Local consistency techniques have been introduced in logic programming in order to extend the application domain of logic programming languages. The existing languages based on these techniques consider arithmetic constraints applied to variables ranging over nite integer domains. This makes difficult a natural and concise modelling as well as an efficient solving of a class of NP-complete combinatorial search problems dealing with sets. To overcome these problems, we propose a solution which consists in extending the notion of integer domains to that of set domains (sets of sets). We specify a set domain by an interval whose lower and upper bounds are known sets, ordered by set inclusion. We define the formal and practical framework of a new constraint logic programming language over set domains, called Conjunto. Conjunto comprises the usual set operation symbols ([ � \ � n), and the set inclusion relation (). Set expressions built using the operation symbols are interpreted as relations (s [ s1 = s2,...). In addition, Conjunto provides us with a set of constraints called graduated constraints (e.g. the set cardinality) which map sets onto arithmetic terms. This allows us to handle optimization problems by applying a cost function to the quantifiable, i.e., arithmetic, terms which are associated to set terms. The constraint solving in Conjunto is based on local consistency techniques using interval reasoning which are extended to handle set constraints. The main contribution of this paper concerns the formal definition of the language and its design and implementation as a practical language.

this paper we describe an interactive software system named SetPlayer

: 81/2 is a declarative data-parallel language designed for the simulation of large dynamical systems. Such simulations are of growing importance and they requires more and more computing power. In consequence, 81/2 introduces a new entity, the web, that combines features of collection-oriented and data-flow language to express data-, stream- and control-parallelism. In this paper, we present the language 81/2, some examples of dynamical systems programmed in 81/2 and we describe the compilation process of a 81/2 programme. Key-words: data-parallelism, collection-oriented languages, declarative languages, synchronous data-flow languages, simulation of dynamical systems. I. Introduction Nowadays, simulation of large dynamical systems represents the majority of supercomputers applications. In this article, a dynamical system refers as any application that modelizes space-time phenomena. Three usual examples are: . numerical resolution of partial differential equations [1] describing con...

A lot of work has been done up to now in designing Constraint Logic Programming Languages in order to solve combinatorial problems. Built-in computational domains in CLP support simple expression of problems and their efficient solution. Building a new computational domain comprising sets and graphs, this paper presents new symbolic constraints on set and graph structures in a CLP environment. Its main aim is to offer to the programmer the possibility to describe and solve in a natural, concise, declarative, expressive and efficient manner real Operations Research problems which are based on set and graph theory. 2 A constraint object is more suitable than a variable Usually the addition of new variables denoting sets to logic programs extends the unification algorithms to the involvment of these formulas [4]. As any added value to a language, it proves to be detrimental to the initial language performances. Moreover set unification is NP-complete [5]. Our constraint handler for sets ...

This paper describes the language 8 1/2 , an embedding of data-parallelism in a declarative framework.

this paper we propose to integrate sets and relations as constrained objects in a CLP framework with finite domains. The domain of discourse for sets is the powerset of the Herbrand universe P(HU). Set constraints and set operators can be simply and efficiently handled. Such an integration of symbolic constrained objects permits Operations Research problems which are based on set algebra as well as relational and graph theory to be solved in a concise and clear manner. Symbolic tools bring expressive power to the language and contribute to reduce the programmer development time. A set variable Our domain of computation P(HU) [ FD permits ground terms of HU to be elements of a set S. Set constraints initialize and refine the domain of such a set. Our set constraints are `; ae; 6ae; 6`, =, disjoint/2,

Abstract. Local consistency techniques have beenintroduced in logic programming in order to extend the application domain of logic programming languages. The existing languages based on these techniques consider arithmetic constraints applied to variables ranging over nite integer domains. This makes di cult a natural and concise modelling as well as an e cient solving of a class of NP-complete combinatorial search problems dealing with sets. To overcome these problems, we propose a solution which consists in extending the notion of integer domains to that of set domains (sets of sets). We specify a set domain by aninterval whose lower and upper bounds are known sets, ordered by set inclusion. We de ne the formal and practical framework of a new constraint logic programming language over set domains, called Conjunto. Conjunto comprises the usual set operation symbols ([ � \ � n), and the set inclusion relation (). Set expressions built using the operation symbols are interpreted as relations (s [ s1 = s2,...). In addition, Conjunto provides us with a set of constraints called graduated constraints (e.g. the set cardinality) which map sets onto arithmetic terms. This allows us to handle optimization problems by applyinga cost function to the quanti able, i.e., arithmetic, terms which are associated to set terms. The constraint solving in Conjunto is based on local consistency techniques using interval reasoning which are extended to handle set constraints. The main contribution of this paper concerns the formal de nition of the language and its design and implementation as a practical language.

Sets play a key role in foundations of mathematics. Why? To what extent is it an accident of history? Imagine that you have a chance to talk to mathematicians from a far-away planet. Would their mathematics be set-based? What are the alternatives to the set-theoretic foundation of mathematics? Besides, set theory seems to play a significant role in computer science; is there a good justification for that? We discuss these and some related issues.