Portability | non-portable (GHC extensions) |
---|---|

Stability | provisional |

Maintainer | nilsson@cs.yale.edu |

Safe Haskell | None |

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 Control.Arrow
- module FRP.Yampa.VectorSpace
- class RandomGen g where
- class Random a where
- (#) :: (a -> b) -> (b -> c) -> a -> c
- dup :: a -> (a, a)
- swap :: (a, b) -> (b, a)
- type Time = Double
- data SF a b
- data Event a
- arrPrim :: (a -> b) -> SF a b
- arrEPrim :: (Event a -> b) -> SF (Event a) b
- identity :: SF a a
- constant :: b -> SF a b
- localTime :: SF a Time
- time :: SF a Time
- (-->) :: b -> SF a b -> SF a b
- (>--) :: a -> SF a b -> SF a b
- (-=>) :: (b -> b) -> SF a b -> SF a b
- (>=-) :: (a -> a) -> SF a b -> SF a b
- initially :: a -> SF a a
- sscan :: (b -> a -> b) -> b -> SF a b
- sscanPrim :: (c -> a -> Maybe (c, b)) -> c -> b -> SF a b
- 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)
- 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)
- 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
- tagWith :: b -> Event a -> Event b
- attach :: Event a -> b -> Event (a, b)
- lMerge :: Event a -> Event a -> Event a
- rMerge :: Event a -> Event a -> Event a
- merge :: Event a -> Event a -> Event a
- 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)
- 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
- switch :: SF a (b, Event c) -> (c -> SF a b) -> SF a b
- dSwitch :: SF a (b, Event c) -> (c -> SF a b) -> SF a b
- rSwitch :: SF a b -> SF (a, Event (SF a b)) b
- drSwitch :: SF a b -> SF (a, Event (SF a b)) b
- kSwitch :: SF a b -> SF (a, b) (Event c) -> (SF a b -> c -> SF a b) -> SF a b
- dkSwitch :: SF a b -> SF (a, b) (Event c) -> (SF a b -> c -> SF a b) -> SF a b
- parB :: Functor col => col (SF a b) -> SF a (col b)
- 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)
- 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 :: Functor col => col (SF a b) -> SF (a, Event (col (SF a b) -> col (SF a b))) (col b)
- drpSwitchB :: Functor col => col (SF a b) -> SF (a, Event (col (SF a b) -> col (SF a b))) (col b)
- par :: Functor col => (forall sf. a -> col sf -> col (b, sf)) -> col (SF b c) -> SF a (col c)
- 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)
- 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)
- 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)
- 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)
- 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
- 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 -> SF (Event a) (Event b)
- accum :: a -> SF (Event (a -> a)) (Event a)
- accumHold :: a -> SF (Event (a -> a)) a
- dAccumHold :: a -> SF (Event (a -> a)) a
- accumBy :: (b -> a -> b) -> b -> SF (Event a) (Event b)
- accumHoldBy :: (b -> a -> b) -> b -> SF (Event a) b
- dAccumHoldBy :: (b -> a -> b) -> b -> SF (Event a) b
- accumFilter :: (c -> a -> (c, Maybe b)) -> c -> SF (Event a) (Event b)
- old_pre :: SF a a
- old_iPre :: a -> SF a a
- pre :: SF a a
- iPre :: a -> SF a a
- delay :: Time -> a -> SF a a
- loopPre :: c -> SF (a, c) (b, c) -> SF a b
- loopIntegral :: VectorSpace c s => SF (a, c) (b, c) -> SF a b
- integral :: VectorSpace a s => SF a a
- derivative :: VectorSpace a s => SF a a
- imIntegral :: VectorSpace a s => a -> SF a a
- noise :: (RandomGen g, Random b) => g -> SF a b
- noiseR :: (RandomGen g, Random b) => (b, b) -> g -> SF a b
- occasionally :: RandomGen g => g -> Time -> b -> SF a (Event b)
- reactimate :: IO a -> (Bool -> IO (DTime, Maybe a)) -> (Bool -> b -> IO Bool) -> SF a b -> IO ()
- type ReactHandle a b = IORef (ReactState a b)
- reactInit :: IO a -> (ReactHandle a b -> Bool -> b -> IO Bool) -> SF a b -> IO (ReactHandle a b)
- react :: ReactHandle a b -> (DTime, Maybe a) -> IO Bool
- type DTime = Double
- 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)])

# Documentation

module Control.Arrow

module FRP.Yampa.VectorSpace

class RandomGen g where

The class `RandomGen`

provides a common interface to random number
generators.

The `next`

operation returns an `Int`

that is uniformly distributed
in the range returned by `genRange`

(including both end points),
and a new generator.

The `genRange`

operation yields the range of values returned by
the generator.

It is required that:

The second condition ensures that `genRange`

cannot examine its
argument, and hence the value it returns can be determined only by the
instance of `RandomGen`

. That in turn allows an implementation to make
a single call to `genRange`

to establish a generator's range, without
being concerned that the generator returned by (say) `next`

might have
a different range to the generator passed to `next`

.

The default definition spans the full range of `Int`

.

split :: g -> (g, g)

The `split`

operation allows one to obtain two distinct random number
generators. This is very useful in functional programs (for example, when
passing a random number generator down to recursive calls), but very
little work has been done on statistically robust implementations of
`split`

([System.Random, System.Random]
are the only examples we know of).

class Random a where

With a source of random number supply in hand, the `Random`

class allows the
programmer to extract random values of a variety of types.

randomR :: RandomGen g => (a, a) -> g -> (a, g)

Takes a range *(lo,hi)* and a random number generator
*g*, and returns a random value uniformly distributed in the closed
interval *[lo,hi]*, together with a new generator. It is unspecified
what happens if *lo>hi*. For continuous types there is no requirement
that the values *lo* and *hi* are ever produced, but they may be,
depending on the implementation and the interval.

random :: RandomGen g => g -> (a, g)

The same as `randomR`

, but using a default range determined by the type:

randomRs :: RandomGen g => (a, a) -> g -> [a]

Plural variant of `randomR`

, producing an infinite list of
random values instead of returning a new generator.

randoms :: RandomGen g => g -> [a]

Plural variant of `random`

, producing an infinite list of
random values instead of returning a new generator.

A variant of `randomR`

that uses the global random number generator
(see System.Random).

A variant of `random`

that uses the global random number generator
(see System.Random).

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.

Signal function that transforms a signal carrying values of some type `a`

into a signal carrying values of some type `b`

. You can think of it as
(Signal a -> Signal b). A signal is, conceptually, a
function from `Time`

to value.

A single possible event occurrence, that is, a value that may or may not occur. Events are used to represent values that are not produced continuously, such as mouse clicks (only produced when the mouse is clicked, as opposed to mouse positions, which are always defined).

# Signal functions

## Basic signal functions

## Initialization

## Simple, stateful signal processing

# Events

## Basic event sources

now :: b -> SF a (Event b)Source

Event source with a single occurrence at time 0. The value of the event is given by the function argument.

:: Time | The time |

-> b | Value to produce at that time |

-> SF a (Event b) |

Event source with a single occurrence at or as soon after (local) time *q*
as possible.

repeatedly :: Time -> b -> SF a (Event b)Source

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.

afterEachCat :: [(Time, b)] -> SF a (Event [b])Source

edge :: SF Bool (Event ())Source

A rising edge detector. Useful for things like detecting key presses.
It is initialised as *up*, meaning that events occuring at time 0 will
not be detected.

## Stateful event suppression

## Pointwise functions on events

Make the NoEvent constructor available. Useful e.g. for initialization, ((-->) & friends), and it's easily available anyway (e.g. mergeEvents []).

noEventFst :: (Event a, b) -> (Event c, b)Source

Suppress any event in the first component of a pair.

noEventSnd :: (a, Event b) -> (a, Event c)Source

Suppress any event in the second component of a pair.

tag :: Event a -> b -> Event bSource

Tags an (occurring) event with a value (replacing the old value).

attach :: Event a -> b -> Event (a, b)Source

Attaches an extra value to the value of an occurring event.

lMerge :: Event a -> Event a -> Event aSource

Left-biased event merge (always prefer left event, if present).

rMerge :: Event a -> Event a -> Event aSource

Right-biased event merge (always prefer right event, if present).

merge :: Event a -> Event a -> Event aSource

Unbiased event merge: simultaneous occurrence is an error.

mergeBy :: (a -> a -> a) -> Event a -> Event a -> Event aSource

Event merge parameterized by a conflict resolution function.

mergeEvents :: [Event a] -> Event aSource

joinE :: Event a -> Event b -> Event (a, b)Source

Join (conjucntion) of two events. Only produces an event if both events exist.

filterE :: (a -> Bool) -> Event a -> Event aSource

Filter out events that don't satisfy some predicate.

mapFilterE :: (a -> Maybe b) -> Event a -> Event bSource

gate :: Event a -> Bool -> Event aSource

Enable/disable event occurences based on an external condition.

# Switching

## Basic switchers

## Parallel composition and switching

### Parallel composition and switching over collections with broadcasting

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)Source

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)Source

rpSwitchB :: Functor col => col (SF a b) -> SF (a, Event (col (SF a b) -> col (SF a b))) (col b)Source

drpSwitchB :: Functor col => col (SF a b) -> SF (a, Event (col (SF a b) -> col (SF a b))) (col b)Source

### Parallel composition and switching over collections with general routing

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)Source

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)Source

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)Source

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)Source

# Discrete to continuous-time signal functions

## Wave-form generation

trackAndHold :: a -> SF (Maybe a) aSource

## Accumulators

old_accumBy :: (b -> a -> b) -> b -> SF (Event a) (Event b)Source

dAccumHold :: a -> SF (Event (a -> a)) aSource

accumHoldBy :: (b -> a -> b) -> b -> SF (Event a) bSource

dAccumHoldBy :: (b -> a -> b) -> b -> SF (Event a) bSource

# Delays

## Basic delays

## Timed delays

# State keeping combinators

## Loops with guaranteed well-defined feedback

loopIntegral :: VectorSpace c s => SF (a, c) (b, c) -> SF a bSource

## Integration and differentiation

integral :: VectorSpace a s => SF a aSource

derivative :: VectorSpace a s => SF a aSource

imIntegral :: VectorSpace a s => a -> SF a aSource

# Noise (random signal) sources and stochastic event sources

# Reactimation

:: IO a | IO initialization action |

-> (Bool -> IO (DTime, Maybe a)) | IO input sensing action |

-> (Bool -> b -> IO Bool) | IO actuaction (output processing) action |

-> SF a b | Signal function |

-> IO () |

Convenience function to run a signal function indefinitely, using a IO actions to obtain new input and process the output.

This function first runs the initialization action, which provides the initial input for the signal transformer at time 0.

Afterwards, an input sensing action is used to obtain new input (if any) and the time since the last iteration. The argument to the input sensing function indicates if it can block. If no new input is received, it is assumed to be the same as in the last iteration.

After applying the signal function to the input, the actuation IO action is executed. The first argument indicates if the output has changed, the second gives the actual output). Actuation functions may choose to ignore the first argument altogether. This action should return True if the reactimation must stop, and False if it should continue.

Note that this becomes the program's *main loop*, which makes using this
function incompatible with GLUT, Gtk and other graphics libraries. It may also
impose a sizeable constraint in larger projects in which different subparts run
at different time steps. If you need to control the main
loop yourself for these or other reasons, use `reactInit`

and `react`

.

type ReactHandle a b = IORef (ReactState a b)Source

reactInit :: IO a -> (ReactHandle a b -> Bool -> b -> IO Bool) -> SF a b -> IO (ReactHandle a b)Source