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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 metalevel substitutions) they were implementing. In this paper we fi ..."
Abstract

Cited by 6 (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 metalevel substitutions) they were implementing. In this paper we first survey previous work in the domain by pointing out the motivations and challenges that guided the development of such calculi. Then we use very simple technology to establish a general theory of explicit substitutions for the lambdacalculus which enjoys fundamental properties such as simulation of onestep betareduction, confluence on metaterms, preservation of betastrong normalisation, strong normalisation of typed terms and full composition. The calculus also admits a natural translation into Linear Logic’s proofnets.
MultiStage Imperative Languages: A Conservative Extension Result
 In [41] (2000
, 2000
"... This paper extends the recent work [CMT00] on the operational semantics and type system for a core language, called MiniML ref , which exploits the notion of closed type (see also [MTBS99]) to safely combine imperative and multistage programming. The main novelties are the identification of a larg ..."
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Cited by 4 (3 self)
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This paper extends the recent work [CMT00] on the operational semantics and type system for a core language, called MiniML ref , which exploits the notion of closed type (see also [MTBS99]) to safely combine imperative and multistage programming. The main novelties are the identification of a larger set of closed types and the addition of a binder for useless variables. The resulting language is a conservative extension of MiniML ref , a simple imperative subset of SML. 1
A Theory of Explicit Substitutions with Safe and Full Composition
 Logical Methods in Computer Science
"... Vol. 5 (3:1) 2009, pp. 1–29 ..."
Resource operators for λcalculus
 INFORM. AND COMPUT
, 2007
"... We present a simple term calculus with an explicit control of erasure and duplication of substitutions, enjoying a sound and complete correspondence with the intuitionistic fragment of Linear Logic’s proofnets. We show the operational behaviour of the calculus and some of its fundamental properties ..."
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Cited by 3 (2 self)
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We present a simple term calculus with an explicit control of erasure and duplication of substitutions, enjoying a sound and complete correspondence with the intuitionistic fragment of Linear Logic’s proofnets. We show the operational behaviour of the calculus and some of its fundamental properties such as confluence, preservation of strong normalisation, strong normalisation of simplytyped terms, step by step simulation of βreduction and full composition.
SHARING IN THE WEAK LAMBDACALCULUS REVISITED
"... Abstract. In a previous paper [2] which appeared in the volume celebrating Klop’s 60th anniversary, we presented a labeled lambdacalculus to characterize the dag implementation of the weak lambdacalculus as described in Wadsworth’s dissertation [11]. In this paper, we simplify this calculus and pr ..."
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Cited by 2 (0 self)
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Abstract. In a previous paper [2] which appeared in the volume celebrating Klop’s 60th anniversary, we presented a labeled lambdacalculus to characterize the dag implementation of the weak lambdacalculus as described in Wadsworth’s dissertation [11]. In this paper, we simplify this calculus and present a simpler proof of the sharing property which allows the dag implementation. In order to avoid duplication of presentations, we mainly show here the modifications brought to the weak labeled lambdacalculus in [2]. The reader is therefore recommended to read first the companion article and later read our present paper. We are happy that this note can therefore be considered as establishing a new bridge between two friends and now senior colleagues, Jan Willem Klop and Henk