Modeling sharing and recursion for weak reduction strategies using explicit substitution

Benaissa, Zine-El-Abidine; Lescanne, Pierre; Rose, Kristoffer H.

doi:10.1007/3-540-61756-6_99

Cited by 16 publications

(19 citation statements)

References 9 publications

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“…In this section, we present the weak λ-calculus of explicit substitution and addresses λσ a w , proposed by Benaissa, Lescanne, and Rose [6].…”

Section: The Calculus λσ a Wmentioning

confidence: 99%

“…The reason for introducing two rules is discussed in [6]. It roughly corresponds to the possibility of changing a term location by pointer indirection (FVarG) versus root copy (FVarE) 1 .…”

Section: Dynamicsmentioning

confidence: 99%

“…Notice that, since a replacement occurs at any place the address of the rewritten term occurs, and due to the use of fresh addresses, simultaneous rewriting preserves term admissibility [6]. …”

Section: Definition 2 (Simultaneous Rewriting)mentioning

confidence: 99%

“…Benaissa, Lescanne, and Rose [6] have identified two variants of call-byneed, called NeedE and NeedG, which differ essentially in the choice between (FVarG) and (FVarE). They are presented in Figure 5.…”

Section: Call-by-needmentioning

confidence: 99%

“…To keep track of sharing, Benaissa, Lescanne, and Rose [6] have proposed a calculus named λσ a w , an extension of λσ w with global term annotations called addresses, accompanied by a specific rewriting relation, named simultaneous rewriting, to model in a single step the computation performed on all shared instances. As a general rewriting system, λσ a w is not attached to a specific strategy: strict and lazy strategies have been defined on top of the calculus, independently of the rewriting rules.…”

Section: Introductionmentioning

confidence: 99%

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Explaining the lazy Krivine machine using explicit substitution and addresses

Lang

2007

Higher-Order Symb Comput

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Abstract. In a previous paper, Benaissa, Lescanne, and Rose, have extended the weak lambda-calculus of explicit substitution λσw with addresses, so that it gives an account of the sharing implemented by lazy functional language interpreters. We show in this paper that their calculus, called λσ a w , fits well to the lazy Krivine machine, which describes the core of a lazy (call-by-need) functional programming language implementation. The lazy Krivine machine implements term evaluation sharing, that is essential for efficiency of such languages. The originality of our proof is that it gives a very detailed account of the implemented strategy.

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“…In this section, we present the weak λ-calculus of explicit substitution and addresses λσ a w , proposed by Benaissa, Lescanne, and Rose [6].…”

Section: The Calculus λσ a Wmentioning

confidence: 99%

“…The reason for introducing two rules is discussed in [6]. It roughly corresponds to the possibility of changing a term location by pointer indirection (FVarG) versus root copy (FVarE) 1 .…”

Section: Dynamicsmentioning

confidence: 99%

Section: Definition 2 (Simultaneous Rewriting)mentioning

confidence: 99%

Section: Call-by-needmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Explaining the lazy Krivine machine using explicit substitution and addresses

Lang

2007

Higher-Order Symb Comput

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Reductions, intersection types, and explicit substitutions

Dougherty

Lescanne

2001

Lecture Notes in Computer Science

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We present a new system of intersection types for a composition-free calculus of explicit substitutions with a rule for garbage collection, and show that it characterizes those terms which are strongly normalizing. This system extends previous work on the natural generalization of the classical intersection types system, which characterized head normalization and weak normalization, but was not complete for strong normalization. An important role is played by the notion of available variable in a term, which is a generalization of the classical notion of free variable.

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A framework for defining Object-Calculi extended abstract

Lang

Lescanne

Liquori

1999

FM’99 — Formal Methods

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In this paper, we give a general framework for the foundation of an operational (small step) semantics of object-based languages with an emphasis on functional and imperative issues. The framework allows classifying very naturally many object-based calculi according to their main implementation techniques of inheritance, namely delegation and embedding, and their particular strategies. This distinction comes easily from a choice in the rules. Our framework is founded on two previous works: λObj + , a version of the Lambda Calculus of Objects of Fischer, Honsell, and Mitchell, for the object aspects, and λσ a w of Benaissa, Lescanne, and Rose, for the description of the operational semantics and sharing. The former is the formalization of a small delegation-based language which contains both lambda calculus and object primitives to create, update, and send messages to objects, while the latter is designed to provide a generic description of functional language implementations and is based on a calculus of explicit substitution extended with addresses to deal with memory management. The framework is presented as a set of modules, each of which captures a particular aspect of object-calculi (functional vs. imperative, delegation vs. embedding, and any combination of them). Above all, it introduces and illustrates a new promising approach to formally reason about the operational semantics of languages with (possibly) mutable states.

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Modeling sharing and recursion for weak reduction strategies using explicit substitution

Cited by 16 publications

References 9 publications

Explaining the lazy Krivine machine using explicit substitution and addresses

Explaining the lazy Krivine machine using explicit substitution and addresses

Reductions, intersection types, and explicit substitutions

A framework for defining Object-Calculi extended abstract

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