We present Clafer (class, feature, reference), a class modeling language with first-class support for feature modeling. We designed Clafer as a concise notation for meta-models, feature models, mixtures of meta- and feature models (such as components with options), and models that couple feature models and meta-models via constraints (such as mapping feature configurations to component configurations or model templates). Clafer allows arranging models into multiple specialization and extension layers via constraints and inheritance. We identify several key mechanisms allowing a meta-modeling language to express feature models concisely. Clafer unifies basic modeling constructs, such as class, association, and property, into a single construct, called clafer. We provide the language with a formal semantics built in a structurally explicit way. The resulting semantics explains the meaning of hierarchical models whereby properties can be arbitrarily nested in the presence of inheritance and feature modeling constructs. The semantics also enables building consistent automated reasoning support for the language: To date, we implemented three reasoners for Clafer based on Alloy, Z3 SMT, and Choco3 CSP solvers. We show that Clafer meets its design objectives using examples and by comparing to other languages.
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