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Data Types as Quotients of Polynomial Functors

Authors Jeremy Avigad , Mario Carneiro , Simon Hudon

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Author Details

Jeremy Avigad
  • Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA, USA
Mario Carneiro
  • Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA, USA
Simon Hudon
  • Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA, USA

Funding

Work partially supported by AFOSR grant FA9550-18-1-0120 and the Sloan Foundation.

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

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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Supplementary Materials

  • Lean formalizations are online at www.github.com/avigad/qpf.

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