The Stratified Loose Approach: A Generalization of Initial and Loose Semantics

Besides the respective advantages and drawbacks of the initial and loose approaches to algebraic semantics, the choice of either initial semantics or loose semantics for a given specification language often relies on methodological considerations. In this paper, we briefly recall the main features of the Pluss specification language, the semantics of which was originally designed following the loose approach. Then we study how far some basic concerns, such as modularity and reusability, interact with the design of the semantics of the Pluss specification-building primitives. We show that neither the initial approach nor the loose one is powerful enough to reflect our intuition and needs about software reusability and modularity, and we introduce a more sophisticated framework, the stratified loose semantics, which can be considered as a generalization of both loose and initial semantics.

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