Abstract: This paper introduces a calculus of state-based software components modelled as concrete coalgebras for some Set endofunctors, with specified initial conditions. The calculus is parametrized by a notion of behaviour, introduced as a strong (usually commutative) monad. The proposed component model and calculus are illustrated through the characterisation of a particular class of components, classified as separable, which includes the ones arising in the so-called model oriented approach to systems’ design.

Coalgebras of Kripke Polynomial Functors have been widely used in modelling various kinds of systems. In this paper, we give a category Coalg KPF which consists of coalgebras of KPFs. Then we present a set of constructions like sequential and parallel composition in a subcategory of Coalg KPF for a restricted family of KPFs by exploiting the canonical operations in category theory. A family of algebraic laws for the properties being satisfied by these operations is provided. Sun Meng is a Fellow at UNU/IIST on leave from the School of Mathematical Science of Beijing University, China, where he is a Ph.D candidate. His research interest include category theory, coalgebra theory, Object-Oriented method, formal method in software development, and formal semantics for modeling languages. His email address is sm@iist.unu.edu.