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Theory and Practice of Constraint Handling Rules
, 1998
"... Constraint Handling Rules (CHR) are our proposal to allow more flexibility and applicationoriented customization of constraint systems. CHR are a declarative language extension especially designed for writing userdefined constraints. CHR are essentially a committedchoice language consisting of mu ..."
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Cited by 396 (35 self)
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Constraint Handling Rules (CHR) are our proposal to allow more flexibility and applicationoriented customization of constraint systems. CHR are a declarative language extension especially designed for writing userdefined constraints. CHR are essentially a committedchoice language consisting of multiheaded guarded rules that rewrite constraints into simpler ones until they are solved. In this broad survey we aim at covering all aspects of CHR as they currently present themselves. Going from theory to practice, we will define syntax and semantics for CHR, introduce an important decidable property, confluence, of CHR programs and define a tight integration of CHR with constraint logic programming languages. This survey then describes implementations of the language before we review several constraint solvers  both traditional and non standard ones  written in the CHR language. Finally we introduce two innovative applications that benefited from using CHR.
Equations and rewrite rules: a survey
 In Formal Language Theory: Perspectives and Open Problems
, 1980
"... bY ..."
ContextSensitive Computations in Functional and Functional Logic Programs
 JOURNAL OF FUNCTIONAL AND LOGIC PROGRAMMING
, 1998
"... ..."
Diagram Groups
, 1996
"... this paper, we study 2dimensional analogies of this idea: semigroup diagrams, monoid pictures, annular diagrams, cylindric pictures and braided pictures. While the groups of linear diagrams are all free, we get a large class of groups which are representable by 2dimensional semigroup diagrams. Sem ..."
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Cited by 38 (6 self)
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this paper, we study 2dimensional analogies of this idea: semigroup diagrams, monoid pictures, annular diagrams, cylindric pictures and braided pictures. While the groups of linear diagrams are all free, we get a large class of groups which are representable by 2dimensional semigroup diagrams. Semigroup diagrams, are wellknown geometrical objects used in the study of Thue systems (=semigroup presentations). They were first formally introduced by Kashintsev [16], see also Remmers [29], Stallings [34] or Higgins [13]. The role of semigroup diagrams in the study of semigroups is similar to the role of van Kampen diagrams in the study of groups (see [22] or [26])
Confluence of Typed Attributed Graph Transformation Systems
 In: Proc. ICGT 2002. Volume 2505 of LNCS
, 2002
"... The issue of confluence is of major importance for the successful application of attributed graph transformation, such as automated translation of UML models into semantic domains. Whereas termination is undecidable in general and must be established by carefully designing the rules, local confl ..."
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Cited by 38 (6 self)
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The issue of confluence is of major importance for the successful application of attributed graph transformation, such as automated translation of UML models into semantic domains. Whereas termination is undecidable in general and must be established by carefully designing the rules, local confluence can be shown for term rewriting and graph rewriting using the concept of critical pairs. In this paper, we discuss typed attributed graph transformation using a new simplified notion of attribution. For this kind of attributed graph transformation systems we establish a definition of critical pairs and prove a critical pair lemma, stating that local confluence follows from confluence of all critical pairs.
Completeness of Combinations of Constructor Systems
 Journal of Symbolic Computation
, 1993
"... this paper we show that it is sufficient to impose the constructor discipline for obtaining the modularity of completeness. This result is a simple consequence of a quite powerful divide and conquer technique for establishing completeness of such constructor systems. Our approach is not limited to s ..."
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Cited by 31 (2 self)
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this paper we show that it is sufficient to impose the constructor discipline for obtaining the modularity of completeness. This result is a simple consequence of a quite powerful divide and conquer technique for establishing completeness of such constructor systems. Our approach is not limited to systems which are composed of disjoint parts. The importance of our method is that we may decompose a given constructor system into parts which possibly share function symbols and rewrite rules in order to infer completeness. We obtain a similar technique for semicompleteness, i.e. the combination of confluence and weak normalisation. 1. Introduction
Birewrite systems
, 1996
"... In this article we propose an extension of term rewriting techniques to automate the deduction in monotone preorder theories. To prove an inclusion a ⊆ b from a given set I of them, we generate from I, using a completion procedure, a birewrite system 〈R⊆, R⊇〉, that is, a pair of rewrite relations ..."
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Cited by 29 (9 self)
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In this article we propose an extension of term rewriting techniques to automate the deduction in monotone preorder theories. To prove an inclusion a ⊆ b from a given set I of them, we generate from I, using a completion procedure, a birewrite system 〈R⊆, R⊇〉, that is, a pair of rewrite relations −−− → R ⊆ and −−− → R ⊇ , and seek a common term c such that a −−−→ R ⊆ c and b −−−→
Lambda calculus with patterns
, 1990
"... The calculus is an extension of the calculus with a pattern matching facility. The form of the argument of a function can be specified and hencecalculus is more convenient than ordinary calculus. We explore the basic theory of calculus, establishing results such as confluence. In doing so, we f ..."
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Cited by 28 (1 self)
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The calculus is an extension of the calculus with a pattern matching facility. The form of the argument of a function can be specified and hencecalculus is more convenient than ordinary calculus. We explore the basic theory of calculus, establishing results such as confluence. In doing so, we find some requirements for patterns that guarantee confluence. Our work can be seen as giving some foundations for implementations of functional programming languages.
On free conformal and vertex algebras
 J. Algebra
, 1999
"... Vertex algebras and conformal algebras have recently attracted a lot of attention due to their connections with physics and Moonshine representations of the Monster. See, for example, [6], [10], [15], [17], [19]. In this paper we describe bases of free conformal and free vertex algebras (as introduc ..."
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Cited by 27 (8 self)
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Vertex algebras and conformal algebras have recently attracted a lot of attention due to their connections with physics and Moonshine representations of the Monster. See, for example, [6], [10], [15], [17], [19]. In this paper we describe bases of free conformal and free vertex algebras (as introduced in [6], see also [20]). All linear spaces are over a field k of characteristic 0. Throughout this paper Z+ will stand for the set of nonnegative integers. In §1 and §2 we give a review of conformal and vertex algebra theory. All statements is these sections are either in [9], [15], [16], [17], [18], [20] or easily follow from results therein. In §3 we investigate free conformal and vertex algebras. 1. Conformal algebras 1.1. Definition of conformal algebras. We first recall some basic definitions and constructions, see [16], [17], [18], [20]. The main object of investigation is defined as follows: Definition 1.1. A Conformal algebra is a linear space C endowed with a linear operator D: C → C and a sequence of bilinear products ○n: C ⊗ C → C, n ∈ Z+, such that for any a, b ∈ C one has (i) (locality) There is a nonnegative integer N = N(a, b) such that a ○n b = 0 for any n � N; (ii) D(a ○n b) = (Da) ○n b + a ○n (Db); (iii) (Da) ○n b = −na n−1 b. 1.2. Spaces of power series. Now let us discuss the main motivation for the Definition 1.1. We closely follow [14] and [18]. 1.2.1. Circle products. Let A be an algebra. Consider the space of power series A[[z, z −1]]. We will write series a ∈ A[[z, z −1]] in the form a(z) = ∑ a(n)z −n−1, a(n) ∈ A. n∈Z On A[[z, z−1]] there is an infinite sequence of bilinear products ○n, n ∈ Z+, given by n a ○n b (z) = Resw a(w)b(z)(z − w) ). (1.1) Explicitly, for a pair of series a(z) = ∑ n∈Z a(n)z−n−1 and b(z) = ∑ n∈Z b(n)z−n−1 we have −m−1 a ○n b (z) = a ○n b (m)z, where
Modularity of Strong Normalization and Confluence in the algebraiclambdacube
, 1994
"... In this paper we present the algebraiccube, an extension of Barendregt's cube with first and higherorder algebraic rewriting. We show that strong normalization is a modular property of all systems in the algebraiccube, provided that the firstorder rewrite rules are nonduplicating and the hig ..."
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Cited by 25 (7 self)
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In this paper we present the algebraiccube, an extension of Barendregt's cube with first and higherorder algebraic rewriting. We show that strong normalization is a modular property of all systems in the algebraiccube, provided that the firstorder rewrite rules are nonduplicating and the higherorder rules satisfy the general schema of Jouannaud and Okada. This result is proven for the algebraic extension of the Calculus of Constructions, which contains all the systems of the algebraiccube. We also prove that local confluence is a modular property of all the systems in the algebraiccube, provided that the higherorder rules do not introduce critical pairs. This property and the strong normalization result imply the modularity of confluence. 1 Introduction Many different computational models have been developed and studied by theoretical computer scientists. One of the main motivations for the development This research was partially supported by ESPRIT Basic Research Act...