Categories of Containers
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We introduce the notion of containers as a mathematical formalisation of the idea that many important datatypes consist of templates where data is stored. We show that containers have good closure properties under a variety of constructions including the formation of initial algebras and final coalgebras. We also show that containers include strictly positive types and shapely types but that there are containers which do not correspond to either of these. Further, we derive a representation result classifying the nature of polymorphic functions between containers. We finish this paper with an application to the theory of shapely types and refer to a forthcoming paper which applies this theory to differentiable types.
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- Categories of Containers
- Book Title
- Foundations of Software Science and Computation Structures
- Book Subtitle
- 6th International Conference, FOSSACS 2003 Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2003 Warsaw, Poland, April 7–11, 2003 Proceedings
- pp 23-38
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
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- Andrew D. Gordon (4)
- Editor Affiliations
- 4. Microsoft Research
- Author Affiliations
- 5. Department of Mathematics and Computer Science, University of Leicester, Leicester
- 6. School of Computer Science and Information Technology, Nottingham University, Nottingham
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