Variant-Based Decidable Satisfiability in Initial Algebras with Predicates

Gutiérrez, Raúl; Meseguer, José

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https://hdl.handle.net/2142/96264 Copy

Description

Title

Variant-Based Decidable Satisfiability in Initial Algebras with Predicates

Author(s)

• Gutiérrez, Raúl
• Meseguer, José

Issue Date

2017-06-27

Keyword(s)

• finite variant property (FVP)
• OS-compactness
• user-definable predicates
• decidable validity and satisfiability in initial algebras

Abstract

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 (Sigma,E U B) under two conditions: (i) E U B has the finite variant property and B has a finitary unification algorithm; and (ii) (Sigma,E U B) protects a constructor subtheory (Omega,E_Omega U B_Omega) 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.

Type of Resource

text

Language

en

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http://hdl.handle.net/2142/96264

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