LIPIcs.ITP.2019.12.pdf
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Formalizing Computability Theory via Partial Recursive Functions
Author
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
I would like to thank my advisor Jeremy Avigad for his support and encouragement, and for his reviews of early drafts of this work, as well as Yannick Forster, Rob Y. Lewis, and the anonymous reviewers for their many helpful comments.
Cite AsGet BibTex
Mario Carneiro. Formalizing Computability Theory via Partial Recursive Functions. In 10th International Conference on Interactive Theorem Proving (ITP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 141, pp. 12:1-12:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ITP.2019.12
https://doi.org/10.4230/LIPIcs.ITP.2019.12
Abstract
We present an extension to the mathlib library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and we use a constructive encoding of partial functions such that they are executable when the programs in question provably halt. Main theorems include the construction of a universal partial recursive function and a proof of the undecidability of the halting problem. Type class inference provides a transparent way to supply Gödel numberings where needed and encapsulate the encoding details.
Subject Classification
ACM Subject Classification
- Theory of computation → Recursive functions
- Theory of computation → Interactive proof systems
Keywords
- Lean
- computability
- halting problem
- primitive recursion
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