frag-1.1: src/AFRPUtilities.hs
{- $Id: AFRPUtilities.hs,v 1.8 2003/12/19 15:31:50 henrik Exp $
******************************************************************************
* A F R P *
* *
* Module: AFRPUtilities *
* Purpose: Derived utility definitions. *
* Authors: Antony Courtney and Henrik Nilsson *
* *
* Copyright (c) Yale University, 2003 *
* *
******************************************************************************
-}
-- 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
-- AFRPArrowUtilities.
-- * I'm not sure structuring the AFRP "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 AFRPUtilities (
-- 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)
-- 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
dHold, -- :: a -> SF (Event a) a
dTrackAndHold, -- :: a -> SF (Maybe a) a
-- Accumulators
accumHold, -- :: a -> SF (Event (a -> a)) a
dAccumHold, -- :: a -> SF (Event (a -> a)) a
accumHoldBy, -- :: (b -> a -> b) -> b -> SF (Event a) b
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
) where
import AFRPDiagnostics
import AFRP
--infixr 1 ^<<, ^>>
--infixl 1 <<^, >>^
--infixr 0 `fby`
------------------------------------------------------------------------------
-- 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.
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.
recur :: SF a (Event b) -> SF a (Event b)
recur sfe = switch (never &&& sfe) recurAux
where
recurAux b = switch (now b &&& sfe) recurAux
------------------------------------------------------------------------------
-- Parallel composition/switchers with "zip" routing
------------------------------------------------------------------------------
safeZip :: String -> [a] -> [b] -> [(a,b)]
safeZip fn as bs = safeZip' as bs
where
safeZip' _ [] = []
safeZip' cs (d:ds) = (head' cs, d) : safeZip' (tail' cs) ds
head' [] = err
head' (e:_) = e
tail' [] = err
tail' (_:es) = es
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).
dHold :: a -> SF (Event a) a
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
------------------------------------------------------------------------------
accumHold :: a -> SF (Event (a -> a)) a
accumHold a_init = accum a_init >>> hold a_init
dAccumHold :: a -> SF (Event (a -> a)) a
dAccumHold a_init = accum a_init >>> dHold a_init
accumHoldBy :: (b -> a -> b) -> b -> SF (Event a) b
accumHoldBy f b_init = accumBy f b_init >>> hold b_init
dAccumHoldBy :: (b -> a -> b) -> b -> SF (Event a) b
dAccumHoldBy f b_init = accumBy f b_init >>> 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 (^+^)