The Theory of Calculi with Explicit Substitutions Revisited

Kesner, Delia

doi:10.1007/978-3-540-74915-8_20

Cited by 38 publications

(40 citation statements)

References 26 publications

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“…Actually, what we obtain is a slightly optimised version of KN that can also work with open terms, and is therefore suitable for use in implementations of proof assistants [7,19,20].…”

Section: Contributionsmentioning

confidence: 99%

Deriving the full-reducing Krivine machine from the small-step operational semantics of normal order

García-Pérez

Nogueira

Moreno-Navarro

2013

Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming

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We derive by program transformation Pierre Cregut's full-reducing Krivine machine KN from the structural operational semantics of the normal order reduction strategy in a closure-converted pure lambda calculus. We thus establish the correspondence between the strategy and the machine, and showcase our technique for deriving full-reducing abstract machines. Actually, the machine we obtain is a slightly optimised version that can work with open terms and may be used in implementations of proof assistants.

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“…Actually, what we obtain is a slightly optimised version of KN that can also work with open terms, and is therefore suitable for use in implementations of proof assistants [7,19,20].…”

Section: Contributionsmentioning

confidence: 99%

Deriving the full-reducing Krivine machine from the small-step operational semantics of normal order

García-Pérez

Nogueira

Moreno-Navarro

2013

Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming

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“…With time, it was realized that the handling of names could be safely left implicit, see Kesner's [28] for a survey. More recently, also the search of the redex has been factored out, bringing it back to the implicit level, making ES act at a distance, without percolating through the term.…”

Section: Cbn Evaluation Contextsmentioning

confidence: 99%

The Negligible and Yet Subtle Cost of Pattern Matching

Accattoli

Barras

2017

Programming Languages and Systems

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Abstract. The model behind functional programming languages is the closed λ-calculus, that is, the fragment of the λ-calculus where evaluation is weak (i.e. out of abstractions) and terms are closed. It is well-known that the number of β (i.e. evaluation) steps is a reasonable cost model in this setting, for all natural evaluation strategies (call-by-name / value / need). In this paper we try to close the gap between the closed λ-calculus and actual languages, by considering an extension of the λ-calculus with pattern matching. It is straightforward to prove that β plus matching steps provide a reasonable cost model. What we do then is finer: we show that β steps only, without matching steps, provide a reasonable cost model also in this extended setting-morally, pattern matching comes for free, complexity-wise. The result is proven for all evaluation strategies (name / value / need), and, while the proof itself is simple, the problem is shown to be subtle. In particular we show that qualitatively equivalent definitions of call-by-need may behave very differently.This work is part of a wider research effort, the COCA HOLA project [3].

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“…More about explicit substitutions can be found in Delia Kesner's recent overview of the field [50]. In this section, we consider an applicative order of Curien's calculus of closures [12,19].…”

Section: A Reduction Semantics For Normalizing Lambda-terms With Intementioning

confidence: 99%

From Reduction-Based to Reduction-Free Normalization

Danvy¹

2004

BRICS

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We document an operational method to construct reduction-free normalization functions. Starting from a reduction-based normalization function from a reduction semantics, i.e., the iteration of a one-step reduction function, we successively subject it to refocusing (i.e., deforestation of the intermediate successive terms in the reduction sequence), equational simplification, refunctionalization (i.e., the converse of defunctionalization), and direct-style transformation (i.e., the converse of the CPS transformation), ending with a reduction-free normalization function of the kind usually crafted by hand. We treat in detail four simple examples: calculating arithmetic expressions, recognizing Dyck words, normalizing lambda-terms with explicit substitutions and call/cc, and flattening binary trees.The overall method builds on previous work by the author and his students on a syntactic correspondence between reduction semantics and abstract machines and on a functional correspondence between evaluators and abstract machines. The measure of success of these two correspondences is that each of the inter-derived semantic artifacts (i.e., man-made constructs) could plausibly have been written by hand, as is the actual case for several ones derived here. *

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The Theory of Calculi with Explicit Substitutions Revisited

Cited by 38 publications

References 26 publications

Deriving the full-reducing Krivine machine from the small-step operational semantics of normal order

Deriving the full-reducing Krivine machine from the small-step operational semantics of normal order

The Negligible and Yet Subtle Cost of Pattern Matching

From Reduction-Based to Reduction-Free Normalization

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