Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof systems in such logical frameworks a cumbersome and awkward task. To address this issue, we propose CoLF, a conservative extension of LF with higher-order rational terms and mixed inductive and coinductive definitions. In this framework, two terms are equal if they unfold to the same infinite regular B\"ohm tree. Both term equality and type checking are decidable in CoLF. We illustrate the elegance and expressive power of the framework with several small case studies.
翻译:逻辑框架LF及其后的发展侧重于有鳍证明系统,使此类逻辑框架的循环证明系统正规化成为一项烦琐和尴尬的任务。为了解决这一问题,我们提议COLF, 将LF保守地扩大,以更高层次的合理术语和混合的感性与感性定义。在这个框架内,如果将LF扩大到同一个无限的常规B\"ohm树,两个术语是平等的。在COLF中,平等术语和类型检查都是可变的。我们用几个小案例研究来说明框架的优雅和明确性。