It's very similar to continuous/discrete DSP. The classic example is the integral or the feedback loop. We often talk about circuits which have continuous logic in terms of integrators and feedback loops. Direct from [0] we have a computation of
Exp[t] = 1 + Integral[Exp[x], {x, 0, t}]
as
exp :: SF () Double
exp = proc () -> do
rec let e = 1 + i
i <- integral −< e
returnA −< e
The integral is approximate (of course) but the algorithm holds to approximation no matter what the sampling rate is---that can be chosen by the consumer of the algorithm. From [1] you have an example from a vision system where the algorithm is specified in physical terms w.r.t. the motion of vehicles within a video frame. Again, the sampling occurs when the FRP computation is executed not when it's constructed.
Probably the most tangible example for this audience is thinking about Javascript GUIs. A Javascript GUI might be thought of as depending upon continuous signals like the mouse position, current time, scroll position, etc and also a set of (instantaneous) events like mouse clicks, new data arriving from asynchronous requests, etc. The output is a continuous "state of the GUI" signal.
Ultimately, the actual mouse position and painting loops are discrete, obviously, but their sample rates may be chosen independently of the actual business logic.
Comments
It's very similar to continuous/discrete DSP. The classic example is the integral or the feedback loop. We often talk about circuits which have continuous logic in terms of integrators and feedback loops. Direct from [0] we have a computation of
as The integral is approximate (of course) but the algorithm holds to approximation no matter what the sampling rate is---that can be chosen by the consumer of the algorithm. From [1] you have an example from a vision system where the algorithm is specified in physical terms w.r.t. the motion of vehicles within a video frame. Again, the sampling occurs when the FRP computation is executed not when it's constructed.Probably the most tangible example for this audience is thinking about Javascript GUIs. A Javascript GUI might be thought of as depending upon continuous signals like the mouse position, current time, scroll position, etc and also a set of (instantaneous) events like mouse clicks, new data arriving from asynchronous requests, etc. The output is a continuous "state of the GUI" signal.
Ultimately, the actual mouse position and painting loops are discrete, obviously, but their sample rates may be chosen independently of the actual business logic.
[0] Liu, Cheng, Hudak. Causal Commutative Arrows and Their Optimization. http://cs.yale.edu/c2/images/uploads/ICFP-CCA.pdf
[1] Nilsson, Courtney, Peterson. Functional Reactive Programming, Continued. http://haskell.cs.yale.edu/wp-content/uploads/2011/02/worksh...
Thanks, that explains a lot. Very interesting indeed.