文章基本信息
- 标题：Multi-level Contextual Type Theory
- 本地全文：下载
- 作者：Mathieu Boespflug ; Brigitte Pientka
- 期刊名称：Electronic Proceedings in Theoretical Computer Science
- 电子版ISSN：2075-2180
- 出版年度：2011
- 卷号：71
- 页码：29-43
- DOI：10.4204/EPTCS.71.3
- 出版社：Open Publishing Association
- 摘要：Contextual type theory distinguishes between bound variables and meta-variables to write potentially incomplete terms in the presence of binders. It has found good use as a framework for concise explanations of higher-order unification, characterize holes in proofs, and in developing a foundation for programming with higher-order abstract syntax, as embodied by the programming and reasoning environment Beluga. However, to reason about these applications, we need to introduce meta^2-variables to characterize the dependency on meta-variables and bound variables. In other words, we must go beyond a two-level system granting only bound variables and meta-variables.
In this paper we generalize contextual type theory to n levels for arbitrary n, so as to obtain a formal system offering bound variables, meta-variables and so on all the way to meta^n-variables. We obtain a uniform account by collapsing all these different kinds of variables into a single notion of variabe indexed by some level k. We give a decidable bi-directional type system which characterizes beta-eta-normal forms together with a generalized substitution operation.
