代数CPS模拟的完备性

Ali Assaf, S. Perdrix
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引用次数: 4

摘要

代数演算和线性代数演算是经典演算的两种扩展,具有项的线性组合。它们在不同的背景下独立出现:前者是微分λ演算的一个片段,后者是量子计算的候选λ演算。它们在处理应用程序参数和代数规则方面有所不同。这两种语言可以使用众所周知的按值调用和按名称调用的CPS翻译的代数扩展来相互模拟。这些模拟是合理的,因为它们保留了减少量。在本文中,我们证明了模拟实际上是完整的,加强了两种语言之间的联系。
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Completeness of algebraic CPS simulations
The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms. They arise independently in distinct contexts: the former is a fragment of the differential lambda calculus, the latter is a candidate lambda calculus for quantum computation. They differ in the handling of application arguments and algebraic rules. The two languages can simulate each other using an algebraic extension of the well-known call-by-value and call-by-name CPS translations. These simulations are sound, in that they preserve reductions. In this paper, we prove that the simulations are actually complete, strengthening the connection between the two languages.
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