Order-sorted Algebra I: equational deduction for multiple inheritance, overloading, exceptions and partial operations
Abstract: "This paper generalizes many-sorted algebra (hereafter, MSA) to order-sorted algebra (hereafter, OSA) by allowing a partial ordering relation on the set of sorts. This supports abstract data types with multiple inheritance (in roughly the sense of object-oriented programming), several...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Menlo Park, Calif.
1989
|
| Schriftenreihe: | Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL
89,10 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "This paper generalizes many-sorted algebra (hereafter, MSA) to order-sorted algebra (hereafter, OSA) by allowing a partial ordering relation on the set of sorts. This supports abstract data types with multiple inheritance (in roughly the sense of object-oriented programming), several forms of polymorphism and overloading, partial operations (as total on equationally defined subsorts), exception handling, and an operational semantics based on term rewriting. We give the basic algebraic constructions for OSA, including quotient, image, product and term algebra, and we prove their basic properties, including Quotient, Homomorphism, and Initiality Theorems. The paper's major mathematical results include a notion of OSA deduction, a Completeness Theorem for it, and an OSA Birkhoff Variety Theorem We also develop conditional OSA, including Initiality, Completeness, and McKinsey-Maclev Quasivariety Theorems, and we reduce OSA to (conditional) MSA, which allows lifting many known MSA results to OSA. Retracts, which intuitively are left inverses to subsort inclusions, provide relatively inexpensive run-time error handling. We show that it is safe to add retracts to any OSA signature, in the sense that it gives rise to a conservative extension. A final section compares and contrasts many different approaches to OSA. This paper also includes several examples demonstrating the flexibility and applicability of OSA, including some standard benchmarks like STACK and LIST, as well as a much more substantial example, the number hierarchy from the naturals up to the quaternions |
| Beschreibung: | 49 S. |
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| 245 | 1 | 0 | |a Order-sorted Algebra I |b equational deduction for multiple inheritance, overloading, exceptions and partial operations |c by Joseph A. Goguen and José Meseguer |
| 264 | 1 | |a Menlo Park, Calif. |c 1989 | |
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL |v 89,10 | |
| 520 | 3 | |a Abstract: "This paper generalizes many-sorted algebra (hereafter, MSA) to order-sorted algebra (hereafter, OSA) by allowing a partial ordering relation on the set of sorts. This supports abstract data types with multiple inheritance (in roughly the sense of object-oriented programming), several forms of polymorphism and overloading, partial operations (as total on equationally defined subsorts), exception handling, and an operational semantics based on term rewriting. We give the basic algebraic constructions for OSA, including quotient, image, product and term algebra, and we prove their basic properties, including Quotient, Homomorphism, and Initiality Theorems. The paper's major mathematical results include a notion of OSA deduction, a Completeness Theorem for it, and an OSA Birkhoff Variety Theorem | |
| 520 | 3 | |a We also develop conditional OSA, including Initiality, Completeness, and McKinsey-Maclev Quasivariety Theorems, and we reduce OSA to (conditional) MSA, which allows lifting many known MSA results to OSA. Retracts, which intuitively are left inverses to subsort inclusions, provide relatively inexpensive run-time error handling. We show that it is safe to add retracts to any OSA signature, in the sense that it gives rise to a conservative extension. A final section compares and contrasts many different approaches to OSA. This paper also includes several examples demonstrating the flexibility and applicability of OSA, including some standard benchmarks like STACK and LIST, as well as a much more substantial example, the number hierarchy from the naturals up to the quaternions | |
| 650 | 4 | |a Logic programming | |
| 650 | 4 | |a Ordered algebraic structures | |
| 700 | 1 | |a Meseguer, José |e Verfasser |4 aut | |
| 830 | 0 | |a Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL |v 89,10 |w (DE-604)BV008930658 |9 89,10 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-005904665 | ||
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| id | DE-604.BV008948944 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:27:17Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005904665 |
| oclc_num | 22168765 |
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| owner_facet | DE-29T |
| physical | 49 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| record_format | marc |
| series | Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL |
| series2 | Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL |
| spelling | Goguen, Joseph 1941-2006 Verfasser (DE-588)172100275 aut Order-sorted Algebra I equational deduction for multiple inheritance, overloading, exceptions and partial operations by Joseph A. Goguen and José Meseguer Menlo Park, Calif. 1989 49 S. txt rdacontent n rdamedia nc rdacarrier Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL 89,10 Abstract: "This paper generalizes many-sorted algebra (hereafter, MSA) to order-sorted algebra (hereafter, OSA) by allowing a partial ordering relation on the set of sorts. This supports abstract data types with multiple inheritance (in roughly the sense of object-oriented programming), several forms of polymorphism and overloading, partial operations (as total on equationally defined subsorts), exception handling, and an operational semantics based on term rewriting. We give the basic algebraic constructions for OSA, including quotient, image, product and term algebra, and we prove their basic properties, including Quotient, Homomorphism, and Initiality Theorems. The paper's major mathematical results include a notion of OSA deduction, a Completeness Theorem for it, and an OSA Birkhoff Variety Theorem We also develop conditional OSA, including Initiality, Completeness, and McKinsey-Maclev Quasivariety Theorems, and we reduce OSA to (conditional) MSA, which allows lifting many known MSA results to OSA. Retracts, which intuitively are left inverses to subsort inclusions, provide relatively inexpensive run-time error handling. We show that it is safe to add retracts to any OSA signature, in the sense that it gives rise to a conservative extension. A final section compares and contrasts many different approaches to OSA. This paper also includes several examples demonstrating the flexibility and applicability of OSA, including some standard benchmarks like STACK and LIST, as well as a much more substantial example, the number hierarchy from the naturals up to the quaternions Logic programming Ordered algebraic structures Meseguer, José Verfasser aut Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL 89,10 (DE-604)BV008930658 89,10 |
| spellingShingle | Goguen, Joseph 1941-2006 Meseguer, José Order-sorted Algebra I equational deduction for multiple inheritance, overloading, exceptions and partial operations Computer Science Laboratory <Menlo Park, Calif.>: SRI-CSL Logic programming Ordered algebraic structures |
| title | Order-sorted Algebra I equational deduction for multiple inheritance, overloading, exceptions and partial operations |
| title_auth | Order-sorted Algebra I equational deduction for multiple inheritance, overloading, exceptions and partial operations |
| title_exact_search | Order-sorted Algebra I equational deduction for multiple inheritance, overloading, exceptions and partial operations |
| title_full | Order-sorted Algebra I equational deduction for multiple inheritance, overloading, exceptions and partial operations by Joseph A. Goguen and José Meseguer |
| title_fullStr | Order-sorted Algebra I equational deduction for multiple inheritance, overloading, exceptions and partial operations by Joseph A. Goguen and José Meseguer |
| title_full_unstemmed | Order-sorted Algebra I equational deduction for multiple inheritance, overloading, exceptions and partial operations by Joseph A. Goguen and José Meseguer |
| title_short | Order-sorted Algebra I |
| title_sort | order sorted algebra i equational deduction for multiple inheritance overloading exceptions and partial operations |
| title_sub | equational deduction for multiple inheritance, overloading, exceptions and partial operations |
| topic | Logic programming Ordered algebraic structures |
| topic_facet | Logic programming Ordered algebraic structures |
| volume_link | (DE-604)BV008930658 |
| work_keys_str_mv | AT goguenjoseph ordersortedalgebraiequationaldeductionformultipleinheritanceoverloadingexceptionsandpartialoperations AT meseguerjose ordersortedalgebraiequationaldeductionformultipleinheritanceoverloadingexceptionsandpartialoperations |