Yampa/reactimate

reactimate :: IO a                          -- init
           -> (Bool -> IO (DTime, Maybe a)) -- input/sense
           -> (Bool -> b -> IO Bool)        -- output/actuate
           -> SF a b                        -- process/signal function
           -> IO ()

The Bool parameter of sense and actuate are unused if you look up the definition of reactimate so just ignore them (cf. the explanations below).

reactimate basically is an input-process-output loop and forms the interface between (pure) Yampa signal functions and the (potentially impure) external world. More specifically, a Yampa signal function of type SF a b is an abstract data type that transforms a signal of type Time -> a into a signal of type Time -> b (note that one does not have direct access to signals in Yampa but just to signal functions). The Time parameter here is assumed to model continuous time but to evaluate a signal function (or a signal for that matter) it is necessary to sample the signals at discrete points in time. This is exactly what reactimate does (among other things).

Further explanations

• The init action is rather self-explanatory; it executes an initial IO action (e.g. print a welcome message), which then yields an initial sample of type a for the signal function that is passed to reactimate as the last argument.
• The sense argument is then evaluated at False and should return an IO action yielding a pair that contains the time passed since the last sample and a new sample of type a (wrapped in a Maybe) for the signal function. If the second component of sense's return value is Nothing then the previous sample is used again.
• actuate is evaluated at True and the signal function's output of type b, obtained by processing the input sample previously provided by sense. actuate's job now is to process the output (e.g. render a collection of objects contained in it) in an IO action that yields a result of type Bool. If this result is True the processing loop stops (i.e. the IO action defined by reactimate returns ()).
• Finally, the last argument of reactimate is the signal function to be run (or "animated"). Keep in mind that the signal function may take pretty complex forms like a parallel switch embedded in a loop.

Example

To illustrate this, here's a simple example of a Hello World program but with some time dependence added. Its purpose is to print "Hello... wait for it..." to the console once and then wait for 2 seconds until it prints "World!" and then stops.

import Control.Monad
import Data.IORef
import Data.Time.Clock
import FRP.Yampa
 
twoSecondsPassed :: SF () Bool
twoSecondsPassed = time >>> arr (> 2)
 
main :: IO ()
main = do
  t <- getCurrentTime
  timeRef <- newIORef t
  reactimate initialize (sense timeRef) actuate twoSecondsPassed

initialize :: IO ()
initialize = putStrLn "Hello... wait for it..." 

actuate :: Bool -> Bool -> IO Bool
actuate _ x = when x (putStrLn "World!") >> return x

sense :: IORef UTCTime -> Bool -> IO (Double, Maybe ())
sense timeRef _ = do
  now      <- getCurrentTime
  lastTime <- readIORef timeRef
  writeIORef timeRef now
  let dt = now `diffUTCTime` lastTime
  return (realToFrac dt, Just ())

Note that as soon as x in the definition of actuate becomes True (that is after 2 seconds), actuate returns True, hence reactimate returns () and the program stops. If we change the definition of actuate to always return False the line "World!" will be print out indefinitely.

Precision Issues

In the above example, we used the standard Data.Time.Clock module to measure time differences. One should not use System.CPUTime because its precision is hardware dependent and can be very low. E.g. on a Core i7-2720QM, the precision is reduced by a factor of 10¹⁰ compared to Data.Time.Clock (10ms vs. 1ps). This hardware dependence and potentially low precision make System.CPUTime unusable even for simple real time applications (like the game Pong) because the integral and derivative signal functions provided by Yampa behave unpredictably. This results in programs being highly system dependent; e.g. the ball in Pong moving significantly faster on faster hardware or even moving through a paddle because a collision is missed.