Abstract
We present an algebraic framework that provides a general notion of recursive types. We characterize those type systems that guarantee the subject reduction property. Finally, we prove a strong normalization and a principle typing result.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barendregt, H. P.: Lambda calculi with types, in S. Abramsky, D. M. Gabbay, and T. S. E. Maibaum (eds.), Handbook of Logic in Computer Science, Vol. 2, Clarendon Press, 1992, pp. 118–309.
Cardone, F. and Coppo, M.: Type inference with recursive types: syntax and semantics, Inform. and Comput. 92 (1991), 48–80.
Courcelle, B.: Fundamental properties of infinite trees, Theoret. Comput. Sci. 25 (1983).
Gunter, C.: Semantics of Programming Languages. Structures and Techniques, Foundations of Computing, MIT Press, 1992.
Marz, M.: Monomorphe Typsysteme des λ-Kalküls, Juni 1995, Diplomarbeit, 46 pp.
Mendler, N. P.: Inductive types and type constraints in the second-order lambda-calculus, Ann. Pure Appl. Logic 51 (1991), 159–172.
Statman, R.: Recursive types and the subject reduction theorem, Technical Report 94–164, Carnegie Mellon University, March 1994.
Urzyczyn, P.: Positive recursive type assignment, Technical Report 95–03(203), Instytut Informatyki, Uniwersytet Warszawski, 1995.
Wells, J. B.: Typability and type checking in the second order λ-calculus are equivalent and undecidable, in 9th LICS conference, IEEE Computer Society Press, 1994, pp. 176–185.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Marz, M. An Algebraic View on Recursive Types. Applied Categorical Structures 7, 147–157 (1999). https://doi.org/10.1023/A:1008648420750
Issue Date:
DOI: https://doi.org/10.1023/A:1008648420750