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12
Comparing Expressiveness of Set Constructor Symbols
, 2000
"... In this paper we consider the relative expressive power of two very common operators applicable to sets and multisets: the with and the union operators. For such operators we prove that they are not mutually expressible by means of existentially quantified formulae. In order to prove our results ..."
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Cited by 9 (7 self)
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In this paper we consider the relative expressive power of two very common operators applicable to sets and multisets: the with and the union operators. For such operators we prove that they are not mutually expressible by means of existentially quantified formulae. In order to prove our results, canonical forms for settheoretic and multisettheoretic formulae are established and a particularly natural axiomatization of multisets is given and studied.
G.: A uniform approach to constraintsolving for lists, multisets, compact lists, and sets
 ACM Trans. Comput. Log
, 2008
"... Lists, multisets, and sets are wellknown data structures whose usefulness is widely recognized in various areas of Computer Science. They have been analyzed from an axiomatic point of view with a parametric approach in [Dovier et al. 1998] where the relevant unification algorithms have been develop ..."
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Cited by 9 (5 self)
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Lists, multisets, and sets are wellknown data structures whose usefulness is widely recognized in various areas of Computer Science. They have been analyzed from an axiomatic point of view with a parametric approach in [Dovier et al. 1998] where the relevant unification algorithms have been developed. In this paper we extend these results considering more general constraints, namely equality and membership constraints and their negative counterparts.
Set Unification
, 2001
"... The goal of this paper is to provide a uniform overview of the unification problem in algebras capable of describing sets. The problem has been tackled, directly and indirectly, by many researchers and it can find important applications in various research areas  e.g., deductive databases, theorem ..."
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Cited by 8 (4 self)
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The goal of this paper is to provide a uniform overview of the unification problem in algebras capable of describing sets. The problem has been tackled, directly and indirectly, by many researchers and it can find important applications in various research areas  e.g., deductive databases, theorem proving, static analysis, rapid software prototyping. The problem has been explored in depth, but the various solutions proposed are spread across a large literature, and some of the approaches have been ignored and/or rediscovered by different researchers. In this
Constructive Negation and Constraint Logic Programming with Sets
 New Generation Computing
"... The aim of this paper is to extend the Constructive Negation technique to the case of CLP (SET ), a Constraint Logic Programming (CLP ) language based on hereditarily (and hybrid) finite sets. The challenging aspects of the problem originate from the fact that the structure on which CLP (SET ) is ba ..."
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Cited by 8 (5 self)
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The aim of this paper is to extend the Constructive Negation technique to the case of CLP (SET ), a Constraint Logic Programming (CLP ) language based on hereditarily (and hybrid) finite sets. The challenging aspects of the problem originate from the fact that the structure on which CLP (SET ) is based is not admissible closed, and this does not allow to reuse the results presented in the literature concerning the relationships between CLP and constructive negation. We propose a new constraint satisfaction algorithm, capable of correctly handling constructive negation for large classes of CLP (SET ) programs; we also provide a syntactic characterization of such classes of programs. The resulting algorithm provides a novel constraint simplification procedure to handle constructive negation, suitable to theories where unification admits multiple most general unifiers. We also show, using a general result, that it is impossible to construct an interpreter...
A Necessary Condition for Constructive Negation in Constraint Logic Programming
, 2000
"... In [15] a sound and complete procedure for Constructive Negation in Constraint Logic Programming has been presented, together with a sufficient condition, called admissible closure, which guarantees an effective implementation. In this paper we analyze this condition and relate it to the decidabilit ..."
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Cited by 1 (1 self)
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In [15] a sound and complete procedure for Constructive Negation in Constraint Logic Programming has been presented, together with a sufficient condition, called admissible closure, which guarantees an effective implementation. In this paper we analyze this condition and relate it to the decidability of the underlying constraint structure. We prove that the admissible closure condition is also necessary to guarantee the existence of an effective implementation of Constructive Negation.
SetBased Constraints
"... The notion of set constraint has been presented in literature with two dierent meanings and aims. Each of them allows to deal with a particular class of set based formulae. We compare the two notions and present their satis ability problem as instances of the more general framework of Computable ..."
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The notion of set constraint has been presented in literature with two dierent meanings and aims. Each of them allows to deal with a particular class of set based formulae. We compare the two notions and present their satis ability problem as instances of the more general framework of Computable Set Theory. We show that there are large classes of formulae for which both proposals provide suitable procedures for testing satis ability with respect to a given privileged interpretation. We show examples of how these constraints can be used for setbased analysis and for problem solving in general.
Towards Correctness of Program Transformations Through Unification and Critical Pair Computation
, 2010
"... Abstract. Correctness of program transformations in extended lambdacalculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach is the combination of a context lemma with the computation of overlaps between pro ..."
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Abstract. Correctness of program transformations in extended lambdacalculi with a contextual semantics is usually based on reasoning about the operational semantics which is a rewrite semantics. A successful approach is the combination of a context lemma with the computation of overlaps between program transformations and the reduction rules, which results in socalled complete sets of diagrams. The method is similar to the computation of critical pairs for the completion of term rewriting systems. We explore cases where the computation of these overlaps can be done in a first order way by variants of critical pair computation that use unification algorithms. As a case study of an application we describe a finitary and decidable unification algorithm for the combination of the equational theory of leftcommutativity modelling multisets, context variables and manysorted unification. Sets of equations are restricted to be almost linear, i.e. every variable and context variable occurs at most once, where we allow one exception: variables of a sort without ground terms may occur several times. Every context variable must have an argumentsort in the free part of the signature. We also extend the unification algorithm by the treatment of bindingchains in let and letrecenvironments and by contextclasses. This results in a unification algorithm that can be applied to all overlaps of normalorder reductions and transformations in an extended lambda calculus with letrec that we use as a case study. 1
Solution Count for Multiset Unification with
"... this paper, we consider the problem of unifying multiset expressions of the form where t i is either a constant a from the support set S or an object variable X that can be instantiated only to elements of S, and R is either the empty multiset or a trailing multiset variable whose values ran ..."
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this paper, we consider the problem of unifying multiset expressions of the form where t i is either a constant a from the support set S or an object variable X that can be instantiated only to elements of S, and R is either the empty multiset or a trailing multiset variable whose values range over multisets over S. Multiset expressions where R = are called simple, and we will abbreviate them as #
Constraint Logic Programming
"... Abstract. Constraint Logic Programming (CLP) is one of the most successful branches of Logic Programming; it attracts the interest of theoreticians and practitioners, and it is currently used in many commercial applications. Since the original proposal, it has developed enormously: many languages an ..."
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Abstract. Constraint Logic Programming (CLP) is one of the most successful branches of Logic Programming; it attracts the interest of theoreticians and practitioners, and it is currently used in many commercial applications. Since the original proposal, it has developed enormously: many languages and systems are now available either as open source programs or as commercial systems. Also, CLP has been one of the technologies able to recruit researchers from other communities to the declarative programming cause. Current CLP engines include technologies and results developed in other communities, which themselves discovered logic as an invaluable tool to model and solve reallife problems. 1 The CLP paradigm Constraint Logic Programming (CLP) [7] represents a successful attempt to merge the best features of logic programming (LP) and constraint solving. Constraint solving [127,6,56,31] includes a variety of expressive modelling