Variant-Based Decidable Satisfiability in Initial Algebras with Predicates

  • Raúl GutiérrezEmail author
  • José Meseguer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10855)


Decision procedures can be either theory-specific, e.g., Presburger arithmetic, or theory-generic, applying to an infinite number of user-definable theories. Variant satisfiability is a theory-generic procedure for quantifier-free satisfiability in the initial algebra of an order-sorted equational theory \((\varSigma ,E \cup B)\) under two conditions: (i) \(E \cup B\) has the finite variant property and B has a finitary unification algorithm; and (ii) \((\varSigma ,E \cup B)\) protects a constructor subtheory \((\varOmega ,E_{\varOmega } \cup B_{\varOmega })\) that is OS-compact. These conditions apply to many user-definable theories, but have a main limitation: they apply well to data structures, but often do not hold for user-definable predicates on such data structures. We present a theory-generic satisfiability decision procedure, and a prototype implementation, extending variant-based satisfiability to initial algebras with user-definable predicates under fairly general conditions.


Finite variant property (fvp) OS-compactness User-definable predicates Decidable validity and satisfiability in initial algebras 


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Authors and Affiliations

  1. 1.Universitat Politècnica de ValènciaValenciaSpain
  2. 2.University of Illinois at Urbana-ChampaignChampaignUSA

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