module React: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.
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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.
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
Some v whenever the event occurs with value
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' with t' the greatest t' < t (resp.
<=) such that [
= Noneif there is no such t'.
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 [
the evaluation of this semantic function at time t.
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
Given an equality function on a type the combinators can be automatically
specialized via a functor.
Ultimately signal updates depend on primitive 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.
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
React.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
3. Those occurrences are printed
on stdout by the effectful event
Primitive signals are created with
let x, send_x = E.create ()
let pr_x = E.map print_int x
let () = List.iter send_x [1; 2; 3]
React.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
xinitially set to
1and updates it three time with values
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
1223. See the discussion on side effects for more details.
The clock example shows how a realtime time flow can be defined.
let x, set_x = S.create 1
let pr_x = S.map print_int x
let () = List.iter set_x [2; 2; 3]
The update cycle 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, React performs an update cycle. The update cycle 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.
To ensure correctness in the presence of threads, update cycles
must be executed in a critical section. Let uset(
p) be the set
of events and signals that need to be updated whenever the
p is updated. Updating two primitives
concurrently is only allowed if uset(
p) and uset(
disjoint. Otherwise the updates must be properly serialized.
Below updates to
y must be serialized, but z can
be updated concurently to both
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
Update cycles are made under a synchrony hypothesis : the update cycle takes no time, it is instantenous.
Two event occurrences are simultaneous if they occur in the same update cycle; in other words if there exists a primitive on which they both depend. By definition a primitive doesn't depend on any primitive it is therefore impossible for two primitive events to occur simultaneously.
In the code below
y will have simultaneous occurrences while
z will never have simultaneous occurrences with them.
let w, send_w = E.create ()
let x = E.map succ w
let y = E.map succ x
let z, send_z = E.create ()
Effectful events and signals perform their side effect exactly once in each update cycle 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 cycle 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
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 transforms a regular function to make it act on signals.
React.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 :
Besides, some of
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 *)
Pervasives's functions and operators are already lifted and availables in submodules of
React.S. They can be be opened in specific scopes. For example if you are dealing with float signals you can open
If you are using OCaml 3.12 or later you can also use the
let f t = sqrt t *. sin t (* f is defined on float signals *)
open Pervasives (* back to pervasives floats *)
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
React.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
In the example below
history s returns a signal whose value
is the history of
s as a list.
When a program has infinitesimally delayed values a primitive may trigger more than one update cycle. For example if a signal
let history ?(eq = ( = )) s =
let push v = function
|  -> [ v ]
| v' :: _ as l when eq v v' -> l
| l -> v :: l
let define h =
let h' = S.l2 push s h in
S.fix  define
sis infinitesimally delayed, then its update in a cycle
cwill trigger a new cycle
c'at the end of the cycle in which the delayed signal of
swill have the value
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 cycles, like in the following examples.
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
let start, send_start = E.create ()
let diverge =
let define e =
let e' = E.select [e; start] in
let () = send_start () (* diverges *)
let diverge = (* diverges *)
let define s =
let s' = S.Int.succ s in
S.fix 0 define
Invalid_argumentif such dependencies are created. This limitation can be circumvented by mapping these values with the identity.
The following program defines a primitive event
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
escape sequence to control the cursor position.
let pr_time t =
let tm = Unix.localtime t in
tm.Unix.tm_hour tm.Unix.tm_min tm.Unix.tm_sec
let seconds, run =
let e, send = E.create () in
let run () =
while true do send (Unix.gettimeofday ()); Unix.sleep 1 done
let printer = E.map pr_time seconds
let () = run ()