Ordered rewriting and confluence:
Abstract: "One of the major problems in term rewriting theory is what to do with an equation which cannot be ordered into a rule. Many solutions have been proposed, including the use of special unification algorithms or of unfailing completion procedures. If an equation cannot be ordered we can...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
1989
|
| Series: | Computer Laboratory <Cambridge>: Technical report
170 |
| Subjects: | |
| Summary: | Abstract: "One of the major problems in term rewriting theory is what to do with an equation which cannot be ordered into a rule. Many solutions have been proposed, including the use of special unification algorithms or of unfailing completion procedures. If an equation cannot be ordered we can still use any instances of it which can be ordered for rewriting. Thus for example x * y = y * x cannot be ordered, but if a,b are constants with b * a [greater than] a * b we may rewrite b * a [approaches] a * b. This idea is used in unfailing completion, and also appears in the Boyer-Moore system. In this paper we define and investigate completeness with respect to this notion of rewriting and show that many familiar systems are complete rewriting systems in this sense This allows us to decide equality without the use of special unification algorithms. We prove completeness by proving termination and local confluence. We describe a confluence test based on recursive properties of the ordering. |
| Physical Description: | 18 S. |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV010410966 | ||
| 003 | DE-604 | ||
| 005 | 20001009 | ||
| 007 | t | ||
| 008 | 951006s1989 |||| 00||| engod | ||
| 035 | |a (OCoLC)20797416 | ||
| 035 | |a (DE-599)BVBBV010410966 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 100 | 1 | |a Martin, Ursula |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Ordered rewriting and confluence |c by Ursula Martin and Tobias Nipkow |
| 264 | 1 | |a Cambridge |c 1989 | |
| 300 | |a 18 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Computer Laboratory <Cambridge>: Technical report |v 170 | |
| 520 | 3 | |a Abstract: "One of the major problems in term rewriting theory is what to do with an equation which cannot be ordered into a rule. Many solutions have been proposed, including the use of special unification algorithms or of unfailing completion procedures. If an equation cannot be ordered we can still use any instances of it which can be ordered for rewriting. Thus for example x * y = y * x cannot be ordered, but if a,b are constants with b * a [greater than] a * b we may rewrite b * a [approaches] a * b. This idea is used in unfailing completion, and also appears in the Boyer-Moore system. In this paper we define and investigate completeness with respect to this notion of rewriting and show that many familiar systems are complete rewriting systems in this sense | |
| 520 | 3 | |a This allows us to decide equality without the use of special unification algorithms. We prove completeness by proving termination and local confluence. We describe a confluence test based on recursive properties of the ordering. | |
| 650 | 7 | |a Information theory |2 sigle | |
| 650 | 7 | |a Mathematics |2 sigle | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Rewriting systems (Computer science) | |
| 700 | 1 | |a Nipkow, Tobias |d 1958- |e Verfasser |0 (DE-588)17275660X |4 aut | |
| 830 | 0 | |a Computer Laboratory <Cambridge>: Technical report |v 170 |w (DE-604)BV004055605 |9 170 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006932956 | ||
Record in the Search Index
| _version_ | 1804124839051526144 |
|---|---|
| any_adam_object | |
| author | Martin, Ursula Nipkow, Tobias 1958- |
| author_GND | (DE-588)17275660X |
| author_facet | Martin, Ursula Nipkow, Tobias 1958- |
| author_role | aut aut |
| author_sort | Martin, Ursula |
| author_variant | u m um t n tn |
| building | Verbundindex |
| bvnumber | BV010410966 |
| ctrlnum | (OCoLC)20797416 (DE-599)BVBBV010410966 |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02053nam a2200337 cb4500</leader><controlfield tag="001">BV010410966</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20001009 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">951006s1989 |||| 00||| engod</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)20797416</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010410966</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Martin, Ursula</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Ordered rewriting and confluence</subfield><subfield code="c">by Ursula Martin and Tobias Nipkow</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge</subfield><subfield code="c">1989</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">18 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Computer Laboratory <Cambridge>: Technical report</subfield><subfield code="v">170</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">Abstract: "One of the major problems in term rewriting theory is what to do with an equation which cannot be ordered into a rule. Many solutions have been proposed, including the use of special unification algorithms or of unfailing completion procedures. If an equation cannot be ordered we can still use any instances of it which can be ordered for rewriting. Thus for example x * y = y * x cannot be ordered, but if a,b are constants with b * a [greater than] a * b we may rewrite b * a [approaches] a * b. This idea is used in unfailing completion, and also appears in the Boyer-Moore system. In this paper we define and investigate completeness with respect to this notion of rewriting and show that many familiar systems are complete rewriting systems in this sense</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">This allows us to decide equality without the use of special unification algorithms. We prove completeness by proving termination and local confluence. We describe a confluence test based on recursive properties of the ordering.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Information theory</subfield><subfield code="2">sigle</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Mathematics</subfield><subfield code="2">sigle</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Rewriting systems (Computer science)</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Nipkow, Tobias</subfield><subfield code="d">1958-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)17275660X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Computer Laboratory <Cambridge>: Technical report</subfield><subfield code="v">170</subfield><subfield code="w">(DE-604)BV004055605</subfield><subfield code="9">170</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-006932956</subfield></datafield></record></collection> |
| id | DE-604.BV010410966 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:52:02Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006932956 |
| oclc_num | 20797416 |
| open_access_boolean | |
| physical | 18 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| record_format | marc |
| series | Computer Laboratory <Cambridge>: Technical report |
| series2 | Computer Laboratory <Cambridge>: Technical report |
| spelling | Martin, Ursula Verfasser aut Ordered rewriting and confluence by Ursula Martin and Tobias Nipkow Cambridge 1989 18 S. txt rdacontent n rdamedia nc rdacarrier Computer Laboratory <Cambridge>: Technical report 170 Abstract: "One of the major problems in term rewriting theory is what to do with an equation which cannot be ordered into a rule. Many solutions have been proposed, including the use of special unification algorithms or of unfailing completion procedures. If an equation cannot be ordered we can still use any instances of it which can be ordered for rewriting. Thus for example x * y = y * x cannot be ordered, but if a,b are constants with b * a [greater than] a * b we may rewrite b * a [approaches] a * b. This idea is used in unfailing completion, and also appears in the Boyer-Moore system. In this paper we define and investigate completeness with respect to this notion of rewriting and show that many familiar systems are complete rewriting systems in this sense This allows us to decide equality without the use of special unification algorithms. We prove completeness by proving termination and local confluence. We describe a confluence test based on recursive properties of the ordering. Information theory sigle Mathematics sigle Mathematik Rewriting systems (Computer science) Nipkow, Tobias 1958- Verfasser (DE-588)17275660X aut Computer Laboratory <Cambridge>: Technical report 170 (DE-604)BV004055605 170 |
| spellingShingle | Martin, Ursula Nipkow, Tobias 1958- Ordered rewriting and confluence Computer Laboratory <Cambridge>: Technical report Information theory sigle Mathematics sigle Mathematik Rewriting systems (Computer science) |
| title | Ordered rewriting and confluence |
| title_auth | Ordered rewriting and confluence |
| title_exact_search | Ordered rewriting and confluence |
| title_full | Ordered rewriting and confluence by Ursula Martin and Tobias Nipkow |
| title_fullStr | Ordered rewriting and confluence by Ursula Martin and Tobias Nipkow |
| title_full_unstemmed | Ordered rewriting and confluence by Ursula Martin and Tobias Nipkow |
| title_short | Ordered rewriting and confluence |
| title_sort | ordered rewriting and confluence |
| topic | Information theory sigle Mathematics sigle Mathematik Rewriting systems (Computer science) |
| topic_facet | Information theory Mathematics Mathematik Rewriting systems (Computer science) |
| volume_link | (DE-604)BV004055605 |
| work_keys_str_mv | AT martinursula orderedrewritingandconfluence AT nipkowtobias orderedrewritingandconfluence |