Concurrent Programming with Effect Handlers

Originally written as materials for the CUFP 17 tutorial.

Setting up

Install a compatible OCaml compiler

Up to date instructions can be found at https://github.com/ocaml-multicore/awesome-multicore-ocaml#installation

Install required tools

$ opam install ocamlbuild ocamlfind

Outline

The tutorial is structured as follows:

Algebraic Effects and Handlers.
1.1. Recovering from errors
1.2. Basics
Shallow vs Deep Handlers.
Delimited Continuations: A deep dive.
3.1. Examining effect handlers through GDB
Generators & Streams.
4.1. Message passing
4.2. Generators from iterators
4.3. Using the generator
4.4. Streams
Cooperative Concurrency.
5.1. Coroutines
5.2. Async/Await
Asynchronous I/O.
6.1. Blocking echo server
6.2. Asynchronous echo server
Conclusion.

The tutorial also includes the following exercises:

Implement exceptions from effects ★☆☆☆☆
Implement state put and history ★★☆☆☆
Derive generator for an arbitrary iterator ★★★★☆
Same fringe problem ★☆☆☆☆
Implement async/await functionality ★★★☆☆
Implement asynchronous accept and send ★☆☆☆☆

1. Algebraic Effects and Handlers

An algebraic effect handler is a programming abstraction for manipulating control-flow in a first-class fashion. They generalise common abstractions such as exceptions, generators, asynchronous I/O, or concurrency, as well as other seemingly esoteric programming abstractions such as transactional memory and probabilistic computations.

Operationally, effect handlers offer a form of first-class, restartable exception mechanism. In this tutorial, we shall introduce gently algebraic effect and handlers with gentle examples and then continue on to more involved examples.

1.1. Recovering from errors

Lets start with an example. Consider a program which reads a list of numbers from standard input and prints the sum of the numbers:

let rec sum_up acc =
    let l = input_line stdin in
    acc := !acc + int_of_string l;
    sum_up acc 

let _ = 
  let r = ref 0 in
  try sum_up r with
  | End_of_file -> Printf.printf "Sum is %d\n" !r

The above program is available in sources/input_line_exn.ml. You can run this program as:

$ cd sources
$ ocaml input_line_exn.ml
10
20
(* ctrl+d *)
Sum is 30

The input_line function returns a string for the input line and raises End_of_file if it encounters end of file character. We use int_of_string to convert the input string to a number. This works as long as the input is a number. If not, int_of_string raises Failure and this program blows up:

$ ocaml input_line_exn.ml
10
20
MMXVII
Fatal error: exception Failure("int_of_string")

We could print a better error message (sources/input_line_exn2.ml):

exception Conversion_failure of string

let int_of_string l =
  try int_of_string l with
  | Failure _ -> raise (Conversion_failure l)

let rec sum_up acc =
    let l = input_line stdin in
    acc := !acc + int_of_string l;
    sum_up acc

let _ =
  let r = ref 0 in
  try sum_up r with
  | End_of_file -> Printf.printf "Sum is %d\n" !r
  | Conversion_failure s ->
      Printf.fprintf stderr "Conversion failure \"%s\"\n%!" s

The program now prints a friendlier error message:

$ ocaml input_line_exn2.ml
10
20
MMXVII
Conversion failure "MMXVII"

and, unfortunately, the program terminates. We really wish the program kept going:

let _ =
  let r = ref 0 in
  try sum_up r with
  | End_of_file -> Printf.printf "Sum is %d\n" !r
  | Conversion_failure s ->
      Printf.fprintf stderr "Conversion failure \"%s\"\n%!" s
      (* Wish it kept going: continue with 0 *)

We could change the code, but if sum_up function was from a third-party library, changing code is generally not an acceptable option. The issue here is that the library determines whether the error is fatal or not. What we would like is for the client of a library determining whether an error is fatal or not.

1.2. Basics

Algebraic effect handlers allow you to recover from errors. The following code is available in sources/input_line_eff.ml

open Effect
open Effect.Deep

type _ Effect.t += Conversion_failure : string -> int Effect.t

let int_of_string l =
  try int_of_string l with
  | Failure _ -> perform (Conversion_failure l)

let rec sum_up acc =
    let l = input_line stdin in
    acc := !acc + int_of_string l;
    sum_up acc

let _ =
  Printf.printf "Starting up. Please input:\n%!";
  let r = ref 0 in
  match_with sum_up r
  { effc = (fun (type c) (eff: c Effect.t) ->
      match eff with
      | Conversion_failure s -> Some (fun (k: (c,_) continuation) ->
              Printf.fprintf stderr "Conversion failure \"%s\"\n%!" s;
              continue k 0)
      | _ -> None
    );
    exnc = (function
        | End_of_file -> Printf.printf "Sum is %d\n" !r
        | e -> raise e
    );
    (* Shouldn't reach here, means sum_up returned a value *)
    retc = fun _ -> failwith "Impossible, sum_up shouldn't return"
  }

First, let’s run this program:

$ ocaml input_line_eff.ml
10
20
MMXVII
Conversion failure "MMXVII"
30
(* ctrl+d *)
Sum is 60

We've recovered from the conversion error and kept going. Algebraic effects and handlers are similar to exceptions in that we can declare new effects:

type _ Effect.t += Conversion_failure : string -> int Effect.t
(* c.f. [exception Conversion_failure of string] *)

Effects are declared by adding constructors to an extensible variant type defined in the Effect module.

Unlike exceptions, performing an effect returns a value. The declaration here says that Conversion_failure is an algebraic effect that takes a string parameter, which when performed, returns an integer.

Just like exceptions, effects are values. The type of Conversion_failure "MMXVII" is int Effect.t, where int is the result of performing the effect. We perform the effect with perform : 'a Effect.t -> 'a primitive (c.f. raise : exn -> 'a (* bottom *)).

Effect handlers are defined in the modules Effect.Deep and Effect.Shallow. We'll discuss the differences between the two later.

module Deep : sig
  (** Some contents omitted *)

  type ('a,'b) handler =
    { retc: 'a -> 'b;
      exnc: exn -> 'b;
      effc: 'c.'c t -> (('c,'b) continuation -> 'b) option }
  (** [('a,'b) handler] is a handler record with three fields -- [retc]
      is the value handler, [exnc] handles exceptions, and [effc] handles the
      effects performed by the computation enclosed by the handler. *)

  val match_with: ('c -> 'a) -> 'c -> ('a,'b) handler -> 'b
  (** [match_with f v h] runs the computation [f v] in the handler [h]. *)

  type 'a effect_handler =
    { effc: 'b. 'b t -> (('b, 'a) continuation -> 'a) option }
  (** ['a effect_handler] is a deep handler with an identity value handler
      [fun x -> x] and an exception handler that raises any exception
      [fun e -> raise e]. *)

  val try_with: ('b -> 'a) -> 'b -> 'a effect_handler -> 'a
  (** [try_with f v h] runs the computation [f v] under the handler [h]. *)
end

module Shallow : sig
  (** Some contents omitted *)

  type ('a,'b) handler =
    { retc: 'a -> 'b;
      exnc: exn -> 'b;
      effc: 'c.'c t -> (('c,'a) continuation -> 'b) option }
  (** [('a,'b) handler] is a handler record with three fields -- [retc]
      is the value handler, [exnc] handles exceptions, and [effc] handles the
      effects performed by the computation enclosed by the handler. *)

  val continue_with : ('c,'a) continuation -> 'c -> ('a,'b) handler -> 'b
  (** [continue_with k v h] resumes the continuation [k] with value [v] with
      the handler [h].
      @raise Continuation_already_resumed if the continuation has already been
      resumed.
   *)
end

The handlers are records with three fields and are called in the context of match_with, try_with, or continue_with:

retc is the function that is called when the computation returns a value - i.e. no effects or exceptions were performed/raised in the computation. The function has one parameter: the value of the computation

exnc is called when the computation throws an exception. It takes the exception as a parameter.

effc is the function that handles the effects. It has type 'c. 'c Effect.t -> ('c, 'a) continuation -> 'b) option

Effects are strongly typed, but the handler function can handle multiple effects and has to be generic over every possible type (which is potentially all of them since the effects variant can always be extended further), hence the 'c existential type. effc returns an option where a None value means ignore the effect (and crash the program if not handled somewhere else). A Some value holds a function that takes a parameter commonly called k

  { effc = (fun (type c) (eff: c Effect.t) ->
      match eff with
      | Conversion_failure s -> Some (fun (k: (c,_) continuation) ->
              Printf.fprintf stderr "Conversion failure \"%s\"\n%!" s;
              continue k 0)
      | _ -> None
    )
   }

We need to declare a locally abstract type c in order to tell the compiler that eff and k are constrained on the same type.

The parameter k, is the delimited continuation between the point of performing the effect and the effect handler. The delimited continuation is like a dynamically defined function, that can be called and returns a value. The type of k in this case is (int, int) continuation, which says that the continuation expects an integer to continue (the first type parameter), and returns with an integer (the second type parameter).

The delimited continuation is resumed with Effect.Deep's continue : ('a,'b) continuation -> 'a -> 'b. In this example, continue k 0 resumes the continuation with 0, and the corresponding perform (Conversion_failure l) returns with 0.

If we do want to consider the error to be fatal (sources/input_line_eff2.ml), then we can discontinue : ('a,'b) continuation -> exn -> 'b the continuation so that it raises an exception at the perform point.

  match_with sum_up r
  { effc = (fun (type a) (e: a t) ->
      match e with
      | Conversion_failure s -> Some (fun (k: (a,_) continuation) ->
          Printf.fprintf stderr "Conversion failure \"%s\"\n%!" s;
          discontinue k (Failure "int_of_string"))
      | _ -> None
    );
    exnc = (function
        | End_of_file -> Printf.printf "Sum is %d\n" !r
        | e -> raise e
    );
    (* Shouldn't reach here, means sum_up returned a value *)
    retc = fun v -> v
  }

Now,

$ ocaml input_line_eff2.ml
10
20
MMXVII
Conversion failure "MMXVII"
Fatal error: exception Failure("int_of_string")

1.2.1. Effects are unchecked

Unlike Eff, Koka, Links, and other languages that support effect handlers, effects in Multicore OCaml are unchecked currently. A program that does not handle a performed effect fails with a runtime error.

Let's fire up the OCaml top-level:

$ ocaml
OCaml version 5.0.0~beta1

# open Effect;;
# type _ Effect.t += E : unit Effect.t;;
type _ Stdlib.Effect.t += E : unit Effect.t
# let f () = perform E;;
val f : unit -> unit = <fun>
# f ();;
Exception: Stdlib.Effect.Unhandled(E)
# open Effect.Deep;;
# try_with f () {effc = (fun (type c) (eff: c Effect.t) ->
      match eff with
      | E -> Some (fun (k: (c,_) continuation) -> continue k ())
      | _ -> None
  )};;
- : unit = ()

Exercise 1: Implement exceptions from effects ★☆☆☆☆

As mentioned before, effects generalise exceptions. Exceptions handlers are effect handlers that ignore the continuation. Your task is to implement exceptions in terms of effects. The source file is sources/exceptions.ml.

2. Shallow vs Deep Handlers

The OCaml standard library provides two different modules for handling effects: Effect.Deep and Effect.Shallow. When a deep handler returns a continuation, the continuation also includes the handler. This means that, when the continuation is resumed, the effect handler is automatically re-installed, and will handle the effect(s) that the computation may perform in the future.

Shallow handlers on the other hand, allow us to change the handlers every time an effect is performed. Let's use them to implement state without refs. The implementation is available in sources/state1.ml.

open Printf
open Effect
open Effect.Shallow

module type STATE = sig
  type t
  val get : unit -> t
  val run : (unit -> unit) -> init:t -> unit
end

module State (S : sig type t end) : STATE with type t = S.t = struct

  type t = S.t

  type _ Effect.t += Get : t Effect.t

  let get () = perform Get

  let run f ~init =
    let rec loop : type a r. t -> (a, r) continuation -> a -> r =
      fun state k x ->
        continue_with k x
        { retc = (fun result -> result);
          exnc = (fun e -> raise e);
          effc = (fun (type b) (eff: b Effect.t) ->
            match eff with
            | Get -> Some (fun (k: (b,r) continuation) ->
                    loop state k state)
            | _ -> None)
        }
    in
    loop init (fiber f) ()
end

We use Effect.Shallow by wrapping calculations with continue_with : ('c,'a) continuation -> 'c -> ('a,'b) handler -> 'b and getting an initial continuation with val fiber : ('a -> 'b) -> ('a, 'b) continuation

In this example, we define an effect Get that returns a value of type t when performed.

module IS = State (struct type t = int end)
module SS = State (struct type t = string end)

let foo () : unit =
  printf "%d\n" (IS.get ());
  printf "%d\n" (IS.get ());
  printf "%d\n" (IS.get ());
  printf "%s\n" (SS.get ());
  printf "%s\n" (SS.get ()) 

let _ = IS.run (fun () -> SS.run foo "forty two") 42

We instantiate two state instances, one with an integer type and another with string type. Running the program returns:

$ ocaml state1.ml
42
42
42
forty two
forty two

Exercise 2: Implement state put and history ★★☆☆☆

Your task it to implement put : t -> unit that updates the state and history : unit -> t list that returns the list of values put. Do not use references. The source file is sources/state2.ml.

3. Delimited Continuations: A deep dive

EDITOR'S NOTE: The implementation has changed since this section was written. Results in gdb will differ, but the concepts of the implementation remain mostly the same.

Algebraic effect handlers in Multicore OCaml are very efficient due to several choices we make in their implementation. Understanding the implementation of delimited continuations also helps to develop a mental model for reasoning about programs that use effect handlers.

Delimited continuations that appear in the effect handler are implemented on top of fibers -- small, heap allocated stack chunks, that grow and shrink on demand. The execution stack is really a stack of fibers.

Execution stack
---------------

+----+   +----+
|    |   |    |
| f1 |<--| f2 |
|    |   |    |<- stack_pointer
+----+   +----+

An effect handler instantiates a new fiber for evaluating the expression.

try ex with
| effect e k -> ....

Execution stack
---------------

+----+   +----+    +----+
|    |   |    |    |    |
| f1 |<--| f2 | <--| ex |
|    |   |    |    |    |<- stack_pointer
+----+   +----+    +----+

Performing an effect may pop one or more of the fibers based on which handler handles the effect. The popped sequence of fibers becomes the delimited continuation.

effect E : unit 

try perform E with
| effect E k -> ....

Execution stack
---------------

+----+   +----+                                 +----+
|    |   |    |---k (delimited continuation)--->|    |
| f1 |<--| f2 |                                 | ex |
|    |   |    |<- stack_pointer                 |    |
+----+   +----+                                 +----+

When you resume the delimited continuation (with continue or discontinue) the fiber sequence that represents the delimited continuation are push on top of the execution stack. Importantly, our continuations are one-shot -- they can only be resumed once. One shotness means that we never have to copy our continuations in the case that we may need it for a future invocation. For this reason, context switching between fibers is really fast and is completely in userland code and the kernel is not involved.

3.1 Examining effect handlers through GDB

The file sources/gdb.ml:

open Effect
open Effect.Deep

type _ Effect.t += Peek : int Effect.t
                 | Poke : unit Effect.t

let rec a i = perform Peek + Random.int i
let rec b i = a i + Random.int i
let rec c i = b i + Random.int i

let rec d i =
  Random.int i +
  try_with c i
  { effc = fun (type a) (e: a t) ->
      match e with
      | Poke -> Some (fun (k: (a,_) continuation) -> continue k ())
      | _ -> None
  }

let rec e i =
  Random.int i +
  try_with d i
  { effc = fun (type a) (e: a t) ->
      match e with
      | Peek -> Some (fun (k: (a,_) continuation) ->
          Printexc.(print_raw_backtrace stdout (Effect.Deep.get_callstack k 100));
          flush stdout;
          continue k 42
        )
      | _ -> None
  }

let _ = Printf.printf "%d\n" (e 100)

illustrates the effect handler stack. Let us compile and examine the file under GDB:

$ make gdb.native 
$ gdb ./gdb.native

caml_resume is the native stub function through which a fiber is attached to the top of the execution stack and control switches to it. This happens when a new handler is installed, a continuation is resumed with continue or discontinue. Similarly caml_perform is the native function which implements perform primitive. We set breakpoints on these two functions to observe the program as it executes.

(gdb) break caml_perform
Breakpoint 1 at 0xaeca8
(gdb) break caml_resume
Breakpoint 2 at 0xaed38
(gdb) r
Starting program: /home/sudha/ocaml/temp/ocaml-effects-tutorial/sources/gdb.native 
[Thread debugging using libthread_db enabled]
Using host libthread_db library "/lib/x86_64-linux-gnu/libthread_db.so.1".

Breakpoint 1, 0x0000555555602ca8 in caml_perform ()
(gdb) bt
#0  0x0000555555602ca8 in caml_perform ()
#1  0x00005555555a3c08 in camlGdb__b_311 () at gdb.ml:7
#2  0x00005555555a3c69 in camlGdb__c_313 () at gdb.ml:9
#3  <signal handler called>
#4  0x00005555555a3cd8 in camlGdb__d_315 () at gdb.ml:13
#5  <signal handler called>
#6  0x00005555555a3db8 in camlGdb__e_329 () at gdb.ml:22
#7  0x00005555555a4034 in camlGdb__entry () at gdb.ml:33
#8  0x00005555555a13ab in caml_program ()
#9  <signal handler called>
#10 0x000055555560252f in caml_startup_common (argv=0x7fffffffda68, pooling=<optimized out>) at runtime/startup_nat.c:129
#11 0x000055555560257b in caml_startup_exn (argv=<optimized out>) at runtime/startup_nat.c:136
#12 caml_startup (argv=<optimized out>) at runtime/startup_nat.c:141
#13 0x00005555555a108c in main (argc=<optimized out>, argv=<optimized out>) at runtime/main.c:37

Enter effect handler in e. The <signal handler called> frames correspond to the transition between C frames to OCaml frames, and between OCaml frames of two different fibers. These signal handler frames have nothing to do with signals, but are just a hack to let GDB know that the execution stack is a linked list of contiguous stack chunks.

(gdb) c
Continuing.
Raised by primitive operation at Gdb.a in file "gdb.ml" (inlined), line 7, characters 14-26
Called from Gdb.b in file "gdb.ml", line 8, characters 14-17
Called from Gdb.c in file "gdb.ml", line 9, characters 14-17
Called from Gdb.d in file "gdb.ml", line 13, characters 2-159

Breakpoint 2, 0x0000555555602d38 in caml_resume ()
(gdb) bt
#0  0x0000555555602d38 in caml_resume ()
#1  0x00005555555a3db8 in camlGdb__e_329 () at gdb.ml:22
#2  0x00005555555a4034 in camlGdb__entry () at gdb.ml:33
#3  0x00005555555a13ab in caml_program ()
#4  <signal handler called>
#5  0x000055555560252f in caml_startup_common (argv=0x7fffffffda68, pooling=<optimized out>) at runtime/startup_nat.c:129
#6  0x000055555560257b in caml_startup_exn (argv=<optimized out>) at runtime/startup_nat.c:136
#7  caml_startup (argv=<optimized out>) at runtime/startup_nat.c:141
#8  0x00005555555a108c in main (argc=<optimized out>, argv=<optimized out>) at runtime/main.c:37

The control switches to the effect handler. In the effect handler for Peek in e, we get the backtrace of the continuation and print it.

This break point corresponds to continue k 42 in e.

The program terminates normally.

Continuing.
329
[Inferior 1 (process 8464) exited normally]

4. Generators & streams.

So far we've seen examples where the handler discards the continuation (exceptions) and immediately resumes the computation (state). Since the continuations are first-class values, we can also keep them around and resume them later, while executing some other code in the mean time. This functionality allows us to implement programming idioms such as generators, async/await, etc.

4.1. Message passing

Let us being with a simple example that illustrates control switching between two tasks. The two tasks run cooperatively, sending messages between each other. The source code is available in sources/msg_passing.ml.

We define an effect Xchg : int -> int for exchanging integer messages with the other task. During an exchange, the task sends as well as receives an integer.

type _ Effect.t += Xchg : int -> int Effect.t

Since the task may suspend, we need a way to represent the status of the task:

type status =
  Done
| Paused of int * (int, status) continuation

The task may either have been Done or is Paused with the message to send as well as the continuation, which expects the message to receive. The continuation results in another status when resumed. We define a step function that runs the function f for one step with argument v.

let step f v () =
  match_with f v
  { retc = (fun _ -> Done);
    exnc = (fun e -> raise e);
    effc = (fun (type b) (eff: b t) ->
        match eff with
        | Xchg m -> Some (fun (k: (b,_) continuation) ->
                Paused (m, k))
        | _ -> None
    )}

The task may perform an Xchg in which case we return its Paused state. We now define a run_both function for running two tasks concurrently.

let rec run_both a b =
  match a (), b () with
  | Done, Done -> ()
  | Paused (v1, k1), Paused (v2, k2) ->
      run_both (fun () -> continue k1 v2) (fun () -> continue k2 v1)
  | _ -> failwith "improper synchronization"

Both of the tasks may run to completion, or both may offer to exchange a message. We consider the other cases to be incorrect programs. In the latter case, we resume both of the computations with the value from the other.

let rec f name = function
  | 0 -> ()
  | n ->
      Printf.printf "%s: sending %d\n%!" name n;
      let v = perform (Xchg n) in
      Printf.printf "%s: received %d\n%!" name v;
      f name (n-1)

let _ = run_both (step (f "a") 3) (step (f "b") 3)

Finally, we test the program with a simple test.

$ ocaml msg_passing.ml
a: sending 3
b: sending 3
a: received 3
a: sending 2
b: received 3
b: sending 2
a: received 2
a: sending 1
b: received 2
b: sending 1
a: received 1
b: received 1

4.2. Generators from iterators

Iterator is a mechanism to traverse a data structure that retains the control of the traversal on the library side. An example is List.iter : ('a -> unit) -> 'a list -> unit that applies the given function to every element in the list. We can provide the following general type for iterators:

type ('elt,'container) iterator = ('elt -> unit) -> 'container-> unit

where 'elt is the type of element and 'container is the type of the container over which the function iterates.

On the other hand, a generator is a function where the client of the library has control over the traversal. We can imagine a List.generator : 'a list -> (unit -> 'a option) that returns a function, which when called returns the next element in the list. The function returns None if there are no more elements. We can provide the following general type for generator:

type 'elt generator = unit -> 'elt option

Several languages, including Python and JavaScript, provide generators as a primitive mechanism, usually through an yield primitive. Typically, the functions that can yield require special annotations (such as function*) in JavaScript, and only yield values to the immediate caller.

As we've seen in the earlier example, algebraic effect handlers provide a mechanism to suspend arbitrary computation and capture it in the continuation. Hence, we can derive the generator for an arbitrary iterator function.

Exercise 3: Derive generator for an arbitrary iterator ★★★★☆

Your task is to implement the function generate : ('elt, 'container) iterator -> 'elt generator which derives the generator for any iterator function.

Hint: Since calling the generator function is an effectful operation, you might think about saving the state of the traversal in a reference.

4.3. Using the generator

4.3.1. Traversal

You can use the generator to traverse a data structure on demand.

$ ocaml
# #use "generator.ml";;
# let gl = generate List.iter [1;2;3];;
val gl : int generator = <fun>
# gl();;
- : int option = Some 1
# gl();;
- : int option = Some 2
# gl();;
- : int option = Some 3
# gl();;
- : int option = None
# let ga = generate Array.iter [| 1.0; 2.0; 3.0 |];;
# ga();;
- : float option = Some 1.
# ga();;
- : float option = Some 2.
# ga();;
- : float option = Some 3.
# ga();;
- : float option = None

Exercise 4: Same fringe problem ★☆☆☆☆

Two binary trees have the same fringe if they have exactly the same leaves reading from left to right. Given two binary trees decide whether they have the same fringe. The source file is sources/fringe.ml.

4.4. Streams

The iterator need not necessarily be defined on finite data structure. Here is an iterator that iterates over infinite list of integers.

let rec nats : int (* init *) -> (int, unit) iterator =
  fun v f () ->
    f v; nats (v+1) f ()

Since the iteration is not over any particular container, the container type is unit. We can make a generator over this iterator, which yields an infinite sequence of integers.

let gen_nats : int generator = generate (nats 0) ()

We know that this generator does not terminate. Hence, the optional return type of generator is unnecessary. Hence, we define a type 'a stream for infinite streams:

type 'a stream = unit -> 'a

We can convert a generator to a stream easily:

let inf : 'a generator -> 'a stream  =
  fun g () ->
    match g () with
    | Some n -> n
    | _ -> assert false

Now, an infinite stream of integers starting from 0 is:

let gen_nats : int stream = inf (generate (nats 0) ());;
assert (0 = gen_nats ());;
assert (1 = gen_nats ());;
assert (2 = gen_nats ());;
assert (3 = gen_nats ());;
(* and so on *)

We can define operators over the stream such as map and filter:

let rec filter : 'a stream -> ('a -> bool) -> 'a stream =
  fun g p () ->
    let v = g () in
    if p v then v
    else filter g p ()

let map : 'a stream -> ('a -> 'b) -> 'b stream =
  fun g f () -> f (g ())

We can manipulate the streams using these operators. For example,

(* Even stream *)
let gen_even : int stream =
  let nat_stream = inf (generate (nats 0) ()) in
  filter nat_stream (fun n -> n mod 2 = 0)
;;

assert (0 = gen_even ());;
assert (2 = gen_even ());;
assert (4 = gen_even ());;
assert (6 = gen_even ());;

(* Odd stream *)
let gen_odd : int stream =
  let nat_stream = inf (generate (nats 1) ()) in
  filter nat_stream (fun n -> n mod 2 == 1)
;;


assert (1 = gen_odd ());;
assert (3 = gen_odd ());;
assert (5 = gen_odd ());;
assert (7 = gen_odd ());;

(* Primes using sieve of Eratosthenes *)
let gen_primes =
  let s = inf (generate (nats 2) ()) in
  let rs = ref s in
  fun () ->
    let s = !rs in
    let prime = s () in
    rs := filter s (fun n -> n mod prime != 0);
    prime

assert ( 2 = gen_primes ());;
assert ( 3 = gen_primes ());;
assert ( 5 = gen_primes ());;
assert ( 7 = gen_primes ());;
assert (11 = gen_primes ());;
assert (13 = gen_primes ());;
assert (17 = gen_primes ());;
assert (19 = gen_primes ());;
assert (23 = gen_primes ());;
assert (29 = gen_primes ());;
assert (31 = gen_primes ());;

5. Cooperative Concurrency

OCaml has two popular libraries for cooperative concurrency: Lwt and Async. Both libraries achieve concurrency through a concurrency monad. As a result, the programs that wish to use these libraries have to be written in monadic style. With effect handlers, the code could be written in direct style but also retain the benefit of asynchronous I/O. While the resultant system closely resembles Goroutines in Go, with effect handlers, all of this is implemented in OCaml as a library.

5.1. Coroutines

Let us begin with a simple cooperative scheduler. The source code is available in sources/cooperative.ml. The interface we'll implement first is:

module type Scheduler = sig
  val async : (unit -> 'a) -> unit
  (** [async f] runs [f] concurrently *)
  val yield : unit -> unit
  (** yields control to another task *)
  val run   : (unit -> 'a) -> unit
  (** Runs the scheduler *)
end

We declare effects for async and yield:

type _ Effect.t += Async : (unit -> 'a) -> unit Effect.t
               | Yield : unit Effect.t

let async f = perform (Async f)

let yield () = perform Yield

We use a queue for the tasks that are ready to run:

let q = Queue.create ()
let enqueue t = Queue.push t q
let dequeue () = 
  if Queue.is_empty q then () 
  else Queue.pop q ()

And finally, the main function is:

let rec run : 'a. (unit -> 'a) -> unit =
fun main ->
  match_with main ()
  { retc = (fun _ -> dequeue ());
    exnc = (fun e -> raise e);
    effc = (fun (type b) (eff: b Effect.t) ->
        match eff with
        | Async f -> Some (fun (k: (b, _) continuation) ->
                enqueue (continue k);
                run f
        )
        | Yield -> Some (fun k ->
                enqueue (continue k);
                dequeue ()
        )
        | _ -> None
    )}

If the task runs to completion (value case), then we dequeue and run the next task from the scheduler. In the case of an Async f effect, the current task is enqueued and the new task f is run. If the scheduler yields, then the current task is enqueued and some other task is dequeued and run from the scheduler. We can now write a cooperative concurrent program:

let main () =
  let mk_task name () =
    printf "starting %s\n%!" name;
    yield ();
    printf "ending %s\n%!" name
  in
  async (mk_task "a");
  async (mk_task "b")

let _ = run main

$ ocaml cooperative.ml
starting a
starting b
ending a
ending b

5.2. Async/await

We can extend the scheduler to implement async/await idiom. The interface we will implement is:

module type Scheduler = sig
  type 'a promise
  (** Type of promises *)
  val async : (unit -> 'a) -> 'a promise
  (** [async f] runs [f] concurrently *)
  val await : 'a promise -> 'a
  (** [await p] returns the result of the promise. *)
  val yield : unit -> unit
  (** yields control to another task *)
  val run   : (unit -> 'a) -> unit
  (** Runs the scheduler *)
end

We model a promise as a mutable reference that either is the list of tasks waiting on this promise to resolve (Waiting) or a resolved promise with the value (Done).

type 'a _promise =
  Waiting of ('a,unit) continuation list
| Done of 'a

type 'a promise = 'a _promise ref

Exercise 5: Implement async/await functionality ★★★☆☆

In this task, you will implement the core async/await functionality. Unlike the previous scheduler, additional work has to be done at the Async handler case to create the promise, and at task termination (value case) to update the promise and resume the waiting threads. In addition, the Await case needs to be implemented. The source file is sources/async_await.ml.

6. Asynchronous I/O

Effect handlers let us write asynchronous I/O libraries in direct-style.

6.1. Blocking echo server

As an example, sources/echo.ml is a implementation of an echo server that accepts client messages and echoes them back. Observe that all of the code is written in direct, function-calling, and apparently blocking style. We will see that the same code can be used to implement a blocking as well as non-blocking server. A non-blocking server can concurrently host multiple client sessions unlike the blocking server which serialises client sessions.

The echo server is functorized over the network interface:

module type Aio = sig
  val accept : Unix.file_descr -> Unix.file_descr * Unix.sockaddr
  val recv   : Unix.file_descr -> bytes -> int -> int -> Unix.msg_flag list -> int
  val send   : Unix.file_descr -> bytes -> int -> int -> Unix.msg_flag list -> int
  val fork   : (unit -> unit) -> unit
  val run    : (unit -> unit) -> unit
  val non_blocking_mode : bool
  (* Are the sockets non-blocking *)
end

We can satisfy this interface with functions from the Unix module:

struct
  let accept = Unix.accept
  let recv = Unix.recv
  let send = Unix.send
  let fork f = f ()
  let run f = f ()
  let non_blocking_mode = false
end

You can test this echo server as follows:

$ make echo_unix.native
$ ./echo_unix.native
Echo server listening on 127.0.0.1:9301

In another terminal, establish a client connection:

(* first client *)
$ telnet localhost 9301
Trying 127.0.0.1...
Connected to localhost.
Escape character is '^]'.
hello
server says: hello
world
server says: world

The server echoes whatever message that is sent. In another terminal, establish a second concurrent client connection:

(* second client *)
$ telnet localhost 9301
Trying 127.0.0.1...
Connected to localhost.
Escape character is '^]'.
hello
world

The server does not echo the messages since it is blocked serving the first client. Now, switch to the first client terminal, and terminate the connection:

(* first client *)
^]
telnet> (* ctrl+d *)
$

At this point, you should see that all of the messages sent by the second client has been echoed:

(* second client *)
server says: hello
server says: world

and further messages from the second client are immediately echoed.

6.2. Asynchronous echo server

We will extend our async/await implementation to support asynchronous I/O operations. The source file is sources/echo_async.ml. As usual, we declare the effects and functions to perform the effects:

type file_descr = Unix.file_descr
type sockaddr = Unix.sockaddr
type msg_flag = Unix.msg_flag

type _ Effect.t += Accept : file_descr -> (file_descr * sockaddr) Effect.t
let accept fd = perform (Accept fd)

type _ Effect.t += Recv : file_descr * bytes * int * int * msg_flag list -> int Effect.t
let recv fd buf pos len mode = perform (Recv (fd, buf, pos, len, mode))

type _ Effect.t += Send : file_descr * bytes * int * int * msg_flag list -> int Effect.t
let send fd bus pos len mode = perform (Send (fd, bus, pos, len, mode))

We define functions to poll whether a file descriptor is ready to read or write:

let ready_to_read fd =
  match Unix.select [fd] [] [] 0. with
  | [], _, _ -> false
  | _ -> true

let ready_to_write fd =
  match Unix.select [] [fd] [] 0. with
  | _, [], _ -> false
  | _ -> true

We define a type for tasks blocked on I/O, and a pair of hash tables to hold the continuations blocked on reads and writes:

type blocked = Blocked : 'a eff * ('a, unit) continuation -> blocked

(* tasks blocked on reads *)
let br = Hashtbl.create 13
(* tasks blocked on writes *)
let bw = Hashtbl.create 13

Now, the handler for Recv is:

| effect (Recv (fd,buf,pos,len,mode) as e) k ->
    if ready_to_read fd then
      continue k (Unix.recv fd buf pos len mode)
    else begin
      Hashtbl.add br fd (Blocked (e, k));
      schedule ()
    end

If the file descriptor is ready to be read, then we perform the read immediately with the blocking read form Unix module knowing that the read would not block. If not, we add the task to the blocked-on-read hash table br, and schedule the next task. The main schedule loop is:

  let rec schedule () =
    if not (Queue.is_empty q) then
      (* runnable tasks available *)
      Queue.pop q ()
    else if Hashtbl.length br = 0 && Hashtbl.length bw = 0 then
      (* no runnable tasks, and no blocked tasks => we're done. *)
      ()
    else begin (* no runnable tasks, but blocked tasks available *)
      let rd_fds = Hashtbl.fold (fun fd _ acc -> fd::acc) br [] in
      let wr_fds = Hashtbl.fold (fun fd _ acc -> fd::acc) bw [] in
      let rdy_rd_fds, rdy_wr_fds, _ = Unix.select rd_fds wr_fds [] (-1.) in
      let rec resume ht = function
        | [] -> ()
        | x::xs ->
            begin match Hashtbl.find ht x with
            | Blocked (Recv (fd, buf, pos, len, mode), k) ->
                enqueue (fun () -> continue k (Unix.recv fd buf pos len mode))
            | Blocked (Accept fd, k) -> failwith "not implemented"
            | Blocked (Send (fd, buf, pos, len, mode), k) -> failwith "not implemented"
            | Blocked _ -> failwith "impossible"
            end;
            Hashtbl.remove ht x
      in
      resume br rdy_rd_fds;
      resume bw rdy_wr_fds;
      schedule ()
    end

The interesting case is when runnable tasks are not available and there are blocked tasks. In this case, we run an iteration of the event loop. This may unblock further tasks and we continue running them.

Exercise 6: Implement asynchronous accept and send ★☆☆☆☆

In the file, sources/echo_async.ml, some of the functionality for handling Accept and Send event are not implemented. Your task is to implement these. Once you implement these primitives, you can run echo_async.native to start the asynchronous echo server. This server is able to respond to multiple concurrent clients.

7. Conclusion

Hopefully you've enjoyed the tutorial on algebraic effect handlers in Multicore OCaml. You should be familiar with:

What algebraic effects and handlers are.
Programming with algebraic effect handlers in Multicore OCaml.
Implementation of algebraic effect handlers in Multicore OCaml.
Developing control-flow abstractions such as restartable exceptions, generators, streams, coroutines, and asynchronous I/O.

7.1 Other resources

OCaml manual on Effects and handlers
effect.mli in OCaml standard library

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