Types of Fireballs

Accattoli, Beniamino; Guerrieri, Giulio

doi:10.1007/978-3-030-02768-1_3

Cited by 22 publications

(39 citation statements)

References 36 publications

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“…The idea for the new calculus is to "fire" a stuck β -redex (λ x.t)u without performing the substitution t{u/x} (as u might not be a value), but just creating an explicit substitution t[u/x] that removes the application but "stores" the stuck β -redex. Such a calculus has been recently introduced in [5].…”

Section: Discussionmentioning

confidence: 99%

“…This work has been presented at the workshop ITRS 2018. Later, the author further investigated this topic with Beniamino Accattoli in [5], where we applied the same type system (and hence the same relational semantics) to a different call-by-value calculus with weak evaluation, λ fire . The techniques used in both papers are similar (but not identical), some differences are due to the distinct calculi the type system is applied to.…”

Section: Discussionmentioning

confidence: 99%

“…Some results are analogous: semantic and logical characterization of termination, extraction of quantitative information from type derivations. In [5] we focused on an abstract characterization of the type derivations that provide an exact bound on the number of steps to reach the normal form. Here, the semantic and logical characterization of termination is more informative than in [5] because the reduction in λ sh is not deterministic, contrary to λ fire (the proof that normalization and strong normalization coincide makes sense only for λ sh ).…”

Section: Discussionmentioning

confidence: 99%

“…In [5] we focused on an abstract characterization of the type derivations that provide an exact bound on the number of steps to reach the normal form. Here, the semantic and logical characterization of termination is more informative than in [5] because the reduction in λ sh is not deterministic, contrary to λ fire (the proof that normalization and strong normalization coincide makes sense only for λ sh ). Moreover here, unlike [5], we investigate in detail the case of terms reducing to values and how the general results for λ sh can be applied to analyze qualitative and quantitative properties of Plotkin's λ v restricted to closed terms (see above).…”

Section: Discussionmentioning

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: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

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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“…The seminal work of de Carvalho [23] (appeared in 2007 but unpublished until 2018, see also [22]) showed how to use multi types to obtain exact bounds on evaluation lengths in CbN. Ehrhard adapted multi types to CbV [34], and very recently Accattoli and Guerrieri adapted de Carvalho's study of exact bounds to Ehrhard's system and CbV evaluation [8]. Kesner used de Carvalho's CbN multi types to obtain a simple proof that CbNeed is termination equivalent to CbN [40] (first proved with other techniques by Maraist, Odersky, and Wadler [48] and Ariola and Felleisen [11] in the nineties), and then Kesner and coauthors continued exploring the theory of CbNeed via CbN multi types [14,15,42].…”

Section: Introductionmentioning

confidence: 99%

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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