Fun with automata
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The document outlines a presentation on automata by John A. De Goes, focusing on deterministic transducers and their benefits, including composability and concurrency. It includes definitions, examples, and exercises for developing deterministic transducer methods and implementing a streaming analytics framework. Additionally, there is a task to create a recognizer for a specific language pattern.
![trait DT[A, B] {
def ! (input: A): (B, DT[A, B])
}
object DT {
def apply[A, B](f: A => (B, DT[A, B])) =
new DT[A, B] { def ! (v: A) = f(v) }
}
Thursday, May 24, 12](https://image.slidesharecdn.com/funwithautomata-120525113133-phpapp02/85/Fun-with-automata-7-320.jpg)
![val d1 = {
def f(b: Boolean): DT[Int, Int] =
DT { v =>
val output = if (b) v * 2 else v
(output, f(!b))
}
f(false)
}
Thursday, May 24, 12](https://image.slidesharecdn.com/funwithautomata-120525113133-phpapp02/85/Fun-with-automata-8-320.jpg)
![trait DT[A, B] {
def ! (input: A): (B, DT[A, B])
def !! (inputs: A*): (List[B], DT[A, B]) read many
def >>> [C] (that: DT[B, C]): DT[A, C] compose
def map[C](f: B => C): DT[A, C] output transform
def contramap[C](f: C => A): DT[C, B] input transform
def & [C, D](that: DT[C, D]): parallelize
DT[(A, C), (B, D)]
}
Thursday, May 24, 12](https://image.slidesharecdn.com/funwithautomata-120525113133-phpapp02/85/Fun-with-automata-10-320.jpg)
![Helpers
def identity[A]: DT[A, A]
def constant[A, B](b: B): DT[A, B]
def rep[A]: DT[A, (A, A)]
def rep3[A]: DT[A, ((A, A), A)]
def merge[A, B, C](f: (A, B) => C): DT[(A, B), C]
def merge3[A, B, C, D](f: (A, B, C) => D): DT[((A, B), C), D]
Thursday, May 24, 12](https://image.slidesharecdn.com/funwithautomata-120525113133-phpapp02/85/Fun-with-automata-11-320.jpg)
Fun with automata
- 1. Frontier Developers 6:00: Pizza & Networking 6:20: Presentation https://github.com/jdegoes/fun-with-automata WIFI: Scriblove / scribble Thursday, May 24, 12
- 2. Fun with Automata! https://github.com/jdegoes/fun-with-automata John A. De Goes @jdegoes http://precog.com Thursday, May 24, 12
- 3. Automata Abstract machines that transition between states based on reading of input. Transducers Automata that read and write. Deterministic Transducers Output deterministically depends on current state and prior input. Thursday, May 24, 12
- 4. DTs vs Functions? Function A B DT A (B, DT) Thursday, May 24, 12
- 5. “Functions with a memory.” Thursday, May 24, 12
- 6. Benefits • Purely-functional yet stateful • Incredibly composable • Safely concurrent • Recoverable Thursday, May 24, 12
- 7. trait DT[A, B] { def ! (input: A): (B, DT[A, B]) } object DT { def apply[A, B](f: A => (B, DT[A, B])) = new DT[A, B] { def ! (v: A) = f(v) } } Thursday, May 24, 12
- 8. val d1 = { def f(b: Boolean): DT[Int, Int] = DT { v => val output = if (b) v * 2 else v (output, f(!b)) } f(false) } Thursday, May 24, 12
- 9. val (v1, d2) = d1 ! 1 // v1 = 1 val (v2, d3) = d2 ! 1 // v2 = 2 ... Thursday, May 24, 12
- 10. trait DT[A, B] { def ! (input: A): (B, DT[A, B]) def !! (inputs: A*): (List[B], DT[A, B]) read many def >>> [C] (that: DT[B, C]): DT[A, C] compose def map[C](f: B => C): DT[A, C] output transform def contramap[C](f: C => A): DT[C, B] input transform def & [C, D](that: DT[C, D]): parallelize DT[(A, C), (B, D)] } Thursday, May 24, 12
- 11. Helpers def identity[A]: DT[A, A] def constant[A, B](b: B): DT[A, B] def rep[A]: DT[A, (A, A)] def rep3[A]: DT[A, ((A, A), A)] def merge[A, B, C](f: (A, B) => C): DT[(A, B), C] def merge3[A, B, C, D](f: (A, B, C) => D): DT[((A, B), C), D] Thursday, May 24, 12
- 12. Exercise 1 Develop DT and some of its helper methods in a language of your choice. Thursday, May 24, 12
- 13. Exercise 2 Develop a simple streaming analytics framework, with aggregation and windowing. Thursday, May 24, 12
- 14. Exercise 3 Create a recognizer for the language defined by the grammar ab* (that is, one ‘a’ character followed by zero or more ‘b’ characters). The recognizer emits true’s until a character breaks the pattern, then emits false’s continuously. Thursday, May 24, 12