Execution time of λ-terms via denotational semantics and intersection types

Carvalho, Daniel de

doi:10.1017/s0960129516000396

Cited by 55 publications

(69 citation statements)

References 26 publications

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“…We recall the non-idempotent intersection type system introduced by Ehrhard [22] (nothing but the callby-value version of de Carvalho's system R [15,16]). We use it to characterize the (strong) normalizable terms for the reduction → sh .…”

Section: A Non-idempotent Intersection Type Systemmentioning

confidence: 99%

“…More recently [24,35,38,15,16] (a survey can be found in [13]), non-idempotent variants of intersection types have been introduced: they are obtained by dropping the equation A ∩ A = A. In a non-idempotent setting, the meaning of the typed term t : A ∩ A ∩ B is refined as "t can be used twice as data of type A and once as data of type B".…”

Section: Introductionmentioning

confidence: 99%

“…Non-idempotent intersection types have two main features, both enlightened by de Carvalho [15,16]: 1. Bounds on the execution time: they go beyond simply qualitative characterisations of termination, as type derivations provide quantitative bounds on the execution time (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Starting from [15,16], research on relational semantics/non-idempotent intersection types has proliferated: various works in the literature explore their power in bounding the execution time or in characterizing normalization [17,12,10,33,9,18,40,34,13,37,3]. All these works study relational semantics/nonidempotent intersection types either in LL proof-nets (the graphical representation of proofs in LL), or in some variant of ordinary (i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Following the same approach used in [16] for the call-by-name λ -calculus and in [17] for LL proofnets, we prove that in the shuffling calculus λ sh : Finally, we show that, differently from the case of LL and call-by-name λ -calculus, we are not able to lift the quantitative information enclosed in type derivations to types (i.e. to the interpretation of terms) following the same technique used in [16,17], as our Ex. 28 shows.…”

Section: Introductionmentioning

confidence: 99%

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Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus

Guerrieri

2019

Electron. Proc. Theor. Comput. Sci.

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We investigate the possibility of a semantic account of the execution time (i.e. the number of β v -steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value λ -calculus. For this purpose, we use a linear logic based denotational model that can be seen as a nonidempotent intersection type system: relational semantics. Our investigation is inspired by similar ones for linear logic proof-nets and untyped call-by-name λ -calculus. We first prove a qualitative result: a (possibly open) term is normalizable for weak reduction (which does not reduce under abstractions) if and only if its interpretation is not empty. We then show that the size of type derivations can be used to measure the execution time. Finally, we show that, differently from the case of linear logic and call-by-name λ -calculus, the quantitative information enclosed in type derivations does not lift to types (i.e. to the interpretation of terms). To get a truly semantic measure of execution time in a call-by-value setting, we conjecture that a refinement of its syntax and operational semantics is needed.

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Section: A Non-idempotent Intersection Type Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus

Guerrieri

2019

Electron. Proc. Theor. Comput. Sci.

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Types of Fireballs

Accattoli

Guerrieri

2018

Programming Languages and Systems

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Types by Need

Accattoli

Guerrieri

Leberle

2019

Programming Languages and Systems

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A cornerstone of the theory of λ-calculus is that intersection types characterise termination properties. They are a flexible tool that can be adapted to various notions of termination, and that also induces adequate denotational models. Since the seminal work of de Carvalho in 2007, it is known that multi types (i.e. non-idempotent intersection types) refine intersection types with quantitative information and a strong connection to linear logic. Typically, type derivations provide bounds for evaluation lengths, and minimal type derivations provide exact bounds. De Carvalho studied call-by-name evaluation, and Kesner used his system to show the termination equivalence of call-by-need and call-byname. De Carvalho's system, however, cannot provide exact bounds on call-by-need evaluation lengths. In this paper we develop a new multi type system for call-by-need. Our system produces exact bounds and induces a denotational model of callby-need, providing the first tight quantitative semantics of call-by-need.

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Execution time of λ-terms via denotational semantics and intersection types

Cited by 55 publications

References 26 publications

Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus

Towards a Semantic Measure of the Execution Time in Call-by-Value lambda-Calculus

Types of Fireballs

Types by Need

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