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Abstract
This paper gives a denotational semantics to FRP, and discusses the
connection between the semantics and a stream-based implementation.
Abstract Functional Reactive Programming, or FRP,
is a general framework for programming hybrid systems in a high-level,
declarative manner. The key ideas in FRP are its notions of behaviors
and events. Behaviors are time-varying, reactive values, while
events are time-ordered sequences of discrete-time event occurrences.
FRP is the essence of Fran, a domain-specific language embedded
in Haskell for programming reactive animations, but FRP is now also being
used in vision, robotics and other control systems applications.
In this paper we explore the formal semantics of FRP and how it relates
to an implementation based on streams that represent (and therefore
only approximate) continuous behaviors. We show that, in the limit
as the sampling interval goes to zero, the implementation is faithful to
the formal, continuous semantics, but only when certain constraints on
behaviors are observed. We explore the nature of these constraints,
which vary amongst the FRP primitives. Our results show both the
power and limitations of this approach to language design and implementation.
As an example of a limitation, we show that streams are incapable of representing
instantaneous predicate events over behaviors.
@InProceedings(wan00:frp,
author = "Zhanyong Wan and Paul Hudak",
title = "{F}unctional {R}eactive {P}rogramming from First
Principles",
year = 2000,
booktitle = "Proc. {ACM} {SIGPLAN'00} Conference on Programming
Language Design and Implementation ({PLDI'00})"
)
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