Closed sets of universal Horn formulas for many-sorted (partial) algebras
Coalgebras for binary methods : properties of bisimulations and invariants
Coalgebras for endofunctors can be used to model classes of object-oriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors . This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation and invariants for coalgebras of extended polynomial functors and proves many standard...
Coalgebras for Binary Methods: Properties of Bisimulations and Invariants
Coalgebras for endofunctors can be used to model classes of object-oriented languages. However, binary methods do not fit directly into this approach. This paper proposes an extension of the coalgebraic framework, namely the use of extended polynomial functors. This extension allows the incorporation of binary methods into coalgebraic class specifications. The paper also discusses how to define bisimulation and invariants for coalgebras of extended polynomial functors and proves many...
Compactness and Löwenheim-Skolem properties in categories of pre-institutions
The abstract model-theoretic concepts of compactness and Löwenheim-Skolem properties are investigated in the "softer" framework of pre-institutions [18]. Two compactness results are presented in this paper: a more informative reformulation of the compactness theorem for pre-institution transformations, and a theorem on natural equivalences with an abstract form of the first-order pre-institution. These results rely on notions of compact transformation, which are introduced as arrow-oriented generalizations...
Complexity of -term reductions
Construction d'un plus petit ordre de simplification
Correctness of horizontal and vertical composition for implementation concepts based on constructors and abstractors.
A new implementation concept for parameterized specifications based on constructors and abstractors was recently introduced by Orejas, Navarro and Sánchez which includes most of the implementation concepts in the literature for initial as well as loose semantics. In this paper we redefine vertical and different kinds of horizontal compositions using the new concept of semi-pushout defined for a mixture of signature and specification morphisms. The main results concerning correctness of horizontal...