Transfinite reductions in orthogonal term rewriting systems:
Abstract: "First we establish some fundamental facts in the theory of infinitary orthogonal term rewriting systems (OTRSs): for strongly convergent reductions we prove the Infinitary Parallel Moves Lemma and the Compression Lemma. Strongness is necessary as shown by counterexamples. Normal form...
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1990
|
| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam>/ Department of Computer Science: Report CS
90,41 |
| Schlagworte: | |
| Online-Zugang: | kostenfrei |
| Zusammenfassung: | Abstract: "First we establish some fundamental facts in the theory of infinitary orthogonal term rewriting systems (OTRSs): for strongly convergent reductions we prove the Infinitary Parallel Moves Lemma and the Compression Lemma. Strongness is necessary as shown by counterexamples. Normal forms (finite or infinite) are unique, in contrast to [omega]-normal forms. Strongly converging, fair reductions result in normal forms. Secondly we address the infinite Church-Rosser property, which in general OTRSs fails both for strongly converging reductions and for converging reductions For OTRSs with no collapsing rules other than one rule of the form [formula] the infinite Church-Rosser Property holds for strongly converging reductions. Non-unifiable OTRSs form a special class of them: here any converging reduction is strongly converging. The top-terminating OTRSs of Dershowitz c.s. are examples of non-unifiable OTRSs. We generalize head normal form, Bohm reduction and Bohm tree from Lambda-Calculus to Term rewriting. For OTRSs any term has a unique Bohm tree, and Bohm reduction satisfies the infinite Church-Rosser property Thirdly, results concerning needed redexes from finitary orthogonal rewriting carry over to the infinite setting by adding fairness considerations: needed-fair reductions are normalizing, parallel-outermost reduction is transfinitely hypernormalizing and depth-increasing reduction is hypernormalizing. Finally the relation between graph rewriting and infinitary term rewriting is considered. The link with infinitary rewriting allows us to treat cyclic graphs as well. Sekar and Ramakrishnan's notion of necessary set is useful to handle needed redexes in a graph: Needed redexes in a graph correspond to necessary sets of redexes in the unraveling of the graph |
| Beschreibung: | 48 S. |
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| 245 | 1 | 0 | |a Transfinite reductions in orthogonal term rewriting systems |c J. R. Kennaway ... |
| 264 | 1 | |a Amsterdam |c 1990 | |
| 300 | |a 48 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Centrum voor Wiskunde en Informatica <Amsterdam>/ Department of Computer Science: Report CS |v 90,41 | |
| 520 | 3 | |a Abstract: "First we establish some fundamental facts in the theory of infinitary orthogonal term rewriting systems (OTRSs): for strongly convergent reductions we prove the Infinitary Parallel Moves Lemma and the Compression Lemma. Strongness is necessary as shown by counterexamples. Normal forms (finite or infinite) are unique, in contrast to [omega]-normal forms. Strongly converging, fair reductions result in normal forms. Secondly we address the infinite Church-Rosser property, which in general OTRSs fails both for strongly converging reductions and for converging reductions | |
| 520 | 3 | |a For OTRSs with no collapsing rules other than one rule of the form [formula] the infinite Church-Rosser Property holds for strongly converging reductions. Non-unifiable OTRSs form a special class of them: here any converging reduction is strongly converging. The top-terminating OTRSs of Dershowitz c.s. are examples of non-unifiable OTRSs. We generalize head normal form, Bohm reduction and Bohm tree from Lambda-Calculus to Term rewriting. For OTRSs any term has a unique Bohm tree, and Bohm reduction satisfies the infinite Church-Rosser property | |
| 520 | 3 | |a Thirdly, results concerning needed redexes from finitary orthogonal rewriting carry over to the infinite setting by adding fairness considerations: needed-fair reductions are normalizing, parallel-outermost reduction is transfinitely hypernormalizing and depth-increasing reduction is hypernormalizing. Finally the relation between graph rewriting and infinitary term rewriting is considered. The link with infinitary rewriting allows us to treat cyclic graphs as well. Sekar and Ramakrishnan's notion of necessary set is useful to handle needed redexes in a graph: Needed redexes in a graph correspond to necessary sets of redexes in the unraveling of the graph | |
| 650 | 4 | |a Rewriting systems (Computer science) | |
| 700 | 1 | |a Kennaway, J. R. |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |
| 830 | 0 | |a Centrum voor Wiskunde en Informatica <Amsterdam>/ Department of Computer Science: Report CS |v 90,41 |w (DE-604)BV008928356 |9 90,41 | |
| 856 | 4 | 1 | |u https://ir.cwi.nl/pub/5615 |x Verlag |z kostenfrei |3 Volltext |
| 912 | |a ebook | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-005926030 | ||
Datensatz im Suchindex
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| id | DE-604.BV008974456 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:27:46Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005926030 |
| oclc_num | 24021693 |
| open_access_boolean | 1 |
| owner | DE-29T DE-91G DE-BY-TUM |
| owner_facet | DE-29T DE-91G DE-BY-TUM |
| physical | 48 S. |
| psigel | ebook |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| record_format | marc |
| series | Centrum voor Wiskunde en Informatica <Amsterdam>/ Department of Computer Science: Report CS |
| series2 | Centrum voor Wiskunde en Informatica <Amsterdam>/ Department of Computer Science: Report CS |
| spelling | Transfinite reductions in orthogonal term rewriting systems J. R. Kennaway ... Amsterdam 1990 48 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam>/ Department of Computer Science: Report CS 90,41 Abstract: "First we establish some fundamental facts in the theory of infinitary orthogonal term rewriting systems (OTRSs): for strongly convergent reductions we prove the Infinitary Parallel Moves Lemma and the Compression Lemma. Strongness is necessary as shown by counterexamples. Normal forms (finite or infinite) are unique, in contrast to [omega]-normal forms. Strongly converging, fair reductions result in normal forms. Secondly we address the infinite Church-Rosser property, which in general OTRSs fails both for strongly converging reductions and for converging reductions For OTRSs with no collapsing rules other than one rule of the form [formula] the infinite Church-Rosser Property holds for strongly converging reductions. Non-unifiable OTRSs form a special class of them: here any converging reduction is strongly converging. The top-terminating OTRSs of Dershowitz c.s. are examples of non-unifiable OTRSs. We generalize head normal form, Bohm reduction and Bohm tree from Lambda-Calculus to Term rewriting. For OTRSs any term has a unique Bohm tree, and Bohm reduction satisfies the infinite Church-Rosser property Thirdly, results concerning needed redexes from finitary orthogonal rewriting carry over to the infinite setting by adding fairness considerations: needed-fair reductions are normalizing, parallel-outermost reduction is transfinitely hypernormalizing and depth-increasing reduction is hypernormalizing. Finally the relation between graph rewriting and infinitary term rewriting is considered. The link with infinitary rewriting allows us to treat cyclic graphs as well. Sekar and Ramakrishnan's notion of necessary set is useful to handle needed redexes in a graph: Needed redexes in a graph correspond to necessary sets of redexes in the unraveling of the graph Rewriting systems (Computer science) Kennaway, J. R. Sonstige oth Erscheint auch als Online-Ausgabe Centrum voor Wiskunde en Informatica <Amsterdam>/ Department of Computer Science: Report CS 90,41 (DE-604)BV008928356 90,41 https://ir.cwi.nl/pub/5615 Verlag kostenfrei Volltext |
| spellingShingle | Transfinite reductions in orthogonal term rewriting systems Centrum voor Wiskunde en Informatica <Amsterdam>/ Department of Computer Science: Report CS Rewriting systems (Computer science) |
| title | Transfinite reductions in orthogonal term rewriting systems |
| title_auth | Transfinite reductions in orthogonal term rewriting systems |
| title_exact_search | Transfinite reductions in orthogonal term rewriting systems |
| title_full | Transfinite reductions in orthogonal term rewriting systems J. R. Kennaway ... |
| title_fullStr | Transfinite reductions in orthogonal term rewriting systems J. R. Kennaway ... |
| title_full_unstemmed | Transfinite reductions in orthogonal term rewriting systems J. R. Kennaway ... |
| title_short | Transfinite reductions in orthogonal term rewriting systems |
| title_sort | transfinite reductions in orthogonal term rewriting systems |
| topic | Rewriting systems (Computer science) |
| topic_facet | Rewriting systems (Computer science) |
| url | https://ir.cwi.nl/pub/5615 |
| volume_link | (DE-604)BV008928356 |
| work_keys_str_mv | AT kennawayjr transfinitereductionsinorthogonaltermrewritingsystems |