A Compositional Semantics for Normal Open Programs

In this paper we propose a semantics for first order modular (open) programs. Modular programs are built as a combination of separate modules, which may evolve separately, and be verified separately. Therefore, in order to reason over such programs, compositionality plays a crucial role: the semantics of the whole program must be obtainable as a simple function from the semantics of its individual modules. In this paper we propose such a compositional semantics for first-order programs. This semantics is correct with respect to the set of logical consequences of the program. Moreoverr, - in contrast with other approaches - it is always computable. Furthermore, we show how our results on firs-order programs may be applied in a straightforward way to normal logic programs, in which case our semantics might be regarded as a compositional counterpart of Kunen's semantics. Finally we discuss and show how these results hav to be modified in order to be applied to normal CLP