Combinatory reduction systems: introduction and survey
Abstract: "Combinatory Reduction Systems, or CRSs for short, were designed to combine the usual first-order format of term rewriting with the presence of bound variables as in pure [lambda]-calculus and various typed [lambda]-calculi. Bound variables are also present in many other rewrite syste...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1993
|
| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS
93,62 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "Combinatory Reduction Systems, or CRSs for short, were designed to combine the usual first-order format of term rewriting with the presence of bound variables as in pure [lambda]-calculus and various typed [lambda]-calculi. Bound variables are also present in many other rewrite systems, such as systems with simplification rules for proof normalization. The original idea of CRSs is due to Aczel, who introduced a restricted class of CRSs and, under the assumption of orthogonality, proved confluence. Orthogonality means that the rules are non-ambiguous (no overlap leading to a critical pair) and left-linear (no global comparison of terms necessary) We introduce the class of orthogonal CRSs, illustrated with many examples, discuss its expressive power, and give an outline of a short proof of confluence. This proof is a direct generalization of Aczel's original proof, which is close to the well-known confluence proof for [lambda]-calculus by Tait and Martin-Lof. There is a well-known connection between the parallel reduction featuring in the latter proof, and the concept of 'developments', and a classical lemma in the theory of [lambda]-calculus is that of 'Finite Developments', a strong normalization result. It turns out that the notion of 'parallel reduction' used in Aczel's proof gives rise to a generalized form of developments, which we call 'superdevelopments' and on which we will briefly comment. We conclude with mentioning the results of a comparison of CRSs with the recently proposed and strongly related format of higher-order rewriting: Nipkow's HRSs (Higher-order Rewrite Systems). |
| Beschreibung: | 26 S. |
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| 100 | 1 | |a Klop, Jan Willem |d 1945- |e Verfasser |0 (DE-588)130644498 |4 aut | |
| 245 | 1 | 0 | |a Combinatory reduction systems |b introduction and survey |c J. W. Klop ; V. van Oostrom ; F. van Raamsdonk |
| 264 | 1 | |a Amsterdam |c 1993 | |
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| 490 | 1 | |a Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS |v 93,62 | |
| 520 | 3 | |a Abstract: "Combinatory Reduction Systems, or CRSs for short, were designed to combine the usual first-order format of term rewriting with the presence of bound variables as in pure [lambda]-calculus and various typed [lambda]-calculi. Bound variables are also present in many other rewrite systems, such as systems with simplification rules for proof normalization. The original idea of CRSs is due to Aczel, who introduced a restricted class of CRSs and, under the assumption of orthogonality, proved confluence. Orthogonality means that the rules are non-ambiguous (no overlap leading to a critical pair) and left-linear (no global comparison of terms necessary) | |
| 520 | 3 | |a We introduce the class of orthogonal CRSs, illustrated with many examples, discuss its expressive power, and give an outline of a short proof of confluence. This proof is a direct generalization of Aczel's original proof, which is close to the well-known confluence proof for [lambda]-calculus by Tait and Martin-Lof. There is a well-known connection between the parallel reduction featuring in the latter proof, and the concept of 'developments', and a classical lemma in the theory of [lambda]-calculus is that of 'Finite Developments', a strong normalization result. It turns out that the notion of 'parallel reduction' used in Aczel's proof gives rise to a generalized form of developments, which we call 'superdevelopments' and on which we will briefly comment. We conclude with mentioning the results of a comparison of CRSs with the recently proposed and strongly related format of higher-order rewriting: Nipkow's HRSs (Higher-order Rewrite Systems). | |
| 650 | 4 | |a Lambda calculus | |
| 650 | 4 | |a Rewriting systems (Computer science) | |
| 700 | 1 | |a Oostrom, Vincent van |e Verfasser |4 aut | |
| 700 | 1 | |a Raamsdonk, Femke van |e Verfasser |4 aut | |
| 810 | 2 | |a Department of Computer Science: Report CS |t Centrum voor Wiskunde en Informatica <Amsterdam> |v 93,62 |w (DE-604)BV008928356 |9 93,62 | |
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| author | Klop, Jan Willem 1945- Oostrom, Vincent van Raamsdonk, Femke van |
| author_GND | (DE-588)130644498 |
| author_facet | Klop, Jan Willem 1945- Oostrom, Vincent van Raamsdonk, Femke van |
| author_role | aut aut aut |
| author_sort | Klop, Jan Willem 1945- |
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| id | DE-604.BV010176874 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:47:50Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006759503 |
| oclc_num | 31129780 |
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| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
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| series2 | Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS |
| spelling | Klop, Jan Willem 1945- Verfasser (DE-588)130644498 aut Combinatory reduction systems introduction and survey J. W. Klop ; V. van Oostrom ; F. van Raamsdonk Amsterdam 1993 26 S. txt rdacontent n rdamedia nc rdacarrier Centrum voor Wiskunde en Informatica <Amsterdam> / Department of Computer Science: Report CS 93,62 Abstract: "Combinatory Reduction Systems, or CRSs for short, were designed to combine the usual first-order format of term rewriting with the presence of bound variables as in pure [lambda]-calculus and various typed [lambda]-calculi. Bound variables are also present in many other rewrite systems, such as systems with simplification rules for proof normalization. The original idea of CRSs is due to Aczel, who introduced a restricted class of CRSs and, under the assumption of orthogonality, proved confluence. Orthogonality means that the rules are non-ambiguous (no overlap leading to a critical pair) and left-linear (no global comparison of terms necessary) We introduce the class of orthogonal CRSs, illustrated with many examples, discuss its expressive power, and give an outline of a short proof of confluence. This proof is a direct generalization of Aczel's original proof, which is close to the well-known confluence proof for [lambda]-calculus by Tait and Martin-Lof. There is a well-known connection between the parallel reduction featuring in the latter proof, and the concept of 'developments', and a classical lemma in the theory of [lambda]-calculus is that of 'Finite Developments', a strong normalization result. It turns out that the notion of 'parallel reduction' used in Aczel's proof gives rise to a generalized form of developments, which we call 'superdevelopments' and on which we will briefly comment. We conclude with mentioning the results of a comparison of CRSs with the recently proposed and strongly related format of higher-order rewriting: Nipkow's HRSs (Higher-order Rewrite Systems). Lambda calculus Rewriting systems (Computer science) Oostrom, Vincent van Verfasser aut Raamsdonk, Femke van Verfasser aut Department of Computer Science: Report CS Centrum voor Wiskunde en Informatica <Amsterdam> 93,62 (DE-604)BV008928356 93,62 |
| spellingShingle | Klop, Jan Willem 1945- Oostrom, Vincent van Raamsdonk, Femke van Combinatory reduction systems introduction and survey Lambda calculus Rewriting systems (Computer science) |
| title | Combinatory reduction systems introduction and survey |
| title_auth | Combinatory reduction systems introduction and survey |
| title_exact_search | Combinatory reduction systems introduction and survey |
| title_full | Combinatory reduction systems introduction and survey J. W. Klop ; V. van Oostrom ; F. van Raamsdonk |
| title_fullStr | Combinatory reduction systems introduction and survey J. W. Klop ; V. van Oostrom ; F. van Raamsdonk |
| title_full_unstemmed | Combinatory reduction systems introduction and survey J. W. Klop ; V. van Oostrom ; F. van Raamsdonk |
| title_short | Combinatory reduction systems |
| title_sort | combinatory reduction systems introduction and survey |
| title_sub | introduction and survey |
| topic | Lambda calculus Rewriting systems (Computer science) |
| topic_facet | Lambda calculus Rewriting systems (Computer science) |
| volume_link | (DE-604)BV008928356 |
| work_keys_str_mv | AT klopjanwillem combinatoryreductionsystemsintroductionandsurvey AT oostromvincentvan combinatoryreductionsystemsintroductionandsurvey AT raamsdonkfemkevan combinatoryreductionsystemsintroductionandsurvey |