## ﻿12.24 Effect handlers

- 12.24.1 Basics
- 12.24.2 Concurrency
- 12.24.3 User-level threads
- 12.24.4 Control inversion
- 12.24.5 Semantics
- 12.24.6 Shallow handlers

(Introduced in 5.0)

Note: Effect handlers in OCaml 5.0 should be considered experimental. Effect handlers are exposed in the standard library as a thin wrapper around their implementations in the runtime. They are not supported as a language feature with new syntax. You can rely on them to build non-local control-flow abstractions such as user-level threading that do not expose the effect handler primitives to the user. Expect breaking changes in the future.

Effect handlers are a mechanism for modular programming with user-defined effects. Effect handlers allow the programmers to describe computations that perform effectful operations, whose meaning is described by handlers that enclose the computations. Effect handlers are a generalization of exception handlers and enable non-local control-flow mechanisms such as resumable exceptions, lightweight threads, coroutines, generators and asynchronous I/O to be composably expressed. In this tutorial, we shall see how some of these mechanisms can be built using effect handlers.

### ﻿12.24.1 Basics

To understand the basics, let us define an effect (that is, an operation) that takes an integer argument and returns an integer result. We name this effect Xchg.

open Effect open Effect.Deep type _ Effect.t += Xchg: int -> int t let comp1 () = perform (Xchg 0) + perform (Xchg 1)

We declare the exchange effect Xchg by extending the pre-defined extensible variant type Effect.t with a new constructor Xchg: int -> int t. The declaration may be intuitively read as “the Xchg effect takes an integer parameter, and when this effect is performed, it returns an integer”. The computation comp1 performs the effect twice using the perform primitive and returns their sum.

We can handle the Xchg effect by implementing a handler that always returns the successor of the offered value:

try_with comp1 () { effc = fun (type a) (eff: a t) -> match eff with | Xchg n -> Some (fun (k: (a, _) continuation) -> continue k (n+1)) | _ -> None }
- : int = 3

try_with runs the computation comp1 () under an effect handler that handles the Xchg effect. As mentioned earlier, effect handlers are a generalization of exception handlers. Similar to exception handlers, when the computation performs the Xchg effect, the control jumps to the corresponding handler. However, unlike exception handlers, the handler is also provided with the delimited continuation k, which represents the suspended computation between the point of perform and this handler.

The handler uses the continue primitive to resume the suspended computation with the successor of the offered value. In this example, the computation comp1 performs Xchg 0 and Xchg 1 and receives the values 1 and 2 from the handler respectively. Hence, the whole expression evaluates to 3.

It is useful to note that the we must use locally abstract type (type a) in the effect handler. The type Effect.t is a GADT, and the effect declarations may have different type parameters for different effects. The type parameter a in the type a Effect.t represents the type of the value returned when performing the effect. From the fact that eff has type a Effect.t and from the fact that Xchg n has type int Effect.t, the type-checker deduces that a must be int, which is why we are allowed to pass the integer value n+1 as an argument to continue k.

Another point to note is that the catch-all case “| _ -> None” is necessary when handling effects. This case may be intuitively read as “forward the unhandled effects to the outer handler”.

In this example, we use the deep version of the effect handlers here as opposed to the shallow version. A deep handler monitors a computation until the computation terminates (either normally or via an exception), and handles all of the effects performed (in sequence) by the computation. In contrast, a shallow handler monitors a computation until either the computation terminates or the computation performs one effect, and it handles this single effect only. In situations where they are applicable, deep handlers are usually preferred. An example that utilises shallow handlers is discussed later in ‍12.24.6.

### ﻿12.24.2 Concurrency

The expressive power of effect handlers comes from the delimited continuation. While the previous example immediately resumed the computation, the computation may be resumed later, running some other computation in the interim. Let us extend the previous example and implement message-passing concurrency between two concurrent computations using the Xchg effect. We call these concurrent computations tasks.

A task either is in a suspended state or is completed. We represent the task status as follows:

type 'a status = Complete of 'a | Suspended of {msg: int; cont: (int, 'a status) continuation}

A task either is complete, with a result of type 'a, or is suspended with the message msg to send and the continuation cont. The type (int,'a status) continuation says that the suspended computation expects an int value to resume and returns a 'a status value when resumed.

Next, we define a step function that executes one step of computation until it completes or suspends:

let step (f : unit -> 'a) () : 'a status = match_with f () { retc = (fun v -> Complete v); exnc = raise; effc = fun (type a) (eff: a t) -> match eff with | Xchg msg -> Some (fun (cont: (a, _) continuation) -> Suspended {msg; cont}) | _ -> None }

The argument to the step function, f, is a computation that can perform an Xchg effect and returns a result of type 'a. The step function itself returns a 'a status value.

In the step function, we use the match_with primitive. Like try_with, match_with primitive installs an effect handler. However, unlike try_with, where only the effect case effc is provided, match_with expects the handlers for the value (retc) and exceptional (exnc) return cases. In fact, try_with can be defined using match_with as follows: let try_with f v {effc} = match_with f v {retc = Fun.id; exnc = raise; effc}.

In the step function,

- Case retc: If the computation returns with a value v, we return Complete v.
- Case exnc: If the computation raises an exception, then the handler raises the same exception.
- Case effc: If the computation performs the effect Xchg msg with the continuation cont, then we return Suspended{msg;cont}. Thus, in this case, the continuation cont is not immediately invoked by the handler; instead, it is stored in a data structure for later use.

Since the step function handles the Xchg effect, step f is a computation that does not perform the Xchg effect. It may however perform other effects. Moreover, since we are using deep handlers, the continuation cont stored in the status does not perform the Xchg effect.

We can now write a simple scheduler that runs a pair of tasks to completion:

let rec run_both a b = match a (), b () with | Complete va, Complete vb -> (va, vb) | Suspended {msg = m1; cont = k1}, Suspended {msg = m2; cont = k2} -> run_both (fun () -> continue k1 m2) (fun () -> continue k2 m1) | _ -> failwith "Improper synchronization"

Both of the tasks may run to completion, or both may offer to exchange a message. In the latter case, each computation receives the value offered by the other computation. The situation where one computation offers an exchange while the other computation terminates is regarded as a programmer error, and causes the handler to raise an exception

We can now define a second computation that also exchanges two messages:

let comp2 () = perform (Xchg 21) * perform (Xchg 21)

Finally, we can run the two computations together:

run_both (step comp1) (step comp2)
- : int * int = (42, 0)

The computation comp1 offers the values 0 and 1 and in exchange receives the values 21 and 21, which it adds, producing 42. The computation comp2 offers the values 21 and 21 and in exchange receives the values 0 and 1, which it multiplies, producing 0. The communication between the two computations is programmed entirely inside run_both. Indeed, the definitions of comp1 and comp2, alone, do not assign any meaning to the Xchg effect.

### ﻿12.24.3 User-level threads

Let us extend the previous example for an arbitrary number of tasks. Many languages such as GHC Haskell and Go provide user-level threads as a primitive feature implemented in the runtime system. With effect handlers, user-level threads and their schedulers can be implemented in OCaml itself. Typically, user-level threading systems provide a fork primitive to spawn off a new concurrent task and a yield primitive to yield control to some other task. Correspondingly, we shall declare two effects as follows:

type _ Effect.t += Fork : (unit -> unit) -> unit t | Yield : unit t

The Fork effect takes a thunk (a suspended computation, represented as a function of type unit -> unit) and returns a unit to the performer. The Yield effect is unparameterized and returns a unit when performed. Let us consider that a task performing an Xchg effect may match with any other task also offering to exchange a value.

We shall also define helper functions that simply perform these effects:

let fork f = perform (Fork f) let yield () = perform Yield let xchg v = perform (Xchg v)

A top-level run function defines the scheduler:

(* A concurrent round-robin scheduler *) let run (main : unit -> unit) : unit = let exchanger = ref None in (* waiting exchanger *) let run_q = Queue.create () in (* scheduler queue *) let enqueue k v = let task () = continue k v in Queue.push task run_q in let dequeue () = if Queue.is_empty run_q then () (* done *) else begin let task = Queue.pop run_q in task () end in let rec spawn (f : unit -> unit) : unit = match_with f () { retc = dequeue; exnc = (fun e -> print_endline (Printexc.to_string e); dequeue ()); effc = fun (type a) (eff : a t) -> match eff with | Yield -> Some (fun (k : (a, unit) continuation) -> enqueue k (); dequeue ()) | Fork f -> Some (fun (k : (a, unit) continuation) -> enqueue k (); spawn f) | Xchg n -> Some (fun (k : (int, unit) continuation) -> begin match !exchanger with | Some (n', k') -> exchanger := None; enqueue k' n; continue k n' | None -> exchanger := Some (n, k); dequeue () end) | _ -> None } in spawn main

We use a mutable queue run_q to hold the scheduler queue. The FIFO queue enables round-robin scheduling of tasks in the scheduler. enqueue inserts tasks into the queue, and dequeue extracts tasks from the queue and runs them. The reference cell exchanger holds a (suspended) task offering to exchange a value. At any time, there is either zero or one suspended task that is offering an exchange.

The heavy lifting is done by the spawn function. The spawn function runs the given computation f in an effect handler. If f returns with a value (case retc), we dequeue and run the next task from the scheduler queue. If the computation f raises an exception (case exnc), we print the exception and run the next task from the scheduler.

The computation f may also perform effects. If f performs the Yield effect, the current task is suspended (inserted into the queue of ready tasks), and the next task from the scheduler queue is run. If the effect is Fork f, then the current task is suspended, and the new task f is executed immediately via a tail call to spawn f. Note that this choice to run the new task first is arbitrary. We could very well have chosen instead to insert the task for f into the ready queue and resumed k immediately.

If the effect is Xchg, then we first check whether there is a task waiting to exchange. If so, we enqueue the waiting task with the current value being offered and immediately resume the current task with the value being offered. If not, we make the current task the waiting exchanger, and run the next task from the scheduler queue.

Note that this scheduler code is not perfect – it can leak resources. We shall explain and fix this in the next section ‍12.24.3.

Now we can write a concurrent program that utilises the newly defined operations:

open Printf let _ = run (fun _ -> fork (fun _ -> printf "[t1] Sending 0\n"; let v = xchg 0 in printf "[t1] received %d\n" v); fork (fun _ -> printf "[t2] Sending 1\n"; let v = xchg 1 in printf "[t2] received %d\n" v))
[t1] Sending 0 [t2] Sending 1 [t2] received 0 [t1] received 1

Observe that the messages from the two tasks are interleaved. Notice also that the snippet above makes no reference to the effect handlers and is in direct style (no monadic operations). This example illustrates that, with effect handlers, the user code in a concurrent program can remain in simple direct style, and the use of effect handlers can be fully contained within the concurrency library implementation.

#### ﻿Resuming with an exception

In addition to resuming a continuation with a value, effect handlers also permit resuming by raising an effect at the point of perform. This is done with the help of the discontinue primitive. The discontinue primitive helps ensure that resources are always eventually deallocated, even in the presence of effects.

For example, consider the dequeue operation in the previous example reproduced below:

… let dequeue () = if Queue.is_empty run_q then () (* done *) else (Queue.pop run_q) ()

If the scheduler queue is empty, dequeue considers that the scheduler is done and returns to the caller. However, there may still be a task waiting to exchange a value (stored in the reference cell exchanger), which remains blocked forever! If the blocked task holds onto resources, these resources are leaked. For example, consider the following task:

let leaky_task () = fork (fun _ -> let oc = open_out "secret.txt" in Fun.protect ~finally:(fun _ -> close_out oc) (fun _ -> output_value oc (xchg 0)))

The task writes the received message to the file secret.txt. It uses Fun.protect to ensure that the output channel oc is closed on both normal and exceptional return cases. Unfortunately, this is not sufficient. If the exchange effect xchg 0 cannot be matched with an exchange effect performed by some other thread, then this task remains blocked forever. Thus, the output channel oc is never closed.

To avoid this problem, one must adhere to a simple discipline: every continuation must be eventually either continued or discontinued. Here, we use discontinue to ensure that the blocked task does not remain blocked forever. By discontinuing this task, we force it to terminate (with an exception):

exception Improper_synchronization let dequeue () = if Queue.is_empty run_q then begin match !exchanger with | None -> () (* done *) | Some (n, k) -> exchanger := None; discontinue k Improper_synchronization end else (Queue.pop run_q) ()

When the scheduler queue is empty and there is a blocked exchanger thread, the dequeue function discontinues the blocked thread with an Improper_synchronization exception. This exception is raised at the blocked xchg function call, which causes the finally block to be run and closes the output channel oc. From the point of view of the user, it seems as though the function call xchg 0 raises the exception Improper_synchronization.

### ﻿12.24.4 Control inversion

When it comes to performing traversals on a data structure, there are two fundamental ways depending on whether the producer or the consumer has the control over the traversal. For example, in List.iter f l, the producer List.iter has the control and pushes the element to the consumer f who processes them. On the other hand, the Seq module provides a mechanism similar to delayed lists where the consumer controls the traversal. For example, Seq.forever Random.bool returns an infinite sequence of random bits where every bit is produced (on demand) when queried by the consumer.

Naturally, producers such as List.iter are easier to write in the former style. The latter style is ergonomically better for the consumer since it is preferable and more natural to be in control. To have the best of both worlds, we would like to write a producer in the former style and automatically convert it to the latter style. The conversion can be written once and for all as a library function, thanks to effect handlers. Let us name this function invert. We will first look at how to use the invert function before looking at its implementation details. The type of this function is given below:

val invert : iter:(('a -> unit) -> unit) -> 'a Seq.t

The invert function takes an iter function (a producer that pushes elements to the consumer) and returns a sequence (where the consumer has the control). For example,

let lst_iter = Fun.flip List.iter [1;2;3]
val lst_iter : (int -> unit) -> unit = <fun>

is an iter function with type (int -> unit) -> unit. The expression lst_iter f pushes the elements 1, 2 and 3 to the consumer f. For example,

lst_iter (fun i -> Printf.printf "%d\n" i)
1 2 3 - : unit = ()

The expression invert lst_iter returns a sequence that allows the consumer to traverse the list on demand. For example,

let s = invert ~iter:lst_iter let next = Seq.to_dispenser s;;
val s : int Seq.t = <fun> val next : unit -> int option = <fun>
next();;
- : int option = Some 1
next();;
- : int option = Some 2
next();;
- : int option = Some 3
next();;
- : int option = None

We can use the same invert function on any iter function. For example,

let s = invert ~iter:(Fun.flip String.iter "OCaml") let next = Seq.to_dispenser s;;
val s : char Seq.t = <fun> val next : unit -> char option = <fun>
next();;
- : char option = Some 'O'
next();;
- : char option = Some 'C'
next();;
- : char option = Some 'a'
next();;
- : char option = Some 'm'
next();;
- : char option = Some 'l'
next();;
- : char option = None

#### ﻿Implementing control inversion

The implementation of the invert function is given below:

let invert (type a) ~(iter : (a -> unit) -> unit) : a Seq.t = let module M = struct type _ Effect.t += Yield : a -> unit t end in let yield v = perform (M.Yield v) in fun () -> match_with iter yield { retc = (fun _ -> Seq.Nil); exnc = raise; effc = fun (type b) (eff : b Effect.t) -> match eff with | M.Yield v -> Some (fun (k: (b,_) continuation) -> Seq.Cons (v, continue k)) | _ -> None }

The invert function declares an effect Yield that takes the element to be yielded as a parameter. The yield function performs the Yield effect. The lambda abstraction fun () -> ... delays all action until the first element of the sequence is demanded. Once this happens, the computation iter yield is executed under an effect handler. Every time the iter function pushes an element to the yield function, the computation is interrupted by the Yield effect. The Yield effect is handled by returning the value Seq.Cons(v,continue k) to the consumer. The consumer gets the element v as well as the suspended computation, which in the consumer’s eyes is just the tail of sequence.

When the consumer demands the next element from the sequence (by applying it to ()), the continuation k is resumed. This allows the computation iter yield to make progress, until it either yields another element or terminates normally. In the latter case, the value Seq.Nil is returned, indicating to the consumer that the iteration is over.

It is important to note that the sequence returned by the invert function is ephemeral (as defined by the Seq module) i.e., the sequence must be used at most once. Additionally, the sequence must be fully consumed (i.e., used at least once) so as to ensure that the captured continuation is used linearly.

### ﻿12.24.5 Semantics

In this section, we shall see the semantics of effect handlers with the help of examples.

#### ﻿Nesting handlers

Like exception handlers, effect handlers can be nested.

type _ Effect.t += E : int t | F : string t let foo () = perform F let bar () = try_with foo () { effc = fun (type a) (eff: a t) -> match eff with | E -> Some (fun (k: (a,_) continuation) -> failwith "impossible") | _ -> None } let baz () = try_with bar () { effc = fun (type a) (eff: a t) -> match eff with | F -> Some (fun (k: (a,_) continuation) -> continue k "Hello, world!") | _ -> None }

In this example, the computation foo performs F, the inner handler handles only E and the outer handler handles F. The call to baz returns Hello, world!.

baz ()
- : string = "Hello, world!"

#### ﻿Fibers

It is useful to know a little bit about the implementation of effect handlers to appreciate the design choices and their performance characteristics. Effect handlers are implemented with the help of runtime-managed, dynamically growing segments of stack called fibers. The program stack in OCaml is a linked list of such fibers.

A new fiber is allocated for evaluating the computation enclosed by an effect handler. The fiber is freed when the computation returns to the caller either normally by returning a value or by raising an exception.

At the point of perform in foo in the previous example, the program stack looks like this:

+-----+ +-----+ +-----+ | | | | | | | baz |<--| bar |<--| foo | | | | | | | | | | | | | +-----+ +-----+ +-----+ <- stack_pointer

The two links correspond to the two effect handlers in the program. When the effect F is handled in baz, the program state looks as follows:

+-----+ +-----+ +-----+ | | | | | | +-+ | baz | | bar |<--| foo |<--|k| | | | | | | +-+ +-----+ <- stack_pointer +-----+ +-----+

The delimited continuation k is an object on the heap that refers to the segment of the stack that corresponds to the suspended computation. Capturing a continuation does not involve copying stack frames. When the continuation is resumed, the stack is restored to the previous state by linking together the segment pointed to by k to the current stack. Since neither continuation capture nor resumption requires copying stack frames, suspending the execution using perform and resuming it using either continue or discontinue are fast.

#### ﻿Unhandled effects

Unlike languages such as Eff and Koka, effect handlers in OCaml do not provide effect safety; the compiler does not statically ensure that all the effects performed by the program are handled. If effects do not have a matching handler, then an Effect.Unhandled exception is raised at the point of the corresponding perform. For example, in the previous example, bar does not handle the effect F. Hence, we will get an Effect.Unhandled F exception when we run bar.

try bar () with Effect.Unhandled F -> "Saw Effect.Unhandled exception"
- : string = "Saw Effect.Unhandled exception"

#### ﻿Linear continuations

As discussed earlier ‍12.24.3, the delimited continuations in OCaml must be used linearly – every captured continuation must be resumed either with a continue or discontinue exactly once. Attempting to use a continuation more than once raises a Continuation_already_resumed exception. For example:

try_with perform (Xchg 0) { effc = fun (type a) (eff : a t) -> match eff with | Xchg n -> Some (fun (k: (a, _) continuation) -> continue k 21 + continue k 21) | _ -> None }
Exception: Stdlib.Effect.Continuation_already_resumed.

The primary motivation for adding effect handlers to OCaml is to enable concurrent programming. One-shot continuations are sufficient for almost all concurrent programming needs. They are also much cheaper to implement compared to multi-shot continuations since they do not require stack frames to be copied. Moreover, OCaml programs may also manipulate linear resources such as sockets and file descriptors. The linearity discipline is easily broken if the continuations are allowed to resume more than once. It would be quite hard to debug such linearity violations on resources due to the lack of static checks for linearity and the non-local nature of control flow. Hence, OCaml does not support multi-shot continuations.

While the “at most once resumption” property of continuations is ensured with a dynamic check, there is no check to ensure that the continuations are resumed “at least once”. It is left to the user to ensure that the captured continuations are resumed at least once. Not resuming continuations will leak the memory allocated for the fibers as well as any resources that the suspended computation may hold.

One may install a finaliser on the captured continuation to ensure that the resources are freed:

exception Unwind Gc.finalise (fun k -> try ignore (discontinue k Unwind) with _ -> ()) k

In this case, if k becomes unreachable, then the finaliser ensures that the continuation stack is unwound by discontinuing with an Unwind exception, allowing the computation to free up resources. However, the runtime cost of finalisers is much more than the cost of capturing a continuation. Hence, it is recommended that the user take care of resuming the continuation exactly once rather than relying on the finaliser.

### ﻿12.24.6 Shallow handlers

The examples that we have seen so far have used deep handlers. A deep handler handles all the effects performed (in sequence) by the computation. Whenever a continuation is captured in a deep handler, the captured 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.

OCaml also provides shallow handlers. Compared to deep handlers, a shallow handler handles only the first effect performed by the computation. The continuation captured in a shallow handler does not include the handler. This means that, when the continuation is resumed, the handler is no longer present. For this reason, when the continuation is resumed, the user is expected to provide a new effect handler (possibly a different one) to handle the next effect that the computation may perform.

Shallow handlers make it easier to express certain kinds of programs. Let us implement a shallow handler that enforces a particular sequence of effects (a protocol) on a computation. For this example, let us consider that the computation may perform the following effects:

type _ Effect.t += Send : int -> unit Effect.t | Recv : int Effect.t

Let us assume that we want to enforce a protocol that only permits an alternating sequence of Send and Recv effects that conform to the regular expression (Send;Recv)*;Send?. Hence, the sequence of effects [] (the empty sequence), [Send], [Send;Recv], [Send;Recv;Send], etc., are allowed, but not [Recv], [Send;Send], [Send;Recv;Recv], etc. The key observation here is that the set of effects handled evolves over time. We can enforce this protocol quite naturally using shallow handlers as shown below:

open Effect.Shallow let run (comp: unit -> unit) : unit = let rec loop_send : type a. (a,unit) continuation -> a -> unit = fun k v -> continue_with k v { retc = Fun.id; exnc = raise; effc = fun (type b) (eff : b Effect.t) -> match eff with | Send n -> Some (fun (k: (b,_) continuation) -> loop_recv n k ()) | Recv -> failwith "protocol violation" | _ -> None } and loop_recv : type a. int -> (a,unit) continuation -> a -> unit = fun n k v -> continue_with k v { retc = Fun.id; exnc = raise; effc = fun (type b) (eff : b Effect.t) -> match eff with | Recv -> Some (fun (k: (b,_) continuation) -> loop_send k n) | Send v -> failwith "protocol violation" | _ -> None } in loop_send (fiber comp) ()

The run function executes the computation comp ensuring that it can only perform an alternating sequence of Send and Recv effects. The shallow handler uses a different set of primitives compared to the deep handler. The primitive fiber (on the last line) takes an 'a -> 'b function and returns a ('a,'b) Effects.Shallow.continuation. The expression continue_with k v h resumes the continuation k with value v under the handler h.

The mutually recursive functions loop_send and loop_recv resume the given continuation k with value v under different handlers. The loop_send function handles the Send effect and tail calls the loop_recv function. If the computation performs the Recv effect, then loop_send aborts the computation by raising an exception. Similarly, the loop_recv function handles the Recv effect and tail calls the loop_send function. If the computation performs the Send effect, then loop_recv aborts the computation. Given that the continuation captured in the shallow handler do not include the handler, there is only ever one handler installed in the dynamic scope of the computation comp.

The computation is initially executed by the loop_send function (see last line in the code above) which ensures that the first effect that the computation is allowed to perform is the Send effect. Note that the computation is free to perform effects other than Send and Recv, which may be handled by an outer handler.

We can see that the run function will permit a computation that follows the protocol:

run (fun () -> printf "Send 42\n"; perform (Send 42); printf "Recv: %d\n" (perform Recv); printf "Send 43\n"; perform (Send 43); printf "Recv: %d\n" (perform Recv))
Send 42 Recv: 42 Send 43 Recv: 43 - : unit = ()

and aborts those that do not:

run (fun () -> Printf.printf "Send 0\n"; perform (Send 0); Printf.printf "Send 1\n"; perform (Send 1) (* protocol violation *))
Send 0 Send 1 Exception: Failure "protocol violation".

We may implement the same example using deep handlers using reference cells (easy, but unsatisfying) or without them (harder). We leave this as an exercise to the reader.