LIPIcs.ITP.2019.6.pdf
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Data Types as Quotients of Polynomial Functors
Authors
Jeremy Avigad 
,
Mario Carneiro ,
-
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Volume:
10th International Conference on Interactive Theorem Proving (ITP 2019)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Interactive Theorem Proving (ITP) - License:
Creative Commons Attribution 3.0 Unported license
- Publication date: 2019-09-05
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Acknowledgements
We are grateful to Andrei Popescu, Dmitriy Traytel, and Jasmin Blanchette for extensive discussions and very helpful advice.
Cite AsGet BibTex
Jeremy Avigad, Mario Carneiro, and Simon Hudon. Data Types as Quotients of Polynomial Functors. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 6:1-6:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ITP.2019.6
https://doi.org/10.4230/LIPIcs.ITP.2019.6
Abstract
A broad class of data types, including arbitrary nestings of inductive types, coinductive types, and quotients, can be represented as quotients of polynomial functors. This provides perspicuous ways of constructing them and reasoning about them in an interactive theorem prover.
Subject Classification
ACM Subject Classification
- Theory of computation → Logic and verification
- Theory of computation → Type theory
- Theory of computation → Data structures design and analysis
Keywords
- data types
- polynomial functors
- inductive types
- coinductive types
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