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Linear Dependent Types in a Call-by-Value Scenario

机译:按值调用方案中的线性从属类型

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摘要

Linear dependent types allow to precisely capture both the extensional behavior and the time complexity of λ-terms, when the latter are evaluated by Krivine's abstract machine. In this work, we show that the same paradigm can be applied to call-by-value computation. A system of linear dependent types for Plotkin's PCF is introduced, called dℓPCF_v, whose types reflect the complexity of evaluating terms in the so-called CEK machine. DℓPCF_v is proved to be sound, but also relatively complete: every true statement about the extensional and intentional behavior of terms can be derived, provided all true index term inequalities can be used as assumptions.
机译:当由Krivine的抽象机器评估λ项时,线性相关类型允许精确地捕获其扩展行为和时间复杂度。在这项工作中,我们证明了相同的范例可以应用于按值调用计算。引入了用于Plotkin的PCF的线性相关类型的系统,称为dℓPCF_v,其类型反映了在所谓的CEK机器中评估项的复杂性。 DℓPCF_v被证明是合理的,但也相对完整:只要可以将所有真实的索引词不等式用作假设,就可以得出有关术语的扩展和故意行为的每条真实陈述。

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