diff --git a/FRP/Yampa.hs b/FRP/Yampa.hs
deleted file mode 100644
--- a/FRP/Yampa.hs
+++ /dev/null
@@ -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!
diff --git a/FRP/Yampa/AffineSpace.hs b/FRP/Yampa/AffineSpace.hs
deleted file mode 100644
--- a/FRP/Yampa/AffineSpace.hs
+++ /dev/null
@@ -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)
diff --git a/FRP/Yampa/Diagnostics.hs b/FRP/Yampa/Diagnostics.hs
deleted file mode 100644
--- a/FRP/Yampa/Diagnostics.hs
+++ /dev/null
@@ -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)
diff --git a/FRP/Yampa/Event.hs b/FRP/Yampa/Event.hs
deleted file mode 100644
--- a/FRP/Yampa/Event.hs
+++ /dev/null
@@ -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
diff --git a/FRP/Yampa/Forceable.hs b/FRP/Yampa/Forceable.hs
deleted file mode 100644
--- a/FRP/Yampa/Forceable.hs
+++ /dev/null
@@ -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
diff --git a/FRP/Yampa/Geometry.hs b/FRP/Yampa/Geometry.hs
deleted file mode 100644
--- a/FRP/Yampa/Geometry.hs
+++ /dev/null
@@ -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
-
-
diff --git a/FRP/Yampa/Internals.hs b/FRP/Yampa/Internals.hs
deleted file mode 100644
--- a/FRP/Yampa/Internals.hs
+++ /dev/null
@@ -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)
-
-
diff --git a/FRP/Yampa/MergeableRecord.hs b/FRP/Yampa/MergeableRecord.hs
deleted file mode 100644
--- a/FRP/Yampa/MergeableRecord.hs
+++ /dev/null
@@ -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
diff --git a/FRP/Yampa/Miscellany.hs b/FRP/Yampa/Miscellany.hs
deleted file mode 100644
--- a/FRP/Yampa/Miscellany.hs
+++ /dev/null
@@ -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
diff --git a/FRP/Yampa/Point2.hs b/FRP/Yampa/Point2.hs
deleted file mode 100644
--- a/FRP/Yampa/Point2.hs
+++ /dev/null
@@ -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
diff --git a/FRP/Yampa/Point3.hs b/FRP/Yampa/Point3.hs
deleted file mode 100644
--- a/FRP/Yampa/Point3.hs
+++ /dev/null
@@ -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
diff --git a/FRP/Yampa/Task.hs b/FRP/Yampa/Task.hs
deleted file mode 100644
--- a/FRP/Yampa/Task.hs
+++ /dev/null
@@ -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???
diff --git a/FRP/Yampa/Utilities.hs b/FRP/Yampa/Utilities.hs
deleted file mode 100644
--- a/FRP/Yampa/Utilities.hs
+++ /dev/null
@@ -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 (^+^)
diff --git a/FRP/Yampa/Vector2.hs b/FRP/Yampa/Vector2.hs
deleted file mode 100644
--- a/FRP/Yampa/Vector2.hs
+++ /dev/null
@@ -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
diff --git a/FRP/Yampa/Vector3.hs b/FRP/Yampa/Vector3.hs
deleted file mode 100644
--- a/FRP/Yampa/Vector3.hs
+++ /dev/null
@@ -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
diff --git a/FRP/Yampa/VectorSpace.hs b/FRP/Yampa/VectorSpace.hs
deleted file mode 100644
--- a/FRP/Yampa/VectorSpace.hs
+++ /dev/null
@@ -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
-
-
-
diff --git a/GameLogic.hs b/GameLogic.hs
--- a/GameLogic.hs
+++ b/GameLogic.hs
@@ -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
diff --git a/cuboid.cabal b/cuboid.cabal
--- a/cuboid.cabal
+++ b/cuboid.cabal
@@ -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
 
