Abstract
Equirecursive types consider a recursive type to be equal to its unrolling and have no explicit term-level coercions to change a term’s type from the former to the latter or vice versa. This equality makes deciding type equality and subtyping more difficult than the other approach—isorecursive types, in which the types are not equal, but isomorphic, witnessed by explicit term-level coercions. Previous work has built intuition, rules, and polynomial-time decision procedures for equirecursive types for first-order type systems. Some work has been done for type systems with parametric polymorphism, but that work is incomplete (see below). This chapter will give an intuitive theory of equirecursive types for second-order type systems, sound and complete rules, and a decision procedure for subtyping.
Keywords
- Decision Procedure
- Free Variable
- Equality Rule
- Ultrametic Space
- Tree Automaton
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Amadio, R., Cardelli, L.: Subtyping recursive types. ACM Transactions on Progamming Languages and Systems 15(4), 575–631 (1993)
Canning, P., Cook, W., Hill, W., Mitchell, J., Olthoff, W.: F-bounded quantification for object-oriented programming. In: 4th ACM Conference on Functional Programming and Computer Architecture, London, UK, pp. 273–280. ACM Press (September 1989)
Colazzo, D., Ghelli, G.: Subtyping recursive types in kernel fun. In: 1999 Symposium on Logic in Computer Science, Trento, Italy, pp. 137–146 (July 1999)
Glew, N.: An efficient class and object encoding. In: ACM Conference on Object-Oriented Programming, Systems, Languages, and Applications, Minneapolis, MN, USA. ACM Press (October 2000)
Glew, N.: A theory of second-order trees. In: European Symposium on Programming 2002, Grenoble, France (April 2002)
Glew, N.: A theory of second-order trees. Technical Report TR2001-1859, Department of Computer Science, Cornell University, 4130 Upson Hall, Ithaca, NY 14853-7501, USA (January 2002)
Glew, N.: Subtyping for F-bounded quantifiers and equirecursive types (extended version). arXiv:1202.2486 (February 2012), http://arXiv.org/
Gauthier, N., Pottier, F.: Numbering matters: First-order canonical forms for second-order recursive types. In: 9th ACM SIGPLAN International Conference on Functional Programming, Snowbird, UT, USA, pp. 150–161. ACM Press (September 2004)
Kozen, D., Palsberg, J., Schwartzbach, M.: Efficient recursive subtyping. Mathematical Structures in Computer Science 5(1), 113–125 (1995)
Pierce, B.: Bounded quantification is undecidable. Information and Computation 112, 131–165 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Glew, N. (2012). Subtyping for F-Bounded Quantifiers and Equirecursive Types. In: Constable, R.L., Silva, A. (eds) Logic and Program Semantics. Lecture Notes in Computer Science, vol 7230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29485-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-29485-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29484-6
Online ISBN: 978-3-642-29485-3
eBook Packages: Computer ScienceComputer Science (R0)
