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We introduce a new concept in the area of formal logic: axioms for model morphisms. We work in the setting of specification languages that define the semantics of a theory as a category of models. While it is routine to use axioms to specify the class of models of a theory, there has so far been no analogue to systematically specify the morphisms between these models. This leads to subtle problems where it is difficult to give a theory that specifies the intended model category, or where seemingly isomorphic theories actually have non-isomorphic model categories. Our morphism axioms remedy this by providing new syntax for axiomatizing and reasoning about the properties of model morphisms. Additionally, our system resolves a subtle incompatibility between theory morphisms and model morphisms: the semantics that maps theories to model categories is functorial. While this result is standard in principle, previous formulations had to restrict the allowed theory morphisms or the allowed model morphisms. Our system allows establishing the result in full generality. [ABSTRACT FROM AUTHOR]

Abstract: Rewriting logic is a flexible and expressive logical framework that unifies algebraic denotational semantics and structural operational semantics (SOS) in a novel way, avoiding their respective limitations and allowing succinct semantic definitions. The fact that a rewrite logic theory’s axioms include both equations and rewrite rules provides a useful “abstraction dial” to find the right balance between abstraction and computational observability in semantic definitions. Such semantic definitions are directly executable as interpreters in a rewriting logic language such as Maude, whose generic formal tools can be used to endow those interpreters with powerful program analysis capabilities. [Copyright &y& Elsevier]

Abstract: We are interested in separation-logic-based static analysis of programs that use shared mutable data structures. In this paper, we introduce backward and forward analysis for a separation logic called , an extension of separation logic [Ishtiaq and O’Hearn, BI as an assertion language for mutable data structures, in: POPL’01, 2001, pp. 14–26], to which we add fixpoint connectives and postponed substitution. This allows us to express recursive definitions within the logic as well as the axiomatic semantics of while statements. [Copyright &y& Elsevier]