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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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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