Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω1

Michael Norrish; Brian Huffman

doi:10.1007/978-3-642-39634-2_12

Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω₁

Michael Norrish
, Brian Huffman

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › peer-review

8 Citations (Scopus)

Abstract

We describe a comprehensive HOL mechanisation of the theory of ordinal numbers, focusing on the basic arithmetic operations. Mechanised results include the existence of fixpoints such as ε ₀, the existence of normal forms, and the validation of algorithms used in the ACL2 theorem-proving system.

Original language	English
Title of host publication	Interactive Theorem Proving - 4th International Conference, ITP 2013, Proceedings
Pages	133-146
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-642-39634-2_12
Publication status	Published - 2013
Event	4th International Conference on Interactive Theorem Proving, ITP 2013 - Rennes, France Duration: 22 Jul 2013 → 26 Jul 2013

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7998 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	4th International Conference on Interactive Theorem Proving, ITP 2013
Country/Territory	France
City	Rennes
Period	22/07/13 → 26/07/13

Access to Document

10.1007/978-3-642-39634-2_12

Cite this

Norrish, M., & Huffman, B. (2013). Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω₁. In Interactive Theorem Proving - 4th International Conference, ITP 2013, Proceedings (pp. 133-146). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7998 LNCS). https://doi.org/10.1007/978-3-642-39634-2_12

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abstract = "We describe a comprehensive HOL mechanisation of the theory of ordinal numbers, focusing on the basic arithmetic operations. Mechanised results include the existence of fixpoints such as ε 0, the existence of normal forms, and the validation of algorithms used in the ACL2 theorem-proving system.",

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Norrish, M & Huffman, B 2013, Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω₁. in Interactive Theorem Proving - 4th International Conference, ITP 2013, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7998 LNCS, pp. 133-146, 4th International Conference on Interactive Theorem Proving, ITP 2013, Rennes, France, 22/07/13. https://doi.org/10.1007/978-3-642-39634-2_12

Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω₁. / Norrish, Michael; Huffman, Brian.
Interactive Theorem Proving - 4th International Conference, ITP 2013, Proceedings. 2013. p. 133-146 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7998 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › peer-review

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