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445
Explicit Substitutions Calculi with One Step Eta-reduction Decided Explicitly
"... It has long been argued that the notion of substitution in the λ-calculus needs to be made explicit. This resulted in many calculi have been developed in which the computational steps of the substitution operation involved in β-contractions 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 λse-calculi of explicit substitutions. Our results can be summarised as follows: 1
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
Comparing Calculi of Explicit . . .
- ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE 67 (2002)
, 2002
"... 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. Three styles of explicit substi ..."
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to preserve termination and conuence of the associated substitution calculus and to correspond to the eta-reductions of the other two calculi. Additionally, we prove that and s e as well as and the suspension calculus are non comparable while s e is more adequate than the suspension calculus.
Explicit Substitutions Calculi with Explicit Eta Rules
"... It has been argued that the notion of substitution in the λ-calculus needs to be made explicit and many calculi have been developed in which the computational steps of the substitution operation involved in β-contractions have been atomised. In contrast to the great variety of developments for makin ..."
Abstract
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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 λse-calculi of explicit substitutions. Our results can be summarised as follows: 1) we introduce
Confluence properties of Weak and Strong Calculi of Explicit Substitutions
- JOURNAL OF THE ACM
, 1996
"... Categorical combinators [12, 21, 43] and more recently oe-calculus [1, 23], have been introduced to provide an explicit treatment of substitutions in the -calculus. We reintroduce here the ingredients of these calculi in a self-contained and stepwise way, with a special emphasis on confluence prope ..."
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Cited by 129 (7 self)
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Categorical combinators [12, 21, 43] and more recently oe-calculus [1, 23], have been introduced to provide an explicit treatment of substitutions in the -calculus. We reintroduce here the ingredients of these calculi in a self-contained and stepwise way, with a special emphasis on confluence
A Practical Analysis of Explicit Substitutions Calculi
- Proceedings of 11 th International Workshop on Unification UNIF'97
, 1997
"... Explicit substitutions calculi provide a method to compute over -expressions by using first-order term rewriting systems. Many calculi have been proposed that differ by their signature, their number of rules and their theoretical properties. Our aim is to compare these systems from an operational ..."
Abstract
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Cited by 1 (1 self)
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Explicit substitutions calculi provide a method to compute over -expressions by using first-order term rewriting systems. Many calculi have been proposed that differ by their signature, their number of rules and their theoretical properties. Our aim is to compare these systems from
SUBSEXPL: A Framework for Simulating and Comparing Explicit Substitutions Calculi A Tutorial
, 2005
"... In this paper we present a framework, called SUBSEXPL, for simulating and comparing explicit substitutions calculi. This framework was developed in Ocaml, a language of the ML family, and it allows the manipulation of expressions of the λ-calculus and of several styles of explicit substitutions calc ..."
Abstract
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Cited by 1 (1 self)
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and the suspension calculus; other explicit substitutions calculi can be easily incorporated into the system. An implementation of the η-reduction is provided for each of these explicit substitutions calculi. This system has been of great help for systematically comparing explicit substitutions calculi, as well
SUBSEXPL: a Tool for Simulating and Comparing Explicit Substitutions Calculi
- Proc. 6th IEEE Symp
, 2006
"... Abstract In this tutorial we present the system SUBSEXPL that is used for simulating and comparing explicit substitutions calculi. This framework was developed in Ocaml, a language of the ML family, and it allows the manipulation of expressions of the λ-calculus and of several styles of explicit su ..."
Abstract
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Cited by 1 (0 self)
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Abstract In this tutorial we present the system SUBSEXPL that is used for simulating and comparing explicit substitutions calculi. This framework was developed in Ocaml, a language of the ML family, and it allows the manipulation of expressions of the λ-calculus and of several styles of explicit
Intersection Type Systems and Explicit Substitutions Calculi
- In Proc. of WRS’09. EPTCS 15:69–82
, 2010
"... calculi ..."
The theory of calculi with explicit substitutions revisited
- CSL 2007
, 2007
"... Calculi with explicit substitutions (ES) are widely used in different areas of computer science. Complex systems with ES were developed these last 15 years to capture the good computational behaviour of the original systems (with meta-level substitutions) they were implementing. In this paper we fi ..."
Abstract
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Cited by 10 (1 self)
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Calculi with explicit substitutions (ES) are widely used in different areas of computer science. Complex systems with ES were developed these last 15 years to capture the good computational behaviour of the original systems (with meta-level substitutions) they were implementing. In this paper we
Results 1 - 10
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445
