[racket] Finite State Machines of Arbitrary Size using Racket's composable control
Marjin,
my attempt at an answer:
Yes, just the two-state machine is presented, but could be used for
larger FSMs.
And, yes, that would be the webserver that is provided with racket.
>> In what way is this solution impossible without it?
I represent the solution provides the following features which are
absent or difficult to implement in typical FSMs
1) no state variables, which has positive implications for threading and
scalability.
2) Related to item (1) the state of the machine is uniquely represented
by the continuation which takes the next signal as its redex
(i.e. (kont (car lst))) in function encoding-scheme-helper) **and
nothing else**.
3) transitions between states are managed entirely by the control
primitives abort and prompt and require no user code.
4) processing a signal by invoking (prompt (kont (car lst))
automatically results in a state transition
(even if just a self-transition) so long as the last statement executed
in a signal handler is an abort.
5) notational & representational fidelity with the problem being
modelled. This point is subjective, but I think the notation for the
signal-handlers associated with each statein infinite-k-pump is clear,
readable, and laconic.
6) A FSM built in this way can easily halt between signals. Jay's done
exactly this with his webserver.
I hope this is helpful and not too subjective. Let me know if
additional clarity desired.
R./
Zack
On Mon, May 21, 2012 at 3:30 AM, Marijn wrote:
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> Hi Zack,
>
> On 15-05-12 18:56, Galler wrote:
>> This code was generated in response to the user who sought to
>> implement run-length encoding of a bit-vector on Sunday night.
>>
>> I didn't post this to the board b/c there's a much easier way to
>> solve problem using regular expressions, which Eli B.
>> demonstrated.
>>
>> But, the (infinite-k-pump) function strikes me as a correct and
>> complete way to implement finite state machines (FSM) of aribtrary
>> size in racket using composable control.
>
> It seems that this function as you present it below is just the
> 2-state state-machine that solves the problem of that user, but that
> it could be used as a template for how to implement arbitrary (larger)
> FSMs.
>
>> Its a toy, but maybe of some pedagogical use.
>>
>> Jay's web server works essentially the same way, though instead of
>> one-byte signals, he's using http-requests.
>
> Interesting. That would be the webserver that's built in to Racket
> right?
>
>> Its a good 10 second answer to "what can you do with composable
>> control" that would be impossible in its absence?
>
> Unfortunately my grasp on composable control is tenuous at best, so
> this 10 second answer goes over my head :(. In what way is this
> solution impossible without it? I mean FSMs can be implemented without
> it (and not just in the theoretical Turing-complete tarpit way).
>
> Marijn
>
>
>> #lang racket
>>
>> ;Finite State Machine of arbitrary size using composable control
>>
>>
>> (require racket/control rackunit rackunit/text-ui)
>>
>> (define/contract (list-of-ranges-of-ones vtr) (-> (vectorof (or/c 1
>> 0)) list?) (read (open-input-string (with-output-to-string (λ _
>> (display "(")
>>
>> (encoding-scheme-helper (prompt (infinite-k-pump))
>>
>> (vector->list (vector-append vtr #(0)))) (display ")"))))))
>>
>> ;recursive function. Note the prompt which is how far the
>> invocation of abort, in (infinite-k-pump) wipes out stack (define
>> (encoding-scheme-helper kont lst) (unless (null? lst)
>> (encoding-scheme-helper (prompt (kont (car lst))) (cdr lst))))
>>
>> (define (infinite-k-pump) (let ((counter 0)) (letrec
>> ((incr-counter (λ _ (set! counter (add1 counter)))) (B (λ
>> (signal) (if (= signal 0) (begin (display (sub1 counter)) (display
>> ")") (incr-counter) (A (let/cc k (abort k)))) (begin
>> (incr-counter) (B (let/cc k (abort k))))))) (A (λ (signal) (if (=
>> signal 0) (begin (incr-counter) (A (let/cc k (abort k)))) (begin
>> (display "( ") (display counter) (display " ") (incr-counter) (B
>> (let/cc k (abort k)))))))) ;init function is A (A (let/cc k (abort
>> k))))))
>>
>> ;(run-tests does-it-work?) ; 12 success(es) 0 failure(s) 0 error(s)
>> 12 test(s) run
>>
>> (define does-it-work? (test-suite "Tests for FSM" (check-equal?
>> (list-of-ranges-of-ones #(0)) '()) (check-equal?
>> (list-of-ranges-of-ones #(0 0))'()) (check-equal?
>> (list-of-ranges-of-ones #(0 0 0)) '()) (check-equal?
>> (list-of-ranges-of-ones #(1)) '((0 0))) (check-equal?
>> (list-of-ranges-of-ones #(1 1)) '((0 1))) (check-equal?
>> (list-of-ranges-of-ones #(1 1 1)) '((0 2))) (check-equal?
>> (list-of-ranges-of-ones #(1 1 1 0)) '((0 2))) (check-equal?
>> (list-of-ranges-of-ones #(0 1 1 1)) '((1 3))) (check-equal?
>> (list-of-ranges-of-ones #(0 1 1 1 0)) '((1 3))) (check-equal?
>> (list-of-ranges-of-ones #( 0 1 1 1 0 0 0 1 1 1 0)) '((1 3) (7 9)))
>> (check-equal? (list-of-ranges-of-ones #( 1 1 1 1 0 0 0 1 1 1 1))
>> '((0 3) (7 10))) (check-equal? (list-of-ranges-of-ones #( 0 1 0 1 0
>> 1 0 1 0 1 0)) '((1 1) (3 3) (5 5) (7 7) (9 9)))))
>>
>> ____________________ Racket Users list:
>> http://lists.racket-lang.org/users
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