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48
Explicit Substitutions Calculi with Explicit Eta Rules
"... It has been argued that the notion of substitution in the λcalculus needs to be made explicit and 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 developments for makin ..."
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for making explicit formalisations of the Beta rule, less work has been done for giving explicit definitions of the conditional Eta rule. In this paper constructive Eta rules are proposed for both the λσ and the λsecalculi of explicit substitutions. Our results can be summarised as follows: 1) we introduce
An explicit Eta rewrite rule
, 1994
"... : In this report, we extend calculi of explicit substitutions by an Eta rule. We do this in the framework of AE, a calculus of explicit substitutions introduced by Lescanne (1994) and thoroughly studied by Lescanne and RouyerDegli (1994). The main feature of such a calculus is that the classical ..."
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: In this report, we extend calculi of explicit substitutions by an Eta rule. We do this in the framework of AE, a calculus of explicit substitutions introduced by Lescanne (1994) and thoroughly studied by Lescanne and RouyerDegli (1994). The main feature of such a calculus is that the classical
Typability is undecidable for F+eta
, 1995
"... System F is the wellknown polymorphicallytypedcalculus with universal quanti ers (\8"). F+ is System F extended with the eta rule, which says that if term M can be given type and Mreduces to N, then N can also be given the type. Adding the eta rule to System F is equivalent to adding the su ..."
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Cited by 11 (6 self)
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System F is the wellknown polymorphicallytypedcalculus with universal quanti ers (\8"). F+ is System F extended with the eta rule, which says that if term M can be given type and Mreduces to N, then N can also be given the type. Adding the eta rule to System F is equivalent to adding
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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of developments for making explicit formalisations of the Beta rule, less work has been done for giving explicit definitions of the conditional Eta rule. In this paper constructive Eta rules are proposed for both the λσ and the λsecalculi of explicit substitutions. Our results can be summarised as follows: 1
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
Decidability of Bounded HigherOrder Unification
, 2002
"... It is shown that unifiability of terms in the simply typed lambda calculus with beta and eta rules becomes decidable if there is a bound on the number of bound variables and lambdas in a unifier in etaexpanded betanormal form. ..."
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Cited by 8 (0 self)
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It is shown that unifiability of terms in the simply typed lambda calculus with beta and eta rules becomes decidable if there is a bound on the number of bound variables and lambdas in a unifier in etaexpanded betanormal form.
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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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
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
EtaExpansions III  F omega
, 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 simultaneously a decision procedure for fij equality and a procedure for the calculat ..."
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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 simultaneously a decision procedure for fij equality and a procedure
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
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