We study two observational equivalences of Fickle programs. Fickle is a class-based object oriented imperative language, which extends Java with object re-classification. The first is a contextual equivalence of expressions with respect to a given program. We provide an adequate coalgebraic semantics for it, which is compositional w.r.t. the operators of the language. The second observational e...

Real number computation in modern computers is mostly done via floating point arithmetic which can sometimes produce wildly erroneous results. An alternative approach is to use exact real arithmetic whose results are guaranteed correct to any user-specified precision. It involves potentially infinite data structures and has therefore in recent years been studied using the mathematical field of ...

This paper shows, that three di erent types of logics for coalgebras are institutions. The logics di er regarding the presentation of their syntax. In the rst framework, abstract behavioural logic, one has a syntax-free representation of behavioural properties. We then turn to coalgebraic logic, the syntax of which is given as an initial algebra. The last framework, which we consider, is coalge...

Labeled state-to-function transition systems, FuTSs for short, capture transition schemes incorporating multiplicities from states to functions of finite support over general semirings. As such FuTSs constitute a convenient modeling instrument to deal with process languages and their stochastic extensions in particular. In this paper, the notion of bisimulation induced by a FuTS is addressed fr...

The coalgebraic approach to modal logic provides a uniform framework that captures the semantics of a large class of structurally different modal logics, including e.g. graded and probabilistic modal logics and coalition logic. In this paper, we introduce the coalgebraic μ-calculus, an extension of the general (coalgebraic) framework with fixpoint operators. Our main results are completeness of...

In this article, we provide three coalgebraic characterizations of the class of context-free languages, each based on the idea of adding coalgebraic structure to an existing algebraic structure by specifying output-derivative pairs. Final coalgebra semantics then gives an interpretation function into the final coalgebra of all languages with the usual output and derivative operations. The first...