Formal executable theory of multilevel modeling

Abstract

Multi-Level Modeling (MLM) conceptualizes software models as layered architectures of sub-models that are inter-related by the instance-of relation, which breaks monolithic class hierarchies midway between subtyping and interfaces. This paper introduces a formal theory of MLM, rooted in a set-theoretic semantics of class models. The MLM theory is validated by a provably correct translation into the FOML executable logic. We show how FOML accounts for inter-level constraints, rules, and queries. In that sense, FOML is an organic executable extension for MLM that incorporates all MLM services. As much as the page budget permits, the paper illustrates how multilevel models are represented and processed in FOML.