LIPIcs.TYPES.2011.16.pdf
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Infinitary Rewriting Coinductively
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18th International Workshop on Types for Proofs and Programs (TYPES 2011)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Types for Proofs and Programs (TYPES) - License:
Creative Commons Attribution-NoDerivs 3.0 Unported license
- Publication Date: 2013-01-21
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Jörg Endrullis and Andrew Polonsky. Infinitary Rewriting Coinductively. In 18th International Workshop on Types for Proofs and Programs (TYPES 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 19, pp. 16-27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
https://doi.org/10.4230/LIPIcs.TYPES.2011.16
https://doi.org/10.4230/LIPIcs.TYPES.2011.16
Abstract
We provide a coinductive definition of strongly convergent reductions between infinite lambda terms. This approach avoids the notions of ordinals and metric convergence which have appeared in the earlier definitions of the concept. As an illustration, we prove the existence part of the infinitary standardization theorem. The proof is fully formalized in Coq using coinductive types. The paper concludes with a characterization of infinite lambda terms which reduce to themselves in a single beta step.
Keywords
- infinitary rewriting
- coinduction
- lambda calculus
- standardization
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