A Relational Model of a Parallel and Non-deterministic λ-Calculus

Bucciarelli, Antonio; Ehrhard, Thomas; Manzonetto, Giulio

doi:10.1007/978-3-540-92687-0_8

Cited by 9 publications

(5 citation statements)

References 15 publications

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“…Unsurprisingly models of linear logic are quantitative. This is already evident in the simplest degenerate model, the relational model [13,39], in which multisets are used to record the number of times a resource is used.…”

Section: An Overview Of Quantitative Modelsmentioning

confidence: 99%

Quantitative semantics of the lambda calculus: Some generalisations of the relational model

Ong

2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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We present an overview of some recent work on the quantitative semantics of the λ-calculus. Our starting point is the fundamental degenerate model of linear logic, the relational model. We show that three quantitative semantics of the simplytyped λ-calculus are equivalent: the relational semantics, HO/N game semantics, and the Taylor expansion semantics. We then consider two recent generalisations of the relational model: first, R-weighted relational models where R is a complete commutative semiring, as studied by Laird et al.; secondly, generalised species of structures, as introduced by Fiore et al. In each case, we briefly discuss some applications to quantitative analysis of higher-order programs.

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Section: An Overview Of Quantitative Modelsmentioning

confidence: 99%

Quantitative semantics of the lambda calculus: Some generalisations of the relational model

Ong

2017

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

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“…The relational model [37,17] is a simple denotational semantics of the λ-calculus induced by the relational model of linear logic, via the representation of the λ-calculus in linear logic. It is a paradigmatic model, underlying many others [30,31,24,45,48], mainly studied by Ehrhard and his students and co-authors [38,18,21,16,32,33,34,26,47,46,49,15], the importance of which has emerged slowly. One of its features is that it admits a handy presentation via an intersection type system.…”

Section: Relational Semantics and Multimentioning

confidence: 99%

Call-by-Value Solvability, Revisited

Accattoli

Paolini

2012

Functional and Logic Programming

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Abstract. In the call-by-value lambda-calculus solvable terms have been characterised by means of call-by-name reductions, which is disappointing and requires complex reasonings. We introduce the valuesubstitution lambda-calculus, a simple calculus borrowing ideas from Herbelin and Zimmerman's call-by-value λCBV calculus and from Accattoli and Kesner's substitution calculus λsub. In this new setting, we characterise solvable terms as those terms having normal form with respect to a suitable restriction of the rewriting relation.

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“…Probabilistic and non-deterministic calculi. Many lambda-calculi, such as Jones and Plotkin (1989) and Bucciarelli et al (2009), are concerned with semantical issues and possess probabilistic or non-deterministic properties. These calculi can be seen as having vectorial constructs based on a module over the semi-ring of positive reals for probabilistic effects, and the semi-ring {0, 1} for non-deterministic effects.…”

Section: The Language Lineal Ofmentioning

confidence: 99%

A typed, algebraic, computational lambda-calculus

Valiron

2013

Math. Struct. Comp. Sci.

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Lambda-calculi with vectorial structures have been studied in various ways, but their semantics remain largely uninvestigated. The main contribution of this paper is to provide a categorical framework for the semantics of such algebraic lambda-calculi. We first develop a categorical analysis of a general simply typed lambda-calculus endowed with the structure of a module. We study the problems arising from the addition of a fixed-point combinator and show how to modify the equational theory to solve them. The categorical analysis carries nicely over to the modified language. We provide various concrete models for both the case without fixpoints and for the case with them.

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A Relational Model of a Parallel and Non-deterministic λ-Calculus

Cited by 9 publications

References 15 publications

Quantitative semantics of the lambda calculus: Some generalisations of the relational model

Quantitative semantics of the lambda calculus: Some generalisations of the relational model

Call-by-Value Solvability, Revisited

A typed, algebraic, computational lambda-calculus

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