Up
# module React

: sig
# Interface

Declarative events and signals.

React is a module for functional reactive programming (frp). It provides support to program with time varying values : declarative events and signals. React doesn't define any primitive event or signal, this lets the client choose the concrete timeline.

Consult the semantics, the basics and examples. Open the module to use it, this defines only two types and modules in your scope.

*Release 1.2.0 - Daniel Bünzli <daniel.buenzl i@erratique.ch>*

#

type 'a event

The type for events of type `'a`

.

#

type 'a signal

The type for signals of type `'a`

.

#

type step

The type for update steps.

#
# Lifting

# Pervasives support

module E : sig

Event combinators.

Consult their semantics.

#
# Primitive and basics

#

val create : unit -> 'a event * (?step:step -> 'a -> unit)

`create ()`

is a primitive event `e`

and a `send`

function. The
function `send`

is such that:

`send v`

generates an occurrence`v`

of`e`

at the time it is called and triggers an update step.`send ~step v`

generates an occurence`v`

of`e`

on the step`step`

when`step`

is executed.`send ~step v`

raises`Invalid_argument`

if it was previously called with a step and this step has not executed yet or if the given`step`

was already executed.

**Warning.** `send`

must not be executed inside an update step.

#

val stop : ?strong:bool -> 'a event -> unit

`stop e`

stops `e`

from occuring. It conceptually becomes
never and cannot be restarted. Allows to
disable effectful events.

The `strong`

argument should only be used on platforms
where weak arrays have a strong semantics (i.e. JavaScript).
See details.

**Note.** If executed in an update step
the event may still occur in the step.

#
# Transforming and filtering

#

val app : ('a -> 'b) event -> 'a event -> 'b event

`app ef e`

occurs when both `ef`

and `e`

occur
simultaneously.
The value is `ef`

's occurence applied to `e`

's one.

- [
`app ef e`

]_{t}`= Some v'`

if [`ef`

]_{t}`= Some f`

and [`e`

]_{t}`= Some v`

and`f v = v'`

. - [
`app ef e`

]_{t}`= None`

otherwise.

#

val diff : ('a -> 'a -> 'b) -> 'a event -> 'b event

`diff f e`

occurs whenever `e`

occurs except on the next occurence.
Occurences are `f v v'`

where `v`

is `e`

's current
occurrence and `v'`

the previous one.

- [
`diff f e`

]_{t}`= Some r`

if [`e`

]_{t}`= Some v`

, [`e`

]_{<t}`= Some v'`

and`f v v' = r`

. - [
`diff f e`

]_{t}`= None`

otherwise.

#

val changes : ?eq:('a -> 'a -> bool) -> 'a event -> 'a event

`changes eq e`

is `e`

's occurrences with occurences equal to
the previous one dropped. Equality is tested with `eq`

(defaults to
structural equality).

- [
`changes eq e`

]_{t}`= Some v`

if [`e`

]_{t}`= Some v`

and either [`e`

]_{<t}`= None`

or [`e`

]_{<t}`= Some v'`

and`eq v v' = false`

. - [
`changes eq e`

]_{t}`= None`

otherwise.

#
# Accumulating

#

val accum : ('a -> 'a) event -> 'a -> 'a event

`accum ef i`

accumulates a value, starting with `i`

, using `e`

's
functional occurrences.

- [
`accum ef i`

]_{t}`= Some (f i)`

if [`ef`

]_{t}`= Some f`

and [`ef`

]_{<t}`= None`

. - [
`accum ef i`

]_{t}`= Some (f acc)`

if [`ef`

]_{t}`= Some f`

and [`accum ef i`

]_{<t}`= Some acc`

. - [
`accum ef i`

]`= None`

otherwise.

#

val fold : ('a -> 'b -> 'a) -> 'a -> 'b event -> 'a event

`fold f i e`

accumulates `e`

's occurrences with `f`

starting with `i`

.

- [
`fold f i e`

]_{t}`= Some (f i v)`

if [`e`

]_{t}`= Some v`

and [`e`

]_{<t}`= None`

. - [
`fold f i e`

]_{t}`= Some (f acc v)`

if [`e`

]_{t}`= Some v`

and [`fold f i e`

]_{<t}`= Some acc`

. - [
`fold f i e`

]_{t}`= None`

otherwise.

#
# Combining

#

val merge : ('a -> 'b -> 'a) -> 'a -> 'b event list -> 'a event

`merge f a el`

merges the simultaneous
occurrences of every event in `el`

using `f`

and the accumulator `a`

.

[`merge f a el`

]_{t}
```
= List.fold_left f a (List.filter (fun o -> o <> None)
(List.map
```

[]_{t}`el))`

.

#

val switch : 'a event -> 'a event event -> 'a event

`switch e ee`

is `e`

's occurrences until there is an
occurrence `e'`

on `ee`

, the occurrences of `e'`

are then used
until there is a new occurrence on `ee`

, etc..

- [
`switch e ee`

]_{t}`=`

[`e`

]_{t}if [`ee`

]_{<=t}`= None`

. - [
`switch e ee`

]_{t}`=`

[`e'`

]_{t}if [`ee`

]_{<=t}`= Some e'`

.

#

val fix : ('a event -> 'a event * 'b) -> 'b

`fix ef`

allows to refer to the value an event had an
infinitesimal amount of time before.

In `fix ef`

, `ef`

is called with an event `e`

that represents
the event returned by `ef`

delayed by an infinitesimal amount of
time. If `e', r = ef e`

then `r`

is returned by `fix`

and `e`

is such that :

- [
`e`

]_{t}`=`

`None`

if t = 0 - [
`e`

]_{t}`=`

[`e'`

]_{t-dt}otherwise

**Raises.** `Invalid_argument`

if `e'`

is directly a delayed event (i.e.
an event given to a fixing function).

Lifting combinators. For a given `n`

the semantics is:

- [
`ln f e1 ... en`

]_{t}`= Some (f v1 ... vn)`

if for all i : [`ei`

]_{t}`= Some vi`

. - [
`ln f e1 ... en`

]_{t}`= None`

otherwise.

#

module Option : sig

Events with option occurences.

#

val value : ?default:'a signal -> 'a option event -> 'a event

`value default e`

either silences `None`

occurences if `default`

is
unspecified or replaces them by the value of `default`

at the occurence
time.

- [
`value ~default e`

]_{t}`= v`

if [`e`

]_{t}`= Some (Some v)`

. - [
`value ?default:None e`

]_{t}`= None`

if [`e`

]_{t}=`None`

. - [
`value ?default:(Some s) e`

]_{t}`= v`

if [`e`

]_{t}=`None`

and [`s`

]_{t}`= v`

.

end

end

#
# From events

module S : sig

Signal combinators.

Consult their semantics.

#
# Primitive and basics

#

val create : ?eq:('a -> 'a -> bool) -> 'a -> 'a signal * (?step:step -> 'a -> unit)

`create i`

is a primitive signal `s`

set to `i`

and a
`set`

function. The function `set`

is such that:

`set v`

sets the signal's value to`v`

at the time it is called and triggers an update step.`set ~step v`

sets the signal's value to`v`

at the time it is called and updates it dependencies when`step`

is executed`set ~step v`

raises`Invalid_argument`

if it was previously called with a step and this step has not executed yet or if the given`step`

was already executed.

**Warning.** `set`

must not be executed inside an update step.

#

val value : 'a signal -> 'a

`value s`

is `s`

's current value.

**Warning.** If executed in an update
step may return a non up-to-date value or raise `Failure`

if
the signal is not yet initialized.

#

val retain : 'a signal -> (unit -> unit) -> [

| `R of unit -> unit

]
`retain s c`

keeps a reference to the closure `c`

in `s`

and
returns the previously retained value. `c`

will *never* be
invoked.

**Raises.** `Invalid_argument`

on constant signals.

#

val stop : ?strong:bool -> 'a signal -> unit

`stop s`

, stops updating `s`

. It conceptually becomes const
with the signal's last value and cannot be restarted. Allows to
disable effectful signals.

The `strong`

argument should only be used on platforms
where weak arrays have a strong semantics (i.e. JavaScript).
See details.

**Note.** If executed in an update step the signal may
still update in the step.

#

val trace : ?iff:bool t -> ('a -> unit) -> 'a signal -> 'a signal

`trace iff tr s`

is `s`

except `tr`

is invoked with `s`

's
current value and on `s`

changes when `iff`

is `true`

(defaults
to `S.const true`

). For all t where [`s`

]_{t} `= v`

and (t = 0
or ([`s`

]_{t-dt}`= v'`

and `eq v v' = false`

)) and
[`iff`

]_{t} = `true`

, `tr`

is invoked with `v`

.

#
# Transforming and filtering

#

val filter : ?eq:('a -> 'a -> bool) -> ('a -> bool) -> 'a -> 'a signal -> 'a signal

`filter f i s`

is `s`

's values that satisfy `p`

. If a value does not
satisfy `p`

it holds the last value that was satisfied or `i`

if
there is none.

- [
`filter p s`

]_{t}`=`

[`s`

]_{t}if`p`

[`s`

]_{t}`= true`

. - [
`filter p s`

]_{t}`=`

[`s`

]_{t'}if`p`

[`s`

]_{t}`= false`

and t' is the greatest t' < t with`p`

[`s`

]_{t'}`= true`

. - [
`filter p e`

]_{t}`= i`

otherwise.

#

val fmap : ?eq:('b -> 'b -> bool) -> ('a -> 'b option) -> 'b -> 'a signal -> 'b signal

`fmap fm i s`

is `s`

filtered and mapped by `fm`

.

- [
`fmap fm i s`

]_{t}`=`

v if`fm`

[`s`

]_{t}`= Some v`

. - [
`fmap fm i s`

]_{t}`=`

[`fmap fm i s`

]_{t'}if`fm`

[`s`

]_{t}`= None`

and t' is the greatest t' < t with`fm`

[`s`

]_{t'}`<> None`

. - [
`fmap fm i s`

]_{t}`= i`

otherwise.

#

val diff : ('a -> 'a -> 'b) -> 'a signal -> 'b event

`diff f s`

is an event with occurrences whenever `s`

changes from
`v'`

to `v`

and `eq v v'`

is `false`

(`eq`

is the signal's equality
function). The value of the occurrence is `f v v'`

.

- [
`diff f s`

]_{t}`= Some d`

if [`s`

]_{t}`= v`

and [`s`

]_{t-dt}`= v'`

and`eq v v' = false`

and`f v v' = d`

. - [
`diff f s`

]_{t}`= None`

otherwise.

#

val on : ?eq:('a -> 'a -> bool) -> bool signal -> 'a -> 'a signal -> 'a signal

`on c i s`

is the signal `s`

whenever `c`

is `true`

.
When `c`

is `false`

it holds the last value `s`

had when
`c`

was the last time `true`

or `i`

if it never was.

- [
`on c i s`

]_{t}`=`

[`s`

]_{t}if [`c`

]_{t}`= true`

- [
`on c i s`

]_{t}`=`

[`s`

]_{t'}if [`c`

]_{t}`= false`

where t' is the greatest t' < t with [`c`

]_{t'}`= true`

. - [
`on c i s`

]_{t}`=`

`i`

otherwise.

#

val dismiss : ?eq:('a -> 'a -> bool) -> 'b event -> 'a -> 'a signal -> 'a signal

`dismiss c i s`

is the signal `s`

except changes when `c`

occurs
are ignored. If `c`

occurs initially `i`

is used.

- [
`dismiss c i s`

]_{t}`=`

[`s`

]_{t'}where t' is the greatest t' <= t with [`c`

]_{t'}`= None`

and [`s`

]_{t'-dt}`<>`

[`s`

]_{t'} - [
`dismiss_ c i s`

]_{0}`=`

`v`

where`v = i`

if [`c`

]_{0}`= Some _`

and`v =`

[`s`

]_{0}otherwise.

#
# Accumulating

#
# Combining

#

val fix : ?eq:('a -> 'a -> bool) -> 'a -> ('a signal -> 'a signal * 'b) -> 'b

`fix i sf`

allow to refer to the value a signal had an
infinitesimal amount of time before.

In `fix sf`

, `sf`

is called with a signal `s`

that represents
the signal returned by `sf`

delayed by an infinitesimal amount
time. If `s', r = sf s`

then `r`

is returned by `fix`

and `s`

is such that :

- [
`s`

]_{t}`=`

`i`

for t = 0. - [
`s`

]_{t}`=`

[`s'`

]_{t-dt}otherwise.

`eq`

is the equality used by `s`

.

**Raises.** `Invalid_argument`

if `s'`

is directly a delayed signal (i.e.
a signal given to a fixing function).

**Note.** Regarding values depending on the result `r`

of
`s', r = sf s`

the following two cases need to be distinguished :

- After
`sf s`

is applied,`s'`

does not depend on a value that is in a step and`s`

has no dependents in a step (e.g in the simple case where`fix`

is applied outside a step).

In that case if the initial value of`s'`

differs from`i`

,`s`

and its dependents need to be updated and a special update step will be triggered for this. Values depending on the result`r`

will be created only after this special update step has finished (e.g. they won't see the`i`

of`s`

if`r = s`

). - Otherwise, values depending on
`r`

will be created in the same step as`s`

and`s'`

(e.g. they will see the`i`

of`s`

if`r = s`

).

#
# Lifting

Lifting combinators. For a given `n`

the semantics is :

[`ln f a1`

... `an`

]_{t} = f [`a1`

]_{t} ... [`an`

]_{t}

The following modules lift some of `Pervasives`

functions and
operators.

#

module Int : sig

end

#

module Option : sig

#

val value : ?eq:('a -> 'a -> bool) -> default:[

| `Init of 'a signal

| `Always of 'a signal

] -> 'a option signal -> 'a signal
`value default s`

is `s`

with only its `Some v`

values.
Whenever `s`

is `None`

, if `default`

is ``Always dv`

then
the current value of `dv`

is used instead. If `default`

is ``Init dv`

the current value of `dv`

is only used
if there's no value at creation time, otherwise the last
`Some v`

value of `s`

is used.

- [
`value ~default s`

]_{t}`= v`

if [`s`

]_{t}`= Some v`

- [
`value ~default:(`Always d) s`

]_{t}`=`

[`d`

]_{t}if [`s`

]_{t}`= None`

- [
`value ~default:(`Init d) s`

]_{0}`=`

[`d`

]_{0}if [`s`

]_{0}`= None`

- [
`value ~default:(`Init d) s`

]_{t}`=`

[`value ~default:(`Init d) s`

]_{t'}if [`s`

]_{t}`= None`

and t' is the greatest t' < t with [`s`

]_{t'}`<> None`

or 0 if there is no such`t'`

.

end

#

module Compare : sig

end

#
# Combinator specialization

Given an equality function `equal`

and a type `t`

, the functor
Make automatically applies the `eq`

parameter of the combinators.
The outcome is combinators whose *results* are signals with
values in `t`

.

Basic types are already specialized in the module Special, open this module to use them.

#

module Special : sig

Specialization for booleans, integers and floats.

Open this module to use it.

end

end

#
# Steps

module Step : sig

Update steps.

Update functions returned by S.create and E.create
implicitely create and execute update steps when used without
specifying their `step`

argument.

Using explicit step values with these functions gives more control on the time when the update step is perfomed and allows to perform simultaneous primitive signal updates and event occurences. See also the documentation about update steps and simultaneous events.

end

#
# Semantics

The following notations are used to give precise meaning to the
combinators. It is important to note that in these semantic
descriptions the origin of time t = 0 is *always* fixed at
the time at which the combinator creates the event or the signal and
the semantics of the dependents is evaluated relative to this timeline.

We use dt to denote an infinitesimal amount of time.

#
## Events

An event is a value with discrete occurrences over time.

The semantic function [] `: 'a event -> time -> 'a option`

gives
meaning to an event `e`

by mapping it to a function of time
[`e`

] returning `Some v`

whenever the event occurs with value
`v`

and `None`

otherwise. We write [`e`

]_{t} the evaluation of
this *semantic* function at time t.

As a shortcut notation we also define _{<t} `: 'a event -> 'a option`

(resp. []_{<=t}) to denote the last occurrence, if any, of an
event before (resp. before or at) `t`

. More precisely :

- [
`e`

]_{<t}`=`

[`e`

]_{t'}with t' the greatest t' < t (resp.`<=`

) such that [`e`

]_{t'}`<> None`

. - [
`e`

]_{<t}`= None`

if there is no such t'.

#
## Signals

A signal is a value that varies continuously over time. In contrast to events which occur at specific point in time, a signal has a value at every point in time.

The semantic function [] `: 'a signal -> time -> 'a`

gives
meaning to a signal `s`

by mapping it to a function of time
[`s`

] that returns its value at a given time. We write [`s`

]_{t}
the evaluation of this *semantic* function at time t.

#
### Equality

Most signal combinators have an optional `eq`

parameter that
defaults to structural equality. `eq`

specifies the equality
function used to detect changes in the value of the resulting
signal. This function is needed for the efficient update of
signals and to deal correctly with signals that perform
side effects.

Given an equality function on a type the combinators can be automatically specialized via a functor.

#
### Continuity

Ultimately signal updates depend on primitives updates. Thus a signal can only approximate a real continuous signal. The accuracy of the approximation depends on the variation rate of the real signal and the primitive's update frequency.

#
# Basics

#
## Primitive events and signals

React doesn't define primitive events and signals, they must be created and updated by the client.

Primitive events are created with E.create. This function
returns a new event and an update function that generates an
occurrence for the event at the time it is called. The following
code creates a primitive integer event `x`

and generates three
occurrences with value `1`

, `2`

, `3`

. Those occurrences are printed
on stdout by the effectful event `pr_x`

.

```
open React;;
let x, send_x = E.create ()
let pr_x = E.map print_int x
let () = List.iter send_x [1; 2; 3]
```

Primitive signals are created with S.create. This function
returns a new signal and an update function that sets the signal's value
at the time it is called. The following code creates an
integer signal `x`

initially set to `1`

and updates it three time with
values `2`

, `2`

, `3`

. The signal's values are printed on stdout by the
effectful signal `pr_x`

. Note that only updates that change
the signal's value are printed, hence the program prints `123`

, not `1223`

.
See the discussion on
side effects for more details.

```
open React;;
let x, set_x = S.create 1
let pr_x = S.map print_int x
let () = List.iter set_x [2; 2; 3]
```

The clock example shows how a realtime time flow can be defined.

#
## Update steps

The E.create and S.create functions return update functions
used to generate primitive event occurences and set the value of
primitive signals. Upon invocation as in the preceding section
these functions immediatly create and invoke an update step.
The *update step* automatically updates events and signals that
transitively depend on the updated primitive. The dependents of a
signal are updated iff the signal's value changed according to its
equality function.

The update functions have an optional `step`

argument. If they are
given a concrete `step`

value created with Step.create, then it
updates the event or signal but doesn't update its dependencies. It
will only do so whenever `step`

is executed with
Step.execute. This allows to make primitive event occurences and
signal changes simultaneous. See next section for an example.

#
## Simultaneous events

Update steps are made under a
synchrony hypothesis :
the update step takes no time, it is instantenous. Two event occurrences
are *simultaneous* if they occur in the same update step.

In the code below `w`

, `x`

and `y`

will always have simultaneous
occurrences. They *may* have simulatenous occurences with `z`

if `send_w`

and `send_z`

are used with the same update step.

```
let w, send_w = E.create ()
let x = E.map succ w
let y = E.map succ x
let z, send_z = E.create ()
let () =
let () = send_w 3 (* w x y occur simultaneously, z doesn't occur *) in
let step = Step.create () in
send_w ~step 3;
send_z ~step 4;
Step.execute step (* w x z y occur simultaneously *)
```

#
## The update step and thread safety

Primitives are the only mean to drive the reactive
system and they are entirely under the control of the client. When
the client invokes a primitive's update function without the
`step`

argument or when it invokes Step.execute on a `step`

value, React performs an update step.

To ensure correctness in the presence of threads, update steps
must be executed in a critical section. Let uset(`p`

) be the set
of events and signals that need to be updated whenever the
primitive `p`

is updated. Updating two primitives `p`

and `p'`

concurrently is only allowed if uset(`p`

) and uset(`p'`

) are
disjoint. Otherwise the updates must be properly serialized.

Below, concurrent, updates to `x`

and `y`

must be serialized (or
performed on the same step if it makes sense semantically), but z
can be updated concurently to both `x`

and `y`

.

```
open React;;
let x, set_x = S.create 0
let y, send_y = E.create ()
let z, set_z = S.create 0
let max_xy = S.l2 (fun x y -> if x > y then x else y) x (S.hold 0 y)
let succ_z = S.map succ z
```

#
## Side effects

Effectful events and signals perform their side effect
exactly *once* in each update step in which there
is an update of at least one of the event or signal it depends on.

Remember that a signal updates in a step iff its equality function determined that the signal value changed. Signal initialization is unconditionally considered as an update.

It is important to keep references on effectful events and
signals. Otherwise they may be reclaimed by the garbage collector.
The following program prints only a `1`

.

```
let x, set_x = S.create 1
let () = ignore (S.map print_int x)
let () = Gc.full_major (); List.iter set_x [2; 2; 3]
```

#
## Lifting

Lifting transforms a regular function to make it act on signals. The combinators S.const and S.app allow to lift functions of arbitrary arity n, but this involves the inefficient creation of n-1 intermediary closure signals. The fixed arity lifting functions are more efficient. For example :

```
let f x y = x mod y
let fl x y = S.app (S.app ~eq:(==) (S.const f) x) y (* inefficient *)
let fl' x y = S.l2 f x y (* efficient *)
```

Besides, some of `Pervasives`

's functions and operators are
already lifted and availables in submodules of S. They can be
be opened in specific scopes. For example if you are dealing with
float signals you can open S.Float.

```
open React
open React.S.Float
let f t = sqrt t *. sin t (* f is defined on float signals *)
...
open Pervasives (* back to pervasives floats *)
```

If you are using OCaml 3.12 or later you can also use the `let open`

construct

```
let open React.S.Float in
let f t = sqrt t *. sin t in (* f is defined on float signals *)
...
```

#
## Mutual and self reference

Mutual and self reference among time varying values occurs naturally in programs. However a mutually recursive definition of two signals in which both need the value of the other at time t to define their value at time t has no least fixed point. To break this tight loop one signal must depend on the value the other had at time t-dt where dt is an infinitesimal delay.

The fixed point combinators E.fix and S.fix allow to refer to
the value an event or signal had an infinitesimal amount of time
before. These fixed point combinators act on a function `f`

that takes
as argument the infinitesimally delayed event or signal that `f`

itself returns.

In the example below `history s`

returns a signal whose value
is the history of `s`

as a list.

```
let history ?(eq = ( = )) s =
let push v = function
| [] -> [ v ]
| v' :: _ as l when eq v v' -> l
| l -> v :: l
in
let define h =
let h' = S.l2 push s h in
h', h'
in
S.fix [] define
```

When a program has infinitesimally delayed values a
primitive may trigger more than one update
step. For example if a signal `s`

is infinitesimally delayed, then
its update in a step `c`

will trigger a new step `c'`

at the end
of the step in which the delayed signal of `s`

will have the value
`s`

had in `c`

. This means that the recursion occuring between a
signal (or event) and its infinitesimally delayed counterpart must
be well-founded otherwise this may trigger an infinite number
of update steps, like in the following examples.

```
let start, send_start = E.create ()
let diverge =
let define e =
let e' = E.select [e; start] in
e', e'
in
E.fix define
let () = send_start () (* diverges *)
let diverge = (* diverges *)
let define s =
let s' = S.Int.succ s in
s', s'
in
S.fix 0 define
```

For technical reasons, delayed events and signals (those given to
fixing functions) are not allowed to directly depend on each
other. Fixed point combinators will raise `Invalid_argument`

if
such dependencies are created. This limitation can be
circumvented by mapping these values with the identity.

#
## Strong stops

Strong stops should only be used on platforms where weak arrays have
a strong semantics (i.e. JavaScript). You can safely ignore that
section and the `strong`

argument of E.stop and S.stop
if that's not the case.

Whenever E.stop and S.stop is called with `~strong:true`

on a
reactive value `v`

, it is first stopped and then it walks over the
list `prods`

of events and signals that it depends on and
unregisters itself from these ones as a dependent (something that is
normally automatically done when `v`

is garbage collected since
dependents are stored in a weak array). Then for each element of
`prod`

that has no dependents anymore and is not a primitive it
stops them aswell and recursively.

A stop call with `~strong:true`

is more involved. But it allows to
prevent memory leaks when used judiciously on the leaves of the
reactive system that are no longer used.

**Warning.** It should be noted that if direct references are kept
on an intermediate event or signal of the reactive system it may
suddenly stop updating if all its dependents were strongly stopped. In
the example below, `e1`

will *never* occur:

```
let e, e_send = E.create ()
let e1 = E.map (fun x -> x + 1) e (* never occurs *)
let () =
let e2 = E.map (fun x -> x + 1) e1 in
E.stop ~strong:true e2
```

This can be side stepped by making an artificial dependency to keep the reference:

```
let e, e_send = E.create ()
let e1 = E.map (fun x -> x + 1) e (* may still occur *)
let e1_ref = E.map (fun x -> x) e1
let () =
let e2 = E.map (fun x -> x + 1) e1 in
E.stop ~strong:true e2
```

#
# Examples

#
## Clock

The following program defines a primitive event `seconds`

holding
the UNIX time and occuring on every second. An effectful event
converts these occurences to local time and prints them on stdout
along with an
ANSI
escape sequence to control the cursor position.

```
let pr_time t =
let tm = Unix.localtime t in
Printf.printf "\x1B[8D%02d:%02d:%02d%!"
tm.Unix.tm_hour tm.Unix.tm_min tm.Unix.tm_sec
open React;;
let seconds, run =
let e, send = E.create () in
let run () =
while true do send (Unix.gettimeofday ()); Unix.sleep 1 done
in
e, run
let printer = E.map pr_time seconds
let () = run ()
```

end