Functional Reactive Programming

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Functional Reactive Programming (FRP) integrates time flow and compositional events into functional programming. This provides an elegant way to express computation in domains such as interactive animations, robotics, computer vision, user interfaces, and simulation.


The original formulation of Functional Reactive Programming can be found in the ICFP 97 paper Functional Reactive Animation by Conal Elliott and Paul Hudak. It introduces the following semantic functions:

  • at : Behaviorα → Time → α
  • occ : Eventα → Time × α

to provide a formal description of operations on values now commonly known as behaviors and events. But what are they?


Traditionally a widget-based user interface is created by a series of imperative actions. First an action is invoked to create an edit widget, then additional actions can be invoked to read its current content, set it to a specific value or to assign an event callback for when the content changes. This is tedious and error-prone.

A better way to represent an edit widget's content is a time-varying value, called a behavior. The basic idea is that a time-varying value can be represented as a function of time:

newtype Behavior a =
    Behavior {
      at :: Time -> a

myTodoList                :: Behavior Text
yesterday                 :: Time
myTodoList `at` yesterday :: Text

This is only a theoretical model, because a time-varying value can represent something impure like the content of an edit widget, the current value of a database entry as well as the system clock's current time. Using this model the current content of an edit widget would be a regular first class value:

myEditWidget :: Behavior Text

In most frameworks there is an applicative interface for behaviors, such that you can combine them easily:

liftA2 (<>) myEdit1 myEdit2

The result is a time-varying value that represents the concatenation of myEdit1 and myEdit2. This could be the value of a third widget, a label, to display the concatenation. The following is a hypothetical example:

do edit1 <- editWidget
   edit2 <- editWidget
   label <- label (liftA2 (<>) edit1 edit2)
   {- ... -}

Without behaviors you would have to write event callback actions for the edit widgets to update the label's content. With behaviors you can express this relationship declaratively.


While behaviours work well for describing properties which are continuous (e.g. the motion of an animated object), other properties are more discrete (e.g. what button on the mouse was clicked or the screen position where it happened). Events more easily accommodate information like this, by associating the data value of interest with a particular time:

newtype Event a =
    Event {
      occ :: (Time, a)

mouseInWindowNow     :: Event Bool
occ mouseInWindowNow :: (Time, Bool)

The concept of an event stream (or simply stream), for representing a series of events, supports a basic model of interactivity:

Suppose that we want to compute a function F on several arguments A0, A1, A2,... appearing consecutively in time [as discrete events]. One can view this so-called stream (A0, A1, A2,...) as a potentially infinite list A = (A0:A1:A2:···:An:⊥) where ⊥ stands for “unspecified” and is interactively updated to An+1:⊥ each time the user has a new argument An+1. Then on this list A, the system applies the function F* defined by

F* (A:B) = (F A):(F* B)


F* A = (F A0:F A1:F A2:···:F An:F* ⊥)

also appearing consecutively in time.

Functional Programming and Lambda Calculus, Henk Barendregt (page 325).

Semantic functions?

From page 6 of the paper:

An early implementation of Fran represented behaviors as implied in the formal semantics:

data Behavior a = Behavior (Time -> a)

This representation, however, leads to a serious inefficiency [a “space-time” leak].

So instead of one canonical implementation of FRP, this tendency to "leak" has led to a variety of implementations, each with its own benefit-cost trade-offs.


A simple, practical comparison between FRP libraries is done by frp-zoo

Publications and talks


Blog posts



A possible predecessor?

In his thesis Functional Real-Time Programming: The Language Ruth And Its Semantics, some parts of the semantics Dave Harrison gives for Ruth bears a curious resemblance to those for FRP:

  • (page 48)

A channel is an infinite stream of timestamped data values, or messages, each message denoting an event in the system. [...]

type Channel a = [Event a]
data Event a   = At Time a
  • (page 61)

In the semantics given in Chapter 5 every Ruth program is supplied with a tree of time values (or clock) as suggested in this paper and each Ruth process is given a different sub-tree of the clock [...]

type Program = Clock -> ...
type Process a = Clock -> a

type Clock = Tree Time
left  :: Clock -> Clock
right :: Clock -> Clock

A clock tree is composed of a node holding a non-negative integer denoting the current time and two sub-trees containing the times of future events. As the tree is (lazily) evaluated each of the nodes is instantiated with the value of system time at the time at which the node is instantiated, thus giving programs reference to the current time. [...]

type Time   = Integer  -- must be zero or larger 
data Tree a = Node { contents :: a,
                     left     :: Tree a,
                     right    :: Tree a }

currentTime :: Clock -> Time
currentTime = contents

Regarding Harrison's semantics:

(page 53)

The semantics of Ruth given in Chapter 5 assume a normal order evaluation strategy such as is provided by the technique of lazy evaluation [...]. Consequently whererec can be used to define infinite data structures.