arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1902.05945cs.LOcs.PLmath.LO
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按需要分类(扩展版)

Types by Need (Extended Version)

Beniamino Accattoli, Giulio Guerrieri, Maico Leberle

摘要:

交叉演算理论的一个基石是交叉类型具有终止性。它们是一种灵活的工具,可以适用于各种终止概念,也可以产生适当的指称模式。自从de Carvalho在2007年的开创性工作以来,人们知道多类型(即非幂等交集类型)用定量信息和与线性逻辑的强联系来细化交集类型。通常,类型派生提供计算长度的界限,而最小类型派生提供精确的界限。De Carvalho研究了按名呼叫评估,Kesner使用他的系统来证明按需呼叫和按名呼叫的终止等价性。然而,De Carvalho的系统无法提供按需调用评估长度的精确界限。本文提出了一种新型的多类型按需呼叫系统。我们的系统产生精确的界限,并诱导一个指称模型的呼叫的需要,提供第一个严格的定量语义呼叫的需要。

英文摘要:

A cornerstone of the theory of lambda-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-by-name. 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 call-by-need, providing the first tight quantitative semantics of call-by-need.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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