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doi:10.22028/D291-40156
Titel: | Order-Sorted Equational Computation |
VerfasserIn: | Smolka, Gert Nutt, Werner Goguen, Joseph A. Meseguer, José |
Sprache: | Englisch |
Erscheinungsjahr: | 1987 |
Erscheinungsort: | Kaiserslautern |
Freie Schlagwörter: | Order-Sorted Equational Logic Algebraic Specification Initial Algebra Semantics Partial Functions Rewriting Unification Subsorts Inheritance Logic Programming |
DDC-Sachgruppe: | 004 Informatik |
Dokumenttyp: | Forschungsbericht (Report zu Forschungsprojekten) |
Abstract: | The expressive power of many-sorted equational logic can be greatly enhanced by allowing for subsorts and multiple function declarations. In this paper we study some computational aspects of such a logic. We start with a self-contained introduction to order-sorted equational logic including initial algebra semantics and deduction rules. We then present a theory of order-sorted term rewriting and show that the key results for unsorted rewriting extend to sort decreasing rewriting. We continue with a review of order-sorted unification and prove the basic results. In the second part of the paper we study hierarchical order-sorted specifications with strict partial functions. We define the appropriate homomorphisms for strict algebras and show that every strict algebra is base isomorphic to a strict algebra with at most one error element. For strict specifications, we show that their categories of strict algebras have initial objects. We validate our approach to partial functions by proving that completely defined total functions can be defined as partial without changing the initial algebra semantics. Finally, we provide decidable sufficient criteria for the consistency and strictness of ground confluent rewriting systems. |
Link zu diesem Datensatz: | urn:nbn:de:bsz:291--ds-401560 hdl:20.500.11880/36231 http://dx.doi.org/10.22028/D291-40156 |
Schriftenreihe: | SEKI-Report / Deutsches Forschungszentrum für Künstliche Intelligenz, DFKI [ISSN 1437-4447] |
Band: | 87,14 |
Datum des Eintrags: | 11-Aug-2023 |
Fakultät: | SE - Sonstige Einrichtungen |
Fachrichtung: | SE - DFKI Deutsches Forschungszentrum für Künstliche Intelligenz |
Professur: | SE - Sonstige |
Sammlung: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
Dateien zu diesem Datensatz:
Datei | Beschreibung | Größe | Format | |
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SEKI-Report-SR-87-14_Smolka_Nutt_Goguen_Meseguer_Order=Sorted-Equational-Computation.pdf | 4,78 MB | Adobe PDF | Öffnen/Anzeigen |
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