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Comparing and Implementing Calculi of Explicit Substitutions with Eta Reduction
 Annals of Pure and Applied Logic
, 2005
"... The past decade has seen an explosion of work on calculi of explicit substitutions. Numerous work has illustrated the usefulness of these calculi for practical notions like the implementation of typed functional programming languages and higher order proof assistants. It has also been shown that e ..."
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Cited by 10 (8 self)
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that eta reduction is useful for adapting substitution calculi for practical problems like higher order uni cation. This paper concentrates on rewrite rules for eta reduction in three dierent styles of explicit substitution calculi: , se and the suspension calculus. Both and se when extended with eta
Explicit Substitutions Calculi with One Step Etareduction Decided Explicitly
"... It has long been argued that the notion of substitution in the λcalculus needs to be made explicit. This resulted in many calculi have been developed in which the computational steps of the substitution operation involved in βcontractions have been atomised. In contrast to the great variety of dev ..."
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) we introduce constructive and explicit definitions of the Eta rule in the λσ and the λsecalculi, 2) we prove that these definitions are correct and preserve basic properties such as subject reduction. In particular, we show that the explicit definitions of the eta rules coincide with the Eta rule
The ChurchRosser Property for Pure Type Systems with βηreduction
, 1992
"... this paper is to give a proof of the ChurchRosser property (or confluence) with respect to ## reduction for type theories with labelled lambda abstraction. This property is interesting in general since many other useful properties of a system depends on it and it is crucial when trying to use such ..."
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Cited by 2 (0 self)
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this paper is to give a proof of the ChurchRosser property (or confluence) with respect to ## reduction for type theories with labelled lambda abstraction. This property is interesting in general since many other useful properties of a system depends on it and it is crucial when trying to use
The Virtues of Etaexpansion
, 1993
"... Interpreting jconversion as an expansion rule in the simplytyped calculus maintains the confluence of reduction in a richer type structure. This use of expansions is supported by categorical models of reduction, where ficontraction, as the local counit, and jexpansion, as the local unit, are li ..."
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Cited by 44 (4 self)
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Interpreting jconversion as an expansion rule in the simplytyped calculus maintains the confluence of reduction in a richer type structure. This use of expansions is supported by categorical models of reduction, where ficontraction, as the local counit, and jexpansion, as the local unit
Published by the Computing Laboratory,
, 2005
"... Abstract This paper introduces a new etareduction rule for λcalculus with dependent types and prove the property of ChurchRosser. 1 ..."
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Abstract This paper introduces a new etareduction rule for λcalculus with dependent types and prove the property of ChurchRosser. 1
The Virtues of Etaexpansion
, 1993
"... Abstract Interpreting jconversion as an expansion rule in the simplytyped *calculus maintains the confluence of reduction in a richer type structure. This use of expansions is supported by categorical models of reduction, where ficontraction, as the local counit, and jexpansion, as the local un ..."
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Abstract Interpreting jconversion as an expansion rule in the simplytyped *calculus maintains the confluence of reduction in a richer type structure. This use of expansions is supported by categorical models of reduction, where ficontraction, as the local counit, and jexpansion, as the local
Eta Expansions in System F
 LIENSDMI, Ecole Normale Superieure
, 1996
"... The use of expansionary jrewrite rules in various typed calculi has become increasingly common in recent years as their advantages over contractive jrewrite rules have become apparent. Not only does one obtain the decidability of fijequality, but rewrite relations based on expansions give a natu ..."
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Cited by 4 (0 self)
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natural interpretation of long fijnormal forms, generalise more easily to other type constructors, retain key properties when combined with other rewrite relations, and are supported by a categorical theory of reduction. This paper extends the initial results concerning the simply typed calculus
of eta We f Me
, 16
"... form line 1 ss tra uced glass, which gives rise to the experimental observation of the drastic decrease in flow temperature while a compressive stress was applied. The significant Tg reduction is attributed to a large activation volume of relaxation DVs under shear stress (126 Å 3), the isentropic ..."
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form line 1 ss tra uced glass, which gives rise to the experimental observation of the drastic decrease in flow temperature while a compressive stress was applied. The significant Tg reduction is attributed to a large activation volume of relaxation DVs under shear stress (126 Å 3), the isentropic
Under consideration for publication in Math. Struct. in Comp. Science The Infinitary Lambda Calculus of the Infinite Eta Böhm
, 2013
"... In this paper we introduce a strong form of eta reduction called etabang that we use to construct a confluent and normalising infinitary lambda calculus, of which the normal forms correspond to Barendregt’s infinite eta Böhm trees. This new infinitary perspective on the set of infinite eta Böhm tr ..."
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In this paper we introduce a strong form of eta reduction called etabang that we use to construct a confluent and normalising infinitary lambda calculus, of which the normal forms correspond to Barendregt’s infinite eta Böhm trees. This new infinitary perspective on the set of infinite eta Böhm
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