当前位置: X-MOL 学术arXiv.cs.LO › 论文详情
Non-idempotent types for classical calculi in natural deduction style
arXiv - CS - Logic in Computer Science Pub Date : 2018-02-15 , DOI: arxiv-1802.05494
Delia Kesner; Pierre Vial

In the first part of this paper, we define two resource aware typing systems for the {\lambda}{\mu}-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial arguments-based on decreasing measures of type derivations-to characterize head and strongly normalizing terms. Moreover, typability provides upper bounds for the lengths of the head reduction and the maximal reduction sequences to normal-form. In the second part of this paper, the {\lambda}{\mu}-calculus is refined to a small-step calculus called {\lambda}{\mu}s, which is inspired by the substitution at a distance paradigm. The {\lambda}{\mu}s-calculus turns out to be compatible with a natural extensionof the non-idempotent interpretations of {\lambda}{\mu}, i.e., {\lambda}{\mu}s-reduction preserves and decreases typing derivations in an extended appropriate typing system. We thus derive a simple arithmetical characterization of strongly {\lambda}{\mu}s-normalizing terms by means of typing.
更新日期:2020-01-14

 

全部期刊列表>>
2020新春特辑
限时免费阅读临床医学内容
ACS材料视界
科学报告最新纳米科学与技术研究
清华大学化学系段昊泓
自然科研论文编辑服务
加州大学洛杉矶分校
上海纽约大学William Glover
南开大学化学院周其林
课题组网站
X-MOL
北京大学分子工程苏南研究院
华东师范大学分子机器及功能材料
中山大学化学工程与技术学院
试剂库存
天合科研
down
wechat
bug