Specializing anti-unification for interaction models composition via gate connections

Abstract

Interaction models describe distributed systems as algebraic terms, with gates marking interaction points between local views. Composing local models into a coherent global one requires aligning these gates while respecting the algebraic laws of interaction operators. We specialize anti-unification (or generalization) via a special constant-preserving variant, which preserves designated constants while generalizing the remaining structure. We develop a dedicated rule-based procedure for computing these generalizations, prove its termination, soundness, and completeness, extend it modulo equational theories, and integrate it into a standard anti-unification framework. A prototype tool demonstrates the approach's ability to recompose global interactions from partial views.

26 pages (21 in the article, 5 pages in appendices), 7 figures, 6 tables, submitted to Formal Methods 2026 (FM 2026)