Characterization of strong normalizability for a sequent lambda calculus with co-control

Proceedings of the 19th International Symposium on Principles and Practice of Declarative Programming Pub Date : 2017-10-09 DOI:10.1145/3131851.3131867

J. E. Santo, S. Ghilezan

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引用次数: 2

Abstract

We study strong normalization in a lambda calculus of proof-terms with co-control for the intuitionistic sequent calculus. In this sequent lambda calculus, the management of formulas on the left hand side of typing judgements is "dual" to the management of formulas on the right hand side of the typing judgements in Parigot's lambdamu calculus - that is why our system has first-class "co-control". The characterization of strong normalization is by means of intersection types, and is obtained by analyzing the relationship with another sequent lambda calculus, without co-control, for which a characterization of strong normalizability has been obtained before. The comparison of the two formulations of the sequent calculus, with or without co-control, is of independent interest. Finally, since it is known how to obtain bidirectional natural deduction systems isomorphic to these sequent calculi, characterizations are obtained of the strongly normalizing proof-terms of such natural deduction systems.

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具有共同控制的序列λ演算的强归一化性质

我们研究了直觉序演算中带有协控制的证明项的λ演算中的强归一化。在接下来的lambda演算中，对输入判断左侧公式的管理与Parigot的lambda演算中输入判断右侧公式的管理是“对偶”的——这就是为什么我们的系统具有一流的“协同控制”。强归一化的表征是利用交集类型，并通过分析与另一个序列λ演算的关系得到的，没有共同控制，之前已经得到了强归一化的表征。有或没有共同控制的两种相继演算公式的比较，具有独立的意义。最后，由于已知如何获得与这些序列演算同构的双向自然演绎系统，得到了这些自然演绎系统的强正规化证明项的刻画。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Proceedings of the 19th International Symposium on Principles and Practice of Declarative Programming

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