Modes of Convergence for Term Graph Rewriting
Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour is impaired by the lack of an appropriate count...
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2012-06-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/935/pdf |
| _version_ | 1797268723262816256 |
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| author | Patrick Bahr |
| author_facet | Patrick Bahr |
| author_sort | Patrick Bahr |
| collection | DOAJ |
| description | Term graph rewriting provides a simple mechanism to finitely represent
restricted forms of infinitary term rewriting. The correspondence between
infinitary term rewriting and term graph rewriting has been studied to some
extent. However, this endeavour is impaired by the lack of an appropriate
counterpart of infinitary rewriting on the side of term graphs. We aim to fill
this gap by devising two modes of convergence based on a partial order
respectively a metric on term graphs. The thus obtained structures generalise
corresponding modes of convergence that are usually studied in infinitary term
rewriting. We argue that this yields a common framework in which both term
rewriting and term graph rewriting can be studied. In order to substantiate our
claim, we compare convergence on term graphs and on terms. In particular, we
show that the modes of convergence on term graphs are conservative extensions
of the corresponding modes of convergence on terms and are preserved under
unravelling term graphs to terms. Moreover, we show that many of the properties
known from infinitary term rewriting are preserved. This includes the intrinsic
completeness of both modes of convergence and the fact that convergence via the
partial order is a conservative extension of the metric convergence. |
| first_indexed | 2024-04-25T01:37:01Z |
| format | Article |
| id | doaj.art-ca676bdad13b46a0958f6cb268cedf7e |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:37:01Z |
| publishDate | 2012-06-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-ca676bdad13b46a0958f6cb268cedf7e2024-03-08T09:27:56ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742012-06-01Volume 8, Issue 210.2168/LMCS-8(2:6)2012935Modes of Convergence for Term Graph RewritingPatrick Bahrhttps://orcid.org/0000-0003-1600-8261Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour is impaired by the lack of an appropriate counterpart of infinitary rewriting on the side of term graphs. We aim to fill this gap by devising two modes of convergence based on a partial order respectively a metric on term graphs. The thus obtained structures generalise corresponding modes of convergence that are usually studied in infinitary term rewriting. We argue that this yields a common framework in which both term rewriting and term graph rewriting can be studied. In order to substantiate our claim, we compare convergence on term graphs and on terms. In particular, we show that the modes of convergence on term graphs are conservative extensions of the corresponding modes of convergence on terms and are preserved under unravelling term graphs to terms. Moreover, we show that many of the properties known from infinitary term rewriting are preserved. This includes the intrinsic completeness of both modes of convergence and the fact that convergence via the partial order is a conservative extension of the metric convergence.https://lmcs.episciences.org/935/pdfcomputer science - logic in computer sciencecomputer science - programming languagesf.4.2, f.1.1 |
| spellingShingle | Patrick Bahr Modes of Convergence for Term Graph Rewriting Logical Methods in Computer Science computer science - logic in computer science computer science - programming languages f.4.2, f.1.1 |
| title | Modes of Convergence for Term Graph Rewriting |
| title_full | Modes of Convergence for Term Graph Rewriting |
| title_fullStr | Modes of Convergence for Term Graph Rewriting |
| title_full_unstemmed | Modes of Convergence for Term Graph Rewriting |
| title_short | Modes of Convergence for Term Graph Rewriting |
| title_sort | modes of convergence for term graph rewriting |
| topic | computer science - logic in computer science computer science - programming languages f.4.2, f.1.1 |
| url | https://lmcs.episciences.org/935/pdf |
| work_keys_str_mv | AT patrickbahr modesofconvergencefortermgraphrewriting |