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A Notation for Lambda Terms I: A Generalization of Environments
 THEORETICAL COMPUTER SCIENCE
, 1994
"... A notation for lambda terms is described that is useful in contexts where the intensions of these terms need to be manipulated. This notation uses the scheme of de Bruijn for eliminating variable names, thus obviating ffconversion in comparing terms. This notation also provides for a class of terms ..."
Abstract

Cited by 33 (12 self)
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A notation for lambda terms is described that is useful in contexts where the intensions of these terms need to be manipulated. This notation uses the scheme of de Bruijn for eliminating variable names, thus obviating ffconversion in comparing terms. This notation also provides for a class of terms that can encode other terms together with substitutions to be performed on them. The notion of an environment is used to realize this `delaying' of substitutions. The precise mechanism employed here is, however, more complex than the usual environment mechanism because it has to support the ability to examine subterms embedded under abstractions. The representation presented permits a ficontraction to be realized via an atomic step that generates a substitution and associated steps that percolate this substitution over the structure of a term. The operations on terms that are described also include ones for combining substitutions so that they might be performed simultaneously. Our notatio...
On Computational Interpretations of the Modal Logic S4 IIIa. Termination, Confluence, Conservativity of λevQ
 INSTITUT FUR LOGIK, KOMPLEXITAT UND DEDUKTIONSSYSTEME, UNIVERSITAT
, 1996
"... A language of constructions for minimal logic is the calculus, where cutelimination is encoded as fireduction. We examine corresponding languages for the minimal version of the modal logic S4, with notions of reduction that encodes cutelimination for the corresponding sequent system. It turns o ..."
Abstract

Cited by 8 (4 self)
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A language of constructions for minimal logic is the calculus, where cutelimination is encoded as fireduction. We examine corresponding languages for the minimal version of the modal logic S4, with notions of reduction that encodes cutelimination for the corresponding sequent system. It turns out that a natural interpretation of the latter constructions is a calculus extended by an idealized version of Lisp's eval and quote constructs. In this Part IIIa, we examine the termination and confluence properties of the evQ and evQ H calculi. Most results are negative: the typed calculi do not terminate, the subsystems \Sigma and \Sigma H that propagate substitutions, quotations and evaluations downwards do not terminate either in the untyped case, and the untyped evQ H calculus is not confluent. However, the typed versions of \Sigma and \Sigma H do terminate, so the typed evQcalculus is confluent. It follows that the typed evQcalculus is a conservative extension of the typed S4cal...
Verification of Newman’s and Yokouchi Lemmas in PVS
 Local Proceedings of Logic and Theory of Algorithms, Fourth Conference on Computability in Europe  CiE 2008 (2008
, 2007
"... Abstract. This paper shows how a previously specified theory for Abstract Reduction Systems (ARSs) in which noetherianity was defined by the notion of wellfoundness over binary relations is used in order to prove results such as the wellknown Newman’s Lemma and the Yokouchi’s Lemma. The former one k ..."
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Cited by 2 (2 self)
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Abstract. This paper shows how a previously specified theory for Abstract Reduction Systems (ARSs) in which noetherianity was defined by the notion of wellfoundness over binary relations is used in order to prove results such as the wellknown Newman’s Lemma and the Yokouchi’s Lemma. The former one known as the diamond lemma and the later which states a property of commutation between ARSs. Thears theory was specified in the Prototype Verification System (PVS) for which to the best of our knowledge there are no available theory for dealing with rewriting techniques in general. In addition to proof techniques available in PVS the verification of these lemmas implies an elaborated use of natural as well as noetherian induction. 1.