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cuboid 0.13 → 0.14

raw patch · 18 files changed

+6/−5149 lines, 18 filesdep +Yampadep −random

Dependencies added: Yampa

Dependencies removed: random

Files

− FRP/Yampa.hs 
@@ -1,3314 +0,0 @@-{-# LANGUAGE GADTs, Rank2Types, CPP #-}--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  non-portable (GHC extensions)------ New version using GADTs.------ ToDo:------ * Specialize def. of repeatedly. Could have an impact on invaders.------ * New defs for accs using SFAcc------ * Make sure opt worked: e.g.------   >     repeatedly >>> count >>> arr (fmap sqr)------ * Introduce SFAccHld.------ * See if possible to unify AccHld wity Acc??? They are so close.------ * Introduce SScan. BUT KEEP IN MIND: Most if not all opts would---   have been possible without GADTs???------ * Look into pairs. At least pairing of SScan ought to be interesting.------ * Would be nice if we could get rid of first & second with impunity---   thanks to Id optimizations. That's a clear win, with or without---   an explicit pair combinator.------ * delayEventCat is a bit complicated ...--------- Random ideas:------ * What if one used rules to optimize---   - (arr :: SF a ()) to (constant ())---   - (arr :: SF a a) to identity---   But inspection of invader source code seem to indicate that---   these are not very common cases at all.------ * It would be nice if it was possible to come up with opt. rules---   that are invariant of how signal function expressions are---   parenthesized. Right now, we have e.g.---       arr f >>> (constant c >>> sf)---   being optimized to---       cpAuxA1 f (cpAuxC1 c sf)---   whereas it clearly should be possible to optimize to just---       cpAuxC1 c sf---   What if we didn't use SF' but---      SFComp :: <tfun> -> SF' a b -> SF' b c -> SF' a c---   ???------ * The transition function would still be optimized in (pretty much)---   the current way, but it would still be possible to look "inside"---   composed signal functions for lost optimization opts.---   Seems to me this could be done without too much extra effort/no dupl.---   work.---   E.g. new cpAux, the general case:------ @---      cpAux sf1 sf2 = SFComp tf sf1 sf2---          where---              tf dt a = (cpAux sf1' sf2', c)---                  where---                      (sf1', b) = (sfTF' sf1) dt a---                      (sf2', c) = (sfTF' sf2) dt b--- @------ * The ONLY change was changing the constructor from SF' to SFComp and---   adding sf1 and sf2 to the constructor app.!------ * An optimized case:---     cpAuxC1 b sf1 sf2               = SFComp tf sf1 sf2---   So cpAuxC1 gets an extra arg, and we change the constructor.---   But how to exploit without writing 1000s of rules???---   Maybe define predicates on SFComp to see if the first or second---   sf are "interesting", and if so, make "reassociate" and make a---   recursive call? E.g. we're in the arr case, and the first sf is another---   arr, so we'd like to combine the two.------ * It would also be intersting, then, to know when to STOP playing this---   game, due to the overhead involved.------ * Why don't we have a "SWITCH" constructor that indicates that the---   structure will change, and thus that it is worthwile to keep---   looking for opt. opportunities, whereas a plain "SF'" would---   indicate that things NEVER are going to change, and thus we can just---   as well give up?--------------------------------------------------------------------------------------------module FRP.Yampa (--- Re-exported module, classes, and types-    module Control.Arrow,-    module FRP.Yampa.VectorSpace,-    RandomGen(..),-    Random(..),---- Reverse function composition and arrow plumbing aids-    ( # ),		-- :: (a -> b) -> (b -> c) -> (a -> c),	infixl 9-    dup,		-- :: a -> (a,a)-    swap,		-- :: (a,b) -> (b,a)---- Main types-    Time,	-- [s] Both for time w.r.t. some reference and intervals.-    --SF,		-- Signal Function.-    Event(..),	-- Events; conceptually similar to Maybe (but abstract).---- Temporray!-    SF(..), sfTF', SF'(..),---- 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---- For optimization-    arrPrim, arrEPrim,---- 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---- 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)---- 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 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)---- 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-    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-    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)---- Delays-    old_pre, old_iPre,-    pre,		-- :: SF a a-    iPre,		-- :: a -> SF a a---- Timed delays-    delay,		-- :: Time -> a -> SF a a---- 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---- 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---- 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---- 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)-    DTime,		-- [s] Sampling interval, always > 0.-    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)])--) 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.)--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.-{-# NOINLINE arrPrim #-}-arrPrim :: (a -> b) -> SF a b-arrPrim f = SF {sfTF = \a -> (sfArrG f, f a)}---{-# 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<X><Y> where  <X> and <Y> 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 <fixed point comp>-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<X><Y> where  <X> and <Y> 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<X><Y> where  <X> and <Y> 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-identity :: SF a a-identity = SF {sfTF = \a -> (sfId, a)}----- Identity: constant b = arr (const b)-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).-(-->) :: b -> SF a b -> SF a b-b0 --> (SF {sfTF = tf10}) = SF {sfTF = \a0 -> (fst (tf10 a0), b0)}----- Input initialization operator.-(>--) :: a -> SF a b -> SF a b-a0 >-- (SF {sfTF = tf10}) = SF {sfTF = \_ -> tf10 a0}----- Transform initial output value.-(-=>) :: (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.-(>=-) :: (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 -> b -> 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--}---- Or keep old def. for efficiency reasons?--- 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)----- 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)--}---- This version is not strict in the input event.-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.--- 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---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----- !!! 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 first event.-once :: SF (Event a) (Event a)-once = takeEvents 1----- Suppress all but 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.-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.--- Or "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.--- !!! 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.-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.--- !!! 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.--- !!! 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---------------------------------------------------------------------------------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.-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).-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---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---rpSwitchB :: Functor col =>-    col (SF a b) -> SF (a, Event (col (SF a b) -> col (SF a b))) (col b)-rpSwitchB = rpSwitch broadcast---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.--- rf .........	Routing function: determines the input to each signal function---		in the collection. IMPORTANT! The routing function MUST---		preserve the structure of the signal function collection.--- sfs0 .......	Signal function collection.--- Returns the spatial parallel composition of the supplied signal functions.--par :: Functor col =>-    (forall sf . (a -> col sf -> col (b, sf)))-    -> col (SF b c)-    -> 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)))-    -> col (SF b c)-    -> SF (a, col c) (Event d)-    -> (col (SF b c) -> d -> SF a (col c))-    -> 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.------ !!! Could be optimized on the event source being SFArr, SFArrE, SFArrEE.----dpSwitch :: 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)-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)--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---------------------------------------------------------------------------------old_accum :: a -> SF (Event (a -> a)) (Event a)-old_accum = accumBy (flip ($))--accum :: a -> SF (Event (a -> a)) (Event a)-accum a_init = epPrim f a_init NoEvent-    where-        f a g = (a', Event a', NoEvent)-            where-                a' = g a---accumHold :: a -> SF (Event (a -> a)) a-accumHold a_init = epPrim f a_init a_init-    where-        f a g = (a', a', a')-            where-                a' = g a--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--}---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)--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--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!--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)--}---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)--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.--- !!! 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_iPre :: a -> SF a a-old_iPre = (--> old_pre)------ !!! 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------------------------------------------------------------------------------------ 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------------------------------------------------------------------------------------ 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)----- This is extremely 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---------------------------------------------------------------------------------loopPre :: c -> SF (a,c) (b,c) -> SF a b-loopPre c_init sf = loop (second (iPre c_init) >>> sf)----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.--reactimate :: IO a-	      -> (Bool -> IO (DTime, Maybe a))-	      -> (Bool -> b -> IO Bool)-              -> SF a b-	      -> 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-  }	      --type ReactHandle a b = IORef (ReactState a b)---- initialize 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 })-     done <- 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.--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--deltaEncode :: Eq a => DTime -> [a] -> (a, [(DTime, Maybe a)])-deltaEncode _  []        = usrErr "AFRP" "deltaEncode" "Empty input list."-deltaEncode dt aas@(_:_) = deltaEncodeBy (==) dt aas---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.--- Suppose a subsystem is super sampled. Then some of the output--- samples will have to be dropped. If we are unlycky, the dropped--- samples could be occurring events that we'd rather not miss.--- This is a real problem.--- Similarly, when feeding input into a super-sampled system,--- we may need to extrapolate the input, assuming that it is--- constant. But if (part of) the input is an occurring event, we'd--- rather not duplicate that!!!--- This suggests that:---    * output samples should be merged through a user-supplied merge---      function.---    * input samples should be extrapolated if necessary through a---      user-supplied extrapolation function.------ Possible signature:------ resample :: Time -> (c -> [a]) -> SF a b -> ([b] -> d) -> SF c d------ But what do we do if the inner system runs more slowly than the--- outer one? Then we need to extrapolate the output from the--- inner system, and we have the same problem with events AGAIN!
− FRP/Yampa/AffineSpace.hs 
@@ -1,43 +0,0 @@-{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances #-}--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.AffineSpace--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  non-portable (GHC extensions)------ Affine space type relation.-----------------------------------------------------------------------------------------------module FRP.Yampa.AffineSpace where--import FRP.Yampa.VectorSpace----------------------------------------------------------------------------------- Affine Space type relation---------------------------------------------------------------------------------infix 6 .+^, .-^, .-.---- Maybe origin should not be a class method, even though an origin--- can be assocoated with any affine space.--- Maybe distance should not be a class method, in which case the constraint--- on the coefficient space (a) could be Fractional (i.e., a Field), which--- seems closer to the mathematical definition of affine space, provided--- the constraint on the coefficient space for VectorSpace is also Fractional.---- Minimal instance: origin, .+^, .^.-class (Floating a, VectorSpace v a) => AffineSpace p v a | p -> v, v -> a where-    origin   :: p-    (.+^)    :: p -> v -> p-    (.-^)    :: p -> v -> p-    (.-.)    :: p -> p -> v-    distance :: p -> p -> a--    p .-^ v = p .+^ (negateVector v)--    distance p1 p2 = norm (p1 .-. p2)
− FRP/Yampa/Diagnostics.hs 
@@ -1,21 +0,0 @@--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.Diagnostics--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  portable------ Standardized error-reporting for Yampa--------------------------------------------------------------------------------------------module FRP.Yampa.Diagnostics where--usrErr :: String -> String -> String -> a-usrErr mn fn msg = error (mn ++ "." ++ fn ++ ": " ++ msg)--intErr :: String -> String -> String -> a-intErr mn fn msg = error ("[internal error] " ++ mn ++ "." ++ fn ++ ": "-                          ++ msg)
− FRP/Yampa/Event.hs 
@@ -1,297 +0,0 @@--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.Event--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  portable------ Definition of Yampa Event type.------ Note on naming conventions used in this module.------ Names here might have to be rethought. It's really a bit messy.--- In general, the aim has been short and convenient names (like 'tag',--- 'attach', 'lMerge') and thus we have tried to stay away from suffixing/--- prefixing conventions. E.g. 'Event' as a common suffix would be very--- verbose.------ However, part of the names come from a desire to stay close to similar--- functions for the Maybe type. e.g. 'event', 'fromEvent', 'isEvent'.--- In many cases, this use of 'Event' can could understood to refer to the--- constructor 'Event', not to the type name 'Event'. Thus this use of--- event should not be seen as a suffixing-with-type-name convention. But--- that is obviously not easy to see, and, more over, interpreting 'Event'--- as the name of the type might make equally good or better sense. E.g.--- 'fromEvent' can also be seen as a function taking an event signal,--- which is a partial function on time, to a normal signal. The latter is--- then undefined when the source event function is undefined.------ In other cases, it has been necessary to somehow stay out of the way of--- names used by the prelude or other commonly imported modules/modules--- which could be expected to be used heavily in Yampa code. In those cases--- a suffix 'E' have been added. Examples are 'filterE' (exists in Prelude)--- and 'joinE' (exists in Monad). Maybe the suffix isn't necessary in the--- last case.------ Some functions (actually only one currently, 'mapFilterE') have got an 'E'--- suffix just because they're closely related (by name or semantics) to one--- which already has an 'E' suffix. Another candidate would be 'splitE' to--- complement 'joinE'. But events carrying pairs could obviously have other--- sources than a 'joinE', so currently it is called 'split'.------ 2003-05-19: Actually, have now changed to 'splitE' to avoid a clash--- with the method 'split' in the class RandomGen.------ 2003-05-19: What about 'gate'? Stands out compared to e.g. 'filterE'.------ Currently the 'E' suffix is considered an exception. Maybe we should use--- completely different names to avoid the 'E' suffix. If the functions--- are not used that often, 'Event' might be approriate. Alternatively the--- suffix 'E' should be adopted globaly (except if the name already contains--- 'event' in some form?).------ Arguably, having both a type 'Event' and a constructor 'Event' is confusing--- since there are more than one constructor. But the name 'Event' for the--- constructor is quite apt. It's really the type name that is wrong. But--- no one has found a better name, and changing it would be a really major--- undertaking. Yes, the constructor 'Event' is not exported, but we still--- need to talk conceptually about them. On the other hand, if we consider--- Event-signals as partial functions on time, maybe it isn't so confusing:--- they just don't have a value between events, so 'NoEvent' does not really--- exist conceptually.------ ToDo:--- - Either: reveal NoEvent and Event---   or:     introcuce 'event = Event', call what's now 'event' 'fromEvent',---           and call what's now called 'fromEvent' something else, like---           'unsafeFromEvent'??? Better, dump it! After all, using current---	     names, 'fromEvent = event undefined'!--------------------------------------------------------------------------------------------module FRP.Yampa.Event where--import FRP.Yampa.Diagnostics-import FRP.Yampa.Forceable---infixl 8 `tag`, `attach`, `gate`-infixl 7 `joinE`-infixl 6 `lMerge`, `rMerge`, `merge`------------------------------------------------------------------------------------ The Event type----------------------------------------------------------------------------------- The type Event represents a single possible event occurrence.--- It is isomorphic to Maybe, but its constructors are not exposed outside--- the AFRP implementation.--- There could possibly be further constructors, but note that the NeverEvent---- idea does not work, at least not in the current AFRP implementation.--- Also note that it unfortunately is possible to partially break the--- abstractions through judicious use of e.g. snap and switching.--data Event a = NoEvent-	     | Event a---             deriving Show----- Make the NoEvent constructor available. Useful e.g. for initialization,--- ((-->) & friends), and it's easily available anyway (e.g. mergeEvents []).-noEvent :: Event a-noEvent = NoEvent----- Suppress any event in the first component of a pair.-noEventFst :: (Event a, b) -> (Event c, b)-noEventFst (_, b) = (NoEvent, b)----- Suppress any event in the second component of a pair.-noEventSnd :: (a, Event b) -> (a, Event c)-noEventSnd (a, _) = (a, NoEvent)------------------------------------------------------------------------------------ Eq instance----------------------------------------------------------------------------------- Right now, we could derive this instance. But that could possibly change.--instance Eq a => Eq (Event a) where-    NoEvent   == NoEvent   = True-    (Event x) == (Event y) = x == y-    _         == _         = False------------------------------------------------------------------------------------ Ord instance---------------------------------------------------------------------------------instance Ord a => Ord (Event a) where-    compare NoEvent   NoEvent   = EQ-    compare NoEvent   (Event _) = LT-    compare (Event _) NoEvent   = GT-    compare (Event x) (Event y) = compare x y------------------------------------------------------------------------------------ Functor instance---------------------------------------------------------------------------------instance Functor Event where-    fmap _ NoEvent   = NoEvent-    fmap f (Event a) = Event (f a)------------------------------------------------------------------------------------ Forceable instance---------------------------------------------------------------------------------instance Forceable a => Forceable (Event a) where-    force ea@NoEvent   = ea-    force ea@(Event a) = force a `seq` ea------------------------------------------------------------------------------------ Internal utilities for event construction----------------------------------------------------------------------------------- These utilities are to be considered strictly internal to AFRP for the--- time being.--maybeToEvent :: Maybe a -> Event a-maybeToEvent Nothing  = NoEvent-maybeToEvent (Just a) = Event a------------------------------------------------------------------------------------ Utility functions similar to those available for Maybe----------------------------------------------------------------------------------- An event-based version of the maybe function.-event :: a -> (b -> a) -> Event b -> a-event a _ NoEvent   = a-event _ f (Event b) = f b--fromEvent :: Event a -> a-fromEvent (Event a) = a-fromEvent NoEvent   = usrErr "AFRP" "fromEvent" "Not an event."--isEvent :: Event a -> Bool-isEvent NoEvent   = False-isEvent (Event _) = True--isNoEvent :: Event a -> Bool-isNoEvent = not . isEvent------------------------------------------------------------------------------------ Event tagging----------------------------------------------------------------------------------- Tags an (occurring) event with a value ("replacing" the old value).-tag :: Event a -> b -> Event b-e `tag` b = fmap (const b) e--tagWith :: b -> Event a -> Event b-tagWith = flip tag---- Attaches an extra value to the value of an occurring event.-attach :: Event a -> b -> Event (a, b)-e `attach` b = fmap (\a -> (a, b)) e------------------------------------------------------------------------------------ Event merging (disjunction) and joining (conjunction)----------------------------------------------------------------------------------- !!! I think this is too complicated. rMerge can be obtained simply by--- !!! swapping the arguments. So the only time it is possibly of any--- !!! interest is for partial app. "merge" is inherently dangerous.--- !!! But this is NOT obvious from its type: it's type is just like--- !!! the others. This is the only example of such a def.--- !!! Finally: mergeEvents is left-biased, but this is not reflected in--- !!! its name.---- Left-biased event merge.-lMerge :: Event a -> Event a -> Event a-le `lMerge` re = event re Event le----- Right-biased event merge.-rMerge :: Event a -> Event a -> Event a-le `rMerge` re = event le Event re----- Unbiased event merge: simultaneous occurrence is an error.-merge :: Event a -> Event a -> Event a-merge = mergeBy (usrErr "AFRP" "merge" "Simultaneous event occurrence.")----- Event merge paramterezied on the conflict resolution function.-mergeBy :: (a -> a -> a) -> Event a -> Event a -> Event a-mergeBy _       NoEvent      NoEvent      = NoEvent-mergeBy _       le@(Event _) NoEvent      = le-mergeBy _       NoEvent      re@(Event _) = re-mergeBy resolve (Event l)    (Event r)    = Event (resolve l r)----- A generic event merge utility:-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)-mapMerge _  _  lrf (Event l) (Event r) = Event (lrf l r)---- Merging of a list of events; foremost event has priority.-mergeEvents :: [Event a] -> Event a-mergeEvents = foldr lMerge NoEvent----- Collects simultaneous event occurrences; no event if none.-catEvents :: [Event a] -> Event [a]-catEvents eas = case [ a | Event a <- eas ] of-		    [] -> NoEvent-		    as -> Event as----- Join (conjucntion) of two events.-joinE :: Event a -> Event b -> Event (a,b)-joinE NoEvent   _         = NoEvent-joinE _         NoEvent   = NoEvent-joinE (Event l) (Event r) = Event (l,r)----- Split event carrying pairs into two events.-splitE :: Event (a,b) -> (Event a, Event b)-splitE NoEvent       = (NoEvent, NoEvent)-splitE (Event (a,b)) = (Event a, Event b)------------------------------------------------------------------------------------ Event filtering----------------------------------------------------------------------------------- Filter out events that don't satisfy some predicate.-filterE :: (a -> Bool) -> Event a -> Event a-filterE p e@(Event a) = if (p a) then e else NoEvent-filterE _ NoEvent     = NoEvent----- Combined event mapping and filtering.-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----- Enable/disable event occurences based on an external condition.-gate :: Event a -> Bool -> Event a-_ `gate` False = NoEvent-e `gate` True  = e
− FRP/Yampa/Forceable.hs 
@@ -1,76 +0,0 @@--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.Forceable--- Copyright   :  (c) Zhanyong Wan, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  portable------ Hyperstrict evaluation.--------------------------------------------------------------------------------------------module FRP.Yampa.Forceable where---class Forceable a where-    force :: a -> a---instance Forceable Int where-  force = id---instance Forceable Integer where-  force = id---instance Forceable Double where-  force = id---instance Forceable Float where-  force = id---instance Forceable Bool where-  force = id---instance Forceable () where-  force = id---instance Forceable Char where-  force = id---instance (Forceable a, Forceable b) => Forceable (a, b) where-  force p@(a, b) = force a `seq` force b `seq` p---instance (Forceable a, Forceable b, Forceable c) => Forceable (a, b, c) where-  force p@(a, b, c) = force a `seq` force b `seq` force c `seq` p---instance (Forceable a, Forceable b, Forceable c, Forceable d) =>-         Forceable (a, b, c, d) where-  force p@(a, b, c, d) =-      force a `seq` force b `seq` force c `seq` force d `seq` p---instance (Forceable a, Forceable b, Forceable c, Forceable d, Forceable e) =>-         Forceable (a, b, c, d, e) where-  force p@(a, b, c, d, e) =-      force a `seq` force b `seq` force c `seq` force d `seq` force e `seq` p---instance (Forceable a) => Forceable [a] where-  force nil@[] = nil-  force xs@(x:xs') = force x `seq` force xs' `seq` xs---instance (Forceable a) => Forceable (Maybe a) where-  force mx@Nothing  = mx-  force mx@(Just x) = force x `seq` mx
− FRP/Yampa/Geometry.hs 
@@ -1,30 +0,0 @@--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.Geometry--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  non-portable (GHC extensions)------ Basic geometrical abstractions.--------------------------------------------------------------------------------------------module FRP.Yampa.Geometry (-    module FRP.Yampa.VectorSpace,-    module FRP.Yampa.AffineSpace,-    module FRP.Yampa.Vector2,-    module FRP.Yampa.Vector3,-    module FRP.Yampa.Point2,-    module FRP.Yampa.Point3-) where--import FRP.Yampa.VectorSpace-import FRP.Yampa.AffineSpace-import FRP.Yampa.Vector2-import FRP.Yampa.Vector3-import FRP.Yampa.Point2-import FRP.Yampa.Point3--
− FRP/Yampa/Internals.hs 
@@ -1,37 +0,0 @@--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.Internals--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  portable------ An interface giving access to some of the internal--- details of the Yampa implementation.------ This interface is indended to be used when the need arises to break--- abstraction barriers, e.g. for interfacing Yampa to the real world, for--- debugging purposes, or the like. Be aware that the internal details--- may change. Relying on this interface means that your code is not--- insulated against such changes.--------------------------------------------------------------------------------------------module FRP.Yampa.Internals (-    Event(..)		-- The event type, its constructors, and instances.-) where--import FRP.Yampa.Event------------------------------------------------------------------------------------ Extra Event instances---------------------------------------------------------------------------------instance Show a => Show (Event a) where-    showsPrec d NoEvent   = showString "NoEvent"-    showsPrec d (Event a) = showParen (d >= 10)-				      (showString "Event " . showsPrec 10 a)--
− FRP/Yampa/MergeableRecord.hs 
@@ -1,86 +0,0 @@--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.Miscellany--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  portable------ Framework for record merging.------ Idea:------ MergeableRecord is intended to be a super class for classes providing--- update operations on records. The ADT induced by such a set of operations--- can be considered a "mergeable record", which can be merged into larger--- mergeable records essentially by function composition. Finalization turns--- a mergeable record into a record.------ Typical use:------ Given------ >  data Foo = Foo {l1 :: T1, l2 :: T2}------ one define a mergeable record type (MR Foo) by the following instance:------ @---   instance MergeableRecord Foo where---       mrDefault = Foo {l1 = v1_dflt, l2 = v2_dflt}--- @------ Typically, one would also provide definitions for setting the fields,--- possibly (but not necessarily) overloaded:------ @---   instance HasL1 Foo where---       setL1 v = mrMake (\foo -> foo {l1 = v})--- @------ Now Foo records can be created as follows:------ @---   let foo1 = setL1 v1---   ...---   let foo2 = setL2 v2 ~+~ foo1---   ...---   let foo<N> = setL1 vN ~+~ foo<N-1>---   let fooFinal = mrFinalize foo<N>--- @--------------------------------------------------------------------------------------------module FRP.Yampa.MergeableRecord (-    MergeableRecord(..),-    MR,			-- Abstract-    mrMake,-    (~+~),-    mrMerge,-    mrFinalize-) where--class MergeableRecord a where-    mrDefault :: a----- Type constructor for mergeable records.-newtype MergeableRecord a => MR a = MR (a -> a)----- Construction of a mergeable record.-mrMake :: MergeableRecord a => (a -> a) -> MR a-mrMake f = (MR f)----- Merge two mergeable records. Left "overrides" in case of conflict.-(~+~) :: MergeableRecord a => MR a -> MR a -> MR a-(MR f1) ~+~ (MR f2) = MR (f1 . f2)--mrMerge :: MergeableRecord a => MR a -> MR a -> MR a-mrMerge = (~+~)----- Finalization: turn a mergeable record into a record.-mrFinalize :: MergeableRecord a => MR a -> a-mrFinalize (MR f) = f mrDefault
− FRP/Yampa/Miscellany.hs 
@@ -1,140 +0,0 @@--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.Miscellany--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  portable------ Collection of entities that really should be part--- of the Haskell 98 prelude or simply have no better--- home.------ !!! Reverse function composition should go.--- !!! Better to use '<<<' and '>>>' for, respectively,--- !!! function composition and reverse function composition.-----------------------------------------------------------------------------------------------module FRP.Yampa.Miscellany (--- Reverse function composition-    ( # ),	-- :: (a -> b) -> (b -> c) -> (a -> c),	infixl 9---- Arrow plumbing aids-    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)]---- Generalized tuple selectors-    sel3_1, sel3_2, sel3_3,-    sel4_1, sel4_2, sel4_3, sel4_4,-    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)-) where--infixl 9 #-infixl 7 `fDiv`, `fMod`------------------------------------------------------------------------------------ Reverse function composition----------------------------------------------------------------------------------- !!! Reverse function composition should go.--- !!! Better to use <<< and >>> for, respectively,--- !!! function composition and reverse function composition.--( # ) :: (a -> b) -> (b -> c) -> (a -> c)-f # g = g . f------------------------------------------------------------------------------------ Arrow plumbing aids---------------------------------------------------------------------------------dup :: a -> (a,a)-dup x = (x,x)--swap :: (a,b) -> (b,a)-swap ~(x,y) = (y,x)------------------------------------------------------------------------------------ Maps over lists of pairs---------------------------------------------------------------------------------mapFst :: (a -> b) -> [(a,c)] -> [(b,c)]-mapFst _ []             = []-mapFst f ((x, y) : xys) = (f x, y) : mapFst f xys--mapSnd :: (a -> b) -> [(c,a)] -> [(c,b)]-mapSnd _ []             = []-mapSnd f ((x, y) : xys) = (x, f y) : mapSnd f xys------------------------------------------------------------------------------------ Generalized tuple selectors----------------------------------------------------------------------------------- Triples-sel3_1 :: (a, b, c) -> a-sel3_1 (x,_,_) = x-sel3_2 :: (a, b, c) -> b-sel3_2 (_,x,_) = x-sel3_3 :: (a, b, c) -> c-sel3_3 (_,_,x) = x----- 4-tuples-sel4_1 :: (a, b, c, d) -> a-sel4_1 (x,_,_,_) = x-sel4_2 :: (a, b, c, d) -> b-sel4_2 (_,x,_,_) = x-sel4_3 :: (a, b, c, d) -> c-sel4_3 (_,_,x,_) = x-sel4_4 :: (a, b, c, d) -> d-sel4_4 (_,_,_,x) = x----- 5-tuples--sel5_1 :: (a, b, c, d, e) -> a-sel5_1 (x,_,_,_,_) = x-sel5_2 :: (a, b, c, d, e) -> b-sel5_2 (_,x,_,_,_) = x-sel5_3 :: (a, b, c, d, e) -> c-sel5_3 (_,_,x,_,_) = x-sel5_4 :: (a, b, c, d, e) -> d-sel5_4 (_,_,_,x,_) = x-sel5_5 :: (a, b, c, d, e) -> e-sel5_5 (_,_,_,_,x) = x------------------------------------------------------------------------------------ Floating point utilities----------------------------------------------------------------------------------- Floating-point div and modulo operators.--fDiv :: (RealFrac a) => a -> a -> Integer-fDiv x y = fst (fDivMod x y)---fMod :: (RealFrac a) => a -> a -> a-fMod x y = snd (fDivMod x y)---fDivMod :: (RealFrac a) => a -> a -> (Integer, a)-fDivMod x y = (q, r)-    where-        q = (floor (x/y))-        r = x - fromIntegral q * y
− FRP/Yampa/Point2.hs 
@@ -1,64 +0,0 @@-{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances #-}--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.Point2--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  non-portable (GHC extensions)------ 2D point abstraction (R^2).------ ToDo: Deriving Show, or provide dedicated show instance?-----------------------------------------------------------------------------------------------module FRP.Yampa.Point2 (-    -- module AFRPVectorSpace,-    -- module AFRPAffineSpace,-    -- module AFRPVector2,-    Point2(..),	-- Non-abstract, instance of AffineSpace-    point2X,	-- :: RealFloat a => Point2 a -> a-    point2Y	-- :: RealFloat a => Point2 a -> a-) where--import FRP.Yampa.VectorSpace ()-import FRP.Yampa.AffineSpace-import FRP.Yampa.Vector2-import FRP.Yampa.Forceable----------------------------------------------------------------------------------- 2D point, constructors and selectors.---------------------------------------------------------------------------------data RealFloat a => Point2 a = Point2 !a !a deriving (Eq, Show)--point2X :: RealFloat a => Point2 a -> a-point2X (Point2 x _) = x--point2Y :: RealFloat a => Point2 a -> a-point2Y (Point2 _ y) = y------------------------------------------------------------------------------------ Affine space instance---------------------------------------------------------------------------------instance RealFloat a => AffineSpace (Point2 a) (Vector2 a) a where-    origin = Point2 0 0--    (Point2 x y) .+^ v = Point2 (x + vector2X v) (y + vector2Y v)--    (Point2 x y) .-^ v = Point2 (x - vector2X v) (y - vector2Y v)--    (Point2 x1 y1) .-. (Point2 x2 y2) = vector2 (x1 - x2) (y1 - y2)------------------------------------------------------------------------------------ Forceable instance---------------------------------------------------------------------------------instance RealFloat a => Forceable (Point2 a) where-     force = id
− FRP/Yampa/Point3.hs 
@@ -1,69 +0,0 @@-{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances #-}--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.Point3--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  non-portable (GHC extensions)------ 3D point abstraction (R^3).-----------------------------------------------------------------------------------------------module FRP.Yampa.Point3 (-    -- 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-) where--import FRP.Yampa.VectorSpace ()-import FRP.Yampa.AffineSpace-import FRP.Yampa.Vector3-import FRP.Yampa.Forceable----------------------------------------------------------------------------------- 3D point, constructors and selectors.---------------------------------------------------------------------------------data RealFloat a => Point3 a = Point3 !a !a !a deriving Eq--point3X :: RealFloat a => Point3 a -> a-point3X (Point3 x _ _) = x--point3Y :: RealFloat a => Point3 a -> a-point3Y (Point3 _ y _) = y--point3Z :: RealFloat a => Point3 a -> a-point3Z (Point3 _ _ z) = z------------------------------------------------------------------------------------ Affine space instance---------------------------------------------------------------------------------instance RealFloat a => AffineSpace (Point3 a) (Vector3 a) a where-    origin = Point3 0 0 0--    (Point3 x y z) .+^ 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 x1 y1 z1) .-. (Point3 x2 y2 z2) =-	vector3 (x1 - x2) (y1 - y2) (z1 - z2)------------------------------------------------------------------------------------ Forceable instance---------------------------------------------------------------------------------instance RealFloat a => Forceable (Point3 a) where-     force = id
− FRP/Yampa/Task.hs 
@@ -1,221 +0,0 @@-{-# LANGUAGE Rank2Types #-}--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.Task--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  non-portable (GHC extensions)------ Task abstraction on top of signal transformers.-----------------------------------------------------------------------------------------------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)-    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-) where--import FRP.Yampa-import FRP.Yampa.Utilities (snap)-import FRP.Yampa.Diagnostics--infixl 0 `timeOut`, `abortWhen`, `repeatUntil`------------------------------------------------------------------------------------ The Task type----------------------------------------------------------------------------------- CPS-based representation allowing a termination to be detected.--- (Note the rank 2 polymorphic type!)--- The representation can be changed if necessary, but the Monad laws--- follow trivially in this case.-newtype Task a b c =-    Task (forall d . (c -> SF a (Either b d)) -> SF a (Either b d))---unTask :: Task a b c -> ((c -> SF a (Either b d)) -> SF a (Either b d))-unTask (Task f) = f---mkTask :: SF a (b, Event c) -> Task a b c-mkTask st = Task (switch (st >>> first (arr Left)))----- "Runs" a task (unusually bad name?). The output from the resulting--- signal transformer is tagged with Left while the underlying task is--- 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))----- Runs a task. The output becomes undefined once the underlying task has--- terminated. Convenient e.g. for tasks which are known not to terminate.-runTask_ :: Task a b c -> SF a b-runTask_ tk = runTask tk-              >>> arr (either id (usrErr "AFRPTask" "runTask_"-                                         "Task terminated!"))----- Seems as if the following is convenient after all. Suitable name???--- Maybe that implies a representation change for Tasks?--- 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))-    where-        isEdge (Left _)  (Left _)  = Nothing-	isEdge (Left _)  (Right c) = Just c-	isEdge (Right _) (Right _) = Nothing-	isEdge (Right _) (Left _)  = Nothing------------------------------------------------------------------------------------ Monad instance---------------------------------------------------------------------------------instance Monad (Task a b) where-    tk >>= f = Task (\k -> (unTask tk) (\c -> unTask (f c) k))-    return x = Task (\k -> k x)--{--Let's check the monad laws:--    t >>= return-    = \k -> t (\c -> return c k)-    = \k -> t (\c -> (\x -> \k -> k x) c k)-    = \k -> t (\c -> (\x -> \k' -> k' x) c k)-    = \k -> t (\c -> k c)-    = \k -> t k-    = t-    QED--    return x >>= f-    = \k -> (return x) (\c -> f c k)-    = \k -> (\k -> k x) (\c -> f c k)-    = \k -> (\k' -> k' x) (\c -> f c k)-    = \k -> (\c -> f c k) x-    = \k -> f x k-    = f x-    QED--    (t >>= f) >>= g-    = \k -> (t >>= f) (\c -> g c k)-    = \k -> (\k' -> t (\c' -> f c' k')) (\c -> g c k)-    = \k -> t (\c' -> f c' (\c -> g c k))-    = \k -> t (\c' -> (\x -> \k' -> f x (\c -> g c k')) c' k)-    = \k -> t (\c' -> (\x -> f x >>= g) c' k)-    = t >>= (\x -> f x >>= g)-    QED--No surprises (obviously, since this is essentially just the CPS monad).--}------------------------------------------------------------------------------------ Basic tasks----------------------------------------------------------------------------------- Non-terminating task with constant output b.-constT :: b -> Task a b c-constT b = mkTask (constant b &&& never)----- "Sleeps" for t seconds with constant output b.-sleepT :: Time -> b -> Task a b ()-sleepT t b = mkTask (constant b &&& after t ())----- Takes a "snapshot" of the input and terminates immediately with the input--- value as the result. No time passes; law:------    snapT >> snapT = snapT----snapT :: Task a b a-snapT = mkTask (constant (intErr "AFRPTask" "snapT" "Bad switch?") &&& snap)------------------------------------------------------------------------------------ Basic tasks combinators----------------------------------------------------------------------------------- Impose a time out on a task.-timeOut :: Task a b c -> Time -> Task a b (Maybe c)-tk `timeOut` t = mkTask ((taskToSF tk &&& after t ()) >>> arr aux)-    where-        aux ((b, ec), et) = (b, (lMerge (fmap Just ec)-					(fmap (const Nothing) et)))----- Run a "guarding" event source (SF a (Event b)) in parallel with a--- (possibly non-terminating) task. The task will be aborted at the--- first occurrence of the event source (if it has not terminated itself--- before that). Useful for separating sequencing and termination concerns.--- E.g. we can do something "useful", but in parallel watch for a (exceptional)--- condition which should terminate that activity, whithout having to check--- for that condition explicitly during each and every phase of the activity.--- Example: tsk `abortWhen` lbp-abortWhen :: Task a b c -> SF a (Event d) -> Task a b (Either c d)-tk `abortWhen` est = mkTask ((taskToSF tk &&& est) >>> arr aux)-    where-        aux ((b, ec), ed) = (b, (lMerge (fmap Left ec) (fmap Right ed)))------------------------------------------------------------------------------------ Loops----------------------------------------------------------------------------------- These are general monadic combinators. Maybe they don't really belong here.---- Repeat m until result satisfies the predicate p-repeatUntil :: Monad m => m a -> (a -> Bool) -> m a-m `repeatUntil` p = m >>= \x -> if not (p x) then repeatUntil m p else return x----- 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 ()----- Perform the monadic operation for each element in the list.-forAll :: Monad m => [a] -> (a -> m b) -> m ()-forAll = flip mapM_----- Repeat m for ever.-forEver :: Monad m => m a -> m b-forEver m = m >> forEver m----- Alternatives/other potentially useful signatures:--- until :: a -> (a -> M a) -> (a -> Bool) -> M a--- for: a -> b -> (a -> b -> a) -> (a -> b -> Bool) -> (a -> b -> M b) -> M b--- while??? It could be:--- while :: a -> (a -> Bool) -> (a -> M a) -> M a------------------------------------------------------------------------------------ Monad transformers?----------------------------------------------------------------------------------- What about monad transformers if we want to compose this monad with--- other capabilities???
− FRP/Yampa/Utilities.hs 
@@ -1,352 +0,0 @@--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.Utilities--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  portable------ Derived utility definitions.------ ToDo:------ * Possibly add---       impulse :: VectorSpace a k => a -> Event a---   But to do that, we need access to Event, which we currently do not have.------ * The general arrow utilities should be moved to a module---   FRP.Yampa.Utilities.------ * I'm not sure structuring the Yampa \"core\" according to what is---   core functionality and what's not is all that useful. There are---   many cases where we want to implement combinators that fairly---   easily could be implemented in terms of others as primitives simply---   because we expect that that implementation is going to be much more---   efficient, and that the combinators are used sufficiently often to---   warrant doing this. E.g. 'switch' should be a primitive, even though---   it could be derived from 'pSwitch'.------ * Reconsider 'recur'. If an event source has an immediate occurrence,---   we'll get into a loop. For example: recur now. Maybe suppress---   initial occurrences? Initial occurrences are rather pointless in this---   case anyway.--------------------------------------------------------------------------------------------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---- 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)---- 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)-    andThen,            -- :: SF a (Event b)->SF a (Event b)->SF a (Event b)-    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]---- Guards and automata-oriented combinators-    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---- 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)---- Delays-    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-) where--import FRP.Yampa.Diagnostics-import FRP.Yampa---infixr 5 `andThen`---infixr 1 ^<<, ^>>---infixr 1 <<^, >>^-infixr 0 `fby`----- Now defined directly in Control.Arrow.--- But while using an old version of Arrows ...---------------------------------------------------------------------------------- General arrow utilities--------------------------------------------------------------------------------{--(^>>) :: Arrow a => (b -> c) -> a c d -> a b d-f ^>> a = arr f >>> a--(>>^) :: Arrow a => a b c -> (c -> d) -> a b d-a >>^ f = a >>> arr f---(^<<) :: Arrow a => (c -> d) -> a b c -> a b d -f ^<< a = arr f <<< a---(<<^) :: Arrow a => a c d -> (b -> c) -> a b d-a <<^ f = a <<< arr f--}----------------------------------------------------------------------------------- Liftings---------------------------------------------------------------------------------arr2 :: Arrow a => (b -> c -> d) -> a (b, c) d-arr2 = arr . uncurry---arr3 :: Arrow a => (b -> c -> d -> e) -> a (b, c, d) e-arr3 = arr . \h (b, c, d) -> h b c d---arr4 :: Arrow a => (b -> c -> d -> e -> f) -> a (b, c, d, e) f-arr4 = arr . \h (b, c, d, e) -> h b c d e---arr5 :: Arrow a => (b -> c -> d -> e -> f -> g) -> a (b, c, d, e, f) g-arr5 = arr . \h (b, c, d, e, f) -> h b c d e f---lift0 :: Arrow a => c -> a b c-lift0 c = arr (const c)---lift1 :: Arrow a => (c -> d) -> (a b c -> a b d)-lift1 f = \a -> a >>> arr f---lift2 :: Arrow a => (c -> d -> e) -> (a b c -> a b d -> a b e)-lift2 f = \a1 a2 -> a1 &&& a2 >>> arr2 f---lift3 :: Arrow a => (c -> d -> e -> f) -> (a b c -> a b d -> a b e -> a b f)-lift3 f = \a1 a2 a3 -> (lift2 f) a1 a2 &&& a3 >>> arr2 ($)---lift4 :: Arrow a => (c->d->e->f->g) -> (a b c->a b d->a b e->a b f->a b g)-lift4 f = \a1 a2 a3 a4 -> (lift3 f) a1 a2 a3 &&& a4 >>> arr2 ($)---lift5 :: Arrow a =>-    (c->d->e->f->g->h) -> (a b c->a b d->a b e->a b f->a b g->a b h)-lift5 f = \a1 a2 a3 a4 a5 ->(lift4 f) a1 a2 a3 a4 &&& a5 >>> arr2 ($)------------------------------------------------------------------------------------ Event sources----------------------------------------------------------------------------------- Event source with a single occurrence at time 0. The value of the event--- is obtained by sampling the input at that time.--- (The outer "switch" ensures that the entire signal function will become--- just "constant" once the sample has been taken.)-snap :: SF a (Event a)-snap = switch (never &&& (identity &&& now () >>^ \(a, e) -> e `tag` a)) now----- Event source with a single occurrence at or as soon after (local) time t_ev--- as possible. The value of the event is obtained by sampling the input a--- that time.-snapAfter :: Time -> SF a (Event a)-snapAfter t_ev = switch (never-			 &&& (identity-			      &&& after t_ev () >>^ \(a, e) -> e `tag` a))-			now----- Sample a signal at regular intervals.-sample :: Time -> SF a (Event a)-sample p_ev = identity &&& repeatedly p_ev () >>^ \(a, e) -> e `tag` a----- Makes an event source recurring by restarting it as soon as it has an--- occurrence.--- !!! What about event sources that have an instantaneous occurrence?--- !!! E.g. recur (now ()). --- !!! Or worse, what about recur identity? (or substitute identity for--- !!! a more sensible definition that e.g. merges any incoming event--- !!! with an internally generated one, for example)--- !!! Possibly we should ignore instantaneous reoccurrences.--- New definition:-recur :: SF a (Event b) -> SF a (Event b)-recur sfe = switch (never &&& sfe) $ \b -> Event b --> (recur (NoEvent-->sfe))--andThen :: SF a (Event b) -> SF a (Event b) -> SF a (Event b)-sfe1 `andThen` sfe2 = dSwitch (sfe1 >>^ dup) (const sfe2)--{--recur :: SF a (Event b) -> SF a (Event b)-recur sfe = switch (never &&& sfe) recurAux-    where-	recurAux b = switch (now b &&& sfe) recurAux--}---- Window sampling--- First argument is the window length wl, second is the sampling interval t.--- The output list should contain (min (truncate (T/t) wl)) samples, where--- T is the time the signal function has been running. This requires some--- care in case of sparse sampling. In case of sparse sampling, the--- current input value is assumed to have been present at all points where--- sampling was missed.--sampleWindow :: Int -> Time -> SF a (Event [a])-sampleWindow wl q =-    identity &&& afterEachCat (repeat (q, ()))-    >>> arr (\(a, e) -> fmap (map (const a)) e)-    >>> accumBy updateWindow []-    where-        updateWindow w as = drop (max (length w' - wl) 0) w'-            where-	        w' = w ++ as------------------------------------------------------------------------------------ Parallel composition/switchers with "zip" routing---------------------------------------------------------------------------------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--	head' []    = err-	head' (a:_) = a--	tail' []     = err-	tail' (_:as) = as--	err = usrErr "AFRPUtilities" fn "Input list too short."---parZ :: [SF a b] -> SF [a] [b]-parZ = par (safeZip "parZ")---pSwitchZ :: [SF a b] -> SF ([a],[b]) (Event c) -> ([SF a b] -> c -> SF [a] [b])-            -> SF [a] [b]-pSwitchZ = pSwitch (safeZip "pSwitchZ")---dpSwitchZ :: [SF a b] -> SF ([a],[b]) (Event c) -> ([SF a b] -> c ->SF [a] [b])-             -> SF [a] [b]-dpSwitchZ = dpSwitch (safeZip "dpSwitchZ")---rpSwitchZ :: [SF a b] -> SF ([a], Event ([SF a b] -> [SF a b])) [b]-rpSwitchZ = rpSwitch (safeZip "rpSwitchZ")---drpSwitchZ :: [SF a b] -> SF ([a], Event ([SF a b] -> [SF a b])) [b]-drpSwitchZ = drpSwitch (safeZip "drpSwitchZ")------------------------------------------------------------------------------------ Guards and automata-oriented combinators----------------------------------------------------------------------------------- Runs sft only when the predicate p is satisfied, otherwise runs sff.-provided :: (a -> Bool) -> SF a b -> SF a b -> SF a b-provided p sft sff =-    switch (constant undefined &&& snap) $ \a0 ->-    if p a0 then stt else stf-    where-	stt = switch (sft &&& (not . p ^>> edge)) (const stf)-        stf = switch (sff &&& (p ^>> edge)) (const stt)------------------------------------------------------------------------------------ Wave-form generation----------------------------------------------------------------------------------- Zero-order hold with delay.--- Identity: dHold a0 = hold a0 >>> iPre a0).-old_dHold :: a -> SF (Event a) a-old_dHold a0 = dSwitch (constant a0 &&& identity) dHold'-    where-	dHold' a = dSwitch (constant a &&& notYet) dHold'---dTrackAndHold :: a -> SF (Maybe a) a-dTrackAndHold a_init = trackAndHold a_init >>> iPre a_init------------------------------------------------------------------------------------ Accumulators---------------------------------------------------------------------------------old_accumHold :: a -> SF (Event (a -> a)) a-old_accumHold a_init = old_accum a_init >>> old_hold a_init---old_dAccumHold :: a -> SF (Event (a -> a)) a-old_dAccumHold a_init = old_accum a_init >>> old_dHold a_init---old_accumHoldBy :: (b -> a -> b) -> b -> SF (Event a) b-old_accumHoldBy f b_init = old_accumBy f b_init >>> old_hold b_init---old_dAccumHoldBy :: (b -> a -> b) -> b -> SF (Event a) b-old_dAccumHoldBy f b_init = old_accumBy f b_init >>> old_dHold b_init---count :: Integral b => SF (Event a) (Event b)-count = accumBy (\n _ -> n + 1) 0------------------------------------------------------------------------------------ Delays----------------------------------------------------------------------------------- Lucid-Synchrone-like initialized delay (read "followed by").-fby :: b -> SF a b -> SF a b-b0 `fby` sf = b0 --> sf >>> pre------------------------------------------------------------------------------------ Integrals---------------------------------------------------------------------------------impulseIntegral :: VectorSpace a k => SF (a, Event a) a-impulseIntegral = (integral *** accumHoldBy (^+^) zeroVector) >>^ uncurry (^+^)--old_impulseIntegral :: VectorSpace a k => SF (a, Event a) a-old_impulseIntegral = (integral *** old_accumHoldBy (^+^) zeroVector) >>^ uncurry (^+^)
− FRP/Yampa/Vector2.hs 
@@ -1,103 +0,0 @@-{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances #-}--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.Vector2--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  non-portable (GHC extensions)------ 2D vector abstraction (R^2).------ ToDo: Deriving Show, or provide dedicated show instance?--------------------------------------------------------------------------------------------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-) where--import FRP.Yampa.VectorSpace-import FRP.Yampa.Forceable------------------------------------------------------------------------------------ 2D vector, constructors and selectors.----------------------------------------------------------------------------------- Restrict coefficient space to RealFloat (rather than Floating) for now.--- While unclear if a complex coefficient space would be useful (and if the--- result really would be a 2d vector), the only thing causing trouble is the--- use of atan2 in vector2Theta. Maybe atan2 can be generalized?--data RealFloat a => Vector2 a = Vector2 !a !a deriving (Eq,Show)--vector2 :: RealFloat a => a -> a -> Vector2 a-vector2 x y = Vector2 x y--vector2X :: RealFloat a => Vector2 a -> a-vector2X (Vector2 x _) = x--vector2Y :: RealFloat a => Vector2 a -> a-vector2Y (Vector2 _ y) = y--vector2XY :: RealFloat a => Vector2 a -> (a, a)-vector2XY (Vector2 x y) = (x, y)--vector2Polar :: RealFloat a => a -> a -> Vector2 a-vector2Polar rho theta = Vector2 (rho * cos theta) (rho * sin theta) --vector2Rho :: RealFloat a => Vector2 a -> a-vector2Rho (Vector2 x y) = sqrt (x * x + y * y)--vector2Theta :: RealFloat a => Vector2 a -> a-vector2Theta (Vector2 x y) = atan2 y x--vector2RhoTheta :: RealFloat a => Vector2 a -> (a, a)-vector2RhoTheta v = (vector2Rho v, vector2Theta v)----------------------------------------------------------------------------------- Vector space instance---------------------------------------------------------------------------------instance RealFloat a => VectorSpace (Vector2 a) a where-    zeroVector = Vector2 0 0--    a *^ (Vector2 x y) = Vector2 (a * x) (a * y)--    (Vector2 x y) ^/ a = Vector2 (x / a) (y / a)--    negateVector (Vector2 x y) = (Vector2 (-x) (-y))--    (Vector2 x1 y1) ^+^ (Vector2 x2 y2) = Vector2 (x1 + x2) (y1 + y2)--    (Vector2 x1 y1) ^-^ (Vector2 x2 y2) = Vector2 (x1 - x2) (y1 - y2)--    (Vector2 x1 y1) `dot` (Vector2 x2 y2) = x1 * x2 + y1 * y2------------------------------------------------------------------------------------ Additional operations---------------------------------------------------------------------------------vector2Rotate :: RealFloat a => a -> Vector2 a -> Vector2 a-vector2Rotate theta' v = vector2Polar (vector2Rho v) (vector2Theta v + theta')------------------------------------------------------------------------------------ Forceable instance---------------------------------------------------------------------------------instance RealFloat a => Forceable (Vector2 a) where-     force = id
− FRP/Yampa/Vector3.hs 
@@ -1,121 +0,0 @@-{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-}--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.Vector3--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  non-portable (GHC extensions)------ 3D vector abstraction (R^3).------ ToDo: Deriving Show, or provide dedicated show instance?--------------------------------------------------------------------------------------------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-) where--import FRP.Yampa.VectorSpace-import FRP.Yampa.Forceable----------------------------------------------------------------------------------- 3D vector, constructors and selectors.----------------------------------------------------------------------------------- Restrict coefficient space to RealFloat (rather than Floating) for now.--- While unclear if a complex coefficient space would be useful (and if the--- result really would be a 3d vector), the only thing causing trouble is the--- use of atan2 in vector3Theta and vector3Phi. Maybe atan2 can be generalized?--data RealFloat a => Vector3 a = Vector3 !a !a !a deriving (Eq, Show)--vector3 :: RealFloat a => a -> a -> a -> Vector3 a-vector3 x y z = Vector3 x y z--vector3X :: RealFloat a => Vector3 a -> a-vector3X (Vector3 x _ _) = x--vector3Y :: RealFloat a => Vector3 a -> a-vector3Y (Vector3 _ y _) = y--vector3Z :: RealFloat a => Vector3 a -> a-vector3Z (Vector3 _ _ z) = z--vector3XYZ :: RealFloat a => Vector3 a -> (a, a, a)-vector3XYZ (Vector3 x y z) = (x, y, z)--vector3Spherical :: RealFloat a => a -> a -> a -> Vector3 a-vector3Spherical rho theta phi =-    Vector3 (rhoSinPhi * cos theta) (rhoSinPhi * sin theta) (rho * cos phi)-    where-	rhoSinPhi = rho * sin phi--vector3Rho :: RealFloat a => Vector3 a -> a-vector3Rho (Vector3 x y z) = sqrt (x * x + y * y + z * z)--vector3Theta :: RealFloat a => Vector3 a -> a-vector3Theta (Vector3 x y _) = atan2 y x--vector3Phi :: RealFloat a => Vector3 a -> a-vector3Phi v@(Vector3 _ _ z) = acos (z / vector3Rho v)--vector3RhoThetaPhi :: RealFloat a => Vector3 a -> (a, a, a)-vector3RhoThetaPhi (Vector3 x y z) = (rho, theta, phi)-    where-        rho   = sqrt (x * x + y * y + z * z)-        theta = atan2 y x-	phi   = acos (z / rho)------------------------------------------------------------------------------------ Vector space instance---------------------------------------------------------------------------------instance RealFloat a => VectorSpace (Vector3 a) a where-    zeroVector = Vector3 0 0 0--    a *^ (Vector3 x y z) = Vector3 (a * x) (a * y) (a * z)--    (Vector3 x y z) ^/ a = Vector3 (x / a) (y / a) (z / a)--    negateVector (Vector3 x y z) = (Vector3 (-x) (-y) (-z))--    (Vector3 x1 y1 z1) ^+^ (Vector3 x2 y2 z2) = Vector3 (x1+x2) (y1+y2) (z1+z2)--    (Vector3 x1 y1 z1) ^-^ (Vector3 x2 y2 z2) = Vector3 (x1-x2) (y1-y2) (z1-z2)--    (Vector3 x1 y1 z1) `dot` (Vector3 x2 y2 z2) = x1 * x2 + y1 * y2 + z1 * z2------------------------------------------------------------------------------------ Additional operations---------------------------------------------------------------------------------vector3Rotate :: RealFloat a => a -> a -> Vector3 a -> Vector3 a-vector3Rotate theta' phi' v =-    vector3Spherical (vector3Rho v)-		     (vector3Theta v + theta')-		     (vector3Phi v + phi')------------------------------------------------------------------------------------ Forceable instance---------------------------------------------------------------------------------instance RealFloat a => Forceable (Vector3 a) where-     force = id
− FRP/Yampa/VectorSpace.hs 
@@ -1,160 +0,0 @@-{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances #-}--------------------------------------------------------------------------------------------- |--- Module      :  FRP.Yampa.VectorSpace--- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003--- License     :  BSD-style (see the LICENSE file in the distribution)------ Maintainer  :  nilsson@cs.yale.edu--- Stability   :  provisional--- Portability :  non-portable (GHC extensions)------ Vector space type relation and basic instances.-----------------------------------------------------------------------------------------------module FRP.Yampa.VectorSpace where----------------------------------------------------------------------------------- Vector space type relation---------------------------------------------------------------------------------infixr *^-infixl ^/-infix 7 `dot`-infixl 6 ^+^, ^-^---- Maybe norm and normalize should not be class methods, in which case--- the constraint on the coefficient space (a) should (or, at least, could)--- be Fractional (roughly a Field) rather than Floating.---- Minimal instance: zeroVector, (*^), (^+^), dot-class Floating a => VectorSpace v a | v -> a where-    zeroVector   :: v-    (*^)         :: a -> v -> v-    (^/)         :: v -> a -> v-    negateVector :: v -> v-    (^+^)        :: v -> v -> v-    (^-^)        :: v -> v -> v-    dot          :: v -> v -> a-    norm	 :: v -> a-    normalize	 :: v -> v--    v ^/ a = (1/a) *^ v--    negateVector v = (-1) *^ v--    v1 ^-^ v2 = v1 ^+^ negateVector v2--    norm v = sqrt (v `dot` v)--    normalize v = if nv /= 0 then v ^/ nv else error "normalize: zero vector"-        where-	    nv = norm v----------------------------------------------------------------------------------- Vector space instances for Float and Double---------------------------------------------------------------------------------instance VectorSpace Float Float where-    zeroVector = 0--    a *^ x = a * x--    x ^/ a = x / a--    negateVector x = (-x)--    x1 ^+^ x2 = x1 + x2--    x1 ^-^ x2 = x1 - x2--    x1 `dot` x2 = x1 * x2---instance VectorSpace Double Double where-    zeroVector = 0--    a *^ x = a * x--    x ^/ a = x / a--    negateVector x = (-x)--    x1 ^+^ x2 = x1 + x2--    x1 ^-^ x2 = x1 - x2--    x1 `dot` x2 = x1 * x2------------------------------------------------------------------------------------ Vector space instances for small tuples of Floating---------------------------------------------------------------------------------instance Floating a => VectorSpace (a,a) a where-    zeroVector = (0,0)--    a *^ (x,y) = (a * x, a * y)--    (x,y) ^/ a = (x / a, y / a)--    negateVector (x,y) = (-x, -y)--    (x1,y1) ^+^ (x2,y2) = (x1 + x2, y1 + y2)--    (x1,y1) ^-^ (x2,y2) = (x1 - x2, y1 - y2)--    (x1,y1) `dot` (x2,y2) = x1 * x2 + y1 * y2---instance Floating a => VectorSpace (a,a,a) a where-    zeroVector = (0,0,0)--    a *^ (x,y,z) = (a * x, a * y, a * z)--    (x,y,z) ^/ a = (x / a, y / a, z / a)--    negateVector (x,y,z) = (-x, -y, -z)--    (x1,y1,z1) ^+^ (x2,y2,z2) = (x1+x2, y1+y2, z1+z2)--    (x1,y1,z1) ^-^ (x2,y2,z2) = (x1-x2, y1-y2, z1-z2)--    (x1,y1,z1) `dot` (x2,y2,z2) = x1 * x2 + y1 * y2 + z1 * z2---instance Floating a => VectorSpace (a,a,a,a) a where-    zeroVector = (0,0,0,0)--    a *^ (x,y,z,u) = (a * x, a * y, a * z, a * u)--    (x,y,z,u) ^/ a = (x / a, y / a, z / a, u / a)--    negateVector (x,y,z,u) = (-x, -y, -z, -u)--    (x1,y1,z1,u1) ^+^ (x2,y2,z2,u2) = (x1+x2, y1+y2, z1+z2, u1+u2)--    (x1,y1,z1,u1) ^-^ (x2,y2,z2,u2) = (x1-x2, y1-y2, z1-z2, u1-u2)--    (x1,y1,z1,u1) `dot` (x2,y2,z2,u2) = x1 * x2 + y1 * y2 + z1 * z2 + u1 * u2---instance Floating a => VectorSpace (a,a,a,a,a) a where-    zeroVector = (0,0,0,0,0)--    a *^ (x,y,z,u,v) = (a * x, a * y, a * z, a * u, a * v)--    (x,y,z,u,v) ^/ a = (x / a, y / a, z / a, u / a, v / a)--    negateVector (x,y,z,u,v) = (-x, -y, -z, -u, -v)--    (x1,y1,z1,u1,v1) ^+^ (x2,y2,z2,u2,v2) = (x1+x2, y1+y2, z1+z2, u1+u2, v1+v2)--    (x1,y1,z1,u1,v1) ^-^ (x2,y2,z2,u2,v2) = (x1-x2, y1-y2, z1-z2, u1-u2, v1-v2)--    (x1,y1,z1,u1,v1) `dot` (x2,y2,z2,u2,v2) =-        x1 * x2 + y1 * y2 + z1 * z2 + u1 * u2 + v1 * v2---
GameLogic.hs view
@@ -14,15 +14,10 @@ data WinLose = Win | Lose deriving (Eq)  -- Snapping integral -{-# INLINE integral' #-}-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' | a_prev == zeroVector = -                                    vectorApply (fromIntegral . round) igrl-                                | otherwise  = igrl ^+^ realToFrac dt *^ a_prev+integral' = (iPre zeroVector &&& time) >>> sscan f (zeroVector, 0) >>> arr fst+    where f (prevVal, prevTime) (val, time) +            | val == zeroVector = (vectorApply (fromIntegral . round) prevVal, time)+            | otherwise        = (prevVal ^+^ (realToFrac $ time - prevTime) *^ val, time)  calculateState :: SF ParsedInput GameState calculateState = proc pi@(ParsedInput ws as ss ds _ _ _ _) -> do
cuboid.cabal view
@@ -14,12 +14,9 @@     In order to add levels check out Game.hs. If you come up with     a great level do send it to me. I plan to extract the levels     into a configuration file in the future.-    .-    A slightly modified version of Yampa was included, which exports-    the constructors that allow building new complex stateful operators  Synopsis:           3D Yampa/GLUT Puzzle Game -Version:            0.13+Version:            0.14 License:            MIT License-file:       LICENSE Copyright:          (C) 2010 Pedro Martins@@ -29,10 +26,9 @@ Stability:          experimental Build-Type:         Simple Cabal-Version:      >= 1.6-Extra-Source-Files: FRP/*.hs, FRP/Yampa/*.hs  Executable cuboid      Main-Is:            Main.hs     Other-Modules:      Game, GameLogic, Graphics, Input-    Build-Depends:      base >= 3 && < 5, random, GLUT+    Build-Depends:      base >= 3 && < 5, Yampa, GLUT