Rn- and Gn-Logics
نویسندگان
چکیده
This paper proposes a simple, set-theoretic framework providing expressive typing, higher-order functions and initial models at the same time. Building upon Russell’s ramified theory of types, we develop the theory of R-logics, which are axiomatisable by an order-sorted equational Horn logic with a membership predicate, and of G-logics, that provide in addition partial functions. The latter are therefore more adapted to the use in the program specification domain, while sharing interesting properties, like existence of an initial model, withR-logics. Operational semantics of R-/G-logics presentations is obtained through order-sorted conditional rewriting.
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