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Very interesting. I certainly have some reading to do. Can you explain a little more the notion discrete values and sampling rates and how that applies to str

by kbeaty 12y ago

Very interesting. I certainly have some reading to do. Can you explain a little more the notion discrete values and sampling rates and how that applies to stream processing? I assume that it applies to sampling values of a process over time, but what would be an example in computation where the value would be considered continuous? Is it similar to continuous vs discrete signal processing?

tel 12y ago
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. [0] Liu, Cheng, Hudak. Causal Commutative Arrows and Their Optimization. http://cs.yale.edu/c2/images/uploads/ICFP-CCA.pdf 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/workshop-02.pdf http://haskell.cs.yale.edu/wp-content/uploads/2011/02/worksh...
- kbeaty 12y ago
  Thanks, that explains a lot. Very interesting indeed.

by kbeaty 12y ago

tel 12y ago

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. [0] Liu, Cheng, Hudak. Causal Commutative Arrows and Their Optimization. http://cs.yale.edu/c2/images/uploads/ICFP-CCA.pdf 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/workshop-02.pdf http://haskell.cs.yale.edu/wp-content/uploads/2011/02/worksh...

kbeaty 12y ago
Thanks, that explains a lot. Very interesting indeed.