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On the value of variables

Authors: Accattoli, Beniamino; SACERDOTI COEN, CLAUDIO;

On the value of variables

Abstract

Call-by-value and call-by-need $λ$-calculi are defined using the distinguished syntactic category of values. In theoretical studies, values are variables and abstractions. In more practical works, values are usually defined simply as abstractions. This paper shows that practical values lead to a more efficient process of substitution—for both call-by-value and call-by-need—once the usual hypothesis for implementations hold (terms are closed, reduction does not go under abstraction , and substitution is done in micro steps, replacing one variable occurrence at a time). Namely, the number of substitution steps becomes linear in the number of $β$-redexes, while theoretical values only provide a quadratic bound. We complete the picture by showing that the same quadratic / linear bounds also hold for theoretical / practical versions of call-by-name.

Countries
Italy, France
Keywords

[INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], call-by-value, values, explicit substitutions, complexity, cost model, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], Cost models; Explicit substitutions; Implementations of functional programming languages; lambda-Calculus; Theoretical Computer Science; Computational Theory and Mathematics

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
23
Top 10%
Top 10%
Top 10%
Green
hybrid