English

A Logical Framework with Infinitary Terms

Logic in Computer Science 2023-12-12 v1 Programming Languages

Abstract

Logical frameworks are successful in modeling proof systems. Recently, CoLF extended the logical framework LF to support higher-order rational terms that enable adequate encoding of circular objects and derivations. In this paper, we propose CoLFω^\omega as an alternative interpretation of CoLF-style signatures where terms are taken to be all possibly infinitary terms that are consistent with a given signature. In particular, we propose the notion of productive B\"ohm trees, a particular kind of typed \bot-free B\"ohm trees that are closed under hereditary substitution. We show that the productive B\"ohm trees are capable of meta-encoding their own structure. Overall, we hope to establish CoLFω^\omega as a new formal framework for the encoding of infinitary regular and non-regular structures.

Keywords

Cite

@article{arxiv.2312.05919,
  title  = {A Logical Framework with Infinitary Terms},
  author = {Zhibo Chen},
  journal= {arXiv preprint arXiv:2312.05919},
  year   = {2023}
}
R2 v1 2026-06-28T13:46:24.431Z