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Workshop on the Specification of Abstract Data Types

Workshop of the ESPRIT Basic Research Working Group COMPASS

ADT 1992, COMPASS 1992: Recent Trends in Data Type Specification pp 321–336Cite as

Second-order proof systems for algebraic specification languages

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 785))

Abstract

Besides explicit axioms, an algebraic specification language contains model-theoretic constraints such as term-generation or initiality. For proving properties of specifications and refining them to programs, an axiomatization of these constraints is needed; unfortunately, no effective, sound and complete proof system can be constructed for most algebraic specification languages.

In this paper, we construct non-effective second-order axiomatizations for constraints commonly found in specification languages, and simplified forms useful for the universal fragment. They are shown to be sound and complete, but not effective, since the underlying second-order logic is not effective. A good level of machine support is still possible using higher-order proof assistants.

This research was mostly carried out at Centre National de la Recherche Scientifique, Centre de Recherche en Informatique de Nancy.

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Authors and Affiliations

  1. Institut d'Informatique, Fac. Univ. Notre-Dame de la Paix, Rue Grandgagnage 21, B-5000, Namur

    Pierre-Yves Schobbens

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  1. Pierre-Yves Schobbens
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Hartmut Ehrig Fernando Orejas

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© 1994 Springer-Verlag Berlin Heidelberg

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Schobbens, PY. (1994). Second-order proof systems for algebraic specification languages. In: Ehrig, H., Orejas, F. (eds) Recent Trends in Data Type Specification. ADT COMPASS 1992 1992. Lecture Notes in Computer Science, vol 785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57867-6_20

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  • DOI: https://doi.org/10.1007/3-540-57867-6_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57867-3

  • Online ISBN: 978-3-540-48361-8

  • eBook Packages: Springer Book Archive

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