Maude is a high-performance reflective language and system supporting both equational and rewriting logic specification and programming for a wide range of applications, and has a relatively large worldwide user and open-source developer base. This paper introduces novel features of Maude 2.4 including support for unification and narrowing. Unification is supported in Core Maude, the core rewri...

Salomaa ((1969) Theory of Automata, page 143) asked whether the equational theory of regular expressions over a singleton alphabet has a finite equational base. In this paper, we provide a negative answer to this long standing question. The proof of our main result rests upon a modeltheoretic argument. For every finite collection of equations, that are sound in the algebra of regular expression...

Kleene algebra with tests (KAT) is an equational system for program verification, which is the combination of Boolean algebra (BA) and Kleene algebra (KA), the algebra of regular expressions. In particular, KAT subsumes the propositional fragment of Hoare logic (PHL) which is a formal system for the specification and verification of programs, and that is currently the base of most tools for che...

Kleene algebra with tests (KAT) is an equational system for program verification, which is the combination of Boolean algebra (BA) and Kleene algebra (KA), the algebra of regular expressions. In particular, KAT subsumes the propositional fragment of Hoare logic (PHL) which is a formal system for the specification and verification of programs, and that is currently the base of most tools for che...

Equational zero vector accounting systems, based on duality principles and the double-entry model, were designed as ontological control systems to help prevent and detect fraud and errors inherent in non-equational, single-entry systems. Non-equational systems lend themselves to fraud and errors to a larger degree because the internal control inherent in an equational zero vector system has no ...

We introduce an abstract general notion of system of equations between terms, called Term Equational System, and develop a sound logical deduction system, called Term Equational Logic, for equational reasoning. Further, we give an analysis of algebraic free constructions that together with an internal completeness result may be used to synthesise complete equational logics. Indeed, as an applic...