A Combinator-based order-sorted higher-order unification algorithm
- This paper develops a sound and complete transformation-based algorithm forunification in an extensional order-sorted combinatory logic supporting constantoverloading and a higher-order sort concept. Appropriate notions of order-sortedweak equality and extensionality - reflecting order-sorted fij-equality in thecorresponding lambda calculus given by Johann and Kohlhase - are defined, andthe typed combinator-based higher-order unification techniques of Dougherty aremodified to accommodate unification with respect to the theory they generate. Thealgorithm presented here can thus be viewed as a combinatory logic counterpartto that of Johann and Kohlhase, as well as a refinement of that of Dougherty, andprovides evidence that combinatory logic is well-suited to serve as a framework forincorporating order-sorted higher-order reasoning into deduction systems aimingto capitalize on both the expressiveness of extensional higher-order logic and theefficiency of order-sorted calculi.
Author: | Patricia Johann |
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URN: | urn:nbn:de:hbz:386-kluedo-3260 |
Series (Serial Number): | SEKI Report (93,16) |
Document Type: | Preprint |
Language of publication: | English |
Year of Completion: | 1999 |
Year of first Publication: | 1999 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2000/04/03 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Informatik |
DDC-Cassification: | 0 Allgemeines, Informatik, Informationswissenschaft / 004 Informatik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |