Contemporary linguistic formalisms have become so rigorous that it is now possible to view them as very high level declarative programming languages. Consequently, grammars for natural languages can be viewed as programs; this view enables the application of various methods and techniques that were proved useful for programming languages to the study of natural languages. This paper adapts the notion of program composition, well developed in the context of logic programming languages, to the domain of linguistic formalisms. We study alternative definitions for the semantics of such formalisms, suggesting a denotational semantics that we show to be compositional and fully-abstract. This facilitates a clear, mathematically sound way for defining grammar modularity.