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Interval propagation to reason about sets: definition and implementation of a practical language
 CONSTRAINTS
, 1997
"... 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 difficu ..."
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Cited by 100 (5 self)
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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 NPcomplete 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.
System for Symbolic Computation on Power Sets
 Journal of Symbolic Computation
, 2000
"... this paper we describe an interactive software system named SetPlayer ..."
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Cited by 10 (5 self)
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this paper we describe an interactive software system named SetPlayer
New structures of symbolic constraint objects: sets and graphs (Extended Abstract)
, 1993
"... A lot of work has been done up to now in designing Constraint Logic Programming Languages in order to solve combinatorial problems. Builtin computational domains in CLP support simple expression of problems and their efficient solution. Building a new computational domain comprising sets and graphs ..."
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Cited by 10 (1 self)
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A lot of work has been done up to now in designing Constraint Logic Programming Languages in order to solve combinatorial problems. Builtin 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 NPcomplete [5]. Our constraint handler for sets ...
A DataParallel Declarative Language for the Simulation of Large Dynamical Systems and Its Compilation
, 1994
"... : 81/2 is a declarative dataparallel 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 collectionoriented and ..."
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Cited by 7 (5 self)
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: 81/2 is a declarative dataparallel 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 collectionoriented and dataflow language to express data, stream and controlparallelism. 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. Keywords: dataparallelism, collectionoriented languages, declarative languages, synchronous dataflow 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 spacetime phenomena. Three usual examples are: . numerical resolution of partial differential equations [1] describing con...
Design and Implementation of a Declarative DataParallel Language
, 1994
"... This paper describes the language 8 1/2 , an embedding of dataparallelism in a declarative framework. ..."
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Cited by 5 (1 self)
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This paper describes the language 8 1/2 , an embedding of dataparallelism in a declarative framework.
Set and Binary Relation Variables Viewed as Constrained Objects (abstract)
, 1993
"... 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 symbol ..."
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Cited by 4 (1 self)
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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,
Interval propagation to reason about sets: de nition and implementation of a practical language
 Constraints
, 1997
"... 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 make ..."
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Cited by 3 (0 self)
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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 NPcomplete 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.
Why sets?
 PILLARS OF COMPUTER SCIENCE: ESSAYS DEDICATED TO BORIS (BOAZ) TRAKHTENBROT ON THE OCCASION OF HIS 85TH BIRTHDAY, VOLUME 4800 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2008
"... 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 faraway planet. Would their mathematics be setbased? What are the alternatives to the settheoretic foundation of mathematics? Besi ..."
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Cited by 2 (0 self)
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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 faraway planet. Would their mathematics be setbased? What are the alternatives to the settheoretic 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.