Results 1  10
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27
InductiveDataType Systems
, 2002
"... In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #calA#Ik enriched by patternmatching definitions folnitio a certain format,calat the "General Schema", whichgenera ..."
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Cited by 755 (22 self)
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In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #calA#Ik enriched by patternmatching definitions folnitio a certain format,calat the "General Schema", whichgeneral39I theusual recursor definitions fornatural numbers and simil9 "basic inductive types". This combined lmbined was shown to bestrongl normalIk39f The purpose of this paper is toreformul33 and extend theGeneral Schema in order to make it easil extensibl3 to capture a more general cler of inductive types, cals, "strictly positive", and to ease the strong normalgAg9Ik proof of theresulGGg system. Thisresul provides a computation model for the combination of anal"DAfGI specification language based on abstract data types and of astrongl typed functional language with strictly positive inductive types.
A Unification Algorithm for the Group DiffieHellman Protocol
 IN PROC. OF WITS 2002
, 2002
"... Equational unification can be an effective tool for the analysis of cryptographic protocols. This, for example ..."
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Cited by 27 (3 self)
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Equational unification can be an effective tool for the analysis of cryptographic protocols. This, for example
Normalized Rewriting: an alternative to Rewriting modulo a Set of Equations
, 1996
"... this paper is to make the similarity between KnuthBendix completion and the Buchberger algorithm explicit, by describing a general algorithm called Snormalized completion where S is a parameter, such that both algorithms are Normalized Rewriting: an alternative to Rewriting modulo a Set of Equatio ..."
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Cited by 27 (0 self)
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this paper is to make the similarity between KnuthBendix completion and the Buchberger algorithm explicit, by describing a general algorithm called Snormalized completion where S is a parameter, such that both algorithms are Normalized Rewriting: an alternative to Rewriting modulo a Set of Equations 3 instances of this general algorithm for a particular choice of S. This has been achieved in two steps.
Normalised Rewriting and Normalised Completion
, 1994
"... We introduce normalised rewriting, a new rewrite relation. It generalises former notions of rewriting modulo E, dropping some conditions on E. For example, E can now be the theory of identity, idempotency, the theory of Abelian groups, the theory of commutative rings. We give a new completion algor ..."
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Cited by 19 (2 self)
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We introduce normalised rewriting, a new rewrite relation. It generalises former notions of rewriting modulo E, dropping some conditions on E. For example, E can now be the theory of identity, idempotency, the theory of Abelian groups, the theory of commutative rings. We give a new completion algorithm for normalised rewriting. It contains as an instance the usual AC completion algorithm, but also the wellknown Buchberger's algorithm for computing standard bases of polynomial ideals. We investigate the particular case of completion of ground equations, In this case we prove by a uniform method that completion modulo E terminates, for some interesting E. As a consequence, we obtain the decidability of the word problem for some classes of equational theories. We give implementation results which shows the efficiency of normalised completion with respect to completion modulo AC. 1 Introduction Equational axioms are very common in most sciences, including computer science. Equations can ...
Abstract canonical inference
 ACM Trans. on Computational Logic
, 2007
"... An abstract framework of canonical inference is used to explore how different proof orderings induce different variants of saturation and completeness. Notions like completion, paramodulation, saturation, redundancy elimination, and rewritesystem reduction are connected to proof orderings. Fairness ..."
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Cited by 17 (10 self)
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An abstract framework of canonical inference is used to explore how different proof orderings induce different variants of saturation and completeness. Notions like completion, paramodulation, saturation, redundancy elimination, and rewritesystem reduction are connected to proof orderings. Fairness of deductive mechanisms is defined in terms of proof orderings, distinguishing between (ordinary) “fairness, ” which yields completeness, and “uniform fairness, ” which yields saturation.
Algebraic intruder deductions
 In Proceedings of LPAR’05, LNAI 3835
, 2005
"... Abstract. Many security protocols fundamentally depend on the algebraic properties of cryptographic operators. It is however difficult to handle these properties when formally analyzing protocols, since basic problems like the equality of terms that represent cryptographic messages are undecidable, ..."
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Cited by 14 (4 self)
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Abstract. Many security protocols fundamentally depend on the algebraic properties of cryptographic operators. It is however difficult to handle these properties when formally analyzing protocols, since basic problems like the equality of terms that represent cryptographic messages are undecidable, even for relatively simple algebraic theories. We present a framework for security protocol analysis that can handle algebraic properties of cryptographic operators in a uniform and modular way. Our framework is based on two ideas: the use of modular rewriting to formalize a generalized equational deduction problem for the DolevYao intruder, and the introduction of two parameters that control the complexity of the equational unification problems that arise during protocol analysis by bounding the depth of message terms and the operations that the intruder can perform when analyzing messages. We motivate the different restrictions made in our model by highlighting different ways in which undecidability arises when incorporating algebraic properties of cryptographic operators into formal protocol analysis. 1
EtaExpansions in Dependent Type Theory  The Calculus of Constructions
 Proceedings of the Third International Conference on Typed Lambda Calculus and Applications (TLCA'97
, 1997
"... . Although the use of expansionary jrewrite has become increasingly common in recent years, one area where jcontractions have until now remained the only possibility is in the more powerful type theories of the cube. This paper rectifies this situation by applying jexpansions to the Calculus of ..."
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Cited by 13 (0 self)
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. Although the use of expansionary jrewrite has become increasingly common in recent years, one area where jcontractions have until now remained the only possibility is in the more powerful type theories of the cube. This paper rectifies this situation by applying jexpansions to the Calculus of Constructions  we discuss some of the difficulties posed by the presence of dependent types, prove that every term rewrites to a unique long fijnormal form and deduce the decidability of fijequality, typeability and type inhabitation as corollaries. 1 Introduction Extensional equality for the simply typed calculus requires jconversion, whose interpretation as a rewrite rule has traditionally been as a contraction x : T:fx ) f where x 6 2 FV(t). When combined with the usual fireduction, the resulting rewrite relation is strongly normalising and confluent, and thus reduction to normal form provides a decision procedure for the associated equational theory. However jcontractions beh...
Abstract saturationbased inference
 IN PROCEEDINGS OF THE 18TH ANNUAL SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE
, 2003
"... Solving goals—like deciding word problems or resolving constraints—is much easier in some theory presentations than in others. What have been called “completion processes”, in particular in the study of equational logic, involve finding appropriate presentations of a given theory to solve easily a g ..."
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Cited by 12 (5 self)
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Solving goals—like deciding word problems or resolving constraints—is much easier in some theory presentations than in others. What have been called “completion processes”, in particular in the study of equational logic, involve finding appropriate presentations of a given theory to solve easily a given class of problems. We provide a general prooftheoretic setting within which completionlike processes can be modelled and studied. This framework centers around wellfounded orderings of proofs. It allows for abstract definitions and very general characterizations of saturation processes and redundancy criteria.
Paramodulation with Builtin ACTheories and Symbolic Constraints
 Journal of Symbolic Computation
, 1996
"... this paper we overcome these drawbacks by working with clauses with symbolic constraints (Kirchner et al., 1990; Nieuwenhuis and Rubio, 1992; Rubio, 1994; Nieuwenhuis and Rubio, 1995) . A constrained clause C [[ T ]] is a shorthand for the set of ground instances of the clause part C satisfying the ..."
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Cited by 11 (6 self)
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this paper we overcome these drawbacks by working with clauses with symbolic constraints (Kirchner et al., 1990; Nieuwenhuis and Rubio, 1992; Rubio, 1994; Nieuwenhuis and Rubio, 1995) . A constrained clause C [[ T ]] is a shorthand for the set of ground instances of the clause part C satisfying the constraint T . In a constrained equation
Termination and Completion modulo Associativity, Commutativity and Identity
 Theoretical Computer Science
, 1992
"... Rewriting with associativity, commutativity and identity has been an open problem for a long time. In 1989, Baird, Peterson and Wilkerson introduced the notion of constrained rewriting, to avoid the problem of nontermination inherent to the use of identities. We build up on this idea in two ways: b ..."
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Cited by 11 (3 self)
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Rewriting with associativity, commutativity and identity has been an open problem for a long time. In 1989, Baird, Peterson and Wilkerson introduced the notion of constrained rewriting, to avoid the problem of nontermination inherent to the use of identities. We build up on this idea in two ways: by giving a complete set of rules for completion modulo these axioms; by showing how to build appropriate orderings for proving termination of constrained rewriting modulo associativity, commutativity and identity. 1 Introduction Equations are ubiquitous in mathematics and the sciences. Among the most common equations are associativity, commutativity and identity (existence of a neutral element). Rewriting is an efficient way of reasoning with equations, introduced by Knuth and Bendix [12]. When rewriting, equations are used in one direction chosen once and for all. Unfortunately, orientation alone is not a complete inference rule: given a set of equational axioms E, there may be equal terms...