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On the discriminating power of tests in resource lambda-calculus

机译:资源λ演算中测试的判别力

摘要

Since its discovery, differential linear logic (DLL) inspired numerous domains. In denotational semantics, categorical models of DLL are now commune, and the simplest one is Rel, the category of sets and relations. In proof theory this naturally gave birth to differential proof nets that are full and complete for DLL. In turn, these tools can naturally be translated to their intuitionistic counterpart. By taking the co-Kleisly category associated to the $!$ comonad, Rel becomes MRel, a model of the Lcalcul that contains a notion of differentiation. Proof nets can be used naturally to extend the Lcalcul into the lambda calculus with resources, a calculus that contains notions of linearity and differentiations. Of course MRel is a model of the Lcalcul with resources, and it has been proved adequate, but is it fully abstract? That was a strong conjecture of Bucciarelli, Carraro, Ehrhard and Manzonetto in cite{BCEM11}. However, in this paper we exhibit a counter-example. Moreover, to give more intuition on the essence of the counter-example and to look for more generality, we will use an extension of the resource Lcalcul also introduced by Bucciarelli {em et al} in cite{BCEM11} for which $Minf$ is fully abstract, the tests.
机译:自发现以来,差分线性逻辑(DLL)启发了许多领域。在指称语义中,DLL的分类模型现在是公社,最简单的是Rel,即集合和关系的类别。在证明理论中,这自然催生了对于DLL来说是完整的和完整的差分证明网。反过来,这些工具自然可以转换为它们的直观工具。通过采用与$!$ comonad相关联的co-Kleisly类别,Rel成为MRel,这是 Lcalcul的模型,其中包含差异概念。证明网可以自然地用于将 Lcalcul扩展到具有资源的lambda演算中,该演算包含线性和微分的概念。当然,MRel是带有资源的 Lcalcul的模型,并且已经被证明是足够的,但是它是完全抽象的吗?在 cite {BCEM11}中,这是Bucciarelli,Carraro,Ehrhard和Manzonetto的强烈推测。但是,在本文中,我们展示了一个反例。此外,为了使更多的直觉了解反例的本质并寻求更多的通用性,我们将使用Bucciarelli { em等人}在 cite {BCEM11}中引入的资源 Lcalcul的扩展,为此, Minf $是完全抽象的测试。

著录项

  • 作者

    Breuvart Flavien;

  • 作者单位
  • 年度 2012
  • 总页数
  • 原文格式 PDF
  • 正文语种 en
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