Abstract
AbstractLogical 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 $$ \text {CoLF} $$
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 Böhm tree. Both term equality and type checking are decidable in $$ \text {CoLF} $$
CoLF
. We illustrate the elegance and expressive power of the framework with several small case studies.
Publisher
Springer Nature Switzerland
Reference29 articles.
1. Amadio, R.M., Cardelli, L.: Subtyping recursive types. ACM Transactions on Programming Languages and Systems 15(4), 575–631 (1993)
2. Ariola, Z.M., Blom, S.: Cyclic lambda calculi. In: Abadi, M., Ito, T. (eds.) Theoretical Aspects of Computer Software, Third International Symposium, TACS ’97, Sendai, Japan, September 23-26, 1997, Proceedings. Lecture Notes in Computer Science, vol. 1281, pp. 77–106. Springer, Sendai, Japan (1997). https://doi.org/10.1007/BFb0014548
3. Ariola, Z.M., Klop, J.W.: Lambda calculus with explicit recursion. Information and Computation 139(2), 154–233 (1997). https://doi.org/10.1006/inco.1997.2651
4. Barendregt, H.P.: The lambda calculus - its syntax and semantics, Studies in logic and the foundations of mathematics, vol. 103. North-Holland (1985)
5. Basold, H.: Mixed Inductive-Coinductive Reasoning Types, Programs and Logic. Ph.D. thesis, Radboud University (Apr 2018), https://hdl.handle.net/2066/190323