Abstract
Many features of current logic programming languages are not captured by conventional semantics. Their fundamentally non-ground character, and the uniform way in which such languages have been extended to typed domains subject to constraints, suggest that a categorical treatment of constraint domains, of programming syntax and of semantics may be closer in spirit to declarative programming than conventional set theoretic semantics.
We generalize the notion of a (many-sorted) logic program and of a resolution proof by defining them both over a (not necessarily free) τ-category, a category with products enriched with a mechanism for canonically manipulating n-ary relations. Computing over this domain includes computing over the Herbrand Universe, and over equationally presented constraint domains as special cases. We give a categorical treatment of the fix-point semantics of Kowalski and van Emden, which establishes completeness in a very general setting.
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© 1995 Springer-Verlag Berlin Heidelberg
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Finkelstein, S.E., Freyd, P., Lipton, J. (1995). Logic programming in Tau Categories. In: Pacholski, L., Tiuryn, J. (eds) Computer Science Logic. CSL 1994. Lecture Notes in Computer Science, vol 933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022261
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DOI: https://doi.org/10.1007/BFb0022261
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