAXA (fdComp fd1 fd21) sf22 fd23 - -- The rationale for the following is that the case analysis - -- is typically not going to be more expensive than applying - -- the function and possibly a bit cheaper. Thus if events - -- are sparse, we might win, and if not, we don't loose to - -- much. - cpEXAux fd1 f1 f1ne sf2 = SFCpAXA tf fd1 sf2 FDI -{- - if sfIsInv sf2 then - cpEXInv fd1 f1 f1ne sf2 - else - SFCpAXA tf False fd1 sf2 FDI --} - where - tf dt ea = (cpEXAux fd1 f1 f1ne sf2', c) - where - (sf2', c) = - case ea of - NoEvent -> (sfTF' sf2) dt f1ne - _ -> (sfTF' sf2) dt (f1 ea) - -{- - cpEXInv fd1 f1 f1ne sf2 = SFCpAXA tf True fd1 sf2 FDI - where - tf dt ea = sf2 `seq` (cpEXInv fd1 f1 f1ne sf2', c) - where - (sf2', c) = - case ea of - NoEvent -> (sfTF' sf2) dt f1ne - _ -> (sfTF' sf2) dt (f1 ea) --} - -cpXE :: SF' a (Event b) -> (Event b -> c) -> c -> SF' a c -cpXE sf1 f2 f2ne = cpXEAux (FDE f2 f2ne) f2 f2ne sf1 - where - cpXEAux :: FunDesc (Event b) c -> (Event b -> c) -> c - -> SF' a (Event b) -> SF' a c - cpXEAux fd2 _ _ (SFArr _ fd1) = sfArr (fdComp fd1 fd2) - cpXEAux _ f2 f2ne (SFSScan _ f s eb) = sfSScan f' s (f2 eb) - where - f' s a = case f s a of - Nothing -> Nothing - Just (s', NoEvent) -> Just (s', f2ne) - Just (s', eb') -> Just (s', f2 eb') - cpXEAux _ f2 f2ne (SFEP _ f1 s ebne) = - sfEP f s (vfyNoEv ebne f2ne) - where - f s a = - case f1 s a of - (s', NoEvent, NoEvent) -> (s', f2ne, f2ne) - (s', eb, NoEvent) -> (s', f2 eb, f2ne) - _ -> usrErr "AFRP" "cpXEAux" "Assertion failed: Functions on events must not map NoEvent to Event." - cpXEAux fd2 _ _ (SFCpAXA _ fd11 sf12 fd13) = - cpAXA fd11 sf12 (fdComp fd13 fd2) - cpXEAux fd2 f2 f2ne sf1 = SFCpAXA tf FDI sf1 fd2 -{- - if sfIsInv sf1 then - cpXEInv fd2 f2 f2ne sf1 - else - SFCpAXA tf False FDI sf1 fd2 --} - where - tf dt a = (cpXEAux fd2 f2 f2ne sf1', - case eb of NoEvent -> f2ne; _ -> f2 eb) - where - (sf1', eb) = (sfTF' sf1) dt a - -{- - cpXEInv fd2 f2 f2ne sf1 = SFCpAXA tf True FDI sf1 fd2 - where - tf dt a = sf1 `seq` (cpXEInv fd2 f2 f2ne sf1', - case eb of NoEvent -> f2ne; _ -> f2 eb) - where - (sf1', eb) = (sfTF' sf1) dt a --} - - --- Widening. --- The definition exploits the following identities: --- first identity = identity -- New --- first (constant b) = arr (\(_, c) -> (b, c)) --- (first (arr f)) = arr (\(a, c) -> (f a, c)) -firstPrim :: SF a b -> SF (a,c) (b,c) -firstPrim (SF {sfTF = tf10}) = SF {sfTF = tf0} - where - tf0 ~(a0, c0) = (fpAux sf1, (b0, c0)) - where - (sf1, b0) = tf10 a0 - - --- Also used in parSplitPrim -fpAux :: SF' a b -> SF' (a,c) (b,c) -fpAux (SFArr _ FDI) = sfId -- New -fpAux (SFArr _ (FDC b)) = sfArrG (\(~(_, c)) -> (b, c)) -fpAux (SFArr _ fd1) = sfArrG (\(~(a, c)) -> ((fdFun fd1) a, c)) -fpAux sf1 = SF' tf - -- if sfIsInv sf1 then fpInv sf1 else SF' tf False - where - tf dt ~(a, c) = (fpAux sf1', (b, c)) - where - (sf1', b) = (sfTF' sf1) dt a - - -{- -fpInv :: SF' a b -> SF' (a,c) (b,c) -fpInv sf1 = SF' tf True - where - tf dt ~(a, c) = sf1 `seq` (fpInv sf1', (b, c)) - where - (sf1', b) = (sfTF' sf1) dt a --} - - --- Mirror image of first. -secondPrim :: SF a b -> SF (c,a) (c,b) -secondPrim (SF {sfTF = tf10}) = SF {sfTF = tf0} - where - tf0 ~(c0, a0) = (spAux sf1, (c0, b0)) - where - (sf1, b0) = tf10 a0 - - --- Also used in parSplitPrim -spAux :: SF' a b -> SF' (c,a) (c,b) -spAux (SFArr _ FDI) = sfId -- New -spAux (SFArr _ (FDC b)) = sfArrG (\(~(c, _)) -> (c, b)) -spAux (SFArr _ fd1) = sfArrG (\(~(c, a)) -> (c, (fdFun fd1) a)) -spAux sf1 = SF' tf - -- if sfIsInv sf1 then spInv sf1 else SF' tf False - where - tf dt ~(c, a) = (spAux sf1', (c, b)) - where - (sf1', b) = (sfTF' sf1) dt a - - -{- -spInv :: SF' a b -> SF' (c,a) (c,b) -spInv sf1 = SF' tf True - where - tf dt ~(c, a) = sf1 `seq` (spInv sf1', (c, b)) - where - (sf1', b) = (sfTF' sf1) dt a --} - - --- Parallel composition. --- The definition exploits the following identities (that hold for SF): --- identity *** identity = identity -- New --- sf *** identity = first sf -- New --- identity *** sf = second sf -- New --- constant b *** constant d = constant (b, d) --- constant b *** arr f2 = arr (\(_, c) -> (b, f2 c) --- arr f1 *** constant d = arr (\(a, _) -> (f1 a, d) --- arr f1 *** arr f2 = arr (\(a, b) -> (f1 a, f2 b) -parSplitPrim :: SF a b -> SF c d -> SF (a,c) (b,d) -parSplitPrim (SF {sfTF = tf10}) (SF {sfTF = tf20}) = SF {sfTF = tf0} - where - tf0 ~(a0, c0) = (psXX sf1 sf2, (b0, d0)) - where - (sf1, b0) = tf10 a0 - (sf2, d0) = tf20 c0 - - -- Naming convention: ps where and is one of: - -- X - arbitrary signal function - -- A - arbitrary pure arrow - -- C - constant arrow - - psXX :: SF' a b -> SF' c d -> SF' (a,c) (b,d) - psXX (SFArr _ fd1) (SFArr _ fd2) = sfArr (fdPar fd1 fd2) - psXX (SFArr _ FDI) sf2 = spAux sf2 -- New - psXX (SFArr _ (FDC b)) sf2 = psCX b sf2 - psXX (SFArr _ fd1) sf2 = psAX (fdFun fd1) sf2 - psXX sf1 (SFArr _ FDI) = fpAux sf1 -- New - psXX sf1 (SFArr _ (FDC d)) = psXC sf1 d - psXX sf1 (SFArr _ fd2) = psXA sf1 (fdFun fd2) --- !!! Unclear if this really is a gain. --- !!! potentially unnecessary tupling and untupling. --- !!! To be investigated. --- !!! 2005-07-01: At least for MEP 6, the corresponding opt for --- !!! &&& was harmfull. On that basis, disable it here too. --- psXX (SFCpAXA _ fd11 sf12 fd13) (SFCpAXA _ fd21 sf22 fd23) = --- cpAXA (fdPar fd11 fd21) (psXX sf12 sf22) (fdPar fd13 fd23) - psXX sf1 sf2 = SF' tf -{- - if sfIsInv sf1 && sfIsInv sf2 then - psXXInv sf1 sf2 - else - SF' tf False --} - where - tf dt ~(a, c) = (psXX sf1' sf2', (b, d)) - where - (sf1', b) = (sfTF' sf1) dt a - (sf2', d) = (sfTF' sf2) dt c - -{- - psXXInv :: SF' a b -> SF' c d -> SF' (a,c) (b,d) - psXXInv sf1 sf2 = SF' tf True - where - tf dt ~(a, c) = sf1 `seq` sf2 `seq` (psXXInv sf1' sf2', - (b, d)) - where - (sf1', b) = (sfTF' sf1) dt a - (sf2', d) = (sfTF' sf2) dt c --} - - psCX :: b -> SF' c d -> SF' (a,c) (b,d) - psCX b (SFArr _ fd2) = sfArr (fdPar (FDC b) fd2) - psCX b sf2 = SF' tf -{- - if sfIsInv sf2 then - psCXInv b sf2 - else - SF' tf False --} - where - tf dt ~(_, c) = (psCX b sf2', (b, d)) - where - (sf2', d) = (sfTF' sf2) dt c - -{- - psCXInv :: b -> SF' c d -> SF' (a,c) (b,d) - psCXInv b sf2 = SF' tf True - where - tf dt ~(_, c) = sf2 `seq` (psCXInv b sf2', (b, d)) - where - (sf2', d) = (sfTF' sf2) dt c --} - - psXC :: SF' a b -> d -> SF' (a,c) (b,d) - psXC (SFArr _ fd1) d = sfArr (fdPar fd1 (FDC d)) - psXC sf1 d = SF' tf -{- - if sfIsInv sf1 then - psXCInv sf1 d - else - SF' tf False --} - where - tf dt ~(a, _) = (psXC sf1' d, (b, d)) - where - (sf1', b) = (sfTF' sf1) dt a - -{- - psXCInv :: SF' a b -> d -> SF' (a,c) (b,d) - psXCInv sf1 d = SF' tf True - where - tf dt ~(a, _) = sf1 `seq` (psXCInv sf1' d, (b, d)) - where - (sf1', b) = (sfTF' sf1) dt a --} - - psAX :: (a -> b) -> SF' c d -> SF' (a,c) (b,d) - psAX f1 (SFArr _ fd2) = sfArr (fdPar (FDG f1) fd2) - psAX f1 sf2 = SF' tf -{- - if sfIsInv sf2 then - psAXInv f1 sf2 - else - SF' tf False --} - where - tf dt ~(a, c) = (psAX f1 sf2', (f1 a, d)) - where - (sf2', d) = (sfTF' sf2) dt c - -{- - psAXInv :: (a -> b) -> SF' c d -> SF' (a,c) (b,d) - psAXInv f1 sf2 = SF' tf True - where - tf dt ~(a, c) = sf2 `seq` (psAXInv f1 sf2', (f1 a, d)) - where - (sf2', d) = (sfTF' sf2) dt c --} - - psXA :: SF' a b -> (c -> d) -> SF' (a,c) (b,d) - psXA (SFArr _ fd1) f2 = sfArr (fdPar fd1 (FDG f2)) - psXA sf1 f2 = SF' tf -{- - if sfIsInv sf1 then - psXAInv sf1 f2 - else - SF' tf False --} - where - tf dt ~(a, c) = (psXA sf1' f2, (b, f2 c)) - where - (sf1', b) = (sfTF' sf1) dt a - -{- - psXAInv :: SF' a b -> (c -> d) -> SF' (a,c) (b,d) - psXAInv sf1 f2 = SF' tf True - where - tf dt ~(a, c) = sf1 `seq` (psXAInv sf1' f2, (b, f2 c)) - where - (sf1', b) = (sfTF' sf1) dt a --} - - --- !!! Hmmm. Why don't we optimize the FDE cases here??? --- !!! Seems pretty obvious that we should! --- !!! It should also be possible to optimize an event processor in --- !!! parallel with another event processor or an Arr FDE. - -parFanOutPrim :: SF a b -> SF a c -> SF a (b, c) -parFanOutPrim (SF {sfTF = tf10}) (SF {sfTF = tf20}) = SF {sfTF = tf0} - where - tf0 a0 = (pfoXX sf1 sf2, (b0, c0)) - where - (sf1, b0) = tf10 a0 - (sf2, c0) = tf20 a0 - - -- Naming convention: pfo where and is one of: - -- X - arbitrary signal function - -- A - arbitrary pure arrow - -- I - identity arrow - -- C - constant arrow - - pfoXX :: SF' a b -> SF' a c -> SF' a (b ,c) - pfoXX (SFArr _ fd1) (SFArr _ fd2) = sfArr(fdFanOut fd1 fd2) - pfoXX (SFArr _ FDI) sf2 = pfoIX sf2 - pfoXX (SFArr _ (FDC b)) sf2 = pfoCX b sf2 - pfoXX (SFArr _ fd1) sf2 = pfoAX (fdFun fd1) sf2 - pfoXX sf1 (SFArr _ FDI) = pfoXI sf1 - pfoXX sf1 (SFArr _ (FDC c)) = pfoXC sf1 c - pfoXX sf1 (SFArr _ fd2) = pfoXA sf1 (fdFun fd2) --- !!! Unclear if this really would be a gain --- !!! 2005-07-01: NOT a win for MEP 6. --- pfoXX (SFCpAXA _ fd11 sf12 fd13) (SFCpAXA _ fd21 sf22 fd23) = --- cpAXA (fdPar fd11 fd21) (psXX sf12 sf22) (fdPar fd13 fd23) - pfoXX sf1 sf2 = SF' tf -{- - if sfIsInv sf1 && sfIsInv sf2 then - pfoXXInv sf1 sf2 - else - SF' tf False --} - where - tf dt a = (pfoXX sf1' sf2', (b, c)) - where - (sf1', b) = (sfTF' sf1) dt a - (sf2', c) = (sfTF' sf2) dt a - -{- - pfoXXInv :: SF' a b -> SF' a c -> SF' a (b ,c) - pfoXXInv sf1 sf2 = SF' tf True - where - tf dt a = sf1 `seq` sf2 `seq` (pfoXXInv sf1' sf2', (b, c)) - where - (sf1', b) = (sfTF' sf1) dt a - (sf2', c) = (sfTF' sf2) dt a --} - - pfoIX :: SF' a c -> SF' a (a ,c) - pfoIX (SFArr _ fd2) = sfArr (fdFanOut FDI fd2) - pfoIX sf2 = SF' tf -{- - if sfIsInv sf2 then - pfoIXInv sf2 - else - SF' tf False --} - where - tf dt a = (pfoIX sf2', (a, c)) - where - (sf2', c) = (sfTF' sf2) dt a - -{- - pfoIXInv :: SF' a c -> SF' a (a ,c) - pfoIXInv sf2 = SF' tf True - where - tf dt a = sf2 `seq` (pfoIXInv sf2', (a, c)) - where - (sf2', c) = (sfTF' sf2) dt a --} - - pfoXI :: SF' a b -> SF' a (b ,a) - pfoXI (SFArr _ fd1) = sfArr (fdFanOut fd1 FDI) - pfoXI sf1 = SF' tf -{- - if sfIsInv sf1 then - pfoXIInv sf1 - else - SF' tf False --} - where - tf dt a = (pfoXI sf1', (b, a)) - where - (sf1', b) = (sfTF' sf1) dt a - -{- - pfoXIInv :: SF' a b -> SF' a (b ,a) - pfoXIInv sf1 = SF' tf True - where - tf dt a = sf1 `seq` (pfoXIInv sf1', (b, a)) - where - (sf1', b) = (sfTF' sf1) dt a --} - - pfoCX :: b -> SF' a c -> SF' a (b ,c) - pfoCX b (SFArr _ fd2) = sfArr (fdFanOut (FDC b) fd2) - pfoCX b sf2 = SF' tf -{- - if sfIsInv sf2 then - pfoCXInv b sf2 - else - SF' tf False --} - where - tf dt a = (pfoCX b sf2', (b, c)) - where - (sf2', c) = (sfTF' sf2) dt a - -{- - pfoCXInv :: b -> SF' a c -> SF' a (b ,c) - pfoCXInv b sf2 = SF' tf True - where - tf dt a = sf2 `seq` (pfoCXInv b sf2', (b, c)) - where - (sf2', c) = (sfTF' sf2) dt a --} - - pfoXC :: SF' a b -> c -> SF' a (b ,c) - pfoXC (SFArr _ fd1) c = sfArr (fdFanOut fd1 (FDC c)) - pfoXC sf1 c = SF' tf -{- - if sfIsInv sf1 then - pfoXCInv sf1 c - else - SF' tf False --} - where - tf dt a = (pfoXC sf1' c, (b, c)) - where - (sf1', b) = (sfTF' sf1) dt a - -{- - pfoXCInv :: SF' a b -> c -> SF' a (b ,c) - pfoXCInv sf1 c = SF' tf True - where - tf dt a = sf1 `seq` (pfoXCInv sf1' c, (b, c)) - where - (sf1', b) = (sfTF' sf1) dt a --} - - pfoAX :: (a -> b) -> SF' a c -> SF' a (b ,c) - pfoAX f1 (SFArr _ fd2) = sfArr (fdFanOut (FDG f1) fd2) - pfoAX f1 sf2 = SF' tf -{- - if sfIsInv sf2 then - pfoAXInv f1 sf2 - else - SF' tf False --} - where - tf dt a = (pfoAX f1 sf2', (f1 a, c)) - where - (sf2', c) = (sfTF' sf2) dt a - -{- - pfoAXInv :: (a -> b) -> SF' a c -> SF' a (b ,c) - pfoAXInv f1 sf2 = SF' tf True - where - tf dt a = sf2 `seq` (pfoAXInv f1 sf2', (f1 a, c)) - where - (sf2', c) = (sfTF' sf2) dt a --} - - pfoXA :: SF' a b -> (a -> c) -> SF' a (b ,c) - pfoXA (SFArr _ fd1) f2 = sfArr (fdFanOut fd1 (FDG f2)) - pfoXA sf1 f2 = SF' tf -{- - if sfIsInv sf1 then - pfoXAInv sf1 f2 - else - SF' tf False --} - where - tf dt a = (pfoXA sf1' f2, (b, f2 a)) - where - (sf1', b) = (sfTF' sf1) dt a - -{- - pfoXAInv :: SF' a b -> (a -> c) -> SF' a (b ,c) - pfoXAInv sf1 f2 = SF' tf True - where - tf dt a = sf1 `seq` (pfoXAInv sf1' f2, (b, f2 a)) - where - (sf1', b) = (sfTF' sf1) dt a --} - - ------------------------------------------------------------------------------- --- ArrowLoop instance and implementation ------------------------------------------------------------------------------- - -instance ArrowLoop SF where - loop = loopPrim - - -loopPrim :: SF (a,c) (b,c) -> SF a b -loopPrim (SF {sfTF = tf10}) = SF {sfTF = tf0} - where - tf0 a0 = (loopAux sf1, b0) - where - (sf1, (b0, c0)) = tf10 (a0, c0) - - loopAux :: SF' (a,c) (b,c) -> SF' a b - loopAux (SFArr _ FDI) = sfId - loopAux (SFArr _ (FDC (b, _))) = sfConst b - loopAux (SFArr _ fd1) = - sfArrG (\a -> let (b,c) = (fdFun fd1) (a,c) in b) - loopAux sf1 = SF' tf -{- - if sfIsInv sf1 then - loopInv sf1 - else - SF' tf False --} - where - tf dt a = (loopAux sf1', b) - where - (sf1', (b, c)) = (sfTF' sf1) dt (a, c) - -{- - loopInv :: SF' (a,c) (b,c) -> SF' a b - loopInv sf1 = SF' tf True - where - tf dt a = sf1 `seq` (loopInv sf1', b) - where - (sf1', (b, c)) = (sfTF' sf1) dt (a, c) --} - - ------------------------------------------------------------------------------- --- Basic signal functions ------------------------------------------------------------------------------- - --- | Identity: identity = arr id --- --- Using 'identity' is preferred over lifting id, since the arrow combinators --- know how to optimise certain networks based on the transformations being --- applied. -identity :: SF a a -identity = SF {sfTF = \a -> (sfId, a)} - --- | Identity: constant b = arr (const b) --- --- Using 'constant' is preferred over lifting const, since the arrow combinators --- know how to optimise certain networks based on the transformations being --- applied. -constant :: b -> SF a b -constant b = SF {sfTF = \_ -> (sfConst b, b)} - --- | Outputs the time passed since the signal function instance was started. -localTime :: SF a Time -localTime = constant 1.0 >>> integral - --- | Alternative name for localTime. -time :: SF a Time -time = localTime - ------------------------------------------------------------------------------- --- Initialization ------------------------------------------------------------------------------- - --- | Initialization operator (cf. Lustre/Lucid Synchrone). --- --- The output at time zero is the first argument, and from --- that point on it behaves like the signal function passed as --- second argument. -(-->) :: b -> SF a b -> SF a b -b0 --> (SF {sfTF = tf10}) = SF {sfTF = \a0 -> (fst (tf10 a0), b0)} - --- | Input initialization operator. --- --- The input at time zero is the first argument, and from --- that point on it behaves like the signal function passed as --- second argument. -(>--) :: a -> SF a b -> SF a b -a0 >-- (SF {sfTF = tf10}) = SF {sfTF = \_ -> tf10 a0} - - --- | Transform initial output value. --- --- Applies a transformation 'f' only to the first output value at --- time zero. -(-=>) :: (b -> b) -> SF a b -> SF a b -f -=> (SF {sfTF = tf10}) = - SF {sfTF = \a0 -> let (sf1, b0) = tf10 a0 in (sf1, f b0)} - - --- | Transform initial input value. --- --- Applies a transformation 'f' only to the first input value at --- time zero. -(>=-) :: (a -> a) -> SF a b -> SF a b -f >=- (SF {sfTF = tf10}) = SF {sfTF = \a0 -> tf10 (f a0)} - --- | Override initial value of input signal. -initially :: a -> SF a a -initially = (--> identity) - - ------------------------------------------------------------------------------- --- Simple, stateful signal processing ------------------------------------------------------------------------------- - --- New sscan primitive. It should be possible to define lots of functions --- in terms of this one. Eventually a new constructor will be introduced if --- this works out. - -sscan :: (b -> a -> b) -> b -> SF a b -sscan f b_init = sscanPrim f' b_init b_init - where - f' b a = let b' = f b a in Just (b', b') - - -{- -sscanPrim :: (c -> a -> Maybe (c, b)) -> c -> b -> SF a b -sscanPrim f c_init b_init = SF {sfTF = tf0} - where - tf0 a0 = case f c_init a0 of - Nothing -> (spAux f c_init b_init, b_init) - Just (c', b') -> (spAux f c' b', b') - - spAux :: (c -> a -> Maybe (c, b)) -> c -> b -> SF' a b - spAux f c b = sf - where - -- sf = SF' tf True - sf = SF' tf - tf _ a = case f c a of - Nothing -> (sf, b) - Just (c', b') -> (spAux f c' b', b') --} - - ------------------------------------------------------------------------------- --- Basic event sources ------------------------------------------------------------------------------- - --- | Event source that never occurs. -never :: SF a (Event b) -never = SF {sfTF = \_ -> (sfNever, NoEvent)} - - --- | Event source with a single occurrence at time 0. The value of the event --- is given by the function argument. -now :: b -> SF a (Event b) -now b0 = (Event b0 --> never) - - --- | Event source with a single occurrence at or as soon after (local) time /q/ --- as possible. -after :: Time -- ^ The time /q/ after which the event should be produced - -> b -- ^ Value to produce at that time - -> SF a (Event b) -after q x = afterEach [(q,x)] - --- | Event source with repeated occurrences with interval q. --- Note: If the interval is too short w.r.t. the sampling intervals, --- the result will be that events occur at every sample. However, no more --- than one event results from any sampling interval, thus avoiding an --- "event backlog" should sampling become more frequent at some later --- point in time. - --- !!! 2005-03-30: This is potentially a bit inefficient since we KNOW --- !!! (at this level) that the SF is going to be invarying. But afterEach --- !!! does NOT know this as the argument list may well be finite. --- !!! We could use sfMkInv, but that's not without problems. --- !!! We're probably better off specializing afterEachCat here. - -repeatedly :: Time -> b -> SF a (Event b) -repeatedly q x | q > 0 = afterEach qxs - | otherwise = usrErr "AFRP" "repeatedly" "Non-positive period." - where - qxs = (q,x):qxs - - --- Event source with consecutive occurrences at the given intervals. --- Should more than one event be scheduled to occur in any sampling interval, --- only the first will in fact occur to avoid an event backlog. --- Question: Should positive periods except for the first one be required? --- Note that periods of length 0 will always be skipped except for the first. --- Right now, periods of length 0 is allowed on the grounds that no attempt --- is made to forbid simultaneous events elsewhere. -{- -afterEach :: [(Time,b)] -> SF a (Event b) -afterEach [] = never -afterEach ((q,x):qxs) - | q < 0 = usrErr "AFRP" "afterEach" "Negative period." - | otherwise = SF {sfTF = tf0} - where - tf0 _ = if q <= 0 then - (scheduleNextEvent 0.0 qxs, Event x) - else - (awaitNextEvent (-q) x qxs, NoEvent) - - scheduleNextEvent t [] = sfNever - scheduleNextEvent t ((q,x):qxs) - | q < 0 = usrErr "AFRP" "afterEach" "Negative period." - | t' >= 0 = scheduleNextEvent t' qxs - | otherwise = awaitNextEvent t' x qxs - where - t' = t - q - awaitNextEvent t x qxs = SF' {sfTF' = tf} - where - tf dt _ | t' >= 0 = (scheduleNextEvent t' qxs, Event x) - | otherwise = (awaitNextEvent t' x qxs, NoEvent) - where - t' = t + dt --} - --- | Event source with consecutive occurrences at the given intervals. --- Should more than one event be scheduled to occur in any sampling interval, --- only the first will in fact occur to avoid an event backlog. - --- After all, after, repeatedly etc. are defined in terms of afterEach. -afterEach :: [(Time,b)] -> SF a (Event b) -afterEach qxs = afterEachCat qxs >>> arr (fmap head) - --- | Event source with consecutive occurrences at the given intervals. --- Should more than one event be scheduled to occur in any sampling interval, --- the output list will contain all events produced during that interval. - --- Guaranteed not to miss any events. -afterEachCat :: [(Time,b)] -> SF a (Event [b]) -afterEachCat [] = never -afterEachCat ((q,x):qxs) - | q < 0 = usrErr "AFRP" "afterEachCat" "Negative period." - | otherwise = SF {sfTF = tf0} - where - tf0 _ = if q <= 0 then - emitEventsScheduleNext 0.0 [x] qxs - else - (awaitNextEvent (-q) x qxs, NoEvent) - - emitEventsScheduleNext _ xs [] = (sfNever, Event (reverse xs)) - emitEventsScheduleNext t xs ((q,x):qxs) - | q < 0 = usrErr "AFRP" "afterEachCat" "Negative period." - | t' >= 0 = emitEventsScheduleNext t' (x:xs) qxs - | otherwise = (awaitNextEvent t' x qxs, Event (reverse xs)) - where - t' = t - q - awaitNextEvent t x qxs = SF' tf -- False - where - tf dt _ | t' >= 0 = emitEventsScheduleNext t' [x] qxs - | otherwise = (awaitNextEvent t' x qxs, NoEvent) - where - t' = t + dt - --- | Delay for events. (Consider it a triggered after, hence /basic/.) - --- Can be implemented fairly cheaply as long as the events are sparse. --- It is a question of rescheduling events for later. Not unlike "afterEach". --- --- It is not exactly the case that delayEvent t = delay t NoEvent --- since the rules for dropping/extrapolating samples are different. --- A single event occurrence will never be duplicated. --- If there is an event occurrence, one will be output as soon as --- possible after the given delay time, but not necessarily that --- one. See delayEventCat. - -delayEvent :: Time -> SF (Event a) (Event a) -delayEvent q | q < 0 = usrErr "AFRP" "delayEvent" "Negative delay." - | q == 0 = identity - | otherwise = delayEventCat q >>> arr (fmap head) - - --- There is no *guarantee* above that every event actually will be --- rescheduled since the sampling frequency (temporarily) might drop. --- The following interface would allow ALL scheduled events to occur --- as soon as possible: --- (Read "delay event and catenate events that occur so closely so as to be --- inseparable".) --- The events in the list are ordered temporally to the extent possible. - -{- --- This version is too strict! -delayEventCat :: Time -> SF (Event a) (Event [a]) -delayEventCat q | q < 0 = usrErr "AFRP" "delayEventCat" "Negative delay." - | q == 0 = arr (fmap (:[])) - | otherwise = SF {sfTF = tf0} - where - tf0 NoEvent = (noPendingEvent, NoEvent) - tf0 (Event x) = (pendingEvents (-q) [] [] (-q) x, NoEvent) - - noPendingEvent = SF' tf -- True - where - tf _ NoEvent = (noPendingEvent, NoEvent) - tf _ (Event x) = (pendingEvents (-q) [] [] (-q) x, NoEvent) - - -- t_next is the present time w.r.t. the next scheduled event. - -- t_last is the present time w.r.t. the last scheduled event. - -- In the event queues, events are associated with their time - -- w.r.t. to preceding event (positive). - pendingEvents t_last rqxs qxs t_next x = SF' tf -- True - where - tf dt NoEvent = tf1 (t_last + dt) rqxs (t_next + dt) - tf dt (Event x') = tf1 (-q) ((q', x') : rqxs) t_next' - where - t_next' = t_next + dt - t_last' = t_last + dt - q' = t_last' + q - - tf1 t_last' rqxs' t_next' - | t_next' >= 0 = - emitEventsScheduleNext t_last' rqxs' qxs t_next' [x] - | otherwise = - (pendingEvents t_last' rqxs' qxs t_next' x, NoEvent) - - -- t_next is the present time w.r.t. the *scheduled* time of the - -- event that is about to be emitted (i.e. >= 0). - -- The time associated with any event at the head of the event - -- queue is also given w.r.t. the event that is about to be emitted. - -- Thus, t_next - q' is the present time w.r.t. the event at the head - -- of the event queue. - emitEventsScheduleNext t_last [] [] t_next rxs = - (noPendingEvent, Event (reverse rxs)) - emitEventsScheduleNext t_last rqxs [] t_next rxs = - emitEventsScheduleNext t_last [] (reverse rqxs) t_next rxs - emitEventsScheduleNext t_last rqxs ((q', x') : qxs') t_next rxs - | q' > t_next = (pendingEvents t_last rqxs qxs' (t_next - q') x', - Event (reverse rxs)) - | otherwise = emitEventsScheduleNext t_last rqxs qxs' (t_next-q') - (x' : rxs) --} - --- | Delay an event by a given delta and catenate events that occur so closely --- so as to be /inseparable/. -delayEventCat :: Time -> SF (Event a) (Event [a]) -delayEventCat q | q < 0 = usrErr "AFRP" "delayEventCat" "Negative delay." - | q == 0 = arr (fmap (:[])) - | otherwise = SF {sfTF = tf0} - where - tf0 e = (case e of - NoEvent -> noPendingEvent - Event x -> pendingEvents (-q) [] [] (-q) x, - NoEvent) - - noPendingEvent = SF' tf -- True - where - tf _ e = (case e of - NoEvent -> noPendingEvent - Event x -> pendingEvents (-q) [] [] (-q) x, - NoEvent) - - -- t_next is the present time w.r.t. the next scheduled event. - -- t_last is the present time w.r.t. the last scheduled event. - -- In the event queues, events are associated with their time - -- w.r.t. to preceding event (positive). - pendingEvents t_last rqxs qxs t_next x = SF' tf -- True - where - tf dt e - | t_next' >= 0 = - emitEventsScheduleNext e t_last' rqxs qxs t_next' [x] - | otherwise = - (pendingEvents t_last'' rqxs' qxs t_next' x, NoEvent) - where - t_next' = t_next + dt - t_last' = t_last + dt - (t_last'', rqxs') = - case e of - NoEvent -> (t_last', rqxs) - Event x' -> (-q, (t_last'+q,x') : rqxs) - - -- t_next is the present time w.r.t. the *scheduled* time of the - -- event that is about to be emitted (i.e. >= 0). - -- The time associated with any event at the head of the event - -- queue is also given w.r.t. the event that is about to be emitted. - -- Thus, t_next - q' is the present time w.r.t. the event at the head - -- of the event queue. - emitEventsScheduleNext e _ [] [] _ rxs = - (case e of - NoEvent -> noPendingEvent - Event x -> pendingEvents (-q) [] [] (-q) x, - Event (reverse rxs)) - emitEventsScheduleNext e t_last rqxs [] t_next rxs = - emitEventsScheduleNext e t_last [] (reverse rqxs) t_next rxs - emitEventsScheduleNext e t_last rqxs ((q', x') : qxs') t_next rxs - | q' > t_next = (case e of - NoEvent -> - pendingEvents t_last - rqxs - qxs' - (t_next - q') - x' - Event x'' -> - pendingEvents (-q) - ((t_last+q, x'') : rqxs) - qxs' - (t_next - q') - x', - Event (reverse rxs)) - | otherwise = emitEventsScheduleNext e - t_last - rqxs - qxs' - (t_next - q') - (x' : rxs) - - --- | A rising edge detector. Useful for things like detecting key presses. --- It is initialised as /up/, meaning that events occuring at time 0 will --- not be detected. - --- Note that we initialize the loop with state set to True so that there --- will not be an occurence at t0 in the logical time frame in which --- this is started. -edge :: SF Bool (Event ()) -edge = iEdge True - --- | A rising edge detector that can be initialized as up ('True', meaning --- that events occurring at time 0 will not be detected) or down --- ('False', meaning that events ocurring at time 0 will be detected). -iEdge :: Bool -> SF Bool (Event ()) --- iEdge i = edgeBy (isBoolRaisingEdge ()) i -iEdge b = sscanPrim f (if b then 2 else 0) NoEvent - where - f :: Int -> Bool -> Maybe (Int, Event ()) - f 0 False = Nothing - f 0 True = Just (1, Event ()) - f 1 False = Just (0, NoEvent) - f 1 True = Just (2, NoEvent) - f 2 False = Just (0, NoEvent) - f 2 True = Nothing - f _ _ = undefined - --- | Like 'edge', but parameterized on the tag value. -edgeTag :: a -> SF Bool (Event a) --- edgeTag a = edgeBy (isBoolRaisingEdge a) True -edgeTag a = edge >>> arr (`tag` a) - - --- Internal utility. --- isBoolRaisingEdge :: a -> Bool -> Bool -> Maybe a --- isBoolRaisingEdge _ False False = Nothing --- isBoolRaisingEdge a False True = Just a --- isBoolRaisingEdge _ True True = Nothing --- isBoolRaisingEdge _ True False = Nothing - - --- | Edge detector particularized for detecting transtitions --- on a 'Maybe' signal from 'Nothing' to 'Just'. - --- !!! 2005-07-09: To be done or eliminated --- !!! Maybe could be kept as is, but could be easy to implement directly --- !!! in terms of sscan? -edgeJust :: SF (Maybe a) (Event a) -edgeJust = edgeBy isJustEdge (Just undefined) - where - isJustEdge Nothing Nothing = Nothing - isJustEdge Nothing ma@(Just _) = ma - isJustEdge (Just _) (Just _) = Nothing - isJustEdge (Just _) Nothing = Nothing - - --- | Edge detector parameterized on the edge detection function and initial --- state, i.e., the previous input sample. The first argument to the --- edge detection function is the previous sample, the second the current one. - --- !!! Is this broken!?! Does not disallow an edge condition that persists --- !!! between consecutive samples. See discussion in ToDo list above. --- !!! 2005-07-09: To be done. -edgeBy :: (a -> a -> Maybe b) -> a -> SF a (Event b) -edgeBy isEdge a_init = SF {sfTF = tf0} - where - tf0 a0 = (ebAux a0, maybeToEvent (isEdge a_init a0)) - - ebAux a_prev = SF' tf -- True - where - tf _ a = (ebAux a, maybeToEvent (isEdge a_prev a)) - - ------------------------------------------------------------------------------- --- Stateful event suppression ------------------------------------------------------------------------------- - --- | Suppression of initial (at local time 0) event. -notYet :: SF (Event a) (Event a) -notYet = initially NoEvent - - --- | Suppress all but the first event. -once :: SF (Event a) (Event a) -once = takeEvents 1 - - --- | Suppress all but the first n events. -takeEvents :: Int -> SF (Event a) (Event a) -takeEvents n | n <= 0 = never -takeEvents n = dSwitch (arr dup) (const (NoEvent >-- takeEvents (n - 1))) - - -{- --- More complicated using "switch" that "dSwitch". -takeEvents :: Int -> SF (Event a) (Event a) -takeEvents 0 = never -takeEvents (n + 1) = switch (never &&& identity) (takeEvents' n) - where - takeEvents' 0 a = now a - takeEvents' (n + 1) a = switch (now a &&& notYet) (takeEvents' n) --} - - --- | Suppress first n events. - --- Here dSwitch or switch does not really matter. -dropEvents :: Int -> SF (Event a) (Event a) -dropEvents n | n <= 0 = identity -dropEvents n = dSwitch (never &&& identity) - (const (NoEvent >-- dropEvents (n - 1))) - - ------------------------------------------------------------------------------- --- Basic switchers ------------------------------------------------------------------------------- - --- !!! Interesting case. It seems we need scoped type variables --- !!! to be able to write down the local type signatures. --- !!! On the other hand, the scoped type variables seem to --- !!! prohibit the kind of unification that is needed for GADTs??? --- !!! Maybe this could be made to wok if it actually WAS known --- !!! that scoped type variables indeed corresponds to universally --- !!! quantified variables? Or if one were to keep track of those --- !!! scoped type variables that actually do? --- !!! --- !!! Find a simpler case to experiment further. For now, elim. --- !!! the free variable. - -{- --- Basic switch. -switch :: SF a (b, Event c) -> (c -> SF a b) -> SF a b -switch (SF {sfTF = tf10} :: SF a (b, Event c)) (k :: c -> SF a b) = SF {sfTF = tf0} - where - tf0 a0 = - case tf10 a0 of - (sf1, (b0, NoEvent)) -> (switchAux sf1, b0) - (_, (_, Event c0)) -> sfTF (k c0) a0 - - -- It would be nice to optimize further here. E.g. if it would be - -- possible to observe the event source only. - switchAux :: SF' a (b, Event c) -> SF' a b - switchAux (SFId _) = switchAuxA1 id -- New - switchAux (SFConst _ (b, NoEvent)) = sfConst b - switchAux (SFArr _ f1) = switchAuxA1 f1 - switchAux sf1 = SF' tf - where - tf dt a = - case (sfTF' sf1) dt a of - (sf1', (b, NoEvent)) -> (switchAux sf1', b) - (_, (_, Event c)) -> sfTF (k c) a - - -- Could be optimized a little bit further by having a case for - -- identity, switchAuxI1 - - -- Note: While switch behaves as a stateless arrow at this point, that - -- could change after a switch. Hence, SF' overall. - switchAuxA1 :: (a -> (b, Event c)) -> SF' a b - switchAuxA1 f1 = sf - where - sf = SF' tf - tf _ a = - case f1 a of - (b, NoEvent) -> (sf, b) - (_, Event c) -> sfTF (k c) a --} - --- | Basic switch. --- --- By default, the first signal function is applied. --- --- Whenever the second value in the pair actually is an event, --- the value carried by the event is used to obtain a new signal --- function to be applied *at that time and at future times*. --- --- Until that happens, the first value in the pair is produced --- in the output signal. --- --- Important note: at the time of switching, the second --- signal function is applied immediately. If that second --- SF can also switch at time zero, then a double (nested) --- switch might take place. If the second SF refers to the --- first one, the switch might take place infinitely many --- times and never be resolved. --- --- Remember: The continuation is evaluated strictly at the time --- of switching! -switch :: SF a (b, Event c) -> (c -> SF a b) -> SF a b -switch (SF {sfTF = tf10}) k = SF {sfTF = tf0} - where - tf0 a0 = - case tf10 a0 of - (sf1, (b0, NoEvent)) -> (switchAux sf1 k, b0) - (_, (_, Event c0)) -> sfTF (k c0) a0 - - -- It would be nice to optimize further here. E.g. if it would be - -- possible to observe the event source only. - switchAux :: SF' a (b, Event c) -> (c -> SF a b) -> SF' a b - switchAux (SFArr _ (FDC (b, NoEvent))) _ = sfConst b - switchAux (SFArr _ fd1) k = switchAuxA1 (fdFun fd1) k - switchAux sf1 k = SF' tf -{- - if sfIsInv sf1 then - switchInv sf1 k - else - SF' tf False --} - where - tf dt a = - case (sfTF' sf1) dt a of - (sf1', (b, NoEvent)) -> (switchAux sf1' k, b) - (_, (_, Event c)) -> sfTF (k c) a - -{- - -- Note: subordinate signal function being invariant does NOT - -- imply that the overall signal function is. - switchInv :: SF' a (b, Event c) -> (c -> SF a b) -> SF' a b - switchInv sf1 k = SF' tf False - where - tf dt a = - case (sfTF' sf1) dt a of - (sf1', (b, NoEvent)) -> (switchInv sf1' k, b) - (_, (_, Event c)) -> sfTF (k c) a --} - - -- !!! Could be optimized a little bit further by having a case for - -- !!! identity, switchAuxI1. But I'd expect identity is so unlikely - -- !!! that there is no point. - - -- Note: While switch behaves as a stateless arrow at this point, that - -- could change after a switch. Hence, SF' overall. - switchAuxA1 :: (a -> (b, Event c)) -> (c -> SF a b) -> SF' a b - switchAuxA1 f1 k = sf - where - sf = SF' tf -- False - tf _ a = - case f1 a of - (b, NoEvent) -> (sf, b) - (_, Event c) -> sfTF (k c) a - - --- | Switch with delayed observation. --- --- By default, the first signal function is applied. --- --- Whenever the second value in the pair actually is an event, --- the value carried by the event is used to obtain a new signal --- function to be applied *at future times*. --- --- Until that happens, the first value in the pair is produced --- in the output signal. --- --- Important note: at the time of switching, the second --- signal function is used immediately, but the current --- input is fed by it (even though the actual output signal --- value at time 0 is discarded). --- --- If that second SF can also switch at time zero, then a --- double (nested) -- switch might take place. If the second SF refers to the --- first one, the switch might take place infinitely many times and never be --- resolved. --- --- Remember: The continuation is evaluated strictly at the time --- of switching! - --- Alternative name: "decoupled switch"? --- (The SFId optimization is highly unlikley to be of much use, but it --- does raise an interesting typing issue.) -dSwitch :: SF a (b, Event c) -> (c -> SF a b) -> SF a b -dSwitch (SF {sfTF = tf10}) k = SF {sfTF = tf0} - where - tf0 a0 = - let (sf1, (b0, ec0)) = tf10 a0 - in (case ec0 of - NoEvent -> dSwitchAux sf1 k - Event c0 -> fst (sfTF (k c0) a0), - b0) - - -- It would be nice to optimize further here. E.g. if it would be - -- possible to observe the event source only. - dSwitchAux :: SF' a (b, Event c) -> (c -> SF a b) -> SF' a b - dSwitchAux (SFArr _ (FDC (b, NoEvent))) _ = sfConst b - dSwitchAux (SFArr _ fd1) k = dSwitchAuxA1 (fdFun fd1) k - dSwitchAux sf1 k = SF' tf -{- - if sfIsInv sf1 then - dSwitchInv sf1 k - else - SF' tf False --} - where - tf dt a = - let (sf1', (b, ec)) = (sfTF' sf1) dt a - in (case ec of - NoEvent -> dSwitchAux sf1' k - Event c -> fst (sfTF (k c) a), - - b) - -{- - -- Note: that the subordinate signal function is invariant does NOT - -- imply that the overall signal function is. - dSwitchInv :: SF' a (b, Event c) -> (c -> SF a b) -> SF' a b - dSwitchInv sf1 k = SF' tf False - where - tf dt a = - let (sf1', (b, ec)) = (sfTF' sf1) dt a - in (case ec of - NoEvent -> dSwitchInv sf1' k - Event c -> fst (sfTF (k c) a), - - b) --} - - -- !!! Could be optimized a little bit further by having a case for - -- !!! identity, switchAuxI1 - - -- Note: While dSwitch behaves as a stateless arrow at this point, that - -- could change after a switch. Hence, SF' overall. - dSwitchAuxA1 :: (a -> (b, Event c)) -> (c -> SF a b) -> SF' a b - dSwitchAuxA1 f1 k = sf - where - sf = SF' tf -- False - tf _ a = - let (b, ec) = f1 a - in (case ec of - NoEvent -> sf - Event c -> fst (sfTF (k c) a), - - b) - - --- | Recurring switch. --- --- See for more --- information on how this switch works. - --- !!! Suboptimal. Overall, the constructor is invarying since rSwitch is --- !!! being invoked recursively on a switch. In fact, we don't even care --- !!! whether the subordinate signal function is invarying or not. --- !!! We could make use of a signal function transformer sfInv to --- !!! mark the constructor as invarying. Would that make sense? --- !!! The price would be an extra loop with case analysis. --- !!! The potential gain is fewer case analyses in superior loops. -rSwitch :: SF a b -> SF (a, Event (SF a b)) b -rSwitch sf = switch (first sf) ((noEventSnd >=-) . rSwitch) - -{- --- Old version. New is more efficient. Which one is clearer? -rSwitch :: SF a b -> SF (a, Event (SF a b)) b -rSwitch sf = switch (first sf) rSwitch' - where - rSwitch' sf = switch (sf *** notYet) rSwitch' --} - - --- | Recurring switch with delayed observation. --- --- See for more --- information on how this switch works. -drSwitch :: SF a b -> SF (a, Event (SF a b)) b -drSwitch sf = dSwitch (first sf) ((noEventSnd >=-) . drSwitch) - -{- --- Old version. New is more efficient. Which one is clearer? -drSwitch :: SF a b -> SF (a, Event (SF a b)) b -drSwitch sf = dSwitch (first sf) drSwitch' - where - drSwitch' sf = dSwitch (sf *** notYet) drSwitch' --} - - --- | "Call-with-current-continuation" switch. --- --- See for more --- information on how this switch works. - --- !!! Has not been optimized properly. --- !!! Nor has opts been tested! --- !!! Don't forget Inv opts! -kSwitch :: SF a b -> SF (a,b) (Event c) -> (SF a b -> c -> SF a b) -> SF a b -kSwitch sf10@(SF {sfTF = tf10}) (SF {sfTF = tfe0}) k = SF {sfTF = tf0} - where - tf0 a0 = - let (sf1, b0) = tf10 a0 - in - case tfe0 (a0, b0) of - (sfe, NoEvent) -> (kSwitchAux sf1 sfe, b0) - (_, Event c0) -> sfTF (k sf10 c0) a0 - --- Same problem as above: must pass k explicitly??? --- kSwitchAux (SFId _) sfe = kSwitchAuxI1 sfe - kSwitchAux (SFArr _ (FDC b)) sfe = kSwitchAuxC1 b sfe - kSwitchAux (SFArr _ fd1) sfe = kSwitchAuxA1 (fdFun fd1) sfe - -- kSwitchAux (SFArrE _ f1) sfe = kSwitchAuxA1 f1 sfe - -- kSwitchAux (SFArrEE _ f1) sfe = kSwitchAuxA1 f1 sfe - kSwitchAux sf1 (SFArr _ (FDC NoEvent)) = sf1 - kSwitchAux sf1 (SFArr _ fde) = kSwitchAuxAE sf1 (fdFun fde) - -- kSwitchAux sf1 (SFArrE _ fe) = kSwitchAuxAE sf1 fe - -- kSwitchAux sf1 (SFArrEE _ fe) = kSwitchAuxAE sf1 fe - kSwitchAux sf1 sfe = SF' tf -- False - where - tf dt a = - let (sf1', b) = (sfTF' sf1) dt a - in - case (sfTF' sfe) dt (a, b) of - (sfe', NoEvent) -> (kSwitchAux sf1' sfe', b) - (_, Event c) -> sfTF (k (freeze sf1 dt) c) a - -{- --- !!! Untested optimization! - kSwitchAuxI1 (SFConst _ NoEvent) = sfId - kSwitchAuxI1 (SFArr _ fe) = kSwitchAuxI1AE fe - kSwitchAuxI1 sfe = SF' tf - where - tf dt a = - case (sfTF' sfe) dt (a, a) of - (sfe', NoEvent) -> (kSwitchAuxI1 sfe', a) - (_, Event c) -> sfTF (k identity c) a --} - --- !!! Untested optimization! - kSwitchAuxC1 b (SFArr _ (FDC NoEvent)) = sfConst b - kSwitchAuxC1 b (SFArr _ fde) = kSwitchAuxC1AE b (fdFun fde) - -- kSwitchAuxC1 b (SFArrE _ fe) = kSwitchAuxC1AE b fe - -- kSwitchAuxC1 b (SFArrEE _ fe) = kSwitchAuxC1AE b fe - kSwitchAuxC1 b sfe = SF' tf -- False - where - tf dt a = - case (sfTF' sfe) dt (a, b) of - (sfe', NoEvent) -> (kSwitchAuxC1 b sfe', b) - (_, Event c) -> sfTF (k (constant b) c) a - --- !!! Untested optimization! - kSwitchAuxA1 f1 (SFArr _ (FDC NoEvent)) = sfArrG f1 - kSwitchAuxA1 f1 (SFArr _ fde) = kSwitchAuxA1AE f1 (fdFun fde) - -- kSwitchAuxA1 f1 (SFArrE _ fe) = kSwitchAuxA1AE f1 fe - -- kSwitchAuxA1 f1 (SFArrEE _ fe) = kSwitchAuxA1AE f1 fe - kSwitchAuxA1 f1 sfe = SF' tf -- False - where - tf dt a = - let b = f1 a - in - case (sfTF' sfe) dt (a, b) of - (sfe', NoEvent) -> (kSwitchAuxA1 f1 sfe', b) - (_, Event c) -> sfTF (k (arr f1) c) a - --- !!! Untested optimization! --- kSwitchAuxAE (SFId _) fe = kSwitchAuxI1AE fe - kSwitchAuxAE (SFArr _ (FDC b)) fe = kSwitchAuxC1AE b fe - kSwitchAuxAE (SFArr _ fd1) fe = kSwitchAuxA1AE (fdFun fd1) fe - -- kSwitchAuxAE (SFArrE _ f1) fe = kSwitchAuxA1AE f1 fe - -- kSwitchAuxAE (SFArrEE _ f1) fe = kSwitchAuxA1AE f1 fe - kSwitchAuxAE sf1 fe = SF' tf -- False - where - tf dt a = - let (sf1', b) = (sfTF' sf1) dt a - in - case fe (a, b) of - NoEvent -> (kSwitchAuxAE sf1' fe, b) - Event c -> sfTF (k (freeze sf1 dt) c) a - -{- --- !!! Untested optimization! - kSwitchAuxI1AE fe = SF' tf -- False - where - tf dt a = - case fe (a, a) of - NoEvent -> (kSwitchAuxI1AE fe, a) - Event c -> sfTF (k identity c) a --} - --- !!! Untested optimization! - kSwitchAuxC1AE b fe = SF' tf -- False - where - tf _ a = - case fe (a, b) of - NoEvent -> (kSwitchAuxC1AE b fe, b) - Event c -> sfTF (k (constant b) c) a - --- !!! Untested optimization! - kSwitchAuxA1AE f1 fe = SF' tf -- False - where - tf _ a = - let b = f1 a - in - case fe (a, b) of - NoEvent -> (kSwitchAuxA1AE f1 fe, b) - Event c -> sfTF (k (arr f1) c) a - - --- | 'kSwitch' with delayed observation. --- --- See for more --- information on how this switch works. - --- !!! Has not been optimized properly. Should be like kSwitch. -dkSwitch :: SF a b -> SF (a,b) (Event c) -> (SF a b -> c -> SF a b) -> SF a b -dkSwitch sf10@(SF {sfTF = tf10}) (SF {sfTF = tfe0}) k = SF {sfTF = tf0} - where - tf0 a0 = - let (sf1, b0) = tf10 a0 - in (case tfe0 (a0, b0) of - (sfe, NoEvent) -> dkSwitchAux sf1 sfe - (_, Event c0) -> fst (sfTF (k sf10 c0) a0), - b0) - - dkSwitchAux sf1 (SFArr _ (FDC NoEvent)) = sf1 - dkSwitchAux sf1 sfe = SF' tf -- False - where - tf dt a = - let (sf1', b) = (sfTF' sf1) dt a - in (case (sfTF' sfe) dt (a, b) of - (sfe', NoEvent) -> dkSwitchAux sf1' sfe' - (_, Event c) -> fst (sfTF (k (freeze sf1 dt) c) a), - b) - - ------------------------------------------------------------------------------- --- Parallel composition and switching over collections with broadcasting ------------------------------------------------------------------------------- - --- | Tuple a value up with every element of a collection of signal --- functions. -broadcast :: Functor col => a -> col sf -> col (a, sf) -broadcast a sfs = fmap (\sf -> (a, sf)) sfs - - --- !!! Hmm. We should really optimize here. --- !!! Check for Arr in parallel! --- !!! Check for Arr FDE in parallel!!! --- !!! Check for EP in parallel!!!!! --- !!! Cf &&&. --- !!! But how??? All we know is that the collection is a functor ... --- !!! Maybe that kind of generality does not make much sense for --- !!! par and parB? (Although it is niceto be able to switch into a --- !!! par or parB from within a pSwitch[B].) --- !!! If we had a parBList, that could be defined in terms of &&&, surely? --- !!! E.g. --- !!! parBList [] = constant [] --- !!! parBList (sf:sfs) = sf &&& parBList sfs >>> arr (\(x,xs) -> x:xs) --- !!! --- !!! This ought to optimize quite well. E.g. --- !!! parBList [arr1,arr2,arr3] --- !!! = arr1 &&& parBList [arr2,arr3] >>> arrX --- !!! = arr1 &&& (arr2 &&& parBList [arr3] >>> arrX) >>> arrX --- !!! = arr1 &&& (arr2 &&& (arr3 &&& parBList [] >>> arrX) >>> arrX) >>> arrX --- !!! = arr1 &&& (arr2 &&& (arr3C >>> arrX) >>> arrX) >>> arrX --- !!! = arr1 &&& (arr2 &&& (arr3CcpX) >>> arrX) >>> arrX --- !!! = arr1 &&& (arr23CcpX >>> arrX) >>> arrX --- !!! = arr1 &&& (arr23CcpXcpX) >>> arrX --- !!! = arr123CcpXcpXcpX - --- | Spatial parallel composition of a signal function collection. --- Given a collection of signal functions, it returns a signal --- function that 'broadcast's its input signal to every element --- of the collection, to return a signal carrying a collection --- of outputs. See 'par'. --- --- For more information on how parallel composition works, check --- -parB :: Functor col => col (SF a b) -> SF a (col b) -parB = par broadcast - --- | Parallel switch (dynamic collection of signal functions spatially composed --- in parallel). See 'pSwitch'. --- --- For more information on how parallel composition works, check --- -pSwitchB :: Functor col => - col (SF a b) -> SF (a,col b) (Event c) -> (col (SF a b)->c-> SF a (col b)) - -> SF a (col b) -pSwitchB = pSwitch broadcast - --- | Delayed parallel switch with broadcasting (dynamic collection of --- signal functions spatially composed in parallel). See 'dpSwitch'. --- --- For more information on how parallel composition works, check --- -dpSwitchB :: Functor col => - col (SF a b) -> SF (a,col b) (Event c) -> (col (SF a b)->c->SF a (col b)) - -> SF a (col b) -dpSwitchB = dpSwitch broadcast - --- For more information on how parallel composition works, check --- -rpSwitchB :: Functor col => - col (SF a b) -> SF (a, Event (col (SF a b) -> col (SF a b))) (col b) -rpSwitchB = rpSwitch broadcast - --- For more information on how parallel composition works, check --- -drpSwitchB :: Functor col => - col (SF a b) -> SF (a, Event (col (SF a b) -> col (SF a b))) (col b) -drpSwitchB = drpSwitch broadcast - - ------------------------------------------------------------------------------- --- Parallel composition and switching over collections with general routing ------------------------------------------------------------------------------- - --- | Spatial parallel composition of a signal function collection parameterized --- on the routing function. --- -par :: Functor col => - (forall sf . (a -> col sf -> col (b, sf))) -- ^ Determines the input to each signal function - -- in the collection. IMPORTANT! The routing function MUST - -- preserve the structure of the signal function collection. - - -> col (SF b c) -- ^ Signal function collection. - -> SF a (col c) -par rf sfs0 = SF {sfTF = tf0} - where - tf0 a0 = - let bsfs0 = rf a0 sfs0 - sfcs0 = fmap (\(b0, sf0) -> (sfTF sf0) b0) bsfs0 - sfs = fmap fst sfcs0 - cs0 = fmap snd sfcs0 - in - (parAux rf sfs, cs0) - - --- Internal definition. Also used in parallel swithers. -parAux :: Functor col => - (forall sf . (a -> col sf -> col (b, sf))) - -> col (SF' b c) - -> SF' a (col c) -parAux rf sfs = SF' tf -- True - where - tf dt a = - let bsfs = rf a sfs - sfcs' = fmap (\(b, sf) -> (sfTF' sf) dt b) bsfs - sfs' = fmap fst sfcs' - cs = fmap snd sfcs' - in - (parAux rf sfs', cs) - - --- | Parallel switch parameterized on the routing function. This is the most --- general switch from which all other (non-delayed) switches in principle --- can be derived. The signal function collection is spatially composed in --- parallel and run until the event signal function has an occurrence. Once --- the switching event occurs, all signal function are "frozen" and their --- continuations are passed to the continuation function, along with the --- event value. --- - --- rf ......... Routing function: determines the input to each signal function --- in the collection. IMPORTANT! The routing function has an --- obligation to preserve the structure of the signal function --- collection. --- sfs0 ....... Signal function collection. --- sfe0 ....... Signal function generating the switching event. --- k .......... Continuation to be invoked once event occurs. --- Returns the resulting signal function. --- --- !!! Could be optimized on the event source being SFArr, SFArrE, SFArrEE -pSwitch :: Functor col - => (forall sf . (a -> col sf -> col (b, sf))) -- ^ Routing function: determines the input to each signal function - -- in the collection. IMPORTANT! The routing function has an - -- obligation to preserve the structure of the signal function - -- collection. - - -> col (SF b c) -- ^ Signal function collection. - -> SF (a, col c) (Event d) -- ^ Signal function generating the switching event. - -> (col (SF b c) -> d -> SF a (col c)) -- ^ Continuation to be invoked once event occurs. - -> SF a (col c) -pSwitch rf sfs0 sfe0 k = SF {sfTF = tf0} - where - tf0 a0 = - let bsfs0 = rf a0 sfs0 - sfcs0 = fmap (\(b0, sf0) -> (sfTF sf0) b0) bsfs0 - sfs = fmap fst sfcs0 - cs0 = fmap snd sfcs0 - in - case (sfTF sfe0) (a0, cs0) of - (sfe, NoEvent) -> (pSwitchAux sfs sfe, cs0) - (_, Event d0) -> sfTF (k sfs0 d0) a0 - - pSwitchAux sfs (SFArr _ (FDC NoEvent)) = parAux rf sfs - pSwitchAux sfs sfe = SF' tf -- False - where - tf dt a = - let bsfs = rf a sfs - sfcs' = fmap (\(b, sf) -> (sfTF' sf) dt b) bsfs - sfs' = fmap fst sfcs' - cs = fmap snd sfcs' - in - case (sfTF' sfe) dt (a, cs) of - (sfe', NoEvent) -> (pSwitchAux sfs' sfe', cs) - (_, Event d) -> sfTF (k (freezeCol sfs dt) d) a - - --- | Parallel switch with delayed observation parameterized on the routing --- function. --- --- The collection argument to the function invoked on the --- switching event is of particular interest: it captures the --- continuations of the signal functions running in the collection --- maintained by 'dpSwitch' at the time of the switching event, --- thus making it possible to preserve their state across a switch. --- Since the continuations are plain, ordinary signal functions, --- they can be resumed, discarded, stored, or combined with --- other signal functions. - --- !!! Could be optimized on the event source being SFArr, SFArrE, SFArrEE. --- -dpSwitch :: Functor col => - (forall sf . (a -> col sf -> col (b, sf))) -- ^ Routing function. Its purpose is - -- to pair up each running signal function in the collection - -- maintained by 'dpSwitch' with the input it is going to see - -- at each point in time. All the routing function can do is specify - -- how the input is distributed. - -> col (SF b c) -- ^ Initial collection of signal functions. - -> SF (a, col c) (Event d) -- ^ Signal function that observes the external - -- input signal and the output signals from the collection in order - -- to produce a switching event. - -> (col (SF b c) -> d -> SF a (col c)) -- ^ The fourth argument is a function that is invoked when the - -- switching event occurs, yielding a new signal function to switch - -- into based on the collection of signal functions previously - -- running and the value carried by the switching event. This - -- allows the collection to be updated and then switched back - -- in, typically by employing 'dpSwitch' again. - -> SF a (col c) -dpSwitch rf sfs0 sfe0 k = SF {sfTF = tf0} - where - tf0 a0 = - let bsfs0 = rf a0 sfs0 - sfcs0 = fmap (\(b0, sf0) -> (sfTF sf0) b0) bsfs0 - cs0 = fmap snd sfcs0 - in - (case (sfTF sfe0) (a0, cs0) of - (sfe, NoEvent) -> dpSwitchAux (fmap fst sfcs0) sfe - (_, Event d0) -> fst (sfTF (k sfs0 d0) a0), - cs0) - - dpSwitchAux sfs (SFArr _ (FDC NoEvent)) = parAux rf sfs - dpSwitchAux sfs sfe = SF' tf -- False - where - tf dt a = - let bsfs = rf a sfs - sfcs' = fmap (\(b, sf) -> (sfTF' sf) dt b) bsfs - cs = fmap snd sfcs' - in - (case (sfTF' sfe) dt (a, cs) of - (sfe', NoEvent) -> dpSwitchAux (fmap fst sfcs') - sfe' - (_, Event d) -> fst (sfTF (k (freezeCol sfs dt) - d) - a), - cs) - - --- Recurring parallel switch parameterized on the routing function. --- rf ......... Routing function: determines the input to each signal function --- in the collection. IMPORTANT! The routing function has an --- obligation to preserve the structure of the signal function --- collection. --- sfs ........ Initial signal function collection. --- Returns the resulting signal function. - -rpSwitch :: Functor col => - (forall sf . (a -> col sf -> col (b, sf))) - -> col (SF b c) -> SF (a, Event (col (SF b c) -> col (SF b c))) (col c) -rpSwitch rf sfs = - pSwitch (rf . fst) sfs (arr (snd . fst)) $ \sfs' f -> - noEventSnd >=- rpSwitch rf (f sfs') - - -{- -rpSwitch rf sfs = pSwitch (rf . fst) sfs (arr (snd . fst)) k - where - k sfs f = rpSwitch' (f sfs) - rpSwitch' sfs = pSwitch (rf . fst) sfs (NoEvent --> arr (snd . fst)) k --} - --- Recurring parallel switch with delayed observation parameterized on the --- routing function. -drpSwitch :: Functor col => - (forall sf . (a -> col sf -> col (b, sf))) - -> col (SF b c) -> SF (a, Event (col (SF b c) -> col (SF b c))) (col c) -drpSwitch rf sfs = - dpSwitch (rf . fst) sfs (arr (snd . fst)) $ \sfs' f -> - noEventSnd >=- drpSwitch rf (f sfs') - -{- -drpSwitch rf sfs = dpSwitch (rf . fst) sfs (arr (snd . fst)) k - where - k sfs f = drpSwitch' (f sfs) - drpSwitch' sfs = dpSwitch (rf . fst) sfs (NoEvent-->arr (snd . fst)) k --} - ------------------------------------------------------------------------------- --- Wave-form generation ------------------------------------------------------------------------------- - --- | Zero-order hold. - --- !!! Should be redone using SFSScan? --- !!! Otherwise, we are missing an invarying case. -old_hold :: a -> SF (Event a) a -old_hold a_init = switch (constant a_init &&& identity) - ((NoEvent >--) . old_hold) - --- | Zero-order hold. -hold :: a -> SF (Event a) a -hold a_init = epPrim f () a_init - where - f _ a = ((), a, a) - --- !!! --- !!! 2005-04-10: I DO NO LONGER THINK THIS IS CORRECT! --- !!! CAN ONE POSSIBLY GET THE DESIRED STRICTNESS PROPERTIES --- !!! ("DECOUPLING") this way??? --- !!! Also applies to the other "d" functions that were tentatively --- !!! defined using only epPrim. --- !!! --- !!! 2005-06-13: Yes, indeed wrong! (But it's subtle, one has to --- !!! make sure that the incoming event (and not just the payload --- !!! of the event) is control dependent on the output of "dHold" --- !!! to observe it. --- !!! --- !!! 2005-06-09: But if iPre can be defined in terms of sscan, --- !!! and ep + sscan = sscan, then things might work, and --- !!! it might be possible to define dHold simply as hold >>> iPre --- !!! without any performance penalty. - --- | Zero-order hold with delay. --- --- Identity: dHold a0 = hold a0 >>> iPre a0). -dHold :: a -> SF (Event a) a -dHold a0 = hold a0 >>> iPre a0 -{- --- THIS IS WRONG! SEE ABOVE. -dHold a_init = epPrim f a_init a_init - where - f a' a = (a, a', a) --} - --- | Tracks input signal when available, holds last value when disappears. --- --- !!! DANGER!!! Event used inside arr! Probably OK because arr will not be --- !!! optimized to arrE. But still. Maybe rewrite this using, say, scan? --- !!! or switch? Switching (in hold) for every input sample does not --- !!! seem like such a great idea anyway. -trackAndHold :: a -> SF (Maybe a) a -trackAndHold a_init = arr (maybe NoEvent Event) >>> hold a_init - - ------------------------------------------------------------------------------- --- Accumulators ------------------------------------------------------------------------------- - --- | See 'accum'. -old_accum :: a -> SF (Event (a -> a)) (Event a) -old_accum = accumBy (flip ($)) - --- | Given an initial value in an accumulator, --- it returns a signal function that processes --- an event carrying transformation functions. --- Every time an 'Event' is received, the function --- inside it is applied to the accumulator, --- whose new value is outputted in an 'Event'. --- -accum :: a -> SF (Event (a -> a)) (Event a) -accum a_init = epPrim f a_init NoEvent - where - f a g = (a', Event a', NoEvent) -- Accumulator, output if Event, output if no event - where - a' = g a - - --- | Zero-order hold accumulator (always produces the last outputted value --- until an event arrives). -accumHold :: a -> SF (Event (a -> a)) a -accumHold a_init = epPrim f a_init a_init - where - f a g = (a', a', a') -- Accumulator, output if Event, output if no event - where - a' = g a - --- | Zero-order hold accumulator with delayed initialization (always produces --- the last outputted value until an event arrives, but the very initial output --- is always the given accumulator). -dAccumHold :: a -> SF (Event (a -> a)) a -dAccumHold a_init = accumHold a_init >>> iPre a_init -{- --- WRONG! --- epPrim DOES and MUST patternmatch --- on the input at every time step. --- Test case to check for this added! -dAccumHold a_init = epPrim f a_init a_init - where - f a g = (a', a, a') - where - a' = g a --} - - --- | See 'accumBy'. -old_accumBy :: (b -> a -> b) -> b -> SF (Event a) (Event b) -old_accumBy f b_init = switch (never &&& identity) $ \a -> abAux (f b_init a) - where - abAux b = switch (now b &&& notYet) $ \a -> abAux (f b a) - --- | Accumulator parameterized by the accumulation function. -accumBy :: (b -> a -> b) -> b -> SF (Event a) (Event b) -accumBy g b_init = epPrim f b_init NoEvent - where - f b a = (b', Event b', NoEvent) - where - b' = g b a - --- | Zero-order hold accumulator parameterized by the accumulation function. -accumHoldBy :: (b -> a -> b) -> b -> SF (Event a) b -accumHoldBy g b_init = epPrim f b_init b_init - where - f b a = (b', b', b') - where - b' = g b a - --- !!! This cannot be right since epPrim DOES and MUST patternmatch --- !!! on the input at every time step. --- !!! Add a test case to check for this! - --- | Zero-order hold accumulator parameterized by the accumulation function --- with delayed initialization (initial output sample is always the --- given accumulator). -dAccumHoldBy :: (b -> a -> b) -> b -> SF (Event a) b -dAccumHoldBy f a_init = accumHoldBy f a_init >>> iPre a_init -{- --- WRONG! --- epPrim DOES and MUST patternmatch --- on the input at every time step. --- Test case to check for this added! -dAccumHoldBy g b_init = epPrim f b_init b_init - where - f b a = (b', b, b') - where - b' = g b a --} - - -{- Untested: - -accumBy f b = switch (never &&& identity) $ \a -> - let b' = f b a in NoEvent >-- Event b' --> accumBy f b' - -But no real improvement in clarity anyway. - --} - --- accumBy f b = accumFilter (\b -> a -> let b' = f b a in (b', Event b')) b - -{- --- Identity: accumBy f = accumFilter (\b a -> let b' = f b a in (b',Just b')) -accumBy :: (b -> a -> b) -> b -> SF (Event a) (Event b) -accumBy f b_init = SF {sfTF = tf0} - where - tf0 NoEvent = (abAux b_init, NoEvent) - tf0 (Event a0) = let b' = f b_init a0 - in (abAux b', Event b') - - abAux b = SF' {sfTF' = tf} - where - tf _ NoEvent = (abAux b, NoEvent) - tf _ (Event a) = let b' = f b a - in (abAux b', Event b') --} - -{- -accumFilter :: (c -> a -> (c, Maybe b)) -> c -> SF (Event a) (Event b) -accumFilter f c_init = SF {sfTF = tf0} - where - tf0 NoEvent = (afAux c_init, NoEvent) - tf0 (Event a0) = case f c_init a0 of - (c', Nothing) -> (afAux c', NoEvent) - (c', Just b0) -> (afAux c', Event b0) - - afAux c = SF' {sfTF' = tf} - where - tf _ NoEvent = (afAux c, NoEvent) - tf _ (Event a) = case f c a of - (c', Nothing) -> (afAux c', NoEvent) - (c', Just b) -> (afAux c', Event b) --} - --- | See 'accumFilter'. -old_accumFilter :: (c -> a -> (c, Maybe b)) -> c -> SF (Event a) (Event b) -old_accumFilter f c_init = switch (never &&& identity) $ \a -> afAux (f c_init a) - where - afAux (c, Nothing) = switch (never &&& notYet) $ \a -> afAux (f c a) - afAux (c, Just b) = switch (now b &&& notYet) $ \a -> afAux (f c a) - --- | Accumulator parameterized by the accumulator function with filtering, --- possibly discarding some of the input events based on whether the second --- component of the result of applying the accumulation function is --- 'Nothing' or 'Just' x for some x. -accumFilter :: (c -> a -> (c, Maybe b)) -> c -> SF (Event a) (Event b) -accumFilter g c_init = epPrim f c_init NoEvent - where - f c a = case g c a of - (c', Nothing) -> (c', NoEvent, NoEvent) - (c', Just b) -> (c', Event b, NoEvent) - - ------------------------------------------------------------------------------- --- Delays ------------------------------------------------------------------------------- - --- | Uninitialized delay operator (old implementation). - --- !!! The seq helps in the dynamic delay line example. But is it a good --- !!! idea in general? Are there other accumulators which should be seq'ed --- !!! as well? E.g. accum? Switch? Anywhere else? What's the underlying --- !!! design principle? What can the user assume? --- -old_pre :: SF a a -old_pre = SF {sfTF = tf0} - where - tf0 a0 = (preAux a0, usrErr "AFRP" "pre" "Uninitialized pre operator.") - - preAux a_prev = SF' tf -- True - where - tf _ a = {- a_prev `seq` -} (preAux a, a_prev) - --- | Initialized delay operator (old implementation). -old_iPre :: a -> SF a a -old_iPre = (--> old_pre) - - - --- | Uninitialized delay operator. - --- !!! Redefined using SFSScan --- !!! About 20% slower than old_pre on its own. -pre :: SF a a -pre = sscanPrim f uninit uninit - where - f c a = Just (a, c) - uninit = usrErr "AFRP" "pre" "Uninitialized pre operator." - - --- | Initialized delay operator. -iPre :: a -> SF a a -iPre = (--> pre) - - ------------------------------------------------------------------------------- --- Timed delays ------------------------------------------------------------------------------- - --- | Delay a signal by a fixed time 't', using the second parameter --- to fill in the initial 't' seconds. - --- Invariants: --- t_diff measure the time since the latest output sample ideally --- should have been output. Whenever that equals or exceeds the --- time delta for the next buffered sample, it is time to output a --- new sample (although not necessarily the one first in the queue: --- it might be necessary to "catch up" by discarding samples. --- 0 <= t_diff < bdt, where bdt is the buffered time delta for the --- sample on the front of the buffer queue. --- --- Sum of time deltas in the queue >= q. - --- !!! PROBLEM! --- Since input samples sometimes need to be duplicated, it is not a --- good idea use a delay on things like events since we then could --- end up with duplication of event occurrences. --- (Thus, we actually NEED delayEvent.) - -delay :: Time -> a -> SF a a -delay q a_init | q < 0 = usrErr "AFRP" "delay" "Negative delay." - | q == 0 = identity - | otherwise = SF {sfTF = tf0} - where - tf0 a0 = (delayAux [] [(q, a0)] 0 a_init, a_init) - - delayAux _ [] _ _ = undefined - delayAux rbuf buf@((bdt, ba) : buf') t_diff a_prev = SF' tf -- True - where - tf dt a | t_diff' < bdt = - (delayAux rbuf' buf t_diff' a_prev, a_prev) - | otherwise = nextSmpl rbuf' buf' (t_diff' - bdt) ba - where - t_diff' = t_diff + dt - rbuf' = (dt, a) : rbuf - - nextSmpl rbuf [] t_diff a = - nextSmpl [] (reverse rbuf) t_diff a - nextSmpl rbuf buf@((bdt, ba) : buf') t_diff a - | t_diff < bdt = (delayAux rbuf buf t_diff a, a) - | otherwise = nextSmpl rbuf buf' (t_diff-bdt) ba - - --- !!! Hmm. Not so easy to do efficiently, it seems ... - --- varDelay :: Time -> a -> SF (a, Time) a --- varDelay = undefined - - ------------------------------------------------------------------------------- --- Variable pause in signal ------------------------------------------------------------------------------- - --- | Given a value in an accumulator (b), a predicate signal function (sfC), --- and a second signal function (sf), pause will produce the accumulator b --- if sfC input is True, and will transform the signal using sf otherwise. --- It acts as a pause with an accumulator for the moments when the --- transformation is paused. -pause :: b -> SF a Bool -> SF a b -> SF a b -pause b_init (SF { sfTF = tfP}) (SF {sfTF = tf10}) = SF {sfTF = tf0} - where - -- Initial transformation (no time delta): - -- If the condition is True, return the accumulator b_init) - -- Otherwise transform the input normally and recurse. - tf0 a0 = case tfP a0 of - (c, True) -> (pauseInit b_init tf10 c, b_init) - (c, False) -> let (k, b0) = tf10 a0 - in (pause' b0 k c, b0) - - -- Similar deal, but with a time delta - pauseInit :: b -> (a -> Transition a b) -> SF' a Bool -> SF' a b - pauseInit b_init' tf10' c = SF' tf0' - where tf0' dt a = - case (sfTF' c) dt a of - (c', True) -> (pauseInit b_init' tf10' c', b_init') - (c', False) -> let (k, b0) = tf10' a - in (pause' b0 k c', b0) - - -- Very same deal (almost alpha-renameable) - pause' :: b -> SF' a b -> SF' a Bool -> SF' a b - pause' b_init' tf10' tfP' = SF' tf0' - where tf0' dt a = - case (sfTF' tfP') dt a of - (tfP'', True) -> (pause' b_init' tf10' tfP'', b_init') - (tfP'', False) -> let (tf10'', b0') = (sfTF' tf10') dt a - in (pause' b0' tf10'' tfP'', b0') - --- if_then_else :: SF a Bool -> SF a b -> SF a b -> SF a b --- if_then_else condSF sfThen sfElse = proc (i) -> do --- cond <- condSF -< i --- ok <- sfThen -< i --- notOk <- sfElse -< i --- returnA -< if cond then ok else notOk - ------------------------------------------------------------------------------- --- Integration and differentiation ------------------------------------------------------------------------------- - --- | Integration using the rectangle rule. -{-# INLINE integral #-} -integral :: VectorSpace a s => SF a a -integral = SF {sfTF = tf0} - where - igrl0 = zeroVector - - tf0 a0 = (integralAux igrl0 a0, igrl0) - - integralAux igrl a_prev = SF' tf -- True - where - tf dt a = (integralAux igrl' a, igrl') - where - igrl' = igrl ^+^ realToFrac dt *^ a_prev - - --- "immediate" integration (using the function's value at the current time) -imIntegral :: VectorSpace a s => a -> SF a a -imIntegral = ((\ _ a' dt v -> v ^+^ realToFrac dt *^ a') `iterFrom`) - -iterFrom :: (a -> a -> DTime -> b -> b) -> b -> SF a b -f `iterFrom` b = SF (iterAux b) where - -- iterAux b a = (SF' (\ dt a' -> iterAux (f a a' dt b) a') True, b) - iterAux b a = (SF' (\ dt a' -> iterAux (f a a' dt b) a'), b) - --- | A very crude version of a derivative. It simply divides the --- value difference by the time difference. As such, it is very --- crude. Use at your own risk. -derivative :: VectorSpace a s => SF a a -derivative = SF {sfTF = tf0} - where - tf0 a0 = (derivativeAux a0, zeroVector) - - derivativeAux a_prev = SF' tf -- True - where - tf dt a = (derivativeAux a, (a ^-^ a_prev) ^/ realToFrac dt) - - ------------------------------------------------------------------------------- --- Loops with guaranteed well-defined feedback ------------------------------------------------------------------------------- - --- | Loop with an initial value for the signal being fed back. -loopPre :: c -> SF (a,c) (b,c) -> SF a b -loopPre c_init sf = loop (second (iPre c_init) >>> sf) - --- | Loop by integrating the second value in the pair and feeding the --- result back. Because the integral at time 0 is zero, this is always --- well defined. -loopIntegral :: VectorSpace c s => SF (a,c) (b,c) -> SF a b -loopIntegral sf = loop (second integral >>> sf) - - ------------------------------------------------------------------------------- --- Noise (i.e. random signal generators) and stochastic processes ------------------------------------------------------------------------------- - --- | Noise (random signal) with default range for type in question; --- based on "randoms". -noise :: (RandomGen g, Random b) => g -> SF a b -noise g0 = streamToSF (randoms g0) - - --- | Noise (random signal) with specified range; based on "randomRs". -noiseR :: (RandomGen g, Random b) => (b,b) -> g -> SF a b -noiseR range g0 = streamToSF (randomRs range g0) - - --- Internal. Not very useful for other purposes since we do not have any --- control over the intervals between each "sample". Or? A version with --- time-stamped samples would be similar to embedSynch (applied to identity). --- The list argument must be a stream (infinite list) at present. - -streamToSF :: [b] -> SF a b -streamToSF [] = intErr "AFRP" "streamToSF" "Empty list!" -streamToSF (b:bs) = SF {sfTF = tf0} - where - tf0 _ = (stsfAux bs, b) - - stsfAux [] = intErr "AFRP" "streamToSF" "Empty list!" - -- Invarying since stsfAux [] is an error. - stsfAux (b:bs) = SF' tf -- True - where - tf _ _ = (stsfAux bs, b) - -{- New def, untested: - -streamToSF = sscan2 f - where - f [] _ = intErr "AFRP" "streamToSF" "Empty list!" - f (b:bs) _ = (bs, b) - --} - - --- | Stochastic event source with events occurring on average once every t_avg --- seconds. However, no more than one event results from any one sampling --- interval in the case of relatively sparse sampling, thus avoiding an --- "event backlog" should sampling become more frequent at some later --- point in time. - --- !!! Maybe it would better to give a frequency? But like this to make --- !!! consitent with "repeatedly". -occasionally :: RandomGen g => g -> Time -> b -> SF a (Event b) -occasionally g t_avg x | t_avg > 0 = SF {sfTF = tf0} - | otherwise = usrErr "AFRP" "occasionally" - "Non-positive average interval." - where - -- Generally, if events occur with an average frequency of f, the - -- probability of at least one event occurring in an interval of t - -- is given by (1 - exp (-f*t)). The goal in the following is to - -- decide whether at least one event occurred in the interval of size - -- dt preceding the current sample point. For the first point, - -- we can think of the preceding interval as being 0, implying - -- no probability of an event occurring. - - tf0 _ = (occAux ((randoms g) :: [Time]), NoEvent) - - occAux [] = undefined - occAux (r:rs) = SF' tf -- True - where - tf dt _ = let p = 1 - exp (-(dt/t_avg)) -- Probability for at least one event. - in (occAux rs, if r < p then Event x else NoEvent) - - - ------------------------------------------------------------------------------- --- Reactimation ------------------------------------------------------------------------------- - --- Reactimation of a signal function. --- init ....... IO action for initialization. Will only be invoked once, --- at (logical) time 0, before first call to "sense". --- Expected to return the value of input at time 0. --- sense ...... IO action for sensing of system input. --- arg. #1 ....... True: action may block, waiting for an OS event. --- False: action must not block. --- res. #1 ....... Time interval since previous invocation of the sensing --- action (or, the first time round, the init action), --- returned. The interval must be _strictly_ greater --- than 0. Thus even a non-blocking invocation must --- ensure that time progresses. --- res. #2 ....... Nothing: input is unchanged w.r.t. the previously --- returned input sample. --- Just i: the input is currently i. --- It is OK to always return "Just", even if input is --- unchanged. --- actuate .... IO action for outputting the system output. --- arg. #1 ....... True: output may have changed from previous output --- sample. --- False: output is definitely unchanged from previous --- output sample. --- It is OK to ignore argument #1 and assume that the --- the output has always changed. --- arg. #2 ....... Current output sample. --- result ....... Termination flag. Once True, reactimate will exit --- the reactimation loop and return to its caller. --- sf ......... Signal function to reactimate. - --- | Convenience function to run a signal function indefinitely, using --- a IO actions to obtain new input and process the output. --- --- This function first runs the initialization action, which provides the --- initial input for the signal transformer at time 0. --- --- Afterwards, an input sensing action is used to obtain new input (if any) and --- the time since the last iteration. The argument to the input sensing function --- indicates if it can block. If no new input is received, it is assumed to be --- the same as in the last iteration. --- --- After applying the signal function to the input, the actuation IO action --- is executed. The first argument indicates if the output has changed, the second --- gives the actual output). Actuation functions may choose to ignore the first --- argument altogether. This action should return True if the reactimation --- must stop, and False if it should continue. --- --- Note that this becomes the program's /main loop/, which makes using this --- function incompatible with GLUT, Gtk and other graphics libraries. It may also --- impose a sizeable constraint in larger projects in which different subparts run --- at different time steps. If you need to control the main --- loop yourself for these or other reasons, use 'reactInit' and 'react'. - -reactimate :: IO a -- ^ IO initialization action - -> (Bool -> IO (DTime, Maybe a)) -- ^ IO input sensing action - -> (Bool -> b -> IO Bool) -- ^ IO actuaction (output processing) action - -> SF a b -- ^ Signal function - -> IO () -reactimate init sense actuate (SF {sfTF = tf0}) = - do - a0 <- init - let (sf, b0) = tf0 a0 - loop sf a0 b0 - where - loop sf a b = do - done <- actuate True b - unless (a `seq` b `seq` done) $ do - (dt, ma') <- sense False - let a' = maybe a id ma' - (sf', b') = (sfTF' sf) dt a' - loop sf' a' b' - - --- An API for animating a signal function when some other library --- needs to own the top-level control flow: - --- reactimate's state, maintained across samples: -data ReactState a b = ReactState { - rsActuate :: ReactHandle a b -> Bool -> b -> IO Bool, - rsSF :: SF' a b, - rsA :: a, - rsB :: b - } - --- | A reference to reactimate's state, maintained across samples. -type ReactHandle a b = IORef (ReactState a b) - --- | Initialize a top-level reaction handle. -reactInit :: IO a -- init - -> (ReactHandle a b -> Bool -> b -> IO Bool) -- actuate - -> SF a b - -> IO (ReactHandle a b) -reactInit init actuate (SF {sfTF = tf0}) = - do a0 <- init - let (sf,b0) = tf0 a0 - -- TODO: really need to fix this interface, since right now we - -- just ignore termination at time 0: - r <- newIORef (ReactState {rsActuate = actuate, rsSF = sf, rsA = a0, rsB = b0 }) - _ <- actuate r True b0 - return r - --- | Process a single input sample. -react :: ReactHandle a b - -> (DTime,Maybe a) - -> IO Bool -react rh (dt,ma') = - do rs@(ReactState {rsActuate = actuate, rsSF = sf, rsA = a, rsB = _b }) <- readIORef rh - let a' = maybe a id ma' - (sf',b') = (sfTF' sf) dt a' - writeIORef rh (rs {rsSF = sf',rsA = a',rsB = b'}) - done <- actuate rh True b' - return done - - ------------------------------------------------------------------------------- --- Embedding ------------------------------------------------------------------------------- - --- New embed interface. We will probably have to revisit this. To run an --- embedded signal function while retaining full control (e.g. start and --- stop at will), one would probably need a continuation-based interface --- (as well as a continuation based underlying implementation). --- --- E.g. here are interesting alternative (or maybe complementary) --- signatures: --- --- sample :: SF a b -> SF (Event a) (Event b) --- sample' :: SF a b -> SF (Event (DTime, a)) (Event b) --- --- Maybe it should be called "subSample", since that's the only thing --- that can be achieved. At least does not have the problem with missing --- events when supersampling. --- --- subSampleSynch :: SF a b -> SF (Event a) (Event b) --- Time progresses at the same rate in the embedded system. --- But it is only sampled on the events. --- E.g. --- repeatedly 0.1 () >>> subSampleSynch sf >>> hold --- --- subSample :: DTime -> SF a b -> SF (Event a) (Event b) --- Time advanced by dt for each event, not synchronized with the outer clock. - --- | Given a signal function and a pair with an initial --- input sample for the input signal, and a list of sampling --- times, possibly with new input samples at those times, --- it produces a list of output samples. --- --- This is a simplified, purely-functional version of 'reactimate'. -embed :: SF a b -> (a, [(DTime, Maybe a)]) -> [b] -embed sf0 (a0, dtas) = b0 : loop a0 sf dtas - where - (sf, b0) = (sfTF sf0) a0 - - loop _ _ [] = [] - loop a_prev sf ((dt, ma) : dtas) = - b : (a `seq` b `seq` (loop a sf' dtas)) - where - a = maybe a_prev id ma - (sf', b) = (sfTF' sf) dt a - - --- | Synchronous embedding. The embedded signal function is run on the supplied --- input and time stream at a given (but variable) ratio >= 0 to the outer --- time flow. When the ratio is 0, the embedded signal function is paused. - --- What about running an embedded signal function at a fixed (guaranteed) --- sampling frequency? E.g. super sampling if the outer sampling is slower, --- subsampling otherwise. AS WELL as at a given ratio to the outer one. --- --- Ah, but that's more or less what embedSync does. --- So just simplify the interface. But maybe it should also be possible --- to feed in input from the enclosing system. - --- !!! Should "dropped frames" be forced to avoid space leaks? --- !!! It's kind of hard to se why, but "frame dropping" was a problem --- !!! in the old robot simulator. Try to find an example! - -embedSynch :: SF a b -> (a, [(DTime, Maybe a)]) -> SF Double b -embedSynch sf0 (a0, dtas) = SF {sfTF = tf0} - where - tts = scanl (\t (dt, _) -> t + dt) 0 dtas - bbs@(b:_) = embed sf0 (a0, dtas) - - tf0 _ = (esAux 0 (zip tts bbs), b) - - esAux _ [] = intErr "AFRP" "embedSynch" "Empty list!" - -- Invarying below since esAux [] is an error. - esAux tp_prev tbtbs = SF' tf -- True - where - tf dt r | r < 0 = usrErr "AFRP" "embedSynch" - "Negative ratio." - | otherwise = let tp = tp_prev + dt * r - (b, tbtbs') = advance tp tbtbs - in - (esAux tp tbtbs', b) - - -- Advance the time stamped stream to the perceived time tp. - -- Under the assumption that the perceived time never goes - -- backwards (non-negative ratio), advance maintains the - -- invariant that the perceived time is always >= the first - -- time stamp. - advance _ tbtbs@[(_, b)] = (b, tbtbs) - advance tp tbtbtbs@((_, b) : tbtbs@((t', _) : _)) - | tp < t' = (b, tbtbtbs) - | t' <= tp = advance tp tbtbs - advance _ _ = undefined - --- | Spaces a list of samples by a fixed time delta, avoiding --- unnecessary samples when the input has not changed since --- the last sample. -deltaEncode :: Eq a => DTime -> [a] -> (a, [(DTime, Maybe a)]) -deltaEncode _ [] = usrErr "AFRP" "deltaEncode" "Empty input list." -deltaEncode dt aas@(_:_) = deltaEncodeBy (==) dt aas - - --- | 'deltaEncode' parameterized by the equality test. -deltaEncodeBy :: (a -> a -> Bool) -> DTime -> [a] -> (a, [(DTime, Maybe a)]) -deltaEncodeBy _ _ [] = usrErr "AFRP" "deltaEncodeBy" "Empty input list." -deltaEncodeBy eq dt (a0:as) = (a0, zip (repeat dt) (debAux a0 as)) - where - debAux _ [] = [] - debAux a_prev (a:as) | a `eq` a_prev = Nothing : debAux a as + Time, -- [s] Both for time w.r.t. some reference and intervals. + DTime, -- [s] Sampling interval, always > 0. + SF, -- Signal Function. + Event(..), -- Events; conceptually similar to Maybe (but abstract). + +-- Temporray! +-- SF(..), sfTF', + +-- Main instances + -- SF is an instance of Arrow and ArrowLoop. Method instances: + -- arr :: (a -> b) -> SF a b + -- (>>>) :: SF a b -> SF b c -> SF a c + -- (<<<) :: SF b c -> SF a b -> SF a c + -- first :: SF a b -> SF (a,c) (b,c) + -- second :: SF a b -> SF (c,a) (c,b) + -- (***) :: SF a b -> SF a' b' -> SF (a,a') (b,b') + -- (&&&) :: SF a b -> SF a b' -> SF a (b,b') + -- returnA :: SF a a + -- loop :: SF (a,c) (b,c) -> SF a b + + -- Event is an instance of Functor, Eq, and Ord. Some method instances: + -- fmap :: (a -> b) -> Event a -> Event b + -- (==) :: Event a -> Event a -> Bool + -- (<=) :: Event a -> Event a -> Bool + + -- ** Lifting + arrPrim, arrEPrim, -- For optimization + +-- * Signal functions + +-- ** Basic signal functions + identity, -- :: SF a a + constant, -- :: b -> SF a b + localTime, -- :: SF a Time + time, -- :: SF a Time, Other name for localTime. + +-- ** Initialization + (-->), -- :: b -> SF a b -> SF a b, infixr 0 + (>--), -- :: a -> SF a b -> SF a b, infixr 0 + (-=>), -- :: (b -> b) -> SF a b -> SF a b infixr 0 + (>=-), -- :: (a -> a) -> SF a b -> SF a b infixr 0 + initially, -- :: a -> SF a a + +-- ** Simple, stateful signal processing + sscan, -- :: (b -> a -> b) -> b -> SF a b + sscanPrim, -- :: (c -> a -> Maybe (c, b)) -> c -> b -> SF a b + +-- * Events +-- ** Basic event sources + never, -- :: SF a (Event b) + now, -- :: b -> SF a (Event b) + after, -- :: Time -> b -> SF a (Event b) + repeatedly, -- :: Time -> b -> SF a (Event b) + afterEach, -- :: [(Time,b)] -> SF a (Event b) + afterEachCat, -- :: [(Time,b)] -> SF a (Event [b]) + delayEvent, -- :: Time -> SF (Event a) (Event a) + delayEventCat, -- :: Time -> SF (Event a) (Event [a]) + edge, -- :: SF Bool (Event ()) + iEdge, -- :: Bool -> SF Bool (Event ()) + edgeTag, -- :: a -> SF Bool (Event a) + edgeJust, -- :: SF (Maybe a) (Event a) + edgeBy, -- :: (a -> a -> Maybe b) -> a -> SF a (Event b) + +-- ** Stateful event suppression + notYet, -- :: SF (Event a) (Event a) + once, -- :: SF (Event a) (Event a) + takeEvents, -- :: Int -> SF (Event a) (Event a) + dropEvents, -- :: Int -> SF (Event a) (Event a) + +-- ** Pointwise functions on events + noEvent, -- :: Event a + noEventFst, -- :: (Event a, b) -> (Event c, b) + noEventSnd, -- :: (a, Event b) -> (a, Event c) + event, -- :: a -> (b -> a) -> Event b -> a + fromEvent, -- :: Event a -> a + isEvent, -- :: Event a -> Bool + isNoEvent, -- :: Event a -> Bool + tag, -- :: Event a -> b -> Event b, infixl 8 + tagWith, -- :: b -> Event a -> Event b, + attach, -- :: Event a -> b -> Event (a, b), infixl 8 + lMerge, -- :: Event a -> Event a -> Event a, infixl 6 + rMerge, -- :: Event a -> Event a -> Event a, infixl 6 + merge, -- :: Event a -> Event a -> Event a, infixl 6 + mergeBy, -- :: (a -> a -> a) -> Event a -> Event a -> Event a + mapMerge, -- :: (a -> c) -> (b -> c) -> (a -> b -> c) + -- -> Event a -> Event b -> Event c + mergeEvents, -- :: [Event a] -> Event a + catEvents, -- :: [Event a] -> Event [a] + joinE, -- :: Event a -> Event b -> Event (a,b),infixl 7 + splitE, -- :: Event (a,b) -> (Event a, Event b) + filterE, -- :: (a -> Bool) -> Event a -> Event a + mapFilterE, -- :: (a -> Maybe b) -> Event a -> Event b + gate, -- :: Event a -> Bool -> Event a, infixl 8 + +-- * Switching +-- ** Basic switchers + switch, dSwitch, -- :: SF a (b, Event c) -> (c -> SF a b) -> SF a b + rSwitch, drSwitch, -- :: SF a b -> SF (a,Event (SF a b)) b + kSwitch, dkSwitch, -- :: SF a b + -- -> SF (a,b) (Event c) + -- -> (SF a b -> c -> SF a b) + -- -> SF a b + +-- ** Parallel composition and switching +-- *** Parallel composition and switching over collections with broadcasting + parB, -- :: Functor col => col (SF a b) -> SF a (col b) + pSwitchB,dpSwitchB, -- :: Functor col => + -- col (SF a b) + -- -> SF (a, col b) (Event c) + -- -> (col (SF a b) -> c -> SF a (col b)) + -- -> SF a (col b) + rpSwitchB,drpSwitchB,-- :: Functor col => + -- col (SF a b) + -- -> SF (a, Event (col (SF a b)->col (SF a b))) + -- (col b) + +-- *** Parallel composition and switching over collections with general routing + par, -- Functor col => + -- (forall sf . (a -> col sf -> col (b, sf))) + -- -> col (SF b c) + -- -> SF a (col c) + pSwitch, dpSwitch, -- pSwitch :: Functor col => + -- (forall sf . (a -> col sf -> col (b, sf))) + -- -> col (SF b c) + -- -> SF (a, col c) (Event d) + -- -> (col (SF b c) -> d -> SF a (col c)) + -- -> SF a (col c) + rpSwitch,drpSwitch, -- Functor col => + -- (forall sf . (a -> col sf -> col (b, sf))) + -- -> col (SF b c) + -- -> SF (a, Event (col (SF b c) -> col (SF b c))) + -- (col c) + +-- * Discrete to continuous-time signal functions +-- ** Wave-form generation + old_hold, -- :: a -> SF (Event a) a + hold, -- :: a -> SF (Event a) a + dHold, -- :: a -> SF (Event a) a + trackAndHold, -- :: a -> SF (Maybe a) a + +-- ** Accumulators + accum, -- :: a -> SF (Event (a -> a)) (Event a) + accumHold, -- :: a -> SF (Event (a -> a)) a + dAccumHold, -- :: a -> SF (Event (a -> a)) a + accumBy, -- :: (b -> a -> b) -> b -> SF (Event a) (Event b) + accumHoldBy, -- :: (b -> a -> b) -> b -> SF (Event a) b + dAccumHoldBy, -- :: (b -> a -> b) -> b -> SF (Event a) b + accumFilter, -- :: (c -> a -> (c, Maybe b)) -> c + -- -> SF (Event a) (Event b) + old_accum, -- :: a -> SF (Event (a -> a)) (Event a) + old_accumBy, -- :: (b -> a -> b) -> b -> SF (Event a) (Event b) + old_accumFilter, -- :: (c -> a -> (c, Maybe b)) -> c + +-- * Delays +-- ** Basic delays + pre, -- :: SF a a + iPre, -- :: a -> SF a a + old_pre, old_iPre, + +-- ** Timed delays + delay, -- :: Time -> a -> SF a a + +-- ** Variable delay + pause, -- :: b -> SF a b -> SF a Bool -> SF a b + +-- * State keeping combinators + +-- ** Loops with guaranteed well-defined feedback + loopPre, -- :: c -> SF (a,c) (b,c) -> SF a b + loopIntegral, -- :: VectorSpace c s => SF (a,c) (b,c) -> SF a b + +-- ** Integration and differentiation + integral, -- :: VectorSpace a s => SF a a + + derivative, -- :: VectorSpace a s => SF a a -- Crude! + imIntegral, -- :: VectorSpace a s => a -> SF a a + + -- Temporarily hidden, but will eventually be made public. + -- iterFrom, -- :: (a -> a -> DTime -> b -> b) -> b -> SF a b + +-- * Noise (random signal) sources and stochastic event sources + noise, -- :: noise :: (RandomGen g, Random b) => + -- g -> SF a b + noiseR, -- :: noise :: (RandomGen g, Random b) => + -- (b,b) -> g -> SF a b + occasionally, -- :: RandomGen g => g -> Time -> b -> SF a (Event b) + +-- * Reactimation + reactimate, -- :: IO a + -- -> (Bool -> IO (DTime, Maybe a)) + -- -> (Bool -> b -> IO Bool) + -- -> SF a b + -- -> IO () + ReactHandle, + reactInit, -- IO a -- init + -- -> (ReactHandle a b -> Bool -> b -> IO Bool) -- actuate + -- -> SF a b + -- -> IO (ReactHandle a b) +-- process a single input sample: + react, -- ReactHandle a b + -- -> (DTime,Maybe a) + -- -> IO Bool + +-- * Embedding + +-- (tentative: will be revisited) + embed, -- :: SF a b -> (a, [(DTime, Maybe a)]) -> [b] + embedSynch, -- :: SF a b -> (a, [(DTime, Maybe a)]) -> SF Double b + deltaEncode, -- :: Eq a => DTime -> [a] -> (a, [(DTime, Maybe a)]) + deltaEncodeBy, -- :: (a -> a -> Bool) -> DTime -> [a] + -- -> (a, [(DTime, Maybe a)]) + + -- * Auxiliary definitions + -- Reverse function composition and arrow plumbing aids + ( # ), -- :: (a -> b) -> (b -> c) -> (a -> c), infixl 9 + dup, -- :: a -> (a,a) + swap, -- :: (a,b) -> (b,a) + + +) where + +import Control.Arrow +#if __GLASGOW_HASKELL__ >= 610 +import qualified Control.Category (Category(..)) +#else +#endif +import Control.Monad (unless) +import Data.IORef +import Data.Maybe (fromMaybe) +import System.Random (RandomGen(..), Random(..)) + + +import FRP.Yampa.Diagnostics +import FRP.Yampa.Miscellany (( # ), dup, swap) +import FRP.Yampa.Event +import FRP.Yampa.VectorSpace + +infixr 0 -->, >--, -=>, >=- + +------------------------------------------------------------------------------ +-- Basic type definitions with associated utilities +------------------------------------------------------------------------------ + +-- The time type is really a bit boguous, since, as time passes, the minimal +-- interval between two consecutive floating-point-represented time points +-- increases. A better approach might be to pick a reasonable resolution +-- and represent time and time intervals by Integer (giving the number of +-- "ticks"). +-- +-- That might also improve the timing of time-based event sources. +-- One might actually pick the overall resolution in reactimate, +-- to be passed down, possibly in the form of a global parameter +-- record, to all signal functions on initialization. (I think only +-- switch would need to remember the record, since it is the only place +-- where signal functions get started. So it wouldn't cost all that much. + + +-- | Time is used both for time intervals (duration), and time w.r.t. some +-- agreed reference point in time. + +-- Conceptually, Time = R, i.e. time can be 0 -- or even negative. +type Time = Double -- [s] + + +-- | DTime is the time type for lengths of sample intervals. Conceptually, +-- DTime = R+ = { x in R | x > 0 }. Don't assume Time and DTime have the +-- same representation. +type DTime = Double -- [s] + +-- Representation of signal function in initial state. +-- (Naming: "TF" stands for Transition Function.) + +-- | Signal function that transforms a signal carrying values of some type 'a' +-- into a signal carrying values of some type 'b'. You can think of it as +-- (Signal a -> Signal b). A signal is, conceptually, a +-- function from 'Time' to value. +data SF a b = SF {sfTF :: a -> Transition a b} + + +-- Representation of signal function in "running" state. +-- +-- Possibly better design for Inv. +-- Problem: tension between on the one hand making use of the +-- invariant property, and on the other keeping track of how something +-- has been constructed (SFCpAXA, in particular). +-- Idea: Add a boolean field to SFCpAXA and SF' that classifies +-- a signal function as being invarying. +-- A function sfIsInv computes to True for SFArr, SFAcc (and SFSScan, +-- possibly more), extracts the field in other cases. +-- +-- Motivation for using a function (Event a -> b) in SFArrE +-- rather than (a -> Event b) or (a -> b) or even (Event a -> Event b). +-- The result type should be just "b" as opposed to "Event b" for +-- increased flexibility (e.g. matching "routing functions"). +-- When the result type actually IS (Event b), and this fact is +-- exploitable, we'll be in a context where is it clear that +-- this is a fact, so we don't lose anything. +-- Since the idea is that the function is only going to be applied +-- when the there is an event, one could imagine the input type +-- just "a". But that's not the type of function we're given, +-- so it would have to be "massaged" a bit (precomposing with Event) +-- to fit. This will gain nothing, and potentially we will lose if +-- we actually need to recover the original function. +-- In fact, we sometimes really need to recover the original function +-- (e.g. currently in switch), and to do it correctly (also handling +-- NoEvent), we'd have to work quite hard introducing further +-- inefficiencies. +-- Summary: Make use of what we are given and only wrap things up later +-- when it is clear whatthe need is going to be, thus avoiding costly +-- "unwrapping". + +-- GADTs needed in particular for SFEP, but also e.g. SFSScan +-- exploits them since there are more type vars than in the type con. +-- But one could use existentials for those. + + +data SF' a b where + SFArr :: !(DTime -> a -> Transition a b) -> !(FunDesc a b) -> SF' a b + -- The b is intentionally unstrict as the initial output sometimes + -- is undefined (e.g. when defining pre). In any case, it isn't + -- necessarily used and should thus not be forced. + SFSScan :: !(DTime -> a -> Transition a b) + -> !(c -> a -> Maybe (c, b)) -> !c -> b + -> SF' a b + SFEP :: !(DTime -> Event a -> Transition (Event a) b) + -> !(c -> a -> (c, b, b)) -> !c -> b + -> SF' (Event a) b + SFCpAXA :: !(DTime -> a -> Transition a d) + -> !(FunDesc a b) -> !(SF' b c) -> !(FunDesc c d) + -> SF' a d + -- SFPair :: ... + SF' :: !(DTime -> a -> Transition a b) -> SF' a b + +-- A transition is a pair of the next state (in the form of a signal +-- function) and the output at the present time step. + +type Transition a b = (SF' a b, b) + + +sfTF' :: SF' a b -> (DTime -> a -> Transition a b) +sfTF' (SFArr tf _) = tf +sfTF' (SFSScan tf _ _ _) = tf +sfTF' (SFEP tf _ _ _) = tf +sfTF' (SFCpAXA tf _ _ _) = tf +sfTF' (SF' tf) = tf + + +-- !!! 2005-06-30 +-- Unclear why, but the isInv mechanism seems to do more +-- harm than good. +-- Disable completely and see what happens. +{- +sfIsInv :: SF' a b -> Bool +-- sfIsInv _ = False +sfIsInv (SFArr _ _) = True +-- sfIsInv (SFAcc _ _ _ _) = True +sfIsInv (SFEP _ _ _ _) = True +-- sfIsInv (SFSScan ...) = True +sfIsInv (SFCpAXA _ inv _ _ _) = inv +sfIsInv (SF' _ inv) = inv +-} + +-- "Smart" constructors. The corresponding "raw" constructors should not +-- be used directly for construction. + +sfArr :: FunDesc a b -> SF' a b +sfArr FDI = sfId +sfArr (FDC b) = sfConst b +sfArr (FDE f fne) = sfArrE f fne +sfArr (FDG f) = sfArrG f + + +sfId :: SF' a a +sfId = sf + where + sf = SFArr (\_ a -> (sf, a)) FDI + + +sfConst :: b -> SF' a b +sfConst b = sf + where + sf = SFArr (\_ _ -> (sf, b)) (FDC b) + + +sfNever :: SF' a (Event b) +sfNever = sfConst NoEvent + +-- Assumption: fne = f NoEvent +sfArrE :: (Event a -> b) -> b -> SF' (Event a) b +sfArrE f fne = sf + where + sf = SFArr (\_ ea -> (sf, case ea of NoEvent -> fne ; _ -> f ea)) + (FDE f fne) + +sfArrG :: (a -> b) -> SF' a b +sfArrG f = sf + where + sf = SFArr (\_ a -> (sf, f a)) (FDG f) + + +sfSScan :: (c -> a -> Maybe (c, b)) -> c -> b -> SF' a b +sfSScan f c b = sf + where + sf = SFSScan tf f c b + tf _ a = case f c a of + Nothing -> (sf, b) + Just (c', b') -> (sfSScan f c' b', b') + +sscanPrim :: (c -> a -> Maybe (c, b)) -> c -> b -> SF a b +sscanPrim f c_init b_init = SF {sfTF = tf0} + where + tf0 a0 = case f c_init a0 of + Nothing -> (sfSScan f c_init b_init, b_init) + Just (c', b') -> (sfSScan f c' b', b') + + +-- The event-processing function *could* accept the present NoEvent +-- output as an extra state argument. That would facilitate composition +-- of event-processing functions somewhat, but would presumably incur an +-- extra cost for the more common and simple case of non-composed event +-- processors. +-- +sfEP :: (c -> a -> (c, b, b)) -> c -> b -> SF' (Event a) b +sfEP f c bne = sf + where + sf = SFEP (\_ ea -> case ea of + NoEvent -> (sf, bne) + Event a -> let + (c', b, bne') = f c a + in + (sfEP f c' bne', b)) + f + c + bne + + +-- epPrim is used to define hold, accum, and other event-processing +-- functions. +epPrim :: (c -> a -> (c, b, b)) -> c -> b -> SF (Event a) b +epPrim f c bne = SF {sfTF = tf0} + where + tf0 NoEvent = (sfEP f c bne, bne) + tf0 (Event a) = let + (c', b, bne') = f c a + in + (sfEP f c' bne', b) + + +{- +-- !!! Maybe something like this? +-- !!! But one problem is that the invarying marking would be lost +-- !!! if the signal function is taken apart and re-constructed from +-- !!! the function description and subordinate signal function in +-- !!! cases like SFCpAXA. +sfMkInv :: SF a b -> SF a b +sfMkInv sf = SF {sfTF = ...} + + sfMkInvAux :: SF' a b -> SF' a b + sfMkInvAux sf@(SFArr _ _) = sf + -- sfMkInvAux sf@(SFAcc _ _ _ _) = sf + sfMkInvAux sf@(SFEP _ _ _ _) = sf + sfMkInvAux sf@(SFCpAXA tf inv fd1 sf2 fd3) + | inv = sf + | otherwise = SFCpAXA tf' True fd1 sf2 fd3 + where + tf' = \dt a -> let (sf', b) = tf dt a in (sfMkInvAux sf', b) + sfMkInvAux sf@(SF' tf inv) + | inv = sf + | otherwise = SF' tf' True + tf' = + +-} + +-- Motivation for event-processing function type +-- (alternative would be function of type a->b plus ensuring that it +-- only ever gets invoked on events): +-- * Now we need to be consistent with other kinds of arrows. +-- * We still want to be able to get hold of the original function. +-- 2005-02-30: OK, for FDE, invarant is that the field of type b = +-- f NoEvent. + +data FunDesc a b where + FDI :: FunDesc a a -- Identity function + FDC :: b -> FunDesc a b -- Constant function + FDE :: (Event a -> b) -> b -> FunDesc (Event a) b -- Event-processing fun + FDG :: (a -> b) -> FunDesc a b -- General function + +fdFun :: FunDesc a b -> (a -> b) +fdFun FDI = id +fdFun (FDC b) = const b +fdFun (FDE f _) = f +fdFun (FDG f) = f + +fdComp :: FunDesc a b -> FunDesc b c -> FunDesc a c +fdComp FDI fd2 = fd2 +fdComp fd1 FDI = fd1 +fdComp (FDC b) fd2 = FDC ((fdFun fd2) b) +fdComp _ (FDC c) = FDC c +-- Hardly worth the effort? +-- 2005-03-30: No, not only not worth the effort as the only thing saved +-- would be an application of f2. Also wrong since current invariant does +-- not imply that f1ne = NoEvent. Moreover, we cannot really adopt that +-- invariant as it is not totally impossible for a user to create a function +-- that breaks it. +-- fdComp (FDE f1 f1ne) (FDE f2 f2ne) = +-- FDE (f2 . f1) (vfyNoEvent (f1 NoEvent) f2ne) +fdComp (FDE f1 f1ne) fd2 = FDE (f2 . f1) (f2 f1ne) + where + f2 = fdFun fd2 +fdComp (FDG f1) (FDE f2 f2ne) = FDG f + where + f a = case f1 a of + NoEvent -> f2ne + f1a -> f2 f1a +fdComp (FDG f1) fd2 = FDG (fdFun fd2 . f1) + + +fdPar :: FunDesc a b -> FunDesc c d -> FunDesc (a,c) (b,d) +fdPar FDI FDI = FDI +fdPar FDI (FDC d) = FDG (\(~(a, _)) -> (a, d)) +fdPar FDI fd2 = FDG (\(~(a, c)) -> (a, (fdFun fd2) c)) +fdPar (FDC b) FDI = FDG (\(~(_, c)) -> (b, c)) +fdPar (FDC b) (FDC d) = FDC (b, d) +fdPar (FDC b) fd2 = FDG (\(~(_, c)) -> (b, (fdFun fd2) c)) +fdPar fd1 fd2 = FDG (\(~(a, c)) -> ((fdFun fd1) a, (fdFun fd2) c)) + + +fdFanOut :: FunDesc a b -> FunDesc a c -> FunDesc a (b,c) +fdFanOut FDI FDI = FDG dup +fdFanOut FDI (FDC c) = FDG (\a -> (a, c)) +fdFanOut FDI fd2 = FDG (\a -> (a, (fdFun fd2) a)) +fdFanOut (FDC b) FDI = FDG (\a -> (b, a)) +fdFanOut (FDC b) (FDC c) = FDC (b, c) +fdFanOut (FDC b) fd2 = FDG (\a -> (b, (fdFun fd2) a)) +fdFanOut (FDE f1 f1ne) (FDE f2 f2ne) = FDE f1f2 f1f2ne + where + f1f2 NoEvent = f1f2ne + f1f2 ea@(Event _) = (f1 ea, f2 ea) + + f1f2ne = (f1ne, f2ne) +fdFanOut fd1 fd2 = + FDG (\a -> ((fdFun fd1) a, (fdFun fd2) a)) + + +-- Verifies that the first argument is NoEvent. Returns the value of the +-- second argument that is the case. Raises an error otherwise. +-- Used to check that functions on events do not map NoEvent to Event +-- wherever that assumption is exploited. +vfyNoEv :: Event a -> b -> b +vfyNoEv NoEvent b = b +vfyNoEv _ _ = usrErr "AFRP" "vfyNoEv" "Assertion failed: Functions on events must not map NoEvent to Event." + + +-- Freezes a "running" signal function, i.e., turns it into a continuation in +-- the form of a plain signal function. +freeze :: SF' a b -> DTime -> SF a b +freeze sf dt = SF {sfTF = (sfTF' sf) dt} + + +freezeCol :: Functor col => col (SF' a b) -> DTime -> col (SF a b) +freezeCol sfs dt = fmap (flip freeze dt) sfs + + +------------------------------------------------------------------------------ +-- Arrow instance and implementation +------------------------------------------------------------------------------ +#if __GLASGOW_HASKELL__ >= 610 +instance Control.Category.Category SF where + (.) = flip compPrim + id = SF $ \x -> (sfId,x) +#else +#endif + +instance Arrow SF where + arr = arrPrim + first = firstPrim + second = secondPrim + (***) = parSplitPrim + (&&&) = parFanOutPrim +#if __GLASGOW_HASKELL__ >= 610 +#else + (>>>) = compPrim +#endif + + +-- Lifting. + +-- | Lifts a pure function into a signal function (applied pointwise). +{-# NOINLINE arrPrim #-} +arrPrim :: (a -> b) -> SF a b +arrPrim f = SF {sfTF = \a -> (sfArrG f, f a)} + +-- | Lifts a pure function into a signal function applied to events +-- (applied pointwise). +{-# RULES "arrPrim/arrEPrim" arrPrim = arrEPrim #-} +arrEPrim :: (Event a -> b) -> SF (Event a) b +arrEPrim f = SF {sfTF = \a -> (sfArrE f (f NoEvent), f a)} + + +-- Composition. +-- The definition exploits the following identities: +-- sf >>> identity = sf -- New +-- identity >>> sf = sf -- New +-- sf >>> constant c = constant c +-- constant c >>> arr f = constant (f c) +-- arr f >>> arr g = arr (g . f) +-- +-- !!! Notes/Questions: +-- !!! How do we know that the optimizations terminate? +-- !!! Probably by some kind of size argument on the SF tree. +-- !!! E.g. (Hopefully) all compPrim optimizations are such that +-- !!! the number of compose nodes decrease. +-- !!! Should verify this! +-- +-- !!! There is a tension between using SFInv to signal to superior +-- !!! signal functions that the subordinate signal function will not +-- !!! change form, and using SFCpAXA to allow fusion in the context +-- !!! of some suitable superior signal function. +compPrim :: SF a b -> SF b c -> SF a c +compPrim (SF {sfTF = tf10}) (SF {sfTF = tf20}) = SF {sfTF = tf0} + where + tf0 a0 = (cpXX sf1 sf2, c0) + where + (sf1, b0) = tf10 a0 + (sf2, c0) = tf20 b0 + +-- The following defs are not local to compPrim because cpAXA needs to be +-- called from parSplitPrim. +-- Naming convention: cp where and is one of: +-- X - arbitrary signal function +-- A - arbitrary pure arrow +-- C - constant arrow +-- E - event-processing arrow +-- G - arrow known not to be identity, constant (C) or +-- event-processing (E). + +cpXX :: SF' a b -> SF' b c -> SF' a c +cpXX (SFArr _ fd1) sf2 = cpAX fd1 sf2 +cpXX sf1 (SFArr _ fd2) = cpXA sf1 fd2 +{- +-- !!! 2005-07-07: Too strict. +-- !!! But the question is if it is worth to define pre in terms of sscan ... +-- !!! It is slower than the simplest possible pre, and the kind of coding +-- !!! required to ensure that the laziness props of the second SF are +-- !!! preserved might just slow things down further ... +cpXX (SFSScan _ f1 s1 b) (SFSScan _ f2 s2 c) = + sfSScan f (s1, b, s2, c) c + where + f (s1, b, s2, c) a = + case f1 s1 a of + Nothing -> + case f2 s2 b of + Nothing -> Nothing + Just (s2', c') -> Just ((s1, b, s2', c'), c') + Just (s1', b') -> + case f2 s2 b' of + Nothing -> Just ((s1', b', s2, c), c) + Just (s2', c') -> Just ((s1', b', s2', c'), c') +-} +-- !!! 2005-07-07: Indeed, this is a bit slower than the code above (14%). +-- !!! But both are better than not composing (35% faster and 26% faster)! +cpXX (SFSScan _ f1 s1 b) (SFSScan _ f2 s2 c) = + sfSScan f (s1, b, s2, c) c + where + f (s1, b, s2, c) a = + let + (u, s1', b') = case f1 s1 a of + Nothing -> (True, s1, b) + Just (s1',b') -> (False, s1', b') + in + case f2 s2 b' of + Nothing | u -> Nothing + | otherwise -> Just ((s1', b', s2, c), c) + Just (s2', c') -> Just ((s1', b', s2', c'), c') +cpXX (SFSScan _ f1 s1 eb) (SFEP _ f2 s2 cne) = + sfSScan f (s1, eb, s2, cne) cne + where + f (s1, eb, s2, cne) a = + case f1 s1 a of + Nothing -> + case eb of + NoEvent -> Nothing + Event b -> + let (s2', c, cne') = f2 s2 b + in + Just ((s1, eb, s2', cne'), c) + Just (s1', eb') -> + case eb' of + NoEvent -> Just ((s1', eb', s2, cne), cne) + Event b -> + let (s2', c, cne') = f2 s2 b + in + Just ((s1', eb', s2', cne'), c) +-- !!! 2005-07-09: This seems to yield only a VERY marginal speedup +-- !!! without seq. With seq, substantial speedup! +cpXX (SFEP _ f1 s1 bne) (SFSScan _ f2 s2 c) = + sfSScan f (s1, bne, s2, c) c + where + f (s1, bne, s2, c) ea = + let (u, s1', b', bne') = case ea of + NoEvent -> (True, s1, bne, bne) + Event a -> + let (s1', b, bne') = f1 s1 a + in + (False, s1', b, bne') + in + case f2 s2 b' of + Nothing | u -> Nothing + | otherwise -> Just (seq s1' (s1', bne', s2, c), c) + Just (s2', c') -> Just (seq s1' (s1', bne', s2', c'), c') +-- The function "f" is invoked whenever an event is to be processed. It then +-- computes the output, the new state, and the new NoEvent output. +-- However, when sequencing event processors, the ones in the latter +-- part of the chain may not get invoked since previous ones may +-- decide not to "fire". But a "new" NoEvent output still has to be +-- produced, i.e. the old one retained. Since it cannot be computed by +-- invoking the last event-processing function in the chain, it has to +-- be remembered. Since the composite event-processing function remains +-- constant/unchanged, the NoEvent output has to be part of the state. +-- An alternarive would be to make the event-processing function take an +-- extra argument. But that is likely to make the simple case more +-- expensive. See note at sfEP. +cpXX (SFEP _ f1 s1 bne) (SFEP _ f2 s2 cne) = + sfEP f (s1, s2, cne) (vfyNoEv bne cne) + where + f (s1, s2, cne) a = + case f1 s1 a of + (s1', NoEvent, NoEvent) -> ((s1', s2, cne), cne, cne) + (s1', Event b, NoEvent) -> + let (s2', c, cne') = f2 s2 b in ((s1', s2', cne'), c, cne') + _ -> usrErr "AFRP" "cpXX" "Assertion failed: Functions on events must not map NoEvent to Event." +-- !!! 2005-06-28: Why isn't SFCpAXA (FDC ...) checked for? +-- !!! No invariant rules that out, and it would allow to drop the +-- !!! event processor ... Does that happen elsewhere? +cpXX sf1@(SFEP _ _ _ _) (SFCpAXA _ (FDE f21 f21ne) sf22 fd23) = + cpXX (cpXE sf1 f21 f21ne) (cpXA sf22 fd23) +-- f21 will (hopefully) be invoked less frequently if merged with the +-- event processor. +cpXX sf1@(SFEP _ _ _ _) (SFCpAXA _ (FDG f21) sf22 fd23) = + cpXX (cpXG sf1 f21) (cpXA sf22 fd23) +-- Only functions whose domain is known to be Event can be merged +-- from the left with event processors. +cpXX (SFCpAXA _ fd11 sf12 (FDE f13 f13ne)) sf2@(SFEP _ _ _ _) = + cpXX (cpAX fd11 sf12) (cpEX f13 f13ne sf2) +-- !!! Other cases to look out for: +-- !!! any sf >>> SFCpAXA = SFCpAXA if first arr is const. +-- !!! But the following will presumably not work due to type restrictions. +-- !!! Need to reconstruct sf2 I think. +-- cpXX sf1 sf2@(SFCpAXA _ _ (FDC b) sf22 fd23) = sf2 +cpXX (SFCpAXA _ fd11 sf12 fd13) (SFCpAXA _ fd21 sf22 fd23) = + -- Termination: The first argument to cpXX is no larger than + -- the current first argument, and the second is smaller. + cpAXA fd11 (cpXX (cpXA sf12 (fdComp fd13 fd21)) sf22) fd23 +-- !!! 2005-06-27: The if below accounts for a significant slowdown. +-- !!! One would really like a cheme where opts only take place +-- !!! after a structural change ... +-- cpXX sf1 sf2 = cpXXInv sf1 sf2 +-- cpXX sf1 sf2 = cpXXAux sf1 sf2 +cpXX sf1 sf2 = SF' tf -- False + -- if sfIsInv sf1 && sfIsInv sf2 then cpXXInv sf1 sf2 else SF' tf False + where + tf dt a = (cpXX sf1' sf2', c) + where + (sf1', b) = (sfTF' sf1) dt a + (sf2', c) = (sfTF' sf2) dt b + + +{- +cpXXAux sf1@(SF' _ _) sf2@(SF' _ _) = SF' tf False + where + tf dt a = (cpXXAux sf1' sf2', c) + where + (sf1', b) = (sfTF' sf1) dt a + (sf2', c) = (sfTF' sf2) dt b +cpXXAux sf1 sf2 = SF' tf False + where + tf dt a = (cpXXAux sf1' sf2', c) + where + (sf1', b) = (sfTF' sf1) dt a + (sf2', c) = (sfTF' sf2) dt b +-} + +{- +cpXXAux sf1 sf2 | unsimplifiable sf1 sf2 = SF' tf False + | otherwise = cpXX sf1 sf2 + where + tf dt a = (cpXXAux sf1' sf2', c) + where + (sf1', b) = (sfTF' sf1) dt a + (sf2', c) = (sfTF' sf2) dt b + + unsimplifiable sf1@(SF' _ _) sf2@(SF' _ _) = True + unsimplifiable sf1 sf2 = True +-} + +{- +-- wrong ... +cpXXAux sf1@(SF' _ False) sf2 = SF' tf False +cpXXAux sf1@(SFCpAXA _ False _ _ _) sf2 = SF' tf False +cpXXAux sf1 sf2@(SF' _ False) = SF' tf False +cpXXAux sf1 sf2@(SFCpAXA _ False _ _ _) = SF' tf False +cpXXAux sf1 sf2 = + if sfIsInv sf1 && sfIsInv sf2 then cpXXInv sf1 sf2 else SF' tf False + where + tf dt a = (cpXXAux sf1' sf2', c) + where + (sf1', b) = (sfTF' sf1) dt a + (sf2', c) = (sfTF' sf2) dt b +-} + +{- +cpXXInv sf1 sf2 = SF' tf True + where + tf dt a = sf1 `seq` sf2 `seq` (cpXXInv sf1' sf2', c) + where + (sf1', b) = (sfTF' sf1) dt a + (sf2', c) = (sfTF' sf2) dt b +-} + +-- !!! No. We need local defs. Keep fd1 and fd2. Extract f1 and f2 +-- !!! once and fo all. Get rid of FDI and FDC at the top level. +-- !!! First local def. analyse sf2. SFArr, SFAcc etc. tf in +-- !!! recursive case just make use of f1 and f3. +-- !!! if sf2 is SFInv, that's delegated to a second local +-- !!! recursive def. that does not analyse sf2. + +cpAXA :: FunDesc a b -> SF' b c -> FunDesc c d -> SF' a d +-- Termination: cpAX/cpXA, via cpCX, cpEX etc. only call cpAXA if sf2 +-- is SFCpAXA, and then on the embedded sf and hence on a smaller arg. +cpAXA FDI sf2 fd3 = cpXA sf2 fd3 +cpAXA fd1 sf2 FDI = cpAX fd1 sf2 +cpAXA (FDC b) sf2 fd3 = cpCXA b sf2 fd3 +cpAXA _ _ (FDC d) = sfConst d +cpAXA fd1 sf2 fd3 = + cpAXAAux fd1 (fdFun fd1) fd3 (fdFun fd3) sf2 + where + -- Really: cpAXAAux :: SF' b c -> SF' a d + -- Note: Event cases are not optimized (EXA etc.) + cpAXAAux :: FunDesc a b -> (a -> b) -> FunDesc c d -> (c -> d) + -> SF' b c -> SF' a d + cpAXAAux fd1 _ fd3 _ (SFArr _ fd2) = + sfArr (fdComp (fdComp fd1 fd2) fd3) + cpAXAAux fd1 _ fd3 _ sf2@(SFSScan _ _ _ _) = + cpAX fd1 (cpXA sf2 fd3) + cpAXAAux fd1 _ fd3 _ sf2@(SFEP _ _ _ _) = + cpAX fd1 (cpXA sf2 fd3) + cpAXAAux fd1 _ fd3 _ (SFCpAXA _ fd21 sf22 fd23) = + cpAXA (fdComp fd1 fd21) sf22 (fdComp fd23 fd3) + cpAXAAux fd1 f1 fd3 f3 sf2 = SFCpAXA tf fd1 sf2 fd3 +{- + if sfIsInv sf2 then + cpAXAInv fd1 f1 fd3 f3 sf2 + else + SFCpAXA tf False fd1 sf2 fd3 +-} + where + tf dt a = (cpAXAAux fd1 f1 fd3 f3 sf2', f3 c) + where + (sf2', c) = (sfTF' sf2) dt (f1 a) + +{- + cpAXAInv fd1 f1 fd3 f3 sf2 = SFCpAXA tf True fd1 sf2 fd3 + where + tf dt a = sf2 `seq` (cpAXAInv fd1 f1 fd3 f3 sf2', f3 c) + where + (sf2', c) = (sfTF' sf2) dt (f1 a) +-} + +cpAX :: FunDesc a b -> SF' b c -> SF' a c +cpAX FDI sf2 = sf2 +cpAX (FDC b) sf2 = cpCX b sf2 +cpAX (FDE f1 f1ne) sf2 = cpEX f1 f1ne sf2 +cpAX (FDG f1) sf2 = cpGX f1 sf2 + +cpXA :: SF' a b -> FunDesc b c -> SF' a c +cpXA sf1 FDI = sf1 +cpXA _ (FDC c) = sfConst c +cpXA sf1 (FDE f2 f2ne) = cpXE sf1 f2 f2ne +cpXA sf1 (FDG f2) = cpXG sf1 f2 + +-- Don't forget that the remaining signal function, if it is +-- SF', later could turn into something else, like SFId. +cpCX :: b -> SF' b c -> SF' a c +cpCX b (SFArr _ fd2) = sfConst ((fdFun fd2) b) +-- 2005-07-01: If we were serious about the semantics of sscan being required +-- to be independent of the sampling interval, I guess one could argue for a +-- fixed-point computation here ... Or maybe not. +-- cpCX b (SFSScan _ _ _ _) = sfConst +cpCX b (SFSScan _ f s c) = sfSScan (\s _ -> f s b) s c +cpCX b (SFEP _ _ _ cne) = sfConst (vfyNoEv b cne) +cpCX b (SFCpAXA _ fd21 sf22 fd23) = + cpCXA ((fdFun fd21) b) sf22 fd23 +cpCX b sf2 = SFCpAXA tf (FDC b) sf2 FDI +{- + if sfIsInv sf2 then + cpCXInv b sf2 + else + SFCpAXA tf False (FDC b) sf2 FDI +-} + where + tf dt _ = (cpCX b sf2', c) + where + (sf2', c) = (sfTF' sf2) dt b + + +{- +cpCXInv b sf2 = SFCpAXA tf True (FDC b) sf2 FDI + where + tf dt _ = sf2 `seq` (cpCXInv b sf2', c) + where + (sf2', c) = (sfTF' sf2) dt b +-} + + +cpCXA :: b -> SF' b c -> FunDesc c d -> SF' a d +cpCXA b sf2 FDI = cpCX b sf2 +cpCXA _ _ (FDC c) = sfConst c +cpCXA b sf2 fd3 = cpCXAAux (FDC b) b fd3 (fdFun fd3) sf2 + where + -- fd1 = FDC b + -- f3 = fdFun fd3 + + -- Really: SF' b c -> SF' a d + cpCXAAux :: FunDesc a b -> b -> FunDesc c d -> (c -> d) + -> SF' b c -> SF' a d + cpCXAAux _ b _ f3 (SFArr _ fd2) = sfConst (f3 ((fdFun fd2) b)) + cpCXAAux _ b _ f3 (SFSScan _ f s c) = sfSScan f' s (f3 c) + where + f' s _ = case f s b of + Nothing -> Nothing + Just (s', c') -> Just (s', f3 c') + cpCXAAux _ b _ f3 (SFEP _ _ _ cne) = sfConst (f3 (vfyNoEv b cne)) + cpCXAAux _ b fd3 _ (SFCpAXA _ fd21 sf22 fd23) = + cpCXA ((fdFun fd21) b) sf22 (fdComp fd23 fd3) + cpCXAAux fd1 b fd3 f3 sf2 = SFCpAXA tf fd1 sf2 fd3 +{- + if sfIsInv sf2 then + cpCXAInv fd1 b fd3 f3 sf2 + else + SFCpAXA tf False fd1 sf2 fd3 +-} + where + tf dt _ = (cpCXAAux fd1 b fd3 f3 sf2', f3 c) + where + (sf2', c) = (sfTF' sf2) dt b + +{- + -- For some reason, seq on sf2' in tf is faster than making + -- cpCXAInv strict in sf2 by seq-ing on the top level (which would + -- be similar to pattern matching on sf2). + cpCXAInv fd1 b fd3 f3 sf2 = SFCpAXA tf True fd1 sf2 fd3 + where + tf dt _ = sf2 `seq` (cpCXAInv fd1 b fd3 f3 sf2', f3 c) + where + (sf2', c) = (sfTF' sf2) dt b +-} + + +cpGX :: (a -> b) -> SF' b c -> SF' a c +cpGX f1 sf2 = cpGXAux (FDG f1) f1 sf2 + where + cpGXAux :: FunDesc a b -> (a -> b) -> SF' b c -> SF' a c + cpGXAux fd1 _ (SFArr _ fd2) = sfArr (fdComp fd1 fd2) + -- We actually do know that (fdComp (FDG f1) fd21) is going to + -- result in an FDG. So we *could* call a cpGXA here. But the + -- price is "inlining" of part of fdComp. + cpGXAux _ f1 (SFSScan _ f s c) = sfSScan (\s a -> f s (f1 a)) s c + -- We really shouldn't see an EP here, as that would mean + -- an arrow INTRODUCING events ... + cpGXAux fd1 _ (SFCpAXA _ fd21 sf22 fd23) = + cpAXA (fdComp fd1 fd21) sf22 fd23 + cpGXAux fd1 f1 sf2 = SFCpAXA tf fd1 sf2 FDI +{- + if sfIsInv sf2 then + cpGXInv fd1 f1 sf2 + else + SFCpAXA tf False fd1 sf2 FDI +-} + where + tf dt a = (cpGXAux fd1 f1 sf2', c) + where + (sf2', c) = (sfTF' sf2) dt (f1 a) + +{- + cpGXInv fd1 f1 sf2 = SFCpAXA tf True fd1 sf2 FDI + where + tf dt a = sf2 `seq` (cpGXInv fd1 f1 sf2', c) + where + (sf2', c) = (sfTF' sf2) dt (f1 a) +-} + + +cpXG :: SF' a b -> (b -> c) -> SF' a c +cpXG sf1 f2 = cpXGAux (FDG f2) f2 sf1 + where + -- Really: cpXGAux :: SF' a b -> SF' a c + cpXGAux :: FunDesc b c -> (b -> c) -> SF' a b -> SF' a c + cpXGAux fd2 _ (SFArr _ fd1) = sfArr (fdComp fd1 fd2) + cpXGAux _ f2 (SFSScan _ f s b) = sfSScan f' s (f2 b) + where + f' s a = case f s a of + Nothing -> Nothing + Just (s', b') -> Just (s', f2 b') + cpXGAux _ f2 (SFEP _ f1 s bne) = sfEP f s (f2 bne) + where + f s a = let (s', b, bne') = f1 s a in (s', f2 b, f2 bne') + cpXGAux fd2 _ (SFCpAXA _ fd11 sf12 fd22) = + cpAXA fd11 sf12 (fdComp fd22 fd2) + cpXGAux fd2 f2 sf1 = SFCpAXA tf FDI sf1 fd2 +{- + if sfIsInv sf1 then + cpXGInv fd2 f2 sf1 + else + SFCpAXA tf False FDI sf1 fd2 +-} + where + tf dt a = (cpXGAux fd2 f2 sf1', f2 b) + where + (sf1', b) = (sfTF' sf1) dt a + +{- + cpXGInv fd2 f2 sf1 = SFCpAXA tf True FDI sf1 fd2 + where + tf dt a = (cpXGInv fd2 f2 sf1', f2 b) + where + (sf1', b) = (sfTF' sf1) dt a +-} + +cpEX :: (Event a -> b) -> b -> SF' b c -> SF' (Event a) c +cpEX f1 f1ne sf2 = cpEXAux (FDE f1 f1ne) f1 f1ne sf2 + where + cpEXAux :: FunDesc (Event a) b -> (Event a -> b) -> b + -> SF' b c -> SF' (Event a) c + cpEXAux fd1 _ _ (SFArr _ fd2) = sfArr (fdComp fd1 fd2) + cpEXAux _ f1 _ (SFSScan _ f s c) = sfSScan (\s a -> f s (f1 a)) s c + -- We must not capture cne in the f closure since cne can change! + -- See cpXX the SFEP/SFEP case for a similar situation. However, + -- FDE represent a state-less signal function, so *its* NoEvent + -- value never changes. Hence we only need to verify that it is + -- NoEvent once. + cpEXAux _ f1 f1ne (SFEP _ f2 s cne) = + sfEP f (s, cne) (vfyNoEv f1ne cne) + where + f scne@(s, cne) a = + case f1 (Event a) of + NoEvent -> (scne, cne, cne) + Event b -> + let (s', c, cne') = f2 s b in ((s', cne'), c, cne') + cpEXAux fd1 _ _ (SFCpAXA _ fd21 sf22 fd23) = + cpAXA (fdComp fd1 fd21) sf22 fd23 + -- The rationale for the following is that the case analysis + -- is typically not going to be more expensive than applying + -- the function and possibly a bit cheaper. Thus if events + -- are sparse, we might win, and if not, we don't loose to + -- much. + cpEXAux fd1 f1 f1ne sf2 = SFCpAXA tf fd1 sf2 FDI +{- + if sfIsInv sf2 then + cpEXInv fd1 f1 f1ne sf2 + else + SFCpAXA tf False fd1 sf2 FDI +-} + where + tf dt ea = (cpEXAux fd1 f1 f1ne sf2', c) + where + (sf2', c) = + case ea of + NoEvent -> (sfTF' sf2) dt f1ne + _ -> (sfTF' sf2) dt (f1 ea) + +{- + cpEXInv fd1 f1 f1ne sf2 = SFCpAXA tf True fd1 sf2 FDI + where + tf dt ea = sf2 `seq` (cpEXInv fd1 f1 f1ne sf2', c) + where + (sf2', c) = + case ea of + NoEvent -> (sfTF' sf2) dt f1ne + _ -> (sfTF' sf2) dt (f1 ea) +-} + +cpXE :: SF' a (Event b) -> (Event b -> c) -> c -> SF' a c +cpXE sf1 f2 f2ne = cpXEAux (FDE f2 f2ne) f2 f2ne sf1 + where + cpXEAux :: FunDesc (Event b) c -> (Event b -> c) -> c + -> SF' a (Event b) -> SF' a c + cpXEAux fd2 _ _ (SFArr _ fd1) = sfArr (fdComp fd1 fd2) + cpXEAux _ f2 f2ne (SFSScan _ f s eb) = sfSScan f' s (f2 eb) + where + f' s a = case f s a of + Nothing -> Nothing + Just (s', NoEvent) -> Just (s', f2ne) + Just (s', eb') -> Just (s', f2 eb') + cpXEAux _ f2 f2ne (SFEP _ f1 s ebne) = + sfEP f s (vfyNoEv ebne f2ne) + where + f s a = + case f1 s a of + (s', NoEvent, NoEvent) -> (s', f2ne, f2ne) + (s', eb, NoEvent) -> (s', f2 eb, f2ne) + _ -> usrErr "AFRP" "cpXEAux" "Assertion failed: Functions on events must not map NoEvent to Event." + cpXEAux fd2 _ _ (SFCpAXA _ fd11 sf12 fd13) = + cpAXA fd11 sf12 (fdComp fd13 fd2) + cpXEAux fd2 f2 f2ne sf1 = SFCpAXA tf FDI sf1 fd2 +{- + if sfIsInv sf1 then + cpXEInv fd2 f2 f2ne sf1 + else + SFCpAXA tf False FDI sf1 fd2 +-} + where + tf dt a = (cpXEAux fd2 f2 f2ne sf1', + case eb of NoEvent -> f2ne; _ -> f2 eb) + where + (sf1', eb) = (sfTF' sf1) dt a + +{- + cpXEInv fd2 f2 f2ne sf1 = SFCpAXA tf True FDI sf1 fd2 + where + tf dt a = sf1 `seq` (cpXEInv fd2 f2 f2ne sf1', + case eb of NoEvent -> f2ne; _ -> f2 eb) + where + (sf1', eb) = (sfTF' sf1) dt a +-} + + +-- Widening. +-- The definition exploits the following identities: +-- first identity = identity -- New +-- first (constant b) = arr (\(_, c) -> (b, c)) +-- (first (arr f)) = arr (\(a, c) -> (f a, c)) +firstPrim :: SF a b -> SF (a,c) (b,c) +firstPrim (SF {sfTF = tf10}) = SF {sfTF = tf0} + where + tf0 ~(a0, c0) = (fpAux sf1, (b0, c0)) + where + (sf1, b0) = tf10 a0 + + +-- Also used in parSplitPrim +fpAux :: SF' a b -> SF' (a,c) (b,c) +fpAux (SFArr _ FDI) = sfId -- New +fpAux (SFArr _ (FDC b)) = sfArrG (\(~(_, c)) -> (b, c)) +fpAux (SFArr _ fd1) = sfArrG (\(~(a, c)) -> ((fdFun fd1) a, c)) +fpAux sf1 = SF' tf + -- if sfIsInv sf1 then fpInv sf1 else SF' tf False + where + tf dt ~(a, c) = (fpAux sf1', (b, c)) + where + (sf1', b) = (sfTF' sf1) dt a + + +{- +fpInv :: SF' a b -> SF' (a,c) (b,c) +fpInv sf1 = SF' tf True + where + tf dt ~(a, c) = sf1 `seq` (fpInv sf1', (b, c)) + where + (sf1', b) = (sfTF' sf1) dt a +-} + + +-- Mirror image of first. +secondPrim :: SF a b -> SF (c,a) (c,b) +secondPrim (SF {sfTF = tf10}) = SF {sfTF = tf0} + where + tf0 ~(c0, a0) = (spAux sf1, (c0, b0)) + where + (sf1, b0) = tf10 a0 + + +-- Also used in parSplitPrim +spAux :: SF' a b -> SF' (c,a) (c,b) +spAux (SFArr _ FDI) = sfId -- New +spAux (SFArr _ (FDC b)) = sfArrG (\(~(c, _)) -> (c, b)) +spAux (SFArr _ fd1) = sfArrG (\(~(c, a)) -> (c, (fdFun fd1) a)) +spAux sf1 = SF' tf + -- if sfIsInv sf1 then spInv sf1 else SF' tf False + where + tf dt ~(c, a) = (spAux sf1', (c, b)) + where + (sf1', b) = (sfTF' sf1) dt a + + +{- +spInv :: SF' a b -> SF' (c,a) (c,b) +spInv sf1 = SF' tf True + where + tf dt ~(c, a) = sf1 `seq` (spInv sf1', (c, b)) + where + (sf1', b) = (sfTF' sf1) dt a +-} + + +-- Parallel composition. +-- The definition exploits the following identities (that hold for SF): +-- identity *** identity = identity -- New +-- sf *** identity = first sf -- New +-- identity *** sf = second sf -- New +-- constant b *** constant d = constant (b, d) +-- constant b *** arr f2 = arr (\(_, c) -> (b, f2 c) +-- arr f1 *** constant d = arr (\(a, _) -> (f1 a, d) +-- arr f1 *** arr f2 = arr (\(a, b) -> (f1 a, f2 b) +parSplitPrim :: SF a b -> SF c d -> SF (a,c) (b,d) +parSplitPrim (SF {sfTF = tf10}) (SF {sfTF = tf20}) = SF {sfTF = tf0} + where + tf0 ~(a0, c0) = (psXX sf1 sf2, (b0, d0)) + where + (sf1, b0) = tf10 a0 + (sf2, d0) = tf20 c0 + + -- Naming convention: ps where and is one of: + -- X - arbitrary signal function + -- A - arbitrary pure arrow + -- C - constant arrow + + psXX :: SF' a b -> SF' c d -> SF' (a,c) (b,d) + psXX (SFArr _ fd1) (SFArr _ fd2) = sfArr (fdPar fd1 fd2) + psXX (SFArr _ FDI) sf2 = spAux sf2 -- New + psXX (SFArr _ (FDC b)) sf2 = psCX b sf2 + psXX (SFArr _ fd1) sf2 = psAX (fdFun fd1) sf2 + psXX sf1 (SFArr _ FDI) = fpAux sf1 -- New + psXX sf1 (SFArr _ (FDC d)) = psXC sf1 d + psXX sf1 (SFArr _ fd2) = psXA sf1 (fdFun fd2) +-- !!! Unclear if this really is a gain. +-- !!! potentially unnecessary tupling and untupling. +-- !!! To be investigated. +-- !!! 2005-07-01: At least for MEP 6, the corresponding opt for +-- !!! &&& was harmfull. On that basis, disable it here too. +-- psXX (SFCpAXA _ fd11 sf12 fd13) (SFCpAXA _ fd21 sf22 fd23) = +-- cpAXA (fdPar fd11 fd21) (psXX sf12 sf22) (fdPar fd13 fd23) + psXX sf1 sf2 = SF' tf +{- + if sfIsInv sf1 && sfIsInv sf2 then + psXXInv sf1 sf2 + else + SF' tf False +-} + where + tf dt ~(a, c) = (psXX sf1' sf2', (b, d)) + where + (sf1', b) = (sfTF' sf1) dt a + (sf2', d) = (sfTF' sf2) dt c + +{- + psXXInv :: SF' a b -> SF' c d -> SF' (a,c) (b,d) + psXXInv sf1 sf2 = SF' tf True + where + tf dt ~(a, c) = sf1 `seq` sf2 `seq` (psXXInv sf1' sf2', + (b, d)) + where + (sf1', b) = (sfTF' sf1) dt a + (sf2', d) = (sfTF' sf2) dt c +-} + + psCX :: b -> SF' c d -> SF' (a,c) (b,d) + psCX b (SFArr _ fd2) = sfArr (fdPar (FDC b) fd2) + psCX b sf2 = SF' tf +{- + if sfIsInv sf2 then + psCXInv b sf2 + else + SF' tf False +-} + where + tf dt ~(_, c) = (psCX b sf2', (b, d)) + where + (sf2', d) = (sfTF' sf2) dt c + +{- + psCXInv :: b -> SF' c d -> SF' (a,c) (b,d) + psCXInv b sf2 = SF' tf True + where + tf dt ~(_, c) = sf2 `seq` (psCXInv b sf2', (b, d)) + where + (sf2', d) = (sfTF' sf2) dt c +-} + + psXC :: SF' a b -> d -> SF' (a,c) (b,d) + psXC (SFArr _ fd1) d = sfArr (fdPar fd1 (FDC d)) + psXC sf1 d = SF' tf +{- + if sfIsInv sf1 then + psXCInv sf1 d + else + SF' tf False +-} + where + tf dt ~(a, _) = (psXC sf1' d, (b, d)) + where + (sf1', b) = (sfTF' sf1) dt a + +{- + psXCInv :: SF' a b -> d -> SF' (a,c) (b,d) + psXCInv sf1 d = SF' tf True + where + tf dt ~(a, _) = sf1 `seq` (psXCInv sf1' d, (b, d)) + where + (sf1', b) = (sfTF' sf1) dt a +-} + + psAX :: (a -> b) -> SF' c d -> SF' (a,c) (b,d) + psAX f1 (SFArr _ fd2) = sfArr (fdPar (FDG f1) fd2) + psAX f1 sf2 = SF' tf +{- + if sfIsInv sf2 then + psAXInv f1 sf2 + else + SF' tf False +-} + where + tf dt ~(a, c) = (psAX f1 sf2', (f1 a, d)) + where + (sf2', d) = (sfTF' sf2) dt c + +{- + psAXInv :: (a -> b) -> SF' c d -> SF' (a,c) (b,d) + psAXInv f1 sf2 = SF' tf True + where + tf dt ~(a, c) = sf2 `seq` (psAXInv f1 sf2', (f1 a, d)) + where + (sf2', d) = (sfTF' sf2) dt c +-} + + psXA :: SF' a b -> (c -> d) -> SF' (a,c) (b,d) + psXA (SFArr _ fd1) f2 = sfArr (fdPar fd1 (FDG f2)) + psXA sf1 f2 = SF' tf +{- + if sfIsInv sf1 then + psXAInv sf1 f2 + else + SF' tf False +-} + where + tf dt ~(a, c) = (psXA sf1' f2, (b, f2 c)) + where + (sf1', b) = (sfTF' sf1) dt a + +{- + psXAInv :: SF' a b -> (c -> d) -> SF' (a,c) (b,d) + psXAInv sf1 f2 = SF' tf True + where + tf dt ~(a, c) = sf1 `seq` (psXAInv sf1' f2, (b, f2 c)) + where + (sf1', b) = (sfTF' sf1) dt a +-} + + +-- !!! Hmmm. Why don't we optimize the FDE cases here??? +-- !!! Seems pretty obvious that we should! +-- !!! It should also be possible to optimize an event processor in +-- !!! parallel with another event processor or an Arr FDE. + +parFanOutPrim :: SF a b -> SF a c -> SF a (b, c) +parFanOutPrim (SF {sfTF = tf10}) (SF {sfTF = tf20}) = SF {sfTF = tf0} + where + tf0 a0 = (pfoXX sf1 sf2, (b0, c0)) + where + (sf1, b0) = tf10 a0 + (sf2, c0) = tf20 a0 + + -- Naming convention: pfo where and is one of: + -- X - arbitrary signal function + -- A - arbitrary pure arrow + -- I - identity arrow + -- C - constant arrow + + pfoXX :: SF' a b -> SF' a c -> SF' a (b ,c) + pfoXX (SFArr _ fd1) (SFArr _ fd2) = sfArr(fdFanOut fd1 fd2) + pfoXX (SFArr _ FDI) sf2 = pfoIX sf2 + pfoXX (SFArr _ (FDC b)) sf2 = pfoCX b sf2 + pfoXX (SFArr _ fd1) sf2 = pfoAX (fdFun fd1) sf2 + pfoXX sf1 (SFArr _ FDI) = pfoXI sf1 + pfoXX sf1 (SFArr _ (FDC c)) = pfoXC sf1 c + pfoXX sf1 (SFArr _ fd2) = pfoXA sf1 (fdFun fd2) +-- !!! Unclear if this really would be a gain +-- !!! 2005-07-01: NOT a win for MEP 6. +-- pfoXX (SFCpAXA _ fd11 sf12 fd13) (SFCpAXA _ fd21 sf22 fd23) = +-- cpAXA (fdPar fd11 fd21) (psXX sf12 sf22) (fdPar fd13 fd23) + pfoXX sf1 sf2 = SF' tf +{- + if sfIsInv sf1 && sfIsInv sf2 then + pfoXXInv sf1 sf2 + else + SF' tf False +-} + where + tf dt a = (pfoXX sf1' sf2', (b, c)) + where + (sf1', b) = (sfTF' sf1) dt a + (sf2', c) = (sfTF' sf2) dt a + +{- + pfoXXInv :: SF' a b -> SF' a c -> SF' a (b ,c) + pfoXXInv sf1 sf2 = SF' tf True + where + tf dt a = sf1 `seq` sf2 `seq` (pfoXXInv sf1' sf2', (b, c)) + where + (sf1', b) = (sfTF' sf1) dt a + (sf2', c) = (sfTF' sf2) dt a +-} + + pfoIX :: SF' a c -> SF' a (a ,c) + pfoIX (SFArr _ fd2) = sfArr (fdFanOut FDI fd2) + pfoIX sf2 = SF' tf +{- + if sfIsInv sf2 then + pfoIXInv sf2 + else + SF' tf False +-} + where + tf dt a = (pfoIX sf2', (a, c)) + where + (sf2', c) = (sfTF' sf2) dt a + +{- + pfoIXInv :: SF' a c -> SF' a (a ,c) + pfoIXInv sf2 = SF' tf True + where + tf dt a = sf2 `seq` (pfoIXInv sf2', (a, c)) + where + (sf2', c) = (sfTF' sf2) dt a +-} + + pfoXI :: SF' a b -> SF' a (b ,a) + pfoXI (SFArr _ fd1) = sfArr (fdFanOut fd1 FDI) + pfoXI sf1 = SF' tf +{- + if sfIsInv sf1 then + pfoXIInv sf1 + else + SF' tf False +-} + where + tf dt a = (pfoXI sf1', (b, a)) + where + (sf1', b) = (sfTF' sf1) dt a + +{- + pfoXIInv :: SF' a b -> SF' a (b ,a) + pfoXIInv sf1 = SF' tf True + where + tf dt a = sf1 `seq` (pfoXIInv sf1', (b, a)) + where + (sf1', b) = (sfTF' sf1) dt a +-} + + pfoCX :: b -> SF' a c -> SF' a (b ,c) + pfoCX b (SFArr _ fd2) = sfArr (fdFanOut (FDC b) fd2) + pfoCX b sf2 = SF' tf +{- + if sfIsInv sf2 then + pfoCXInv b sf2 + else + SF' tf False +-} + where + tf dt a = (pfoCX b sf2', (b, c)) + where + (sf2', c) = (sfTF' sf2) dt a + +{- + pfoCXInv :: b -> SF' a c -> SF' a (b ,c) + pfoCXInv b sf2 = SF' tf True + where + tf dt a = sf2 `seq` (pfoCXInv b sf2', (b, c)) + where + (sf2', c) = (sfTF' sf2) dt a +-} + + pfoXC :: SF' a b -> c -> SF' a (b ,c) + pfoXC (SFArr _ fd1) c = sfArr (fdFanOut fd1 (FDC c)) + pfoXC sf1 c = SF' tf +{- + if sfIsInv sf1 then + pfoXCInv sf1 c + else + SF' tf False +-} + where + tf dt a = (pfoXC sf1' c, (b, c)) + where + (sf1', b) = (sfTF' sf1) dt a + +{- + pfoXCInv :: SF' a b -> c -> SF' a (b ,c) + pfoXCInv sf1 c = SF' tf True + where + tf dt a = sf1 `seq` (pfoXCInv sf1' c, (b, c)) + where + (sf1', b) = (sfTF' sf1) dt a +-} + + pfoAX :: (a -> b) -> SF' a c -> SF' a (b ,c) + pfoAX f1 (SFArr _ fd2) = sfArr (fdFanOut (FDG f1) fd2) + pfoAX f1 sf2 = SF' tf +{- + if sfIsInv sf2 then + pfoAXInv f1 sf2 + else + SF' tf False +-} + where + tf dt a = (pfoAX f1 sf2', (f1 a, c)) + where + (sf2', c) = (sfTF' sf2) dt a + +{- + pfoAXInv :: (a -> b) -> SF' a c -> SF' a (b ,c) + pfoAXInv f1 sf2 = SF' tf True + where + tf dt a = sf2 `seq` (pfoAXInv f1 sf2', (f1 a, c)) + where + (sf2', c) = (sfTF' sf2) dt a +-} + + pfoXA :: SF' a b -> (a -> c) -> SF' a (b ,c) + pfoXA (SFArr _ fd1) f2 = sfArr (fdFanOut fd1 (FDG f2)) + pfoXA sf1 f2 = SF' tf +{- + if sfIsInv sf1 then + pfoXAInv sf1 f2 + else + SF' tf False +-} + where + tf dt a = (pfoXA sf1' f2, (b, f2 a)) + where + (sf1', b) = (sfTF' sf1) dt a + +{- + pfoXAInv :: SF' a b -> (a -> c) -> SF' a (b ,c) + pfoXAInv sf1 f2 = SF' tf True + where + tf dt a = sf1 `seq` (pfoXAInv sf1' f2, (b, f2 a)) + where + (sf1', b) = (sfTF' sf1) dt a +-} + + +------------------------------------------------------------------------------ +-- ArrowLoop instance and implementation +------------------------------------------------------------------------------ + +instance ArrowLoop SF where + loop = loopPrim + + +loopPrim :: SF (a,c) (b,c) -> SF a b +loopPrim (SF {sfTF = tf10}) = SF {sfTF = tf0} + where + tf0 a0 = (loopAux sf1, b0) + where + (sf1, (b0, c0)) = tf10 (a0, c0) + + loopAux :: SF' (a,c) (b,c) -> SF' a b + loopAux (SFArr _ FDI) = sfId + loopAux (SFArr _ (FDC (b, _))) = sfConst b + loopAux (SFArr _ fd1) = + sfArrG (\a -> let (b,c) = (fdFun fd1) (a,c) in b) + loopAux sf1 = SF' tf +{- + if sfIsInv sf1 then + loopInv sf1 + else + SF' tf False +-} + where + tf dt a = (loopAux sf1', b) + where + (sf1', (b, c)) = (sfTF' sf1) dt (a, c) + +{- + loopInv :: SF' (a,c) (b,c) -> SF' a b + loopInv sf1 = SF' tf True + where + tf dt a = sf1 `seq` (loopInv sf1', b) + where + (sf1', (b, c)) = (sfTF' sf1) dt (a, c) +-} + + +------------------------------------------------------------------------------ +-- Basic signal functions +------------------------------------------------------------------------------ + +-- | Identity: identity = arr id +-- +-- Using 'identity' is preferred over lifting id, since the arrow combinators +-- know how to optimise certain networks based on the transformations being +-- applied. +identity :: SF a a +identity = SF {sfTF = \a -> (sfId, a)} + +-- | Identity: constant b = arr (const b) +-- +-- Using 'constant' is preferred over lifting const, since the arrow combinators +-- know how to optimise certain networks based on the transformations being +-- applied. +constant :: b -> SF a b +constant b = SF {sfTF = \_ -> (sfConst b, b)} + +-- | Outputs the time passed since the signal function instance was started. +localTime :: SF a Time +localTime = constant 1.0 >>> integral + +-- | Alternative name for localTime. +time :: SF a Time +time = localTime + +------------------------------------------------------------------------------ +-- Initialization +------------------------------------------------------------------------------ + +-- | Initialization operator (cf. Lustre/Lucid Synchrone). +-- +-- The output at time zero is the first argument, and from +-- that point on it behaves like the signal function passed as +-- second argument. +(-->) :: b -> SF a b -> SF a b +b0 --> (SF {sfTF = tf10}) = SF {sfTF = \a0 -> (fst (tf10 a0), b0)} + +-- | Input initialization operator. +-- +-- The input at time zero is the first argument, and from +-- that point on it behaves like the signal function passed as +-- second argument. +(>--) :: a -> SF a b -> SF a b +a0 >-- (SF {sfTF = tf10}) = SF {sfTF = \_ -> tf10 a0} + + +-- | Transform initial output value. +-- +-- Applies a transformation 'f' only to the first output value at +-- time zero. +(-=>) :: (b -> b) -> SF a b -> SF a b +f -=> (SF {sfTF = tf10}) = + SF {sfTF = \a0 -> let (sf1, b0) = tf10 a0 in (sf1, f b0)} + + +-- | Transform initial input value. +-- +-- Applies a transformation 'f' only to the first input value at +-- time zero. +(>=-) :: (a -> a) -> SF a b -> SF a b +f >=- (SF {sfTF = tf10}) = SF {sfTF = \a0 -> tf10 (f a0)} + +-- | Override initial value of input signal. +initially :: a -> SF a a +initially = (--> identity) + + +------------------------------------------------------------------------------ +-- Simple, stateful signal processing +------------------------------------------------------------------------------ + +-- New sscan primitive. It should be possible to define lots of functions +-- in terms of this one. Eventually a new constructor will be introduced if +-- this works out. + +sscan :: (b -> a -> b) -> b -> SF a b +sscan f b_init = sscanPrim f' b_init b_init + where + f' b a = let b' = f b a in Just (b', b') + + +{- +sscanPrim :: (c -> a -> Maybe (c, b)) -> c -> b -> SF a b +sscanPrim f c_init b_init = SF {sfTF = tf0} + where + tf0 a0 = case f c_init a0 of + Nothing -> (spAux f c_init b_init, b_init) + Just (c', b') -> (spAux f c' b', b') + + spAux :: (c -> a -> Maybe (c, b)) -> c -> b -> SF' a b + spAux f c b = sf + where + -- sf = SF' tf True + sf = SF' tf + tf _ a = case f c a of + Nothing -> (sf, b) + Just (c', b') -> (spAux f c' b', b') +-} + + +------------------------------------------------------------------------------ +-- Basic event sources +------------------------------------------------------------------------------ + +-- | Event source that never occurs. +never :: SF a (Event b) +never = SF {sfTF = \_ -> (sfNever, NoEvent)} + + +-- | Event source with a single occurrence at time 0. The value of the event +-- is given by the function argument. +now :: b -> SF a (Event b) +now b0 = (Event b0 --> never) + + +-- | Event source with a single occurrence at or as soon after (local) time /q/ +-- as possible. +after :: Time -- ^ The time /q/ after which the event should be produced + -> b -- ^ Value to produce at that time + -> SF a (Event b) +after q x = afterEach [(q,x)] + +-- | Event source with repeated occurrences with interval q. +-- Note: If the interval is too short w.r.t. the sampling intervals, +-- the result will be that events occur at every sample. However, no more +-- than one event results from any sampling interval, thus avoiding an +-- "event backlog" should sampling become more frequent at some later +-- point in time. + +-- !!! 2005-03-30: This is potentially a bit inefficient since we KNOW +-- !!! (at this level) that the SF is going to be invarying. But afterEach +-- !!! does NOT know this as the argument list may well be finite. +-- !!! We could use sfMkInv, but that's not without problems. +-- !!! We're probably better off specializing afterEachCat here. + +repeatedly :: Time -> b -> SF a (Event b) +repeatedly q x | q > 0 = afterEach qxs + | otherwise = usrErr "AFRP" "repeatedly" "Non-positive period." + where + qxs = (q,x):qxs + + +-- Event source with consecutive occurrences at the given intervals. +-- Should more than one event be scheduled to occur in any sampling interval, +-- only the first will in fact occur to avoid an event backlog. +-- Question: Should positive periods except for the first one be required? +-- Note that periods of length 0 will always be skipped except for the first. +-- Right now, periods of length 0 is allowed on the grounds that no attempt +-- is made to forbid simultaneous events elsewhere. +{- +afterEach :: [(Time,b)] -> SF a (Event b) +afterEach [] = never +afterEach ((q,x):qxs) + | q < 0 = usrErr "AFRP" "afterEach" "Negative period." + | otherwise = SF {sfTF = tf0} + where + tf0 _ = if q <= 0 then + (scheduleNextEvent 0.0 qxs, Event x) + else + (awaitNextEvent (-q) x qxs, NoEvent) + + scheduleNextEvent t [] = sfNever + scheduleNextEvent t ((q,x):qxs) + | q < 0 = usrErr "AFRP" "afterEach" "Negative period." + | t' >= 0 = scheduleNextEvent t' qxs + | otherwise = awaitNextEvent t' x qxs + where + t' = t - q + awaitNextEvent t x qxs = SF' {sfTF' = tf} + where + tf dt _ | t' >= 0 = (scheduleNextEvent t' qxs, Event x) + | otherwise = (awaitNextEvent t' x qxs, NoEvent) + where + t' = t + dt +-} + +-- | Event source with consecutive occurrences at the given intervals. +-- Should more than one event be scheduled to occur in any sampling interval, +-- only the first will in fact occur to avoid an event backlog. + +-- After all, after, repeatedly etc. are defined in terms of afterEach. +afterEach :: [(Time,b)] -> SF a (Event b) +afterEach qxs = afterEachCat qxs >>> arr (fmap head) + +-- | Event source with consecutive occurrences at the given intervals. +-- Should more than one event be scheduled to occur in any sampling interval, +-- the output list will contain all events produced during that interval. + +-- Guaranteed not to miss any events. +afterEachCat :: [(Time,b)] -> SF a (Event [b]) +afterEachCat [] = never +afterEachCat ((q,x):qxs) + | q < 0 = usrErr "AFRP" "afterEachCat" "Negative period." + | otherwise = SF {sfTF = tf0} + where + tf0 _ = if q <= 0 then + emitEventsScheduleNext 0.0 [x] qxs + else + (awaitNextEvent (-q) x qxs, NoEvent) + + emitEventsScheduleNext _ xs [] = (sfNever, Event (reverse xs)) + emitEventsScheduleNext t xs ((q,x):qxs) + | q < 0 = usrErr "AFRP" "afterEachCat" "Negative period." + | t' >= 0 = emitEventsScheduleNext t' (x:xs) qxs + | otherwise = (awaitNextEvent t' x qxs, Event (reverse xs)) + where + t' = t - q + awaitNextEvent t x qxs = SF' tf -- False + where + tf dt _ | t' >= 0 = emitEventsScheduleNext t' [x] qxs + | otherwise = (awaitNextEvent t' x qxs, NoEvent) + where + t' = t + dt + +-- | Delay for events. (Consider it a triggered after, hence /basic/.) + +-- Can be implemented fairly cheaply as long as the events are sparse. +-- It is a question of rescheduling events for later. Not unlike "afterEach". +-- +-- It is not exactly the case that delayEvent t = delay t NoEvent +-- since the rules for dropping/extrapolating samples are different. +-- A single event occurrence will never be duplicated. +-- If there is an event occurrence, one will be output as soon as +-- possible after the given delay time, but not necessarily that +-- one. See delayEventCat. + +delayEvent :: Time -> SF (Event a) (Event a) +delayEvent q | q < 0 = usrErr "AFRP" "delayEvent" "Negative delay." + | q == 0 = identity + | otherwise = delayEventCat q >>> arr (fmap head) + + +-- There is no *guarantee* above that every event actually will be +-- rescheduled since the sampling frequency (temporarily) might drop. +-- The following interface would allow ALL scheduled events to occur +-- as soon as possible: +-- (Read "delay event and catenate events that occur so closely so as to be +-- inseparable".) +-- The events in the list are ordered temporally to the extent possible. + +{- +-- This version is too strict! +delayEventCat :: Time -> SF (Event a) (Event [a]) +delayEventCat q | q < 0 = usrErr "AFRP" "delayEventCat" "Negative delay." + | q == 0 = arr (fmap (:[])) + | otherwise = SF {sfTF = tf0} + where + tf0 NoEvent = (noPendingEvent, NoEvent) + tf0 (Event x) = (pendingEvents (-q) [] [] (-q) x, NoEvent) + + noPendingEvent = SF' tf -- True + where + tf _ NoEvent = (noPendingEvent, NoEvent) + tf _ (Event x) = (pendingEvents (-q) [] [] (-q) x, NoEvent) + + -- t_next is the present time w.r.t. the next scheduled event. + -- t_last is the present time w.r.t. the last scheduled event. + -- In the event queues, events are associated with their time + -- w.r.t. to preceding event (positive). + pendingEvents t_last rqxs qxs t_next x = SF' tf -- True + where + tf dt NoEvent = tf1 (t_last + dt) rqxs (t_next + dt) + tf dt (Event x') = tf1 (-q) ((q', x') : rqxs) t_next' + where + t_next' = t_next + dt + t_last' = t_last + dt + q' = t_last' + q + + tf1 t_last' rqxs' t_next' + | t_next' >= 0 = + emitEventsScheduleNext t_last' rqxs' qxs t_next' [x] + | otherwise = + (pendingEvents t_last' rqxs' qxs t_next' x, NoEvent) + + -- t_next is the present time w.r.t. the *scheduled* time of the + -- event that is about to be emitted (i.e. >= 0). + -- The time associated with any event at the head of the event + -- queue is also given w.r.t. the event that is about to be emitted. + -- Thus, t_next - q' is the present time w.r.t. the event at the head + -- of the event queue. + emitEventsScheduleNext t_last [] [] t_next rxs = + (noPendingEvent, Event (reverse rxs)) + emitEventsScheduleNext t_last rqxs [] t_next rxs = + emitEventsScheduleNext t_last [] (reverse rqxs) t_next rxs + emitEventsScheduleNext t_last rqxs ((q', x') : qxs') t_next rxs + | q' > t_next = (pendingEvents t_last rqxs qxs' (t_next - q') x', + Event (reverse rxs)) + | otherwise = emitEventsScheduleNext t_last rqxs qxs' (t_next-q') + (x' : rxs) +-} + +-- | Delay an event by a given delta and catenate events that occur so closely +-- so as to be /inseparable/. +delayEventCat :: Time -> SF (Event a) (Event [a]) +delayEventCat q | q < 0 = usrErr "AFRP" "delayEventCat" "Negative delay." + | q == 0 = arr (fmap (:[])) + | otherwise = SF {sfTF = tf0} + where + tf0 e = (case e of + NoEvent -> noPendingEvent + Event x -> pendingEvents (-q) [] [] (-q) x, + NoEvent) + + noPendingEvent = SF' tf -- True + where + tf _ e = (case e of + NoEvent -> noPendingEvent + Event x -> pendingEvents (-q) [] [] (-q) x, + NoEvent) + + -- t_next is the present time w.r.t. the next scheduled event. + -- t_last is the present time w.r.t. the last scheduled event. + -- In the event queues, events are associated with their time + -- w.r.t. to preceding event (positive). + pendingEvents t_last rqxs qxs t_next x = SF' tf -- True + where + tf dt e + | t_next' >= 0 = + emitEventsScheduleNext e t_last' rqxs qxs t_next' [x] + | otherwise = + (pendingEvents t_last'' rqxs' qxs t_next' x, NoEvent) + where + t_next' = t_next + dt + t_last' = t_last + dt + (t_last'', rqxs') = + case e of + NoEvent -> (t_last', rqxs) + Event x' -> (-q, (t_last'+q,x') : rqxs) + + -- t_next is the present time w.r.t. the *scheduled* time of the + -- event that is about to be emitted (i.e. >= 0). + -- The time associated with any event at the head of the event + -- queue is also given w.r.t. the event that is about to be emitted. + -- Thus, t_next - q' is the present time w.r.t. the event at the head + -- of the event queue. + emitEventsScheduleNext e _ [] [] _ rxs = + (case e of + NoEvent -> noPendingEvent + Event x -> pendingEvents (-q) [] [] (-q) x, + Event (reverse rxs)) + emitEventsScheduleNext e t_last rqxs [] t_next rxs = + emitEventsScheduleNext e t_last [] (reverse rqxs) t_next rxs + emitEventsScheduleNext e t_last rqxs ((q', x') : qxs') t_next rxs + | q' > t_next = (case e of + NoEvent -> + pendingEvents t_last + rqxs + qxs' + (t_next - q') + x' + Event x'' -> + pendingEvents (-q) + ((t_last+q, x'') : rqxs) + qxs' + (t_next - q') + x', + Event (reverse rxs)) + | otherwise = emitEventsScheduleNext e + t_last + rqxs + qxs' + (t_next - q') + (x' : rxs) + + +-- | A rising edge detector. Useful for things like detecting key presses. +-- It is initialised as /up/, meaning that events occuring at time 0 will +-- not be detected. + +-- Note that we initialize the loop with state set to True so that there +-- will not be an occurence at t0 in the logical time frame in which +-- this is started. +edge :: SF Bool (Event ()) +edge = iEdge True + +-- | A rising edge detector that can be initialized as up ('True', meaning +-- that events occurring at time 0 will not be detected) or down +-- ('False', meaning that events ocurring at time 0 will be detected). +iEdge :: Bool -> SF Bool (Event ()) +-- iEdge i = edgeBy (isBoolRaisingEdge ()) i +iEdge b = sscanPrim f (if b then 2 else 0) NoEvent + where + f :: Int -> Bool -> Maybe (Int, Event ()) + f 0 False = Nothing + f 0 True = Just (1, Event ()) + f 1 False = Just (0, NoEvent) + f 1 True = Just (2, NoEvent) + f 2 False = Just (0, NoEvent) + f 2 True = Nothing + f _ _ = undefined + +-- | Like 'edge', but parameterized on the tag value. +edgeTag :: a -> SF Bool (Event a) +-- edgeTag a = edgeBy (isBoolRaisingEdge a) True +edgeTag a = edge >>> arr (`tag` a) + + +-- Internal utility. +-- isBoolRaisingEdge :: a -> Bool -> Bool -> Maybe a +-- isBoolRaisingEdge _ False False = Nothing +-- isBoolRaisingEdge a False True = Just a +-- isBoolRaisingEdge _ True True = Nothing +-- isBoolRaisingEdge _ True False = Nothing + + +-- | Edge detector particularized for detecting transtitions +-- on a 'Maybe' signal from 'Nothing' to 'Just'. + +-- !!! 2005-07-09: To be done or eliminated +-- !!! Maybe could be kept as is, but could be easy to implement directly +-- !!! in terms of sscan? +edgeJust :: SF (Maybe a) (Event a) +edgeJust = edgeBy isJustEdge (Just undefined) + where + isJustEdge Nothing Nothing = Nothing + isJustEdge Nothing ma@(Just _) = ma + isJustEdge (Just _) (Just _) = Nothing + isJustEdge (Just _) Nothing = Nothing + + +-- | Edge detector parameterized on the edge detection function and initial +-- state, i.e., the previous input sample. The first argument to the +-- edge detection function is the previous sample, the second the current one. + +-- !!! Is this broken!?! Does not disallow an edge condition that persists +-- !!! between consecutive samples. See discussion in ToDo list above. +-- !!! 2005-07-09: To be done. +edgeBy :: (a -> a -> Maybe b) -> a -> SF a (Event b) +edgeBy isEdge a_init = SF {sfTF = tf0} + where + tf0 a0 = (ebAux a0, maybeToEvent (isEdge a_init a0)) + + ebAux a_prev = SF' tf -- True + where + tf _ a = (ebAux a, maybeToEvent (isEdge a_prev a)) + + +------------------------------------------------------------------------------ +-- Stateful event suppression +------------------------------------------------------------------------------ + +-- | Suppression of initial (at local time 0) event. +notYet :: SF (Event a) (Event a) +notYet = initially NoEvent + + +-- | Suppress all but the first event. +once :: SF (Event a) (Event a) +once = takeEvents 1 + + +-- | Suppress all but the first n events. +takeEvents :: Int -> SF (Event a) (Event a) +takeEvents n | n <= 0 = never +takeEvents n = dSwitch (arr dup) (const (NoEvent >-- takeEvents (n - 1))) + + +{- +-- More complicated using "switch" that "dSwitch". +takeEvents :: Int -> SF (Event a) (Event a) +takeEvents 0 = never +takeEvents (n + 1) = switch (never &&& identity) (takeEvents' n) + where + takeEvents' 0 a = now a + takeEvents' (n + 1) a = switch (now a &&& notYet) (takeEvents' n) +-} + + +-- | Suppress first n events. + +-- Here dSwitch or switch does not really matter. +dropEvents :: Int -> SF (Event a) (Event a) +dropEvents n | n <= 0 = identity +dropEvents n = dSwitch (never &&& identity) + (const (NoEvent >-- dropEvents (n - 1))) + + +------------------------------------------------------------------------------ +-- Basic switchers +------------------------------------------------------------------------------ + +-- !!! Interesting case. It seems we need scoped type variables +-- !!! to be able to write down the local type signatures. +-- !!! On the other hand, the scoped type variables seem to +-- !!! prohibit the kind of unification that is needed for GADTs??? +-- !!! Maybe this could be made to wok if it actually WAS known +-- !!! that scoped type variables indeed corresponds to universally +-- !!! quantified variables? Or if one were to keep track of those +-- !!! scoped type variables that actually do? +-- !!! +-- !!! Find a simpler case to experiment further. For now, elim. +-- !!! the free variable. + +{- +-- Basic switch. +switch :: SF a (b, Event c) -> (c -> SF a b) -> SF a b +switch (SF {sfTF = tf10} :: SF a (b, Event c)) (k :: c -> SF a b) = SF {sfTF = tf0} + where + tf0 a0 = + case tf10 a0 of + (sf1, (b0, NoEvent)) -> (switchAux sf1, b0) + (_, (_, Event c0)) -> sfTF (k c0) a0 + + -- It would be nice to optimize further here. E.g. if it would be + -- possible to observe the event source only. + switchAux :: SF' a (b, Event c) -> SF' a b + switchAux (SFId _) = switchAuxA1 id -- New + switchAux (SFConst _ (b, NoEvent)) = sfConst b + switchAux (SFArr _ f1) = switchAuxA1 f1 + switchAux sf1 = SF' tf + where + tf dt a = + case (sfTF' sf1) dt a of + (sf1', (b, NoEvent)) -> (switchAux sf1', b) + (_, (_, Event c)) -> sfTF (k c) a + + -- Could be optimized a little bit further by having a case for + -- identity, switchAuxI1 + + -- Note: While switch behaves as a stateless arrow at this point, that + -- could change after a switch. Hence, SF' overall. + switchAuxA1 :: (a -> (b, Event c)) -> SF' a b + switchAuxA1 f1 = sf + where + sf = SF' tf + tf _ a = + case f1 a of + (b, NoEvent) -> (sf, b) + (_, Event c) -> sfTF (k c) a +-} + +-- | Basic switch. +-- +-- By default, the first signal function is applied. +-- +-- Whenever the second value in the pair actually is an event, +-- the value carried by the event is used to obtain a new signal +-- function to be applied *at that time and at future times*. +-- +-- Until that happens, the first value in the pair is produced +-- in the output signal. +-- +-- Important note: at the time of switching, the second +-- signal function is applied immediately. If that second +-- SF can also switch at time zero, then a double (nested) +-- switch might take place. If the second SF refers to the +-- first one, the switch might take place infinitely many +-- times and never be resolved. +-- +-- Remember: The continuation is evaluated strictly at the time +-- of switching! +switch :: SF a (b, Event c) -> (c -> SF a b) -> SF a b +switch (SF {sfTF = tf10}) k = SF {sfTF = tf0} + where + tf0 a0 = + case tf10 a0 of + (sf1, (b0, NoEvent)) -> (switchAux sf1 k, b0) + (_, (_, Event c0)) -> sfTF (k c0) a0 + + -- It would be nice to optimize further here. E.g. if it would be + -- possible to observe the event source only. + switchAux :: SF' a (b, Event c) -> (c -> SF a b) -> SF' a b + switchAux (SFArr _ (FDC (b, NoEvent))) _ = sfConst b + switchAux (SFArr _ fd1) k = switchAuxA1 (fdFun fd1) k + switchAux sf1 k = SF' tf +{- + if sfIsInv sf1 then + switchInv sf1 k + else + SF' tf False +-} + where + tf dt a = + case (sfTF' sf1) dt a of + (sf1', (b, NoEvent)) -> (switchAux sf1' k, b) + (_, (_, Event c)) -> sfTF (k c) a + +{- + -- Note: subordinate signal function being invariant does NOT + -- imply that the overall signal function is. + switchInv :: SF' a (b, Event c) -> (c -> SF a b) -> SF' a b + switchInv sf1 k = SF' tf False + where + tf dt a = + case (sfTF' sf1) dt a of + (sf1', (b, NoEvent)) -> (switchInv sf1' k, b) + (_, (_, Event c)) -> sfTF (k c) a +-} + + -- !!! Could be optimized a little bit further by having a case for + -- !!! identity, switchAuxI1. But I'd expect identity is so unlikely + -- !!! that there is no point. + + -- Note: While switch behaves as a stateless arrow at this point, that + -- could change after a switch. Hence, SF' overall. + switchAuxA1 :: (a -> (b, Event c)) -> (c -> SF a b) -> SF' a b + switchAuxA1 f1 k = sf + where + sf = SF' tf -- False + tf _ a = + case f1 a of + (b, NoEvent) -> (sf, b) + (_, Event c) -> sfTF (k c) a + + +-- | Switch with delayed observation. +-- +-- By default, the first signal function is applied. +-- +-- Whenever the second value in the pair actually is an event, +-- the value carried by the event is used to obtain a new signal +-- function to be applied *at future times*. +-- +-- Until that happens, the first value in the pair is produced +-- in the output signal. +-- +-- Important note: at the time of switching, the second +-- signal function is used immediately, but the current +-- input is fed by it (even though the actual output signal +-- value at time 0 is discarded). +-- +-- If that second SF can also switch at time zero, then a +-- double (nested) -- switch might take place. If the second SF refers to the +-- first one, the switch might take place infinitely many times and never be +-- resolved. +-- +-- Remember: The continuation is evaluated strictly at the time +-- of switching! + +-- Alternative name: "decoupled switch"? +-- (The SFId optimization is highly unlikley to be of much use, but it +-- does raise an interesting typing issue.) +dSwitch :: SF a (b, Event c) -> (c -> SF a b) -> SF a b +dSwitch (SF {sfTF = tf10}) k = SF {sfTF = tf0} + where + tf0 a0 = + let (sf1, (b0, ec0)) = tf10 a0 + in (case ec0 of + NoEvent -> dSwitchAux sf1 k + Event c0 -> fst (sfTF (k c0) a0), + b0) + + -- It would be nice to optimize further here. E.g. if it would be + -- possible to observe the event source only. + dSwitchAux :: SF' a (b, Event c) -> (c -> SF a b) -> SF' a b + dSwitchAux (SFArr _ (FDC (b, NoEvent))) _ = sfConst b + dSwitchAux (SFArr _ fd1) k = dSwitchAuxA1 (fdFun fd1) k + dSwitchAux sf1 k = SF' tf +{- + if sfIsInv sf1 then + dSwitchInv sf1 k + else + SF' tf False +-} + where + tf dt a = + let (sf1', (b, ec)) = (sfTF' sf1) dt a + in (case ec of + NoEvent -> dSwitchAux sf1' k + Event c -> fst (sfTF (k c) a), + + b) + +{- + -- Note: that the subordinate signal function is invariant does NOT + -- imply that the overall signal function is. + dSwitchInv :: SF' a (b, Event c) -> (c -> SF a b) -> SF' a b + dSwitchInv sf1 k = SF' tf False + where + tf dt a = + let (sf1', (b, ec)) = (sfTF' sf1) dt a + in (case ec of + NoEvent -> dSwitchInv sf1' k + Event c -> fst (sfTF (k c) a), + + b) +-} + + -- !!! Could be optimized a little bit further by having a case for + -- !!! identity, switchAuxI1 + + -- Note: While dSwitch behaves as a stateless arrow at this point, that + -- could change after a switch. Hence, SF' overall. + dSwitchAuxA1 :: (a -> (b, Event c)) -> (c -> SF a b) -> SF' a b + dSwitchAuxA1 f1 k = sf + where + sf = SF' tf -- False + tf _ a = + let (b, ec) = f1 a + in (case ec of + NoEvent -> sf + Event c -> fst (sfTF (k c) a), + + b) + + +-- | Recurring switch. +-- +-- See for more +-- information on how this switch works. + +-- !!! Suboptimal. Overall, the constructor is invarying since rSwitch is +-- !!! being invoked recursively on a switch. In fact, we don't even care +-- !!! whether the subordinate signal function is invarying or not. +-- !!! We could make use of a signal function transformer sfInv to +-- !!! mark the constructor as invarying. Would that make sense? +-- !!! The price would be an extra loop with case analysis. +-- !!! The potential gain is fewer case analyses in superior loops. +rSwitch :: SF a b -> SF (a, Event (SF a b)) b +rSwitch sf = switch (first sf) ((noEventSnd >=-) . rSwitch) + +{- +-- Old version. New is more efficient. Which one is clearer? +rSwitch :: SF a b -> SF (a, Event (SF a b)) b +rSwitch sf = switch (first sf) rSwitch' + where + rSwitch' sf = switch (sf *** notYet) rSwitch' +-} + + +-- | Recurring switch with delayed observation. +-- +-- See for more +-- information on how this switch works. +drSwitch :: SF a b -> SF (a, Event (SF a b)) b +drSwitch sf = dSwitch (first sf) ((noEventSnd >=-) . drSwitch) + +{- +-- Old version. New is more efficient. Which one is clearer? +drSwitch :: SF a b -> SF (a, Event (SF a b)) b +drSwitch sf = dSwitch (first sf) drSwitch' + where + drSwitch' sf = dSwitch (sf *** notYet) drSwitch' +-} + + +-- | "Call-with-current-continuation" switch. +-- +-- See for more +-- information on how this switch works. + +-- !!! Has not been optimized properly. +-- !!! Nor has opts been tested! +-- !!! Don't forget Inv opts! +kSwitch :: SF a b -> SF (a,b) (Event c) -> (SF a b -> c -> SF a b) -> SF a b +kSwitch sf10@(SF {sfTF = tf10}) (SF {sfTF = tfe0}) k = SF {sfTF = tf0} + where + tf0 a0 = + let (sf1, b0) = tf10 a0 + in + case tfe0 (a0, b0) of + (sfe, NoEvent) -> (kSwitchAux sf1 sfe, b0) + (_, Event c0) -> sfTF (k sf10 c0) a0 + +-- Same problem as above: must pass k explicitly??? +-- kSwitchAux (SFId _) sfe = kSwitchAuxI1 sfe + kSwitchAux (SFArr _ (FDC b)) sfe = kSwitchAuxC1 b sfe + kSwitchAux (SFArr _ fd1) sfe = kSwitchAuxA1 (fdFun fd1) sfe + -- kSwitchAux (SFArrE _ f1) sfe = kSwitchAuxA1 f1 sfe + -- kSwitchAux (SFArrEE _ f1) sfe = kSwitchAuxA1 f1 sfe + kSwitchAux sf1 (SFArr _ (FDC NoEvent)) = sf1 + kSwitchAux sf1 (SFArr _ fde) = kSwitchAuxAE sf1 (fdFun fde) + -- kSwitchAux sf1 (SFArrE _ fe) = kSwitchAuxAE sf1 fe + -- kSwitchAux sf1 (SFArrEE _ fe) = kSwitchAuxAE sf1 fe + kSwitchAux sf1 sfe = SF' tf -- False + where + tf dt a = + let (sf1', b) = (sfTF' sf1) dt a + in + case (sfTF' sfe) dt (a, b) of + (sfe', NoEvent) -> (kSwitchAux sf1' sfe', b) + (_, Event c) -> sfTF (k (freeze sf1 dt) c) a + +{- +-- !!! Untested optimization! + kSwitchAuxI1 (SFConst _ NoEvent) = sfId + kSwitchAuxI1 (SFArr _ fe) = kSwitchAuxI1AE fe + kSwitchAuxI1 sfe = SF' tf + where + tf dt a = + case (sfTF' sfe) dt (a, a) of + (sfe', NoEvent) -> (kSwitchAuxI1 sfe', a) + (_, Event c) -> sfTF (k identity c) a +-} + +-- !!! Untested optimization! + kSwitchAuxC1 b (SFArr _ (FDC NoEvent)) = sfConst b + kSwitchAuxC1 b (SFArr _ fde) = kSwitchAuxC1AE b (fdFun fde) + -- kSwitchAuxC1 b (SFArrE _ fe) = kSwitchAuxC1AE b fe + -- kSwitchAuxC1 b (SFArrEE _ fe) = kSwitchAuxC1AE b fe + kSwitchAuxC1 b sfe = SF' tf -- False + where + tf dt a = + case (sfTF' sfe) dt (a, b) of + (sfe', NoEvent) -> (kSwitchAuxC1 b sfe', b) + (_, Event c) -> sfTF (k (constant b) c) a + +-- !!! Untested optimization! + kSwitchAuxA1 f1 (SFArr _ (FDC NoEvent)) = sfArrG f1 + kSwitchAuxA1 f1 (SFArr _ fde) = kSwitchAuxA1AE f1 (fdFun fde) + -- kSwitchAuxA1 f1 (SFArrE _ fe) = kSwitchAuxA1AE f1 fe + -- kSwitchAuxA1 f1 (SFArrEE _ fe) = kSwitchAuxA1AE f1 fe + kSwitchAuxA1 f1 sfe = SF' tf -- False + where + tf dt a = + let b = f1 a + in + case (sfTF' sfe) dt (a, b) of + (sfe', NoEvent) -> (kSwitchAuxA1 f1 sfe', b) + (_, Event c) -> sfTF (k (arr f1) c) a + +-- !!! Untested optimization! +-- kSwitchAuxAE (SFId _) fe = kSwitchAuxI1AE fe + kSwitchAuxAE (SFArr _ (FDC b)) fe = kSwitchAuxC1AE b fe + kSwitchAuxAE (SFArr _ fd1) fe = kSwitchAuxA1AE (fdFun fd1) fe + -- kSwitchAuxAE (SFArrE _ f1) fe = kSwitchAuxA1AE f1 fe + -- kSwitchAuxAE (SFArrEE _ f1) fe = kSwitchAuxA1AE f1 fe + kSwitchAuxAE sf1 fe = SF' tf -- False + where + tf dt a = + let (sf1', b) = (sfTF' sf1) dt a + in + case fe (a, b) of + NoEvent -> (kSwitchAuxAE sf1' fe, b) + Event c -> sfTF (k (freeze sf1 dt) c) a + +{- +-- !!! Untested optimization! + kSwitchAuxI1AE fe = SF' tf -- False + where + tf dt a = + case fe (a, a) of + NoEvent -> (kSwitchAuxI1AE fe, a) + Event c -> sfTF (k identity c) a +-} + +-- !!! Untested optimization! + kSwitchAuxC1AE b fe = SF' tf -- False + where + tf _ a = + case fe (a, b) of + NoEvent -> (kSwitchAuxC1AE b fe, b) + Event c -> sfTF (k (constant b) c) a + +-- !!! Untested optimization! + kSwitchAuxA1AE f1 fe = SF' tf -- False + where + tf _ a = + let b = f1 a + in + case fe (a, b) of + NoEvent -> (kSwitchAuxA1AE f1 fe, b) + Event c -> sfTF (k (arr f1) c) a + + +-- | 'kSwitch' with delayed observation. +-- +-- See for more +-- information on how this switch works. + +-- !!! Has not been optimized properly. Should be like kSwitch. +dkSwitch :: SF a b -> SF (a,b) (Event c) -> (SF a b -> c -> SF a b) -> SF a b +dkSwitch sf10@(SF {sfTF = tf10}) (SF {sfTF = tfe0}) k = SF {sfTF = tf0} + where + tf0 a0 = + let (sf1, b0) = tf10 a0 + in (case tfe0 (a0, b0) of + (sfe, NoEvent) -> dkSwitchAux sf1 sfe + (_, Event c0) -> fst (sfTF (k sf10 c0) a0), + b0) + + dkSwitchAux sf1 (SFArr _ (FDC NoEvent)) = sf1 + dkSwitchAux sf1 sfe = SF' tf -- False + where + tf dt a = + let (sf1', b) = (sfTF' sf1) dt a + in (case (sfTF' sfe) dt (a, b) of + (sfe', NoEvent) -> dkSwitchAux sf1' sfe' + (_, Event c) -> fst (sfTF (k (freeze sf1 dt) c) a), + b) + + +------------------------------------------------------------------------------ +-- Parallel composition and switching over collections with broadcasting +------------------------------------------------------------------------------ + +-- | Tuple a value up with every element of a collection of signal +-- functions. +broadcast :: Functor col => a -> col sf -> col (a, sf) +broadcast a sfs = fmap (\sf -> (a, sf)) sfs + + +-- !!! Hmm. We should really optimize here. +-- !!! Check for Arr in parallel! +-- !!! Check for Arr FDE in parallel!!! +-- !!! Check for EP in parallel!!!!! +-- !!! Cf &&&. +-- !!! But how??? All we know is that the collection is a functor ... +-- !!! Maybe that kind of generality does not make much sense for +-- !!! par and parB? (Although it is niceto be able to switch into a +-- !!! par or parB from within a pSwitch[B].) +-- !!! If we had a parBList, that could be defined in terms of &&&, surely? +-- !!! E.g. +-- !!! parBList [] = constant [] +-- !!! parBList (sf:sfs) = sf &&& parBList sfs >>> arr (\(x,xs) -> x:xs) +-- !!! +-- !!! This ought to optimize quite well. E.g. +-- !!! parBList [arr1,arr2,arr3] +-- !!! = arr1 &&& parBList [arr2,arr3] >>> arrX +-- !!! = arr1 &&& (arr2 &&& parBList [arr3] >>> arrX) >>> arrX +-- !!! = arr1 &&& (arr2 &&& (arr3 &&& parBList [] >>> arrX) >>> arrX) >>> arrX +-- !!! = arr1 &&& (arr2 &&& (arr3C >>> arrX) >>> arrX) >>> arrX +-- !!! = arr1 &&& (arr2 &&& (arr3CcpX) >>> arrX) >>> arrX +-- !!! = arr1 &&& (arr23CcpX >>> arrX) >>> arrX +-- !!! = arr1 &&& (arr23CcpXcpX) >>> arrX +-- !!! = arr123CcpXcpXcpX + +-- | Spatial parallel composition of a signal function collection. +-- Given a collection of signal functions, it returns a signal +-- function that 'broadcast's its input signal to every element +-- of the collection, to return a signal carrying a collection +-- of outputs. See 'par'. +-- +-- For more information on how parallel composition works, check +-- +parB :: Functor col => col (SF a b) -> SF a (col b) +parB = par broadcast + +-- | Parallel switch (dynamic collection of signal functions spatially composed +-- in parallel). See 'pSwitch'. +-- +-- For more information on how parallel composition works, check +-- +pSwitchB :: Functor col => + col (SF a b) -> SF (a,col b) (Event c) -> (col (SF a b)->c-> SF a (col b)) + -> SF a (col b) +pSwitchB = pSwitch broadcast + +-- | Delayed parallel switch with broadcasting (dynamic collection of +-- signal functions spatially composed in parallel). See 'dpSwitch'. +-- +-- For more information on how parallel composition works, check +-- +dpSwitchB :: Functor col => + col (SF a b) -> SF (a,col b) (Event c) -> (col (SF a b)->c->SF a (col b)) + -> SF a (col b) +dpSwitchB = dpSwitch broadcast + +-- For more information on how parallel composition works, check +-- +rpSwitchB :: Functor col => + col (SF a b) -> SF (a, Event (col (SF a b) -> col (SF a b))) (col b) +rpSwitchB = rpSwitch broadcast + +-- For more information on how parallel composition works, check +-- +drpSwitchB :: Functor col => + col (SF a b) -> SF (a, Event (col (SF a b) -> col (SF a b))) (col b) +drpSwitchB = drpSwitch broadcast + + +------------------------------------------------------------------------------ +-- Parallel composition and switching over collections with general routing +------------------------------------------------------------------------------ + +-- | Spatial parallel composition of a signal function collection parameterized +-- on the routing function. +-- +par :: Functor col => + (forall sf . (a -> col sf -> col (b, sf))) -- ^ Determines the input to each signal function + -- in the collection. IMPORTANT! The routing function MUST + -- preserve the structure of the signal function collection. + + -> col (SF b c) -- ^ Signal function collection. + -> SF a (col c) +par rf sfs0 = SF {sfTF = tf0} + where + tf0 a0 = + let bsfs0 = rf a0 sfs0 + sfcs0 = fmap (\(b0, sf0) -> (sfTF sf0) b0) bsfs0 + sfs = fmap fst sfcs0 + cs0 = fmap snd sfcs0 + in + (parAux rf sfs, cs0) + + +-- Internal definition. Also used in parallel swithers. +parAux :: Functor col => + (forall sf . (a -> col sf -> col (b, sf))) + -> col (SF' b c) + -> SF' a (col c) +parAux rf sfs = SF' tf -- True + where + tf dt a = + let bsfs = rf a sfs + sfcs' = fmap (\(b, sf) -> (sfTF' sf) dt b) bsfs + sfs' = fmap fst sfcs' + cs = fmap snd sfcs' + in + (parAux rf sfs', cs) + + +-- | Parallel switch parameterized on the routing function. This is the most +-- general switch from which all other (non-delayed) switches in principle +-- can be derived. The signal function collection is spatially composed in +-- parallel and run until the event signal function has an occurrence. Once +-- the switching event occurs, all signal function are "frozen" and their +-- continuations are passed to the continuation function, along with the +-- event value. +-- + +-- rf ......... Routing function: determines the input to each signal function +-- in the collection. IMPORTANT! The routing function has an +-- obligation to preserve the structure of the signal function +-- collection. +-- sfs0 ....... Signal function collection. +-- sfe0 ....... Signal function generating the switching event. +-- k .......... Continuation to be invoked once event occurs. +-- Returns the resulting signal function. +-- +-- !!! Could be optimized on the event source being SFArr, SFArrE, SFArrEE +pSwitch :: Functor col + => (forall sf . (a -> col sf -> col (b, sf))) -- ^ Routing function: determines the input to each signal function + -- in the collection. IMPORTANT! The routing function has an + -- obligation to preserve the structure of the signal function + -- collection. + + -> col (SF b c) -- ^ Signal function collection. + -> SF (a, col c) (Event d) -- ^ Signal function generating the switching event. + -> (col (SF b c) -> d -> SF a (col c)) -- ^ Continuation to be invoked once event occurs. + -> SF a (col c) +pSwitch rf sfs0 sfe0 k = SF {sfTF = tf0} + where + tf0 a0 = + let bsfs0 = rf a0 sfs0 + sfcs0 = fmap (\(b0, sf0) -> (sfTF sf0) b0) bsfs0 + sfs = fmap fst sfcs0 + cs0 = fmap snd sfcs0 + in + case (sfTF sfe0) (a0, cs0) of + (sfe, NoEvent) -> (pSwitchAux sfs sfe, cs0) + (_, Event d0) -> sfTF (k sfs0 d0) a0 + + pSwitchAux sfs (SFArr _ (FDC NoEvent)) = parAux rf sfs + pSwitchAux sfs sfe = SF' tf -- False + where + tf dt a = + let bsfs = rf a sfs + sfcs' = fmap (\(b, sf) -> (sfTF' sf) dt b) bsfs + sfs' = fmap fst sfcs' + cs = fmap snd sfcs' + in + case (sfTF' sfe) dt (a, cs) of + (sfe', NoEvent) -> (pSwitchAux sfs' sfe', cs) + (_, Event d) -> sfTF (k (freezeCol sfs dt) d) a + + +-- | Parallel switch with delayed observation parameterized on the routing +-- function. +-- +-- The collection argument to the function invoked on the +-- switching event is of particular interest: it captures the +-- continuations of the signal functions running in the collection +-- maintained by 'dpSwitch' at the time of the switching event, +-- thus making it possible to preserve their state across a switch. +-- Since the continuations are plain, ordinary signal functions, +-- they can be resumed, discarded, stored, or combined with +-- other signal functions. + +-- !!! Could be optimized on the event source being SFArr, SFArrE, SFArrEE. +-- +dpSwitch :: Functor col => + (forall sf . (a -> col sf -> col (b, sf))) -- ^ Routing function. Its purpose is + -- to pair up each running signal function in the collection + -- maintained by 'dpSwitch' with the input it is going to see + -- at each point in time. All the routing function can do is specify + -- how the input is distributed. + -> col (SF b c) -- ^ Initial collection of signal functions. + -> SF (a, col c) (Event d) -- ^ Signal function that observes the external + -- input signal and the output signals from the collection in order + -- to produce a switching event. + -> (col (SF b c) -> d -> SF a (col c)) -- ^ The fourth argument is a function that is invoked when the + -- switching event occurs, yielding a new signal function to switch + -- into based on the collection of signal functions previously + -- running and the value carried by the switching event. This + -- allows the collection to be updated and then switched back + -- in, typically by employing 'dpSwitch' again. + -> SF a (col c) +dpSwitch rf sfs0 sfe0 k = SF {sfTF = tf0} + where + tf0 a0 = + let bsfs0 = rf a0 sfs0 + sfcs0 = fmap (\(b0, sf0) -> (sfTF sf0) b0) bsfs0 + cs0 = fmap snd sfcs0 + in + (case (sfTF sfe0) (a0, cs0) of + (sfe, NoEvent) -> dpSwitchAux (fmap fst sfcs0) sfe + (_, Event d0) -> fst (sfTF (k sfs0 d0) a0), + cs0) + + dpSwitchAux sfs (SFArr _ (FDC NoEvent)) = parAux rf sfs + dpSwitchAux sfs sfe = SF' tf -- False + where + tf dt a = + let bsfs = rf a sfs + sfcs' = fmap (\(b, sf) -> (sfTF' sf) dt b) bsfs + cs = fmap snd sfcs' + in + (case (sfTF' sfe) dt (a, cs) of + (sfe', NoEvent) -> dpSwitchAux (fmap fst sfcs') + sfe' + (_, Event d) -> fst (sfTF (k (freezeCol sfs dt) + d) + a), + cs) + + +-- Recurring parallel switch parameterized on the routing function. +-- rf ......... Routing function: determines the input to each signal function +-- in the collection. IMPORTANT! The routing function has an +-- obligation to preserve the structure of the signal function +-- collection. +-- sfs ........ Initial signal function collection. +-- Returns the resulting signal function. + +rpSwitch :: Functor col => + (forall sf . (a -> col sf -> col (b, sf))) + -> col (SF b c) -> SF (a, Event (col (SF b c) -> col (SF b c))) (col c) +rpSwitch rf sfs = + pSwitch (rf . fst) sfs (arr (snd . fst)) $ \sfs' f -> + noEventSnd >=- rpSwitch rf (f sfs') + + +{- +rpSwitch rf sfs = pSwitch (rf . fst) sfs (arr (snd . fst)) k + where + k sfs f = rpSwitch' (f sfs) + rpSwitch' sfs = pSwitch (rf . fst) sfs (NoEvent --> arr (snd . fst)) k +-} + +-- Recurring parallel switch with delayed observation parameterized on the +-- routing function. +drpSwitch :: Functor col => + (forall sf . (a -> col sf -> col (b, sf))) + -> col (SF b c) -> SF (a, Event (col (SF b c) -> col (SF b c))) (col c) +drpSwitch rf sfs = + dpSwitch (rf . fst) sfs (arr (snd . fst)) $ \sfs' f -> + noEventSnd >=- drpSwitch rf (f sfs') + +{- +drpSwitch rf sfs = dpSwitch (rf . fst) sfs (arr (snd . fst)) k + where + k sfs f = drpSwitch' (f sfs) + drpSwitch' sfs = dpSwitch (rf . fst) sfs (NoEvent-->arr (snd . fst)) k +-} + +------------------------------------------------------------------------------ +-- Wave-form generation +------------------------------------------------------------------------------ + +-- | Zero-order hold. + +-- !!! Should be redone using SFSScan? +-- !!! Otherwise, we are missing an invarying case. +old_hold :: a -> SF (Event a) a +old_hold a_init = switch (constant a_init &&& identity) + ((NoEvent >--) . old_hold) + +-- | Zero-order hold. +hold :: a -> SF (Event a) a +hold a_init = epPrim f () a_init + where + f _ a = ((), a, a) + +-- !!! +-- !!! 2005-04-10: I DO NO LONGER THINK THIS IS CORRECT! +-- !!! CAN ONE POSSIBLY GET THE DESIRED STRICTNESS PROPERTIES +-- !!! ("DECOUPLING") this way??? +-- !!! Also applies to the other "d" functions that were tentatively +-- !!! defined using only epPrim. +-- !!! +-- !!! 2005-06-13: Yes, indeed wrong! (But it's subtle, one has to +-- !!! make sure that the incoming event (and not just the payload +-- !!! of the event) is control dependent on the output of "dHold" +-- !!! to observe it. +-- !!! +-- !!! 2005-06-09: But if iPre can be defined in terms of sscan, +-- !!! and ep + sscan = sscan, then things might work, and +-- !!! it might be possible to define dHold simply as hold >>> iPre +-- !!! without any performance penalty. + +-- | Zero-order hold with delay. +-- +-- Identity: dHold a0 = hold a0 >>> iPre a0). +dHold :: a -> SF (Event a) a +dHold a0 = hold a0 >>> iPre a0 +{- +-- THIS IS WRONG! SEE ABOVE. +dHold a_init = epPrim f a_init a_init + where + f a' a = (a, a', a) +-} + +-- | Tracks input signal when available, holds last value when disappears. +-- +-- !!! DANGER!!! Event used inside arr! Probably OK because arr will not be +-- !!! optimized to arrE. But still. Maybe rewrite this using, say, scan? +-- !!! or switch? Switching (in hold) for every input sample does not +-- !!! seem like such a great idea anyway. +trackAndHold :: a -> SF (Maybe a) a +trackAndHold a_init = arr (maybe NoEvent Event) >>> hold a_init + + +------------------------------------------------------------------------------ +-- Accumulators +------------------------------------------------------------------------------ + +-- | See 'accum'. +old_accum :: a -> SF (Event (a -> a)) (Event a) +old_accum = accumBy (flip ($)) + +-- | Given an initial value in an accumulator, +-- it returns a signal function that processes +-- an event carrying transformation functions. +-- Every time an 'Event' is received, the function +-- inside it is applied to the accumulator, +-- whose new value is outputted in an 'Event'. +-- +accum :: a -> SF (Event (a -> a)) (Event a) +accum a_init = epPrim f a_init NoEvent + where + f a g = (a', Event a', NoEvent) -- Accumulator, output if Event, output if no event + where + a' = g a + + +-- | Zero-order hold accumulator (always produces the last outputted value +-- until an event arrives). +accumHold :: a -> SF (Event (a -> a)) a +accumHold a_init = epPrim f a_init a_init + where + f a g = (a', a', a') -- Accumulator, output if Event, output if no event + where + a' = g a + +-- | Zero-order hold accumulator with delayed initialization (always produces +-- the last outputted value until an event arrives, but the very initial output +-- is always the given accumulator). +dAccumHold :: a -> SF (Event (a -> a)) a +dAccumHold a_init = accumHold a_init >>> iPre a_init +{- +-- WRONG! +-- epPrim DOES and MUST patternmatch +-- on the input at every time step. +-- Test case to check for this added! +dAccumHold a_init = epPrim f a_init a_init + where + f a g = (a', a, a') + where + a' = g a +-} + + +-- | See 'accumBy'. +old_accumBy :: (b -> a -> b) -> b -> SF (Event a) (Event b) +old_accumBy f b_init = switch (never &&& identity) $ \a -> abAux (f b_init a) + where + abAux b = switch (now b &&& notYet) $ \a -> abAux (f b a) + +-- | Accumulator parameterized by the accumulation function. +accumBy :: (b -> a -> b) -> b -> SF (Event a) (Event b) +accumBy g b_init = epPrim f b_init NoEvent + where + f b a = (b', Event b', NoEvent) + where + b' = g b a + +-- | Zero-order hold accumulator parameterized by the accumulation function. +accumHoldBy :: (b -> a -> b) -> b -> SF (Event a) b +accumHoldBy g b_init = epPrim f b_init b_init + where + f b a = (b', b', b') + where + b' = g b a + +-- !!! This cannot be right since epPrim DOES and MUST patternmatch +-- !!! on the input at every time step. +-- !!! Add a test case to check for this! + +-- | Zero-order hold accumulator parameterized by the accumulation function +-- with delayed initialization (initial output sample is always the +-- given accumulator). +dAccumHoldBy :: (b -> a -> b) -> b -> SF (Event a) b +dAccumHoldBy f a_init = accumHoldBy f a_init >>> iPre a_init +{- +-- WRONG! +-- epPrim DOES and MUST patternmatch +-- on the input at every time step. +-- Test case to check for this added! +dAccumHoldBy g b_init = epPrim f b_init b_init + where + f b a = (b', b, b') + where + b' = g b a +-} + + +{- Untested: + +accumBy f b = switch (never &&& identity) $ \a -> + let b' = f b a in NoEvent >-- Event b' --> accumBy f b' + +But no real improvement in clarity anyway. + +-} + +-- accumBy f b = accumFilter (\b -> a -> let b' = f b a in (b', Event b')) b + +{- +-- Identity: accumBy f = accumFilter (\b a -> let b' = f b a in (b',Just b')) +accumBy :: (b -> a -> b) -> b -> SF (Event a) (Event b) +accumBy f b_init = SF {sfTF = tf0} + where + tf0 NoEvent = (abAux b_init, NoEvent) + tf0 (Event a0) = let b' = f b_init a0 + in (abAux b', Event b') + + abAux b = SF' {sfTF' = tf} + where + tf _ NoEvent = (abAux b, NoEvent) + tf _ (Event a) = let b' = f b a + in (abAux b', Event b') +-} + +{- +accumFilter :: (c -> a -> (c, Maybe b)) -> c -> SF (Event a) (Event b) +accumFilter f c_init = SF {sfTF = tf0} + where + tf0 NoEvent = (afAux c_init, NoEvent) + tf0 (Event a0) = case f c_init a0 of + (c', Nothing) -> (afAux c', NoEvent) + (c', Just b0) -> (afAux c', Event b0) + + afAux c = SF' {sfTF' = tf} + where + tf _ NoEvent = (afAux c, NoEvent) + tf _ (Event a) = case f c a of + (c', Nothing) -> (afAux c', NoEvent) + (c', Just b) -> (afAux c', Event b) +-} + +-- | See 'accumFilter'. +old_accumFilter :: (c -> a -> (c, Maybe b)) -> c -> SF (Event a) (Event b) +old_accumFilter f c_init = switch (never &&& identity) $ \a -> afAux (f c_init a) + where + afAux (c, Nothing) = switch (never &&& notYet) $ \a -> afAux (f c a) + afAux (c, Just b) = switch (now b &&& notYet) $ \a -> afAux (f c a) + +-- | Accumulator parameterized by the accumulator function with filtering, +-- possibly discarding some of the input events based on whether the second +-- component of the result of applying the accumulation function is +-- 'Nothing' or 'Just' x for some x. +accumFilter :: (c -> a -> (c, Maybe b)) -> c -> SF (Event a) (Event b) +accumFilter g c_init = epPrim f c_init NoEvent + where + f c a = case g c a of + (c', Nothing) -> (c', NoEvent, NoEvent) + (c', Just b) -> (c', Event b, NoEvent) + + +------------------------------------------------------------------------------ +-- Delays +------------------------------------------------------------------------------ + +-- | Uninitialized delay operator (old implementation). + +-- !!! The seq helps in the dynamic delay line example. But is it a good +-- !!! idea in general? Are there other accumulators which should be seq'ed +-- !!! as well? E.g. accum? Switch? Anywhere else? What's the underlying +-- !!! design principle? What can the user assume? +-- +old_pre :: SF a a +old_pre = SF {sfTF = tf0} + where + tf0 a0 = (preAux a0, usrErr "AFRP" "pre" "Uninitialized pre operator.") + + preAux a_prev = SF' tf -- True + where + tf _ a = {- a_prev `seq` -} (preAux a, a_prev) + +-- | Initialized delay operator (old implementation). +old_iPre :: a -> SF a a +old_iPre = (--> old_pre) + + + +-- | Uninitialized delay operator. + +-- !!! Redefined using SFSScan +-- !!! About 20% slower than old_pre on its own. +pre :: SF a a +pre = sscanPrim f uninit uninit + where + f c a = Just (a, c) + uninit = usrErr "AFRP" "pre" "Uninitialized pre operator." + + +-- | Initialized delay operator. +iPre :: a -> SF a a +iPre = (--> pre) + + +------------------------------------------------------------------------------ +-- Timed delays +------------------------------------------------------------------------------ + +-- | Delay a signal by a fixed time 't', using the second parameter +-- to fill in the initial 't' seconds. + +-- Invariants: +-- t_diff measure the time since the latest output sample ideally +-- should have been output. Whenever that equals or exceeds the +-- time delta for the next buffered sample, it is time to output a +-- new sample (although not necessarily the one first in the queue: +-- it might be necessary to "catch up" by discarding samples. +-- 0 <= t_diff < bdt, where bdt is the buffered time delta for the +-- sample on the front of the buffer queue. +-- +-- Sum of time deltas in the queue >= q. + +-- !!! PROBLEM! +-- Since input samples sometimes need to be duplicated, it is not a +-- good idea use a delay on things like events since we then could +-- end up with duplication of event occurrences. +-- (Thus, we actually NEED delayEvent.) + +delay :: Time -> a -> SF a a +delay q a_init | q < 0 = usrErr "AFRP" "delay" "Negative delay." + | q == 0 = identity + | otherwise = SF {sfTF = tf0} + where + tf0 a0 = (delayAux [] [(q, a0)] 0 a_init, a_init) + + delayAux _ [] _ _ = undefined + delayAux rbuf buf@((bdt, ba) : buf') t_diff a_prev = SF' tf -- True + where + tf dt a | t_diff' < bdt = + (delayAux rbuf' buf t_diff' a_prev, a_prev) + | otherwise = nextSmpl rbuf' buf' (t_diff' - bdt) ba + where + t_diff' = t_diff + dt + rbuf' = (dt, a) : rbuf + + nextSmpl rbuf [] t_diff a = + nextSmpl [] (reverse rbuf) t_diff a + nextSmpl rbuf buf@((bdt, ba) : buf') t_diff a + | t_diff < bdt = (delayAux rbuf buf t_diff a, a) + | otherwise = nextSmpl rbuf buf' (t_diff-bdt) ba + + +-- !!! Hmm. Not so easy to do efficiently, it seems ... + +-- varDelay :: Time -> a -> SF (a, Time) a +-- varDelay = undefined + + +------------------------------------------------------------------------------ +-- Variable pause in signal +------------------------------------------------------------------------------ + +-- | Given a value in an accumulator (b), a predicate signal function (sfC), +-- and a second signal function (sf), pause will produce the accumulator b +-- if sfC input is True, and will transform the signal using sf otherwise. +-- It acts as a pause with an accumulator for the moments when the +-- transformation is paused. +pause :: b -> SF a Bool -> SF a b -> SF a b +pause b_init (SF { sfTF = tfP}) (SF {sfTF = tf10}) = SF {sfTF = tf0} + where + -- Initial transformation (no time delta): + -- If the condition is True, return the accumulator b_init) + -- Otherwise transform the input normally and recurse. + tf0 a0 = case tfP a0 of + (c, True) -> (pauseInit b_init tf10 c, b_init) + (c, False) -> let (k, b0) = tf10 a0 + in (pause' b0 k c, b0) + + -- Similar deal, but with a time delta + pauseInit :: b -> (a -> Transition a b) -> SF' a Bool -> SF' a b + pauseInit b_init' tf10' c = SF' tf0' + where tf0' dt a = + case (sfTF' c) dt a of + (c', True) -> (pauseInit b_init' tf10' c', b_init') + (c', False) -> let (k, b0) = tf10' a + in (pause' b0 k c', b0) + + -- Very same deal (almost alpha-renameable) + pause' :: b -> SF' a b -> SF' a Bool -> SF' a b + pause' b_init' tf10' tfP' = SF' tf0' + where tf0' dt a = + case (sfTF' tfP') dt a of + (tfP'', True) -> (pause' b_init' tf10' tfP'', b_init') + (tfP'', False) -> let (tf10'', b0') = (sfTF' tf10') dt a + in (pause' b0' tf10'' tfP'', b0') + +-- if_then_else :: SF a Bool -> SF a b -> SF a b -> SF a b +-- if_then_else condSF sfThen sfElse = proc (i) -> do +-- cond <- condSF -< i +-- ok <- sfThen -< i +-- notOk <- sfElse -< i +-- returnA -< if cond then ok else notOk + +------------------------------------------------------------------------------ +-- Integration and differentiation +------------------------------------------------------------------------------ + +-- | Integration using the rectangle rule. +{-# INLINE integral #-} +integral :: VectorSpace a s => SF a a +integral = SF {sfTF = tf0} + where + igrl0 = zeroVector + + tf0 a0 = (integralAux igrl0 a0, igrl0) + + integralAux igrl a_prev = SF' tf -- True + where + tf dt a = (integralAux igrl' a, igrl') + where + igrl' = igrl ^+^ realToFrac dt *^ a_prev + + +-- "immediate" integration (using the function's value at the current time) +imIntegral :: VectorSpace a s => a -> SF a a +imIntegral = ((\ _ a' dt v -> v ^+^ realToFrac dt *^ a') `iterFrom`) + +iterFrom :: (a -> a -> DTime -> b -> b) -> b -> SF a b +f `iterFrom` b = SF (iterAux b) where + -- iterAux b a = (SF' (\ dt a' -> iterAux (f a a' dt b) a') True, b) + iterAux b a = (SF' (\ dt a' -> iterAux (f a a' dt b) a'), b) + +-- | A very crude version of a derivative. It simply divides the +-- value difference by the time difference. As such, it is very +-- crude. Use at your own risk. +derivative :: VectorSpace a s => SF a a +derivative = SF {sfTF = tf0} + where + tf0 a0 = (derivativeAux a0, zeroVector) + + derivativeAux a_prev = SF' tf -- True + where + tf dt a = (derivativeAux a, (a ^-^ a_prev) ^/ realToFrac dt) + + +------------------------------------------------------------------------------ +-- Loops with guaranteed well-defined feedback +------------------------------------------------------------------------------ + +-- | Loop with an initial value for the signal being fed back. +loopPre :: c -> SF (a,c) (b,c) -> SF a b +loopPre c_init sf = loop (second (iPre c_init) >>> sf) + +-- | Loop by integrating the second value in the pair and feeding the +-- result back. Because the integral at time 0 is zero, this is always +-- well defined. +loopIntegral :: VectorSpace c s => SF (a,c) (b,c) -> SF a b +loopIntegral sf = loop (second integral >>> sf) + + +------------------------------------------------------------------------------ +-- Noise (i.e. random signal generators) and stochastic processes +------------------------------------------------------------------------------ + +-- | Noise (random signal) with default range for type in question; +-- based on "randoms". +noise :: (RandomGen g, Random b) => g -> SF a b +noise g0 = streamToSF (randoms g0) + + +-- | Noise (random signal) with specified range; based on "randomRs". +noiseR :: (RandomGen g, Random b) => (b,b) -> g -> SF a b +noiseR range g0 = streamToSF (randomRs range g0) + + +-- Internal. Not very useful for other purposes since we do not have any +-- control over the intervals between each "sample". Or? A version with +-- time-stamped samples would be similar to embedSynch (applied to identity). +-- The list argument must be a stream (infinite list) at present. + +streamToSF :: [b] -> SF a b +streamToSF [] = intErr "AFRP" "streamToSF" "Empty list!" +streamToSF (b:bs) = SF {sfTF = tf0} + where + tf0 _ = (stsfAux bs, b) + + stsfAux [] = intErr "AFRP" "streamToSF" "Empty list!" + -- Invarying since stsfAux [] is an error. + stsfAux (b:bs) = SF' tf -- True + where + tf _ _ = (stsfAux bs, b) + +{- New def, untested: + +streamToSF = sscan2 f + where + f [] _ = intErr "AFRP" "streamToSF" "Empty list!" + f (b:bs) _ = (bs, b) + +-} + + +-- | Stochastic event source with events occurring on average once every t_avg +-- seconds. However, no more than one event results from any one sampling +-- interval in the case of relatively sparse sampling, thus avoiding an +-- "event backlog" should sampling become more frequent at some later +-- point in time. + +-- !!! Maybe it would better to give a frequency? But like this to make +-- !!! consitent with "repeatedly". +occasionally :: RandomGen g => g -> Time -> b -> SF a (Event b) +occasionally g t_avg x | t_avg > 0 = SF {sfTF = tf0} + | otherwise = usrErr "AFRP" "occasionally" + "Non-positive average interval." + where + -- Generally, if events occur with an average frequency of f, the + -- probability of at least one event occurring in an interval of t + -- is given by (1 - exp (-f*t)). The goal in the following is to + -- decide whether at least one event occurred in the interval of size + -- dt preceding the current sample point. For the first point, + -- we can think of the preceding interval as being 0, implying + -- no probability of an event occurring. + + tf0 _ = (occAux ((randoms g) :: [Time]), NoEvent) + + occAux [] = undefined + occAux (r:rs) = SF' tf -- True + where + tf dt _ = let p = 1 - exp (-(dt/t_avg)) -- Probability for at least one event. + in (occAux rs, if r < p then Event x else NoEvent) + + + +------------------------------------------------------------------------------ +-- Reactimation +------------------------------------------------------------------------------ + +-- Reactimation of a signal function. +-- init ....... IO action for initialization. Will only be invoked once, +-- at (logical) time 0, before first call to "sense". +-- Expected to return the value of input at time 0. +-- sense ...... IO action for sensing of system input. +-- arg. #1 ....... True: action may block, waiting for an OS event. +-- False: action must not block. +-- res. #1 ....... Time interval since previous invocation of the sensing +-- action (or, the first time round, the init action), +-- returned. The interval must be _strictly_ greater +-- than 0. Thus even a non-blocking invocation must +-- ensure that time progresses. +-- res. #2 ....... Nothing: input is unchanged w.r.t. the previously +-- returned input sample. +-- Just i: the input is currently i. +-- It is OK to always return "Just", even if input is +-- unchanged. +-- actuate .... IO action for outputting the system output. +-- arg. #1 ....... True: output may have changed from previous output +-- sample. +-- False: output is definitely unchanged from previous +-- output sample. +-- It is OK to ignore argument #1 and assume that the +-- the output has always changed. +-- arg. #2 ....... Current output sample. +-- result ....... Termination flag. Once True, reactimate will exit +-- the reactimation loop and return to its caller. +-- sf ......... Signal function to reactimate. + +-- | Convenience function to run a signal function indefinitely, using +-- a IO actions to obtain new input and process the output. +-- +-- This function first runs the initialization action, which provides the +-- initial input for the signal transformer at time 0. +-- +-- Afterwards, an input sensing action is used to obtain new input (if any) and +-- the time since the last iteration. The argument to the input sensing function +-- indicates if it can block. If no new input is received, it is assumed to be +-- the same as in the last iteration. +-- +-- After applying the signal function to the input, the actuation IO action +-- is executed. The first argument indicates if the output has changed, the second +-- gives the actual output). Actuation functions may choose to ignore the first +-- argument altogether. This action should return True if the reactimation +-- must stop, and False if it should continue. +-- +-- Note that this becomes the program's /main loop/, which makes using this +-- function incompatible with GLUT, Gtk and other graphics libraries. It may also +-- impose a sizeable constraint in larger projects in which different subparts run +-- at different time steps. If you need to control the main +-- loop yourself for these or other reasons, use 'reactInit' and 'react'. + +reactimate :: IO a -- ^ IO initialization action + -> (Bool -> IO (DTime, Maybe a)) -- ^ IO input sensing action + -> (Bool -> b -> IO Bool) -- ^ IO actuaction (output processing) action + -> SF a b -- ^ Signal function + -> IO () +reactimate init sense actuate (SF {sfTF = tf0}) = + do + a0 <- init + let (sf, b0) = tf0 a0 + loop sf a0 b0 + where + loop sf a b = do + done <- actuate True b + unless (a `seq` b `seq` done) $ do + (dt, ma') <- sense False + let a' = maybe a id ma' + (sf', b') = (sfTF' sf) dt a' + loop sf' a' b' + + +-- An API for animating a signal function when some other library +-- needs to own the top-level control flow: + +-- reactimate's state, maintained across samples: +data ReactState a b = ReactState { + rsActuate :: ReactHandle a b -> Bool -> b -> IO Bool, + rsSF :: SF' a b, + rsA :: a, + rsB :: b + } + +-- | A reference to reactimate's state, maintained across samples. +type ReactHandle a b = IORef (ReactState a b) + +-- | Initialize a top-level reaction handle. +reactInit :: IO a -- init + -> (ReactHandle a b -> Bool -> b -> IO Bool) -- actuate + -> SF a b + -> IO (ReactHandle a b) +reactInit init actuate (SF {sfTF = tf0}) = + do a0 <- init + let (sf,b0) = tf0 a0 + -- TODO: really need to fix this interface, since right now we + -- just ignore termination at time 0: + r <- newIORef (ReactState {rsActuate = actuate, rsSF = sf, rsA = a0, rsB = b0 }) + _ <- actuate r True b0 + return r + +-- | Process a single input sample. +react :: ReactHandle a b + -> (DTime,Maybe a) + -> IO Bool +react rh (dt,ma') = + do rs@(ReactState {rsActuate = actuate, rsSF = sf, rsA = a, rsB = _b }) <- readIORef rh + let a' = fromMaybe a ma' + (sf',b') = (sfTF' sf) dt a' + writeIORef rh (rs {rsSF = sf',rsA = a',rsB = b'}) + done <- actuate rh True b' + return done + + +------------------------------------------------------------------------------ +-- Embedding +------------------------------------------------------------------------------ + +-- New embed interface. We will probably have to revisit this. To run an +-- embedded signal function while retaining full control (e.g. start and +-- stop at will), one would probably need a continuation-based interface +-- (as well as a continuation based underlying implementation). +-- +-- E.g. here are interesting alternative (or maybe complementary) +-- signatures: +-- +-- sample :: SF a b -> SF (Event a) (Event b) +-- sample' :: SF a b -> SF (Event (DTime, a)) (Event b) +-- +-- Maybe it should be called "subSample", since that's the only thing +-- that can be achieved. At least does not have the problem with missing +-- events when supersampling. +-- +-- subSampleSynch :: SF a b -> SF (Event a) (Event b) +-- Time progresses at the same rate in the embedded system. +-- But it is only sampled on the events. +-- E.g. +-- repeatedly 0.1 () >>> subSampleSynch sf >>> hold +-- +-- subSample :: DTime -> SF a b -> SF (Event a) (Event b) +-- Time advanced by dt for each event, not synchronized with the outer clock. + +-- | Given a signal function and a pair with an initial +-- input sample for the input signal, and a list of sampling +-- times, possibly with new input samples at those times, +-- it produces a list of output samples. +-- +-- This is a simplified, purely-functional version of 'reactimate'. +embed :: SF a b -> (a, [(DTime, Maybe a)]) -> [b] +embed sf0 (a0, dtas) = b0 : loop a0 sf dtas + where + (sf, b0) = (sfTF sf0) a0 + + loop _ _ [] = [] + loop a_prev sf ((dt, ma) : dtas) = + b : (a `seq` b `seq` (loop a sf' dtas)) + where + a = maybe a_prev id ma + (sf', b) = (sfTF' sf) dt a + + +-- | Synchronous embedding. The embedded signal function is run on the supplied +-- input and time stream at a given (but variable) ratio >= 0 to the outer +-- time flow. When the ratio is 0, the embedded signal function is paused. + +-- What about running an embedded signal function at a fixed (guaranteed) +-- sampling frequency? E.g. super sampling if the outer sampling is slower, +-- subsampling otherwise. AS WELL as at a given ratio to the outer one. +-- +-- Ah, but that's more or less what embedSync does. +-- So just simplify the interface. But maybe it should also be possible +-- to feed in input from the enclosing system. + +-- !!! Should "dropped frames" be forced to avoid space leaks? +-- !!! It's kind of hard to se why, but "frame dropping" was a problem +-- !!! in the old robot simulator. Try to find an example! + +embedSynch :: SF a b -> (a, [(DTime, Maybe a)]) -> SF Double b +embedSynch sf0 (a0, dtas) = SF {sfTF = tf0} + where + tts = scanl (\t (dt, _) -> t + dt) 0 dtas + bbs@(b:_) = embed sf0 (a0, dtas) + + tf0 _ = (esAux 0 (zip tts bbs), b) + + esAux _ [] = intErr "AFRP" "embedSynch" "Empty list!" + -- Invarying below since esAux [] is an error. + esAux tp_prev tbtbs = SF' tf -- True + where + tf dt r | r < 0 = usrErr "AFRP" "embedSynch" + "Negative ratio." + | otherwise = let tp = tp_prev + dt * r + (b, tbtbs') = advance tp tbtbs + in + (esAux tp tbtbs', b) + + -- Advance the time stamped stream to the perceived time tp. + -- Under the assumption that the perceived time never goes + -- backwards (non-negative ratio), advance maintains the + -- invariant that the perceived time is always >= the first + -- time stamp. + advance _ tbtbs@[(_, b)] = (b, tbtbs) + advance tp tbtbtbs@((_, b) : tbtbs@((t', _) : _)) + | tp < t' = (b, tbtbtbs) + | t' <= tp = advance tp tbtbs + advance _ _ = undefined + +-- | Spaces a list of samples by a fixed time delta, avoiding +-- unnecessary samples when the input has not changed since +-- the last sample. +deltaEncode :: Eq a => DTime -> [a] -> (a, [(DTime, Maybe a)]) +deltaEncode _ [] = usrErr "AFRP" "deltaEncode" "Empty input list." +deltaEncode dt aas@(_:_) = deltaEncodeBy (==) dt aas + + +-- | 'deltaEncode' parameterized by the equality test. +deltaEncodeBy :: (a -> a -> Bool) -> DTime -> [a] -> (a, [(DTime, Maybe a)]) +deltaEncodeBy _ _ [] = usrErr "AFRP" "deltaEncodeBy" "Empty input list." +deltaEncodeBy eq dt (a0:as) = (a0, zip (repeat dt) (debAux a0 as)) + where + debAux _ [] = [] + debAux a_prev (a:as) | a `eq` a_prev = Nothing : debAux a as | otherwise = Just a : debAux a as -- Embedding and missing events. diff --git a/src/FRP/Yampa/Event.hs b/src/FRP/Yampa/Event.hs --- a/src/FRP/Yampa/Event.hs +++ b/src/FRP/Yampa/Event.hs @@ -249,8 +249,8 @@ -- merging the results. The first three arguments are mapping functions, -- the third of which will only be used when both events are present. -- Therefore, 'mergeBy' = 'mapMerge' 'id' 'id' -mapMerge :: (a -> c) -> (b -> c) -> (a -> b -> c) - -> Event a -> Event b -> Event c +mapMerge :: (a -> c) -> (b -> c) -> (a -> b -> c) + -> Event a -> Event b -> Event c mapMerge _ _ _ NoEvent NoEvent = NoEvent mapMerge lf _ _ (Event l) NoEvent = Event (lf l) mapMerge _ rf _ NoEvent (Event r) = Event (rf r) @@ -263,8 +263,8 @@ -- | Collect simultaneous event occurrences; no event if none. catEvents :: [Event a] -> Event [a] catEvents eas = case [ a | Event a <- eas ] of - [] -> NoEvent - as -> Event as + [] -> NoEvent + as -> Event as -- | Join (conjunction) of two events. Only produces an event -- if both events exist. @@ -295,8 +295,8 @@ mapFilterE :: (a -> Maybe b) -> Event a -> Event b mapFilterE _ NoEvent = NoEvent mapFilterE f (Event a) = case f a of - Nothing -> NoEvent - Just b -> Event b + Nothing -> NoEvent + Just b -> Event b -- | Enable/disable event occurences based on an external condition. diff --git a/src/FRP/Yampa/MergeableRecord.hs b/src/FRP/Yampa/MergeableRecord.hs --- a/src/FRP/Yampa/MergeableRecord.hs +++ b/src/FRP/Yampa/MergeableRecord.hs @@ -53,7 +53,7 @@ module FRP.Yampa.MergeableRecord ( MergeableRecord(..), - MR, -- Abstract + MR, -- Abstract mrMake, (~+~), mrMerge, diff --git a/src/FRP/Yampa/Miscellany.hs b/src/FRP/Yampa/Miscellany.hs --- a/src/FRP/Yampa/Miscellany.hs +++ b/src/FRP/Yampa/Miscellany.hs @@ -20,15 +20,15 @@ module FRP.Yampa.Miscellany ( -- Reverse function composition - ( # ), -- :: (a -> b) -> (b -> c) -> (a -> c), infixl 9 + ( # ), -- :: (a -> b) -> (b -> c) -> (a -> c), infixl 9 -- Arrow plumbing aids - dup, -- :: a -> (a,a) - swap, -- :: (a,b) -> (b,a) + dup, -- :: a -> (a,a) + swap, -- :: (a,b) -> (b,a) -- Maps over lists of pairs - mapFst, -- :: (a -> b) -> [(a,c)] -> [(b,c)] - mapSnd, -- :: (a -> b) -> [(c,a)] -> [(c,b)] + mapFst, -- :: (a -> b) -> [(a,c)] -> [(b,c)] + mapSnd, -- :: (a -> b) -> [(c,a)] -> [(c,b)] -- Generalized tuple selectors sel3_1, sel3_2, sel3_3, @@ -36,9 +36,9 @@ sel5_1, sel5_2, sel5_3, sel5_4, sel5_5, -- Floating point utilities - fDiv, -- :: (RealFrac a, Integral b) => a -> a -> b - fMod, -- :: RealFrac a => a -> a -> a - fDivMod -- :: (RealFrac a, Integral b) => a -> a -> (b, a) + fDiv, -- :: (RealFrac a, Integral b) => a -> a -> b + fMod, -- :: RealFrac a => a -> a -> a + fDivMod -- :: (RealFrac a, Integral b) => a -> a -> (b, a) ) where infixl 9 # @@ -73,12 +73,10 @@ ------------------------------------------------------------------------------ mapFst :: (a -> b) -> [(a,c)] -> [(b,c)] -mapFst _ [] = [] -mapFst f ((x, y) : xys) = (f x, y) : mapFst f xys +mapFst f = map (\(x,y) -> (f x, y)) mapSnd :: (a -> b) -> [(c,a)] -> [(c,b)] -mapSnd _ [] = [] -mapSnd f ((x, y) : xys) = (x, f y) : mapSnd f xys +mapSnd f = map (\(x,y) -> (x, f y)) ------------------------------------------------------------------------------ diff --git a/src/FRP/Yampa/Point2.hs b/src/FRP/Yampa/Point2.hs --- a/src/FRP/Yampa/Point2.hs +++ b/src/FRP/Yampa/Point2.hs @@ -19,9 +19,9 @@ -- module AFRPVectorSpace, -- module AFRPAffineSpace, -- module AFRPVector2, - Point2(..), -- Non-abstract, instance of AffineSpace - point2X, -- :: RealFloat a => Point2 a -> a - point2Y -- :: RealFloat a => Point2 a -> a + Point2(..), -- Non-abstract, instance of AffineSpace + point2X, -- :: RealFloat a => Point2 a -> a + point2Y -- :: RealFloat a => Point2 a -> a ) where import FRP.Yampa.VectorSpace () diff --git a/src/FRP/Yampa/Point3.hs b/src/FRP/Yampa/Point3.hs --- a/src/FRP/Yampa/Point3.hs +++ b/src/FRP/Yampa/Point3.hs @@ -17,10 +17,10 @@ -- module AFRPVectorSpace, -- module AFRPAffineSpace, -- module AFRPVector3, - Point3(..), -- Non-abstract, instance of AffineSpace - point3X, -- :: RealFloat a => Point3 a -> a - point3Y, -- :: RealFloat a => Point3 a -> a - point3Z -- :: RealFloat a => Point3 a -> a + Point3(..), -- Non-abstract, instance of AffineSpace + point3X, -- :: RealFloat a => Point3 a -> a + point3Y, -- :: RealFloat a => Point3 a -> a + point3Z -- :: RealFloat a => Point3 a -> a ) where import FRP.Yampa.VectorSpace () @@ -52,13 +52,13 @@ origin = Point3 0 0 0 (Point3 x y z) .+^ v = - Point3 (x + vector3X v) (y + vector3Y v) (z + vector3Z v) + Point3 (x + vector3X v) (y + vector3Y v) (z + vector3Z v) (Point3 x y z) .-^ v = - Point3 (x - vector3X v) (y - vector3Y v) (z - vector3Z v) + Point3 (x - vector3X v) (y - vector3Y v) (z - vector3Z v) (Point3 x1 y1 z1) .-. (Point3 x2 y2 z2) = - vector3 (x1 - x2) (y1 - y2) (z1 - z2) + vector3 (x1 - x2) (y1 - y2) (z1 - z2) ------------------------------------------------------------------------------ diff --git a/src/FRP/Yampa/Task.hs b/src/FRP/Yampa/Task.hs --- a/src/FRP/Yampa/Task.hs +++ b/src/FRP/Yampa/Task.hs @@ -1,4 +1,4 @@ -{-# LANGUAGE Rank2Types #-} +{-# LANGUAGE CPP, Rank2Types #-} ----------------------------------------------------------------------------------------- -- | -- Module : FRP.Yampa.Task @@ -15,21 +15,26 @@ module FRP.Yampa.Task ( Task, - mkTask, -- :: SF a (b, Event c) -> Task a b c - runTask, -- :: Task a b c -> SF a (Either b c) -- Might change. - runTask_, -- :: Task a b c -> SF a b - taskToSF, -- :: Task a b c -> SF a (b, Event c) -- Might change. - constT, -- :: b -> Task a b c - sleepT, -- :: Time -> b -> Task a b () - snapT, -- :: Task a b a - timeOut, -- :: Task a b c -> Time -> Task a b (Maybe c) - abortWhen, -- :: Task a b c -> SF a (Event d) -> Task a b (Either c d) + mkTask, -- :: SF a (b, Event c) -> Task a b c + runTask, -- :: Task a b c -> SF a (Either b c) -- Might change. + runTask_, -- :: Task a b c -> SF a b + taskToSF, -- :: Task a b c -> SF a (b, Event c) -- Might change. + constT, -- :: b -> Task a b c + sleepT, -- :: Time -> b -> Task a b () + snapT, -- :: Task a b a + timeOut, -- :: Task a b c -> Time -> Task a b (Maybe c) + abortWhen, -- :: Task a b c -> SF a (Event d) -> Task a b (Either c d) repeatUntil,-- :: Monad m => m a -> (a -> Bool) -> m a - for, -- :: Monad m => a -> (a -> a) -> (a -> Bool) -> m b -> m () - forAll, -- :: Monad m => [a] -> (a -> m b) -> m () - forEver -- :: Monad m => m a -> m b + for, -- :: Monad m => a -> (a -> a) -> (a -> Bool) -> m b -> m () + forAll, -- :: Monad m => [a] -> (a -> m b) -> m () + forEver -- :: Monad m => m a -> m b ) where +import Control.Monad (when, forM_) +#if __GLASGOW_HASKELL__ < 710 +import Control.Applicative (Applicative(..)) +#endif + import FRP.Yampa import FRP.Yampa.Utilities (snap) import FRP.Yampa.Diagnostics @@ -62,7 +67,7 @@ -- running. Once the task has terminated, the output goes constant with -- the value Right x, where x is the value of the terminating event. runTask :: Task a b c -> SF a (Either b c) -runTask tk = (unTask tk) (\c -> constant (Right c)) +runTask tk = (unTask tk) (constant . Right) -- Runs a task. The output becomes undefined once the underlying task has @@ -78,20 +83,27 @@ -- Law: mkTask (taskToSF task) = task (but not (quite) vice versa.) taskToSF :: Task a b c -> SF a (b, Event c) taskToSF tk = runTask tk - >>> (arr (either id ((usrErr "AFRPTask" "runTask_" - "Task terminated!"))) - &&& edgeBy isEdge (Left undefined)) + >>> (arr (either id (usrErr "AFRPTask" "runTask_" + "Task terminated!")) + &&& edgeBy isEdge (Left undefined)) where isEdge (Left _) (Left _) = Nothing - isEdge (Left _) (Right c) = Just c - isEdge (Right _) (Right _) = Nothing - isEdge (Right _) (Left _) = Nothing + isEdge (Left _) (Right c) = Just c + isEdge (Right _) (Right _) = Nothing + isEdge (Right _) (Left _) = Nothing ------------------------------------------------------------------------------ --- Monad instance +-- Functor, Applicative, and Monad instances ------------------------------------------------------------------------------ +instance Functor (Task a b) where + fmap f tk = Task (\k -> unTask tk (k . f)) + +instance Applicative (Task a b) where + pure x = Task (\k -> k x) + f <*> v = Task (\k -> (unTask f) (\c -> unTask v (k . c))) + instance Monad (Task a b) where tk >>= f = Task (\k -> (unTask tk) (\c -> unTask (f c) k)) return x = Task (\k -> k x) @@ -162,7 +174,7 @@ tk `timeOut` t = mkTask ((taskToSF tk &&& after t ()) >>> arr aux) where aux ((b, ec), et) = (b, (lMerge (fmap Just ec) - (fmap (const Nothing) et))) + (fmap (const Nothing) et))) -- Run a "guarding" event source (SF a (Event b)) in parallel with a @@ -193,12 +205,12 @@ -- C-style for-loop. -- Example: for 0 (+1) (>=10) ... for :: Monad m => a -> (a -> a) -> (a -> Bool) -> m b -> m () -for i f p m = if p i then m >> for (f i) f p m else return () +for i f p m = when (p i) $ m >> for (f i) f p m -- Perform the monadic operation for each element in the list. forAll :: Monad m => [a] -> (a -> m b) -> m () -forAll = flip mapM_ +forAll = forM_ -- Repeat m for ever. diff --git a/src/FRP/Yampa/Utilities.hs b/src/FRP/Yampa/Utilities.hs --- a/src/FRP/Yampa/Utilities.hs +++ b/src/FRP/Yampa/Utilities.hs @@ -37,60 +37,60 @@ module FRP.Yampa.Utilities ( -- Now defined in Control.Arrow -- General arrow utilities - (^>>), -- :: Arrow a => (b -> c) -> a c d -> a b d - (>>^), -- :: Arrow a => a b c -> (c -> d) -> a b d - (^<<), -- :: Arrow a => (c -> d) -> a b c -> a b d - (<<^), -- :: Arrow a => a c d -> (b -> c) -> a b d + (^>>), -- :: Arrow a => (b -> c) -> a c d -> a b d + (>>^), -- :: Arrow a => a b c -> (c -> d) -> a b d + (^<<), -- :: Arrow a => (c -> d) -> a b c -> a b d + (<<^), -- :: Arrow a => a c d -> (b -> c) -> a b d -- Liftings - arr2, -- :: Arrow a => (b->c->d) -> a (b,c) d - arr3, -- :: Arrow a => (b->c->d->e) -> a (b,c,d) e - arr4, -- :: Arrow a => (b->c->d->e->f) -> a (b,c,d,e) f - arr5, -- :: Arrow a => (b->c->d->e->f->g) -> a (b,c,d,e,f) g - lift0, -- :: Arrow a => c -> a b c - lift1, -- :: Arrow a => (c->d) -> (a b c->a b d) - lift2, -- :: Arrow a => (c->d->e) -> (a b c->a b d->a b e) - lift3, -- :: Arrow a => (c->d->e->f) -> (a b c-> ... ->a b f) - lift4, -- :: Arrow a => (c->d->e->f->g) -> (a b c->...->a b g) - lift5, -- :: Arrow a => (c->d->e->f->g->h)->(a b c->...a b h) + arr2, -- :: Arrow a => (b->c->d) -> a (b,c) d + arr3, -- :: Arrow a => (b->c->d->e) -> a (b,c,d) e + arr4, -- :: Arrow a => (b->c->d->e->f) -> a (b,c,d,e) f + arr5, -- :: Arrow a => (b->c->d->e->f->g) -> a (b,c,d,e,f) g + lift0, -- :: Arrow a => c -> a b c + lift1, -- :: Arrow a => (c->d) -> (a b c->a b d) + lift2, -- :: Arrow a => (c->d->e) -> (a b c->a b d->a b e) + lift3, -- :: Arrow a => (c->d->e->f) -> (a b c-> ... ->a b f) + lift4, -- :: Arrow a => (c->d->e->f->g) -> (a b c->...->a b g) + lift5, -- :: Arrow a => (c->d->e->f->g->h)->(a b c->...a b h) -- Event sources - snap, -- :: SF a (Event a) - snapAfter, -- :: Time -> SF a (Event a) - sample, -- :: Time -> SF a (Event a) - recur, -- :: SF a (Event b) -> SF a (Event b) + snap, -- :: SF a (Event a) + snapAfter, -- :: Time -> SF a (Event a) + sample, -- :: Time -> SF a (Event a) + recur, -- :: SF a (Event b) -> SF a (Event b) andThen, -- :: SF a (Event b)->SF a (Event b)->SF a (Event b) - sampleWindow, -- :: Int -> Time -> SF a (Event [a]) + sampleWindow, -- :: Int -> Time -> SF a (Event [a]) -- Parallel composition/switchers with "zip" routing - parZ, -- [SF a b] -> SF [a] [b] - pSwitchZ, -- [SF a b] -> SF ([a],[b]) (Event c) - -- -> ([SF a b] -> c -> SF [a] [b]) -> SF [a] [b] - dpSwitchZ, -- [SF a b] -> SF ([a],[b]) (Event c) - -- -> ([SF a b] -> c ->SF [a] [b]) -> SF [a] [b] - rpSwitchZ, -- [SF a b] -> SF ([a], Event ([SF a b]->[SF a b])) [b] - drpSwitchZ, -- [SF a b] -> SF ([a], Event ([SF a b]->[SF a b])) [b] + parZ, -- [SF a b] -> SF [a] [b] + pSwitchZ, -- [SF a b] -> SF ([a],[b]) (Event c) + -- -> ([SF a b] -> c -> SF [a] [b]) -> SF [a] [b] + dpSwitchZ, -- [SF a b] -> SF ([a],[b]) (Event c) + -- -> ([SF a b] -> c ->SF [a] [b]) -> SF [a] [b] + rpSwitchZ, -- [SF a b] -> SF ([a], Event ([SF a b]->[SF a b])) [b] + drpSwitchZ, -- [SF a b] -> SF ([a], Event ([SF a b]->[SF a b])) [b] -- Guards and automata-oriented combinators - provided, -- :: (a -> Bool) -> SF a b -> SF a b -> SF a b + provided, -- :: (a -> Bool) -> SF a b -> SF a b -> SF a b -- Wave-form generation - old_dHold, -- :: a -> SF (Event a) a - dTrackAndHold, -- :: a -> SF (Maybe a) a + old_dHold, -- :: a -> SF (Event a) a + dTrackAndHold, -- :: a -> SF (Maybe a) a -- Accumulators - old_accumHold, -- :: a -> SF (Event (a -> a)) a - old_dAccumHold, -- :: a -> SF (Event (a -> a)) a - old_accumHoldBy, -- :: (b -> a -> b) -> b -> SF (Event a) b - old_dAccumHoldBy, -- :: (b -> a -> b) -> b -> SF (Event a) b - count, -- :: Integral b => SF (Event a) (Event b) + old_accumHold, -- :: a -> SF (Event (a -> a)) a + old_dAccumHold, -- :: a -> SF (Event (a -> a)) a + old_accumHoldBy, -- :: (b -> a -> b) -> b -> SF (Event a) b + old_dAccumHoldBy, -- :: (b -> a -> b) -> b -> SF (Event a) b + count, -- :: Integral b => SF (Event a) (Event b) -- Delays - fby, -- :: b -> SF a b -> SF a b, infixr 0 + fby, -- :: b -> SF a b -> SF a b, infixr 0 -- Integrals - impulseIntegral, -- :: VectorSpace a k => SF (a, Event a) a - old_impulseIntegral -- :: VectorSpace a k => SF (a, Event a) a + impulseIntegral, -- :: VectorSpace a k => SF (a, Event a) a + old_impulseIntegral -- :: VectorSpace a k => SF (a, Event a) a ) where import FRP.Yampa.Diagnostics @@ -186,9 +186,9 @@ -- that time. snapAfter :: Time -> SF a (Event a) snapAfter t_ev = switch (never - &&& (identity - &&& after t_ev () >>^ \(a, e) -> e `tag` a)) - now + &&& (identity + &&& after t_ev () >>^ \(a, e) -> e `tag` a)) + now -- Sample a signal at regular intervals. @@ -234,7 +234,7 @@ where updateWindow w as = drop (max (length w' - wl) 0) w' where - w' = w ++ as + w' = w ++ as ------------------------------------------------------------------------------ @@ -244,16 +244,16 @@ safeZip :: String -> [a] -> [b] -> [(a,b)] safeZip fn as bs = safeZip' as bs where - safeZip' _ [] = [] - safeZip' as (b:bs) = (head' as, b) : safeZip' (tail' as) bs + safeZip' _ [] = [] + safeZip' as (b:bs) = (head' as, b) : safeZip' (tail' as) bs - head' [] = err - head' (a:_) = a + head' [] = err + head' (a:_) = a - tail' [] = err - tail' (_:as) = as + tail' [] = err + tail' (_:as) = as - err = usrErr "AFRPUtilities" fn "Input list too short." + err = usrErr "AFRPUtilities" fn "Input list too short." parZ :: [SF a b] -> SF [a] [b] @@ -288,7 +288,7 @@ switch (constant undefined &&& snap) $ \a0 -> if p a0 then stt else stf where - stt = switch (sft &&& (not . p ^>> edge)) (const stf) + stt = switch (sft &&& (not . p ^>> edge)) (const stf) stf = switch (sff &&& (p ^>> edge)) (const stt) @@ -301,7 +301,7 @@ old_dHold :: a -> SF (Event a) a old_dHold a0 = dSwitch (constant a0 &&& identity) dHold' where - dHold' a = dSwitch (constant a &&& notYet) dHold' + dHold' a = dSwitch (constant a &&& notYet) dHold' dTrackAndHold :: a -> SF (Maybe a) a diff --git a/src/FRP/Yampa/Vector2.hs b/src/FRP/Yampa/Vector2.hs --- a/src/FRP/Yampa/Vector2.hs +++ b/src/FRP/Yampa/Vector2.hs @@ -16,16 +16,16 @@ module FRP.Yampa.Vector2 ( -- module AFRPVectorSpace, - Vector2, -- Abstract, instance of VectorSpace - vector2, -- :: RealFloat a => a -> a -> Vector2 a - vector2X, -- :: RealFloat a => Vector2 a -> a - vector2Y, -- :: RealFloat a => Vector2 a -> a - vector2XY, -- :: RealFloat a => Vector2 a -> (a, a) - vector2Polar, -- :: RealFloat a => a -> a -> Vector2 a - vector2Rho, -- :: RealFloat a => Vector2 a -> a - vector2Theta, -- :: RealFloat a => Vector2 a -> a - vector2RhoTheta, -- :: RealFloat a => Vector2 a -> (a, a) - vector2Rotate -- :: RealFloat a => a -> Vector2 a -> Vector2 a + Vector2, -- Abstract, instance of VectorSpace + vector2, -- :: RealFloat a => a -> a -> Vector2 a + vector2X, -- :: RealFloat a => Vector2 a -> a + vector2Y, -- :: RealFloat a => Vector2 a -> a + vector2XY, -- :: RealFloat a => Vector2 a -> (a, a) + vector2Polar, -- :: RealFloat a => a -> a -> Vector2 a + vector2Rho, -- :: RealFloat a => Vector2 a -> a + vector2Theta, -- :: RealFloat a => Vector2 a -> a + vector2RhoTheta, -- :: RealFloat a => Vector2 a -> (a, a) + vector2Rotate -- :: RealFloat a => a -> Vector2 a -> Vector2 a ) where import FRP.Yampa.VectorSpace diff --git a/src/FRP/Yampa/Vector3.hs b/src/FRP/Yampa/Vector3.hs --- a/src/FRP/Yampa/Vector3.hs +++ b/src/FRP/Yampa/Vector3.hs @@ -16,18 +16,18 @@ module FRP.Yampa.Vector3 ( -- module AFRPVectorSpace, - Vector3, -- Abstract, instance of VectorSpace - vector3, -- :: RealFloat a => a -> a -> a -> Vector3 a - vector3X, -- :: RealFloat a => Vector3 a -> a - vector3Y, -- :: RealFloat a => Vector3 a -> a - vector3Z, -- :: RealFloat a => Vector3 a -> a - vector3XYZ, -- :: RealFloat a => Vector3 a -> (a, a, a) - vector3Spherical, -- :: RealFloat a => a -> a -> a -> Vector3 a - vector3Rho, -- :: RealFloat a => Vector3 a -> a - vector3Theta, -- :: RealFloat a => Vector3 a -> a - vector3Phi, -- :: RealFloat a => Vector3 a -> a - vector3RhoThetaPhi, -- :: RealFloat a => Vector3 a -> (a, a, a) - vector3Rotate -- :: RealFloat a => a -> a -> Vector3 a -> Vector3 a + Vector3, -- Abstract, instance of VectorSpace + vector3, -- :: RealFloat a => a -> a -> a -> Vector3 a + vector3X, -- :: RealFloat a => Vector3 a -> a + vector3Y, -- :: RealFloat a => Vector3 a -> a + vector3Z, -- :: RealFloat a => Vector3 a -> a + vector3XYZ, -- :: RealFloat a => Vector3 a -> (a, a, a) + vector3Spherical, -- :: RealFloat a => a -> a -> a -> Vector3 a + vector3Rho, -- :: RealFloat a => Vector3 a -> a + vector3Theta, -- :: RealFloat a => Vector3 a -> a + vector3Phi, -- :: RealFloat a => Vector3 a -> a + vector3RhoThetaPhi, -- :: RealFloat a => Vector3 a -> (a, a, a) + vector3Rotate -- :: RealFloat a => a -> a -> Vector3 a -> Vector3 a ) where import FRP.Yampa.VectorSpace @@ -63,7 +63,7 @@ vector3Spherical rho theta phi = Vector3 (rhoSinPhi * cos theta) (rhoSinPhi * sin theta) (rho * cos phi) where - rhoSinPhi = rho * sin phi + rhoSinPhi = rho * sin phi vector3Rho :: RealFloat a => Vector3 a -> a vector3Rho (Vector3 x y z) = sqrt (x * x + y * y + z * z) @@ -79,7 +79,7 @@ where rho = sqrt (x * x + y * y + z * z) theta = atan2 y x - phi = acos (z / rho) + phi = acos (z / rho) ------------------------------------------------------------------------------ @@ -109,8 +109,8 @@ vector3Rotate :: RealFloat a => a -> a -> Vector3 a -> Vector3 a vector3Rotate theta' phi' v = vector3Spherical (vector3Rho v) - (vector3Theta v + theta') - (vector3Phi v + phi') + (vector3Theta v + theta') + (vector3Phi v + phi') ------------------------------------------------------------------------------ diff --git a/src/FRP/Yampa/VectorSpace.hs b/src/FRP/Yampa/VectorSpace.hs --- a/src/FRP/Yampa/VectorSpace.hs +++ b/src/FRP/Yampa/VectorSpace.hs @@ -37,8 +37,8 @@ (^+^) :: v -> v -> v (^-^) :: v -> v -> v dot :: v -> v -> a - norm :: v -> a - normalize :: v -> v + norm :: v -> a + normalize :: v -> v v ^/ a = (1/a) *^ v @@ -50,7 +50,7 @@ normalize v = if nv /= 0 then v ^/ nv else error "normalize: zero vector" where - nv = norm v + nv = norm v ------------------------------------------------------------------------------ -- Vector space instances for Float and Double diff --git a/tests/AFRPTestsCommon.hs b/tests/AFRPTestsCommon.hs --- a/tests/AFRPTestsCommon.hs +++ b/tests/AFRPTestsCommon.hs @@ -17,7 +17,6 @@ import Data.IORef (newIORef, writeIORef, readIORef) import FRP.Yampa -import FRP.Yampa.Internals (Event(NoEvent, Event)) ------------------------------------------------------------------------------ -- Rough equality with instances @@ -70,6 +69,7 @@ && x2 ~= y2 && x3 ~= y3 && x4 ~= y4 + && x5 ~= y5 instance REq a => REq (Maybe a) where Nothing ~= Nothing = True @@ -105,7 +105,7 @@ where -- The initial 0.0 is just for result compatibility with an older -- version. - input = 0.0 : [ fromIntegral (b `div` freq) | b <- [1..] ] + input = 0.0 : [ fromIntegral (b `div` freq) | b <- [1..] :: [Int] ] freq = 5 @@ -148,18 +148,20 @@ return (0.25, Just input') actuate _ output = do writeIORef outputr output - input <- readIORef inputr - count <- readIORef countr + _input <- readIORef inputr + count <- readIORef countr return (count >= n) reactimate init sense actuate sf - output <- readIORef outputr - return output + -- return output + readIORef outputr ------------------------------------------------------------------------------ -- Some utilities used for testing laws ------------------------------------------------------------------------------ -fun_prod f g = \(x,y) -> (f x, g y) +assoc :: ((a,b),c) -> (a,(b,c)) assoc ((a,b),c) = (a,(b,c)) -assoc_inv (a,(b,c)) = ((a,b),c) + +assocInv :: (a,(b,c)) -> ((a,b),c) +assocInv (a,(b,c)) = ((a,b),c) diff --git a/tests/AFRPTestsLaws.hs b/tests/AFRPTestsLaws.hs --- a/tests/AFRPTestsLaws.hs +++ b/tests/AFRPTestsLaws.hs @@ -49,7 +49,7 @@ laws_t4_lhs :: [(Double, Double)] laws_t4_lhs = testSF1 (arr dup >>> first (arr (*2.5))) laws_t4_rhs :: [(Double, Double)] -laws_t4_rhs = testSF1 (arr dup >>> arr (fun_prod (*2.5) id)) +laws_t4_rhs = testSF1 (arr dup >>> arr ((*2.5) *** id)) laws_t5_lhs :: [(Double, Double)] laws_t5_lhs = testSF1 (arr dup >>> (first (integral >>> arr (+3.0)))) @@ -57,9 +57,9 @@ laws_t5_rhs = testSF1 (arr dup >>> (first integral >>> first (arr (+3.0)))) laws_t6_lhs :: [(Double, Double)] -laws_t6_lhs = testSF1 (arr dup >>> (first integral>>>arr (fun_prod id (+3.0)))) +laws_t6_lhs = testSF1 (arr dup >>> (first integral >>> arr (id *** (+3.0)))) laws_t6_rhs :: [(Double, Double)] -laws_t6_rhs = testSF1 (arr dup >>> (arr (fun_prod id (+3.0))>>>first integral)) +laws_t6_rhs = testSF1 (arr dup >>> (arr (id *** (+3.0)) >>> first integral)) laws_t7_lhs :: [Double] laws_t7_lhs = testSF1 (arr dup >>> (first integral >>> arr fst)) diff --git a/tests/AFRPTestsLoopLaws.hs b/tests/AFRPTestsLoopLaws.hs --- a/tests/AFRPTestsLoopLaws.hs +++ b/tests/AFRPTestsLoopLaws.hs @@ -56,7 +56,7 @@ -- Used to work with only signature t2_f :: Fractional a -> SF a a looplaws_t2_f :: SF (Double, Double) (Double, Double) looplaws_t2_f = integral -looplaws_t2_k = fun_prod id (+42.0) +looplaws_t2_k = id *** (+42.0) looplaws_t2_lhs :: [Double] looplaws_t2_lhs = testSF1 (loop (looplaws_t2_f >>> arr looplaws_t2_k)) looplaws_t2_rhs :: [Double] @@ -74,7 +74,7 @@ looplaws_t3_lhs :: [Double] looplaws_t3_lhs = testSF1 (loop (loop looplaws_t3_f)) looplaws_t3_rhs :: [Double] -looplaws_t3_rhs = testSF1 (loop (arr assoc_inv >>> looplaws_t3_f >>>arr assoc)) +looplaws_t3_rhs = testSF1 (loop (arr assocInv >>> looplaws_t3_f >>> arr assoc)) -- Superposing @@ -84,7 +84,7 @@ looplaws_t4_rhs :: [(Double, Double)] looplaws_t4_rhs = testSF1 (arr dup >>> (loop (arr assoc >>> second looplaws_t4_f - >>> arr assoc_inv))) + >>> arr assocInv))) -- Extension