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Typed Generic Traversal With Term Rewriting Strategies
 Journal of Logic and Algebraic Programming
, 2002
"... A typed model of strategic term rewriting is developed. The key innovation is that generic. The calculus traversal is covered. To this end, we define a typed rewriting calculus S ′ γ employs a manysorted type system extended by designated generic strategy types γ. We consider two generic strategy t ..."
Abstract

Cited by 26 (8 self)
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A typed model of strategic term rewriting is developed. The key innovation is that generic. The calculus traversal is covered. To this end, we define a typed rewriting calculus S ′ γ employs a manysorted type system extended by designated generic strategy types γ. We consider two generic strategy types, namely the types of typepreserving and typeunifying strategies. S ′ γ offers traversal combinators to construct traversals or schemes thereof from manysorted and generic strategies. The traversal combinators model different forms of onestep traversal, that is, they process the immediate subterms of a given term without anticipating any scheme of recursion into terms. To inhabit generic types, we need to add a fundamental combinator to lift a manysorted strategy s to a generic type γ. This step is called strategy extension. The semantics of the corresponding combinator states that s is only applied if the type of the term at hand fits, otherwise the extended strategy fails. This approach dictates that the semantics of strategy application must be typedependent to a certain extent. Typed strategic term rewriting with coverage of generic term traversal is a simple but expressive model of generic programming. It has applications in program
Specifying authentication protocols using elan
, 1999
"... The NeedhamSchroeder publickey protocol [NS78] has been already analyzed using several methodologies from modelcheckers like FDR [Ros94] to approaches based on theorem proving like NRL [Mea96]. Although this protocol is simple it has been proved insecure only in 1995 by G. Lowe [Low95]. After the ..."
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Cited by 8 (3 self)
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The NeedhamSchroeder publickey protocol [NS78] has been already analyzed using several methodologies from modelcheckers like FDR [Ros94] to approaches based on theorem proving like NRL [Mea96]. Although this protocol is simple it has been proved insecure only in 1995 by G. Lowe [Low95]. After the discover of the security problem and the correctness proof of a modified version in [Low96] several other approaches have been used in order to discover the attack and obtain correct versions like [Mea96, Mon99, Den98]. The protocol is described by defining the messages exchanged between the participants. Each agent sends a message and goes into a new state in which it possibly expects a confirmation message. We can thus say that the protocol consists in the sequence of states describing the agents and the communication network. Therefore it seems natural to use rewrite rules in order to describe the transition from one state to another and strategies in order to describe the way these rules are applied. In order to describe a computational version of a certain logic we use computational systems that can express the proof calculus of the given logic. A computational system ([KKV95]) is a combination of a rewrite theory and a strategy describing the intended set of computations. These ideas are implemented in the language ELAN ([BKK+ 98]) which allows to describe computational systems. In our approach the whole formalization is done as the same level: the state transitions of the agents and of
Generic typepreserving traversal strategies
 PROC. INTERNATIONAL WORKSHOP ON REDUCTION STRATEGIES IN REWRITING AND PROGRAMMING (WRS 2001), VOLUME SPUPV 2359
, 2001
"... A typed model of strategic rewriting with coverage of generic traversals is developed. The corresponding calculus offers, for example, a strategy operator 2 (), which applies the argument strategy to all immediate subterms. To provide a typeful model for generic strategies, one has to identify signa ..."
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Cited by 5 (2 self)
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A typed model of strategic rewriting with coverage of generic traversals is developed. The corresponding calculus offers, for example, a strategy operator 2 (), which applies the argument strategy to all immediate subterms. To provide a typeful model for generic strategies, one has to identify signatureindependent, that is, generic types. In the present article, we restrict ourselves to TP  the generic type of all TypePreserving strategies. TP is easily integrated into a standard manysorted type system for rewriting. To inhabit TP, we need to introduce a (leftbiased) typedriven choice operator & ,. The operator applies its left argument (corresponding to a manysorted strategy) if the type of the given term ts, and the operator resorts to the right argument (corresponding to a generic default) otherwise. This approach dictates that the semantics of strategy application must be typedependent to a certain extent.
Explicit Substitutions and All That
, 2000
"... Explicit substitution calculi are extensions of the lambdacalculus where the substitution mechanism is internalized into the theory. This feature makes them suitable for implementation and theoretical study of logic based tools as strongly typed programming languages and proof assistant systems. In ..."
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Cited by 3 (3 self)
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Explicit substitution calculi are extensions of the lambdacalculus where the substitution mechanism is internalized into the theory. This feature makes them suitable for implementation and theoretical study of logic based tools as strongly typed programming languages and proof assistant systems. In this paper we explore new developments on two of the most successful styles of explicit substitution calculi: the lambdasigma and lambda_secalculi.
Using Rewriting and Strategies for Describing the B Predicate Prover
 in Arithmetic, Proof Theory and Computational Complexity, P. Clote and
, 1998
"... Rules controlled by strategies is the main paradigm of the language ELAN that we are using here as a logical framework to describe the propositional and predicate prover of the B system. The inference rules for the provers are described by conditional rewrite rules and their application is controlle ..."
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Cited by 3 (1 self)
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Rules controlled by strategies is the main paradigm of the language ELAN that we are using here as a logical framework to describe the propositional and predicate prover of the B system. The inference rules for the provers are described by conditional rewrite rules and their application is controlled by strategies. We show how different strategies using the same set of rewrite rules lead to different proof methods and how this could be finely controlled by the user.
Abstract
, 2002
"... A typed model of strategic term rewriting is developed. The key innovation is that generic. The calculus traversal is covered. To this end, we define a typed rewriting calculus S ′ γ employs a manysorted type system extended by designated generic strategy types γ. We consider two generic strategy t ..."
Abstract
 Add to MetaCart
A typed model of strategic term rewriting is developed. The key innovation is that generic. The calculus traversal is covered. To this end, we define a typed rewriting calculus S ′ γ employs a manysorted type system extended by designated generic strategy types γ. We consider two generic strategy types, namely the types of typepreserving and typeunifying strategies. S ′ γ offers traversal combinators to construct traversals or schemes thereof from manysorted and generic strategies. The traversal combinators model different forms of onestep traversal, that is, they process the immediate subterms of a given term without anticipating any scheme of recursion into terms. To inhabit generic types, we need to add a fundamental combinator to lift a manysorted strategy s to a generic type γ. This step is called strategy extension. The semantics of the corresponding combinator states that s is only applied if the type of the term at hand fits, otherwise the extended strategy fails. This approach dictates that the semantics of strategy application must be typedependent to a certain extent. Typed strategic term rewriting with coverage of generic term traversal is a simple but expressive model of generic programming. It has applications in program