Abstract. In this paper, we present a theory of synchronous data-flow languages. Our theory is supported by both some heuristic analysis of applications and some theoretical investigation of the data-flow paradigm. Our model covers both behavioural and operational aspects, and allows both synchronous and asynchronous styles of implementation for synchronous programs. This model served as a basis to establish the gc common format for synchronous data-flow languages.

Abstract: We propose a novel discipline for programming stream functions and for the semantic description of stream manipulation languages based on the observation that both general and causal stream functions can be characterized as coKleisli arrows of comonads. This seems to be a promising application for the old, but very little exploited idea that if monads abstract notions of computation of a value, comonads ought to be useable as an abstraction of notions of value in a context. We also show that causal partial-stream functions can be described in terms of a combination of a comonad and a monad.

Introduction 1.1. Flots de donn'ees Dans les ann'ees 70, le langage Lucid a 'et'e propos'e [2, 1], pour pallier l'inefficacit'e des langages fonctionnels, en introduisant un style d'it'eration fond'e sur les suites de valeurs. A peu pr`es `a la meme 'epoque, Gilles Kahn montrait [13] que la s'emantique de r'eseaux de processus asynchrones et d'eterministes, communiquant par des files d'attente, pouvait se d'ecrire comme des syst`emes d"equations de suites, tr`es voisins des programmes Lucid. Parall`element, le concept d"evaluation paresseuse 'emergeait comme un outil pratique [10, 16], permettant d'introduire dans les langages de programmation des types de donn'ees infinis, comme les suites, et maintenant, des langages fonctionnels modernes, comme Lazy ML ou Haskell permettent d"ecrire tr`es facilement des programmes `a la Lucid ou `a la Kahn, en apportant de nombreuse facilit'es d'expression, tels la curryfic