Timed Denotational Semantics for Causal Functions over Timed Streams

David Janin 1 Bernard Paul Serpette 2
1 PoSET - Models for a Structured Programming of Space and Time
LaBRI - Laboratoire Bordelais de Recherche en Informatique, SCRIME - Studio de Création et de Recherche en Informatique et Musique Électroacoustique, Inria Bordeaux - Sud-Ouest
2 INDES - Secure Diffuse Programming
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We consider timed system behaviors seen as functions acting over streams of timed events (timed streams) that satisfy a temporal causality property: at every instant, current outputs only depends on inputs that have already been received. We aim at defining a timed model for describing their denotational semantics in the style of Strachey’s and Scott’s domain approach. For such a purpose, we extend timed streams with a notion of partial timed streams that form together a directed complete partial order (DCPO). Continuous functions over these DCPOs are then natural candidates for modeling timed denotational semantics of causal functions. Indeed, restricting to some notion of pre-synchronous continuous functions, we show that every causal function admits a non empty lattice of possible semantics which least element corresponds to a latest or laziest semantics and which greatest element corresponds a earliest or eagerest semantics. These operational aspects are then made explicit by defining a operational semantics model for causal functions that is inspired by timed-IO automata theory.
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https://hal.archives-ouvertes.fr/hal-01402209
Contributor : David Janin <>
Submitted on : Thursday, November 24, 2016 - 1:50:02 PM
Last modification on : Tuesday, May 29, 2018 - 9:14:04 AM

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  • HAL Id : hal-01402209, version 1

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David Janin, Bernard Paul Serpette. Timed Denotational Semantics for Causal Functions over Timed Streams. [Research Report] LaBRI - Laboratoire Bordelais de Recherche en Informatique. 2016. ⟨hal-01402209⟩

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