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Confluence properties of Weak and Strong Calculi of Explicit Substitutions
 JOURNAL OF THE ACM
, 1996
"... Categorical combinators [12, 21, 43] and more recently oecalculus [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 selfcontained and stepwise way, with a special emphasis on confluence prope ..."
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Cited by 120 (7 self)
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Categorical combinators [12, 21, 43] and more recently oecalculus [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 selfcontained and stepwise way, with a special emphasis on confluence properties. The main new results of the paper w.r.t. [12, 21, 1, 23] are the following: 1. We present a confluent weak calculus of substitutions, where no variable clashes can be feared. 2. We solve a conjecture raised in [1]: oecalculus is not confluent (it is confluent on ground terms only). This unfortunate result is "repaired" by presenting a confluent version of oecalculus, named the Envcalculus in [23], called here the confluent oecalculus.
Abstract machines for programming language implementation
 FUTURE GENERATION COMPUTER SYSTEMS
, 2000
"... We present an extensive, annotated bibliography of the abstract machines designed for each of the main programming paradigms (imperative, object oriented, functional, logic and concurrent). We conclude that whilst a large number of efficient abstract machines have been designed for particular langua ..."
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Cited by 20 (0 self)
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We present an extensive, annotated bibliography of the abstract machines designed for each of the main programming paradigms (imperative, object oriented, functional, logic and concurrent). We conclude that whilst a large number of efficient abstract machines have been designed for particular language implementations, relatively little work has been done to design abstract machines in a systematic fashion.
The Soundness of Explicit Substitution with Nameless Variables
, 1995
"... We show the soundness of a λcalculus B where de Bruijn indices are used, substitution is explicit, and reduction is stepwise. This is done by interpreting B in the classical calculus where the explicit substitution becomes implicit and de Bruijn indices become named variables. This is the first fl ..."
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Cited by 2 (1 self)
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We show the soundness of a λcalculus B where de Bruijn indices are used, substitution is explicit, and reduction is stepwise. This is done by interpreting B in the classical calculus where the explicit substitution becomes implicit and de Bruijn indices become named variables. This is the first flat semantics of explicit substitution and stepwise reduction and the first clear account of exactly when ffreduction is needed.
A Semantics for stepwise substitution and reduction
, 1995
"... We show the soundness of a calculus B where de Bruijn indices are used, substitution is explicit, and reduction is stepwise. This is done by interpreting B in the classical calculus where the explicit substitution becomes implicit and de Bruijn indices become named variables. This is the first fla ..."
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We show the soundness of a calculus B where de Bruijn indices are used, substitution is explicit, and reduction is stepwise. This is done by interpreting B in the classical calculus where the explicit substitution becomes implicit and de Bruijn indices become named variables. This is the first flat semantics of explicit substitution and stepwise reduction and the first clear account of exactly when ffreduction is needed. Keywords: De Bruijn's indices, variable updating, substitution, reduction, soundness. 1 Introduction Variables play a very demanding role in the reduction and substitution of the calculus. This has lead in many cases to using implicit rather than explicit substitution. Implementations of the calculus provide their own explicit substitution procedures as in HOL [GM 93], Nuprl [Con 86] and Authomath [NGdV 94]. Furthermore, research on theories of explicit substitution has been striving lately ([HL 89], [ACCL 91], [KN 93], [Mel 95], [BBLR 95] and [KR 95]). In this...