School of Computing

Infinitary rewriting: Foundations revisited

Stefan Kahrs

In Christopher Lynch, editor, Proceedings of the 21st International Conference on Rewriting Techniques and Applications, volume 6 of Leibniz International Proceedings in Informatics (LIPIcs), pages 182-196, Dagstuhl, Germany, July 2010. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik.


Infinitary Term Rewriting allows to express infinitary terms and infinitary reductions that converge to them. As their notion of transfinite reduction in general, and as binary relations in particular two concepts have been studied in the past: strongly and weakly convergent reductions, and in the last decade research has mostly focused around the former.

Finitary rewriting has a strong connection to the equational theory of its rule set: if the rewrite system is confluent this (implies consistency of the theory and) gives rise to a semi-decision procedure for the theory, and if the rewrite system is in addition terminating this becomes a decision procedure. This connection is the original reason for the study of these properties in rewriting.

For infinitary rewriting there is barely an established notion of an equational theory. The reason this issue is not trivial is that such a theory would need to include some form of ``getting to limits'', and there are different options one can pursue. These options are being looked at here, as well as several alternatives for the notion of reduction relation and their relationships to these equational theories.

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Bibtex Record

author = {Stefan Kahrs},
title = {Infinitary Rewriting: Foundations Revisited},
month = {July},
year = {2010},
pages = {182-196},
keywords = {determinacy analysis, Craig interpolants},
note = {},
doi = {},
url = {},
    publication_type = {inproceedings},
    submission_id = {24768_1279195559},
    ISBN = {978-3-939897-18-7},
    booktitle = {Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
    editor = {Christopher Lynch},
    volume = {6},
    series = {Leibniz International Proceedings in Informatics (LIPIcs)},
    address = {Dagstuhl, Germany},
    publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
    ISSN = {1868-8969},
    refereed = {Yes},

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