Abstract
Coalgebraic specification and semantics, as used earlier for object-oriented programming, is extended with temporal aspects. The (non-temporal) expression s.meth expressing that method meth is applied in state s is extended to an expression s.meth@α, where α is a time parameter. It means: in state s let the state evolve for α units of time, and then apply method meth. With this formalism we specify various (elementary) deterministic hybrid systems (and give a few simulations). We also define a notion of model for such a specification, and define what it means for a model to be terminal. Terminal models are “optimal” in the sense that they involve a minimal set of states, as will be illustrated in a number of examples. This shows that standard model theory can be applied to temporal (coalgebraic) specifications.
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Jacobs, B. (1996). Coalgebraic specifications and models of deterministic hybrid systems. In: Wirsing, M., Nivat, M. (eds) Algebraic Methodology and Software Technology. AMAST 1996. Lecture Notes in Computer Science, vol 1101. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014337
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DOI: https://doi.org/10.1007/BFb0014337
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