Friday, August 20, 2010

Mixing monadic and direct-style code with delimited continuations

The Lwt library is a really nice way to write concurrent programs. A big downside, however, is that you can’t use direct-style libraries with it. Suppose we’re writing an XMPP server, and we want to parse XML as it arrives over a network connection, using Daniel Bünzli’s nice xmlm library. Xmlm can read from a string, or from a Pervasives.in_channel, or you can give it a function of type (unit -> int) to return the next character of input. But there is no way to have it read from an Lwt thread; that is, we can’t give it a function of type (unit -> int Lwt.t), since it doesn’t know what do with an Lwt.t. To keep track of the parser state at the point the input blocks, the whole library would need to be rewritten in Lwt style (i.e. monadic style).

Now, Lwt does provide the Lwt_preemptive module, which gives you a way to spin off a preemptive thread (implemented as an ordinary OCaml thread) and wait for its result in the usual Lwt way with bind. This is useful, but has two drawbacks: preemptive threads are preemptive, so you’re back to traditional locking if you want to operate on shared data; and preemptive threads are threads, so they are much heavier than Lwt threads, and (continuing the XMPP hypothetical) it may not be feasible to use one per open connection.


What we would really like is to be able spin off a cooperative, direct-style thread. The thread needs a way to block on Lwt threads, but when it blocks we need to be able to schedule another Lwt thread. As a cooperative thread it of course has exclusive access to the process state while it is running. A cooperative, direct-style thread is sometimes called a coroutine (although to me that word connotes a particular style of inter-thread communication as well, where values are yielded between coroutines), or a fiber.

Here’s an API for mixing Lwt threads with fibers:

  val start : (unit -> 'a) -> 'a Lwt.t 
  val await : 'a Lwt.t -> 'a 

The start function spins off a fiber, returning an Lwt thread which is woken with the result of the fiber once it completes. The await function (which may be called only from within a fiber) blocks on the result of an Lwt thread, allowing another Lwt thread to be scheduled while it is waiting.

With this API we could implement our XMPP server by calling xmlm from within a fiber, and passing it a function that awaits the next character available on the network connection. But how do we implement it?

Delimited continuations

Oleg Kiselyov’s recent announcement of a native-code version of his Delimcc library for delimited continuations in OCaml reminded me of two things:

  1. I should find out what delimited continuations are.
  2. They sound useful for implementing fibers.

The paper describing the library, Delimited Control in OCaml, Abstractly and Concretely, has a pretty good overview of delimited continuations, and section 2 of A Monadic Framework for Delimited Continuations is helpful too.

The core API is small:

  type 'a prompt 
  type ('a,'b) subcont 
  val new_prompt   : unit -> 'a prompt 
  val push_prompt  : 'a prompt -> (unit -> 'a) -> 'a 
  val take_subcont : 
    'b prompt -> (('a,'b) subcont -> unit -> 'b) -> 'a 
  val push_subcont : ('a,'b) subcont -> (unit -> 'a) -> 'b 

I find it easiest to think about these functions as operations on the stack. A prompt is an identifier used to mark a point on the stack (the stack can be marked more than once with the same prompt). The function new_prompt makes a new prompt which is not equal to any other prompt.

The call push_prompt p f marks the stack with p then runs f, so the stack, growing to the right, looks like


where ABCD are stack frames in the continuation of the call to push_prompt, and EFGH are frames created while running f. If f returns normally (that is, without calling take_subcont) then its return value is returned by push_prompt, and we are back to the original stack ABCD.

If take_subcont p g is called while running f, the stack fragment EFGH is packaged up as an ('a,'b) subcont and passed to g. You can think of an ('a,'b) subcont as a function of type 'a -> 'b, where 'a is the return type of the call to take_subcont and 'b is the return type of the call to push_prompt. Take_subcont removes the fragment pEFGH from the stack, and there are some new frames IJKL from running g, so we have


Now g can make use of the passed-in subcont using push_subcont. (Thinking of a subcont as a function, push_subcont is just a weird function application operator, which takes the argument as a thunk). Then the stack becomes


Of course g can call the subcont as many times as you like.

A common pattern is to re-mark the stack with push_prompt before calling push_subcont (so take_subcont may be called again). There is an optimized version of this combination called push_delim_subcont, which produces the stack


The idea that a subcont is a kind of function is realized by shift0, which is like take_subcont except that instead of passing a subcont to g it passes an ordinary function. The passed function just wraps a call to push_delim_subcont. (It is push_delim_subcont rather than push_subcont for historical reasons I think—see the Monadic Framework paper for a comparison of various delimited continuation primitives.)

Implementing fibers

To implement fibers, we want start f to mark the stack, then run f; and await t to unwind the stack back to the mark, wait for t to complete, then restore the stack. Here is start:

  let active_prompt = ref None 
  let start f = 
    let t, u = Lwt.wait () in 
    let p = Delimcc.new_prompt () in 
    active_prompt := Some p; 
    Delimcc.push_prompt p begin fun () -> 
      let r = 
        try Lwt.Return (f ()) 
        with e -> Lwt.Fail e in 
      active_prompt := None; 
      match r with 
        | Lwt.Return v -> Lwt.wakeup u v 
        | Lwt.Fail e -> Lwt.wakeup_exn u e 
        | Lwt.Sleep -> assert false 

We make a sleeping Lwt thread, and store a new prompt in a global (this is OK because we won’t yield control to another Lwt thread before using it; of course this is not safe with OCaml threads). Then we mark the stack with push_prompt and run the fiber. (The let r = ... match r with ... is to avoid calling Lwt.wakeup{,_exn} in the scope of the try; we use Lwt.state as a handy type to store either a result or an exception.) If the fiber completes without calling await then all we do is wake up the Lwt thread with the returned value or exception.

Here is await:

  let await t = 
    let p = 
      match !active_prompt with 
        | None -> failwith "await called outside start" 
        | Some p -> p in 
    active_prompt := None; 
    match Lwt.poll t with 
      | Some v -> v 
      | None -> 
          Delimcc.shift0 p begin fun k -> 
            let ready _ = 
              active_prompt := Some p; 
              k (); 
              Lwt.return () in 
            ignore (Lwt.try_bind (fun () -> t) ready ready) 
          match Lwt.poll t with 
            | Some v -> v 
            | None -> assert false 

We first check to be sure that we are in the scope of start, and that t isn’t already completed (in which case we just return its result). If we actually need to wait for t, we call shift0, which capture the stack fragment back to the push_prompt call in start (this continuation includes the subsequent match Lwt.poll t and everything after the call to await), then try_bind so we can restore the stack fragment when t completes (whether by success or failure). When t completes, the ready function restores the global active_prompt, in case the fiber calls await again, then restores the stack by calling k (recall that this also re-marks the stack with p, which is needed if the fiber calls await again).

It’s pretty difficult to follow what’s going on here, so let’s try it with stacks. After calling start we have


where ABCD is the continuation of push_prompt in start (just the return of t) and EFGH are frames created by the thunk passed to start. Now, a call to await (on an uncompleted thread) calls shift0, which packs up EFGH as k and unwinds the stack to p. The function passed to shift0 stores k in ready but doesn’t call it, and control returns to start (since the stack has been unwound).

The program continues normally until t completes. Now control is in Lwt.run_waiters running threads that were waiting on t; one of them is our ready function. When it is called, the stack is re-marked and EFGH is restored, so we have


where QRST is wherever we happen to be in the main program, ending in Lwt.run_waiters. Now, EFGH ends with the second call to match Lwt.poll in await, which returns the value of t and continues the thunk passed to start. The stack is now marked with p inside Lwt.run_waiters, so when await is called again control returns there.

Events vs. threads

We have seen that we can use fibers to write Lwt threads in direct style. Should we abandon Lwt’s monadic style entirely, and use Lwt only for its event handling?

First, how does each style perform? Every time a fiber blocks and resumes, we have to copy, unwind, and restore its entire stack. With Lwt threads, the “stack” is a bunch of linked closures in the heap, so we don’t need to do anything to block or resume. On the other hand, building and garbage-collecting the closures is more expensive than pushing and popping the stack. We can imagine that which style performs better depends on the thread: if it blocks infrequently enough, the amortized cost of copying and restoring the stack might be lower than the cost of building and garbage-collecting the closures. (We can also imagine that a different implementation of delimited continuations might change this tradeoff.)

Second, how does the code look? The paper Cooperative Task Management without Manual Stack Management considers this question in the context of the “events vs. threads” debate. Many of its points lose their force when translated to OCaml and Lwt—closures, the >>= operator, and Lwt’s syntax extension go a long way toward making Lwt code look like direct style—but some are still germane. In favor of fibers is that existing direct-style code need not be rewritten to work with Lwt (what motivated us in the first place). In favor of monadic style is that the type of a function reflects the possibility that it might block, yield control to another thread, and disturb state invariants.

Direct-style FRP

We could apply this idea, of replacing monadic style with direct style using delimited continuations, to other monads—in particular to the froc library for functional reactive programming. (The Scala.React FRP library also uses delimited continuations to implement direct style; see Deprecating the Observer Pattern for details.)

Here’s the API:

  val direct : (unit -> 'a) -> 'a Froc.behavior 
  val read : 'a Froc.behavior -> 'a 

Not surprisingly, it’s just the same as for Lwt, but with a different monad and different names (I don’t know if direct is quite right but it is better than start). There is already a function Froc.sample with the same type as read, but it has a different meaning: sample takes a snapshot of a behavior but creates no dependency on it.

The implementation is very similar as well:

  let active_prompt = ref None 
  let direct f = 
    let t, u = Froc_ddg.make_changeable () in 
    let p = Delimcc.new_prompt () in 
    active_prompt := Some p; 
    Delimcc.push_prompt p begin fun () -> 
      let r = 
        try Froc_ddg.Value (f ()) 
        with e -> Froc_ddg.Fail e in 
      active_prompt := None; 
      Froc_ddg.write_result u r 
    (Obj.magic t : _ Froc.behavior) 

This is essentially the same code as start, modulo the change of monad. However, some of the functions we need aren’t exported from Froc, so we need to use the underlying Froc_ddg module and magic the result at the end. Froc_ddg.make_changeable is the equivalent of Lwt.wait: it returns an “uninitialized” monadic value along with a writer for that value. We use Froc_ddg.result instead of Lwt.state to store a value or exception, and Froc_ddg.write_result instead of the pattern match and Lwt.wakeup{,_exn}.

  let read t = 
    let p = 
      match !active_prompt with 
        | None -> failwith "read called outside direct" 
        | Some p -> p in 
    active_prompt := None; 
    Delimcc.shift0 p begin fun k -> 
      Froc.notify_result_b t begin fun _ -> 
        active_prompt := Some p; 
        k () 
    Froc.sample t 

And this is essentially the same code as await. A Froc.behavior always has a value, so we don’t poll it as we did with Lwt.t, but go straight to shift0. We have Froc.try_bind but it’s a little more compact to use use notify_result_b, which passes a result.

Monadic reflection

The similarity between these implementations suggests that we could use the same code to get a direct style version of any monad; we only need a way to create an uninitialized monadic value, then set it. The call to Lwt.poll in await is an optimization which we would have to forgo. (In both these examples we have a monad with failure, and try_bind, but we could do without it.)

A little googling turns up Andrzej Filinski’s paper Representing Monads, which reaches the same conclusion, with a lot more rigor. In that work start/direct are called reify, and await/read are called reflect. Reflect is close to the implementations above, but in reify the paper marks the stack inside a function passed to bind rather than creating an uninitialized monadic value and later setting it.

This makes sense—inside bind an uninitialized monadic value is created, then set from the result of the function passed to bind. So we are partially duplicating bind in the code above. If we mark the stack in the right place we should be able to use bind directly. It is hard to see how to make the details work out, however, since Lwt.bind and Froc.bind each have some cases where uninitialized values are not created.

(You can find the complete code for Lwt fibers here and direct-style froc here.)

(revised 10/22)

1 comment:

  1. Very nice post! It must have been quite a bit of work, Thank You. I'm still reading it. Nice that you bring up FRP.

    BTW I've been watching recently Channel9 lectures involving monads: and -- rather basic material but very entertaining.