吉拉德翻译与LC的计算分析

[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science Pub Date : 1992-06-22 DOI:10.1109/LICS.1992.185523

Chetan R. Murthy

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引用次数: 48

摘要

J.-Y。吉拉德(1992)从古典逻辑到建构逻辑的新翻译。给出了一个兼容的连续传递样式(CPS)翻译，并将其转换为用于控制算子程序的c重写机器求值器和一组足以表示该求值器的约简/计算规则。发现有必要在M. Felleisen(博士论文，Indiana university, 1987)的微积分(lambda -抽象下的求值)中增加一条约简规则。这个约简规则来自于一个经过修改的按名称调用的cps转换。转向吉拉德的新经典逻辑LC，为其提供了一种直观的术语提取程序，生成了CPS函数程序。利用该语言的句法性质，可以对LC的证据性质给出简单的证明。这项工作揭示了cps翻译的设计空间，扩展了控制算子语言和经典逻辑之间的关系。

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A computational analysis of Girard's translation and LC

J.-Y. Girard's (1992) new translation from classical to constructive logic is explained. A compatible continuation-passing-style (CPS) translation is given and converted to a C-rewriting machine evaluator for control-operator programs and a set of reduction/computation rules sufficient to represent the evaluator. It is found necessary to add one reduction rule to M. Felleisen's (Ph.D. thesis, Indiana Univ., 1987) calculus (evaluation under lambda -abstraction). This reduction rule arises from a modified call-by-name CPS-translation. Turning to Girard's new classical logic LC, an intuitionistic term-extraction procedure is provided for it, producing CPS functional programs. Using the syntactic properties of this language, it is possible to give simple proofs for the evidence properties of LC. This work sheds light on the design space of CPS-translations and extends the relation between control-operator languages and classical logic.<>

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[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science

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