On phase semantics and denotational semantics: the exponentials

Bucciarelli, Antonio; Ehrhard, Thomas

doi:10.1016/s0168-0072(00)00056-7

Cited by 61 publications

(105 citation statements)

References 5 publications

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“…We conclude, applying Pascal's formula (2) for the first of these three sums, and observing that, in the two last sums, the binomial coefficients are equal to T U . Indeed, when U and V are such that U V = T , t ∈ U and t / ∈ V , we have…”

Section: Leibniz Law and Partial Derivativementioning

confidence: 69%

“…Up to some minor variations, the resource terms which are in some T (M) are those called well formed in [16]. We characterise these terms as those which are coherent with themselves for a coherence relation on simple resource terms, and call them uniform (not ''well formed'', because we are very much interested in the other terms as well, and also because this usage of the word ''uniform'' is reminiscent of a corresponding notion in denotational semantics, see the discussions in [2]). The main purpose of the paper is then to study the behaviour of the Taylor expansion of an ordinary lambda-term M when one reduces its simple summands, which are all strongly normalising, even if M is not.…”

Section: Outlinementioning

confidence: 99%

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Uniformity and the Taylor expansion of ordinary lambda-terms

Ehrhard

Regnier

2008

Theoretical Computer Science

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109

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International audienceWe define the complete Taylor expansion of an ordinary lambda-term as an infinite linear combination --- with rational coefficients --- of terms of a resource calculus similar to Boudol's resource lambda-calculus. In this calculus, all applications are (multi-)linear in the algebraic sense, i.e. commute with linear combination of the function or the argument. We study the collective behaviour of the beta-reducts of the terms occurring in the Taylor expansion of any ordinary lambda-term, using a uniformity property that they enjoy

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Section: Leibniz Law and Partial Derivativementioning

confidence: 69%

Section: Outlinementioning

confidence: 99%

Uniformity and the Taylor expansion of ordinary lambda-terms

Ehrhard

Regnier

2008

Theoretical Computer Science

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109

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“…A (still) open question is whether the general construction introduced in Bucciarelli and Ehrhard (2001) can be modified to give the co-free exponentials directly and in a general way. Another related issue concerns full completeness for static semantics.…”

Section: Extending Non-uniform Static Semanticsmentioning

confidence: 99%

Non-uniform (hyper/multi)coherence spaces

Boudes¹

2010

Math. Struct. Comp. Sci.

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In (hyper)coherence semantics, proofs/terms are cliques in (hyper)graphs. Intuitively, the vertices represent the results of computations and the edge relation witnesses the ability to carry out the computation assembled into a single piece of data or a single (strongly) stable function, at arrow types. In (hyper)coherence semantics, the argument of a (strongly) stable functional is always a (strongly) stable function. As a consequence, compared to the relational semantics where there is no edge relation, some vertices are missing. Recovering these vertices is essential if we are to reconstruct proofs/terms from their interpretations. It will also be useful for comparing with other semantics, such as game semantics. Bucciarelli and Ehrhard (2001) introduced a non-uniform coherence space semantics, where no vertex is missing. By constructing the co-free exponential, we get a new version of this semantics, together with non-uniform versions of hypercoherences and multicoherences. This provides a new semantics in which an edge is a finite multiset. Thanks to the co-free construction, these non-uniform semantics are deterministic in the sense that the intersection of a clique and an anti-clique contains at most one vertex, which is a result of interaction, and they then extensionally collapse onto the corresponding uniform semantics.

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“…Linear logic interpretation: non-idempotent intersection types are deeply linked to linear logic (LL) [20]. Relational semantics [21,7] -the category Rel of sets and relations endowed with the comonad ! of finite multisets -is a sort of "canonical" denotational model of LL; the Kleisli category Rel !…”

Section: Introductionmentioning

confidence: 99%

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

Guerrieri¹

2018

EasyChair Preprints

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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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On phase semantics and denotational semantics: the exponentials

Cited by 61 publications

References 5 publications

Uniformity and the Taylor expansion of ordinary lambda-terms

Uniformity and the Taylor expansion of ordinary lambda-terms

Non-uniform (hyper/multi)coherence spaces

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

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