A Coequational Approach to Specifying Behaviours

A coalgebraic, equational approach to the specification of observational structures allowing for a choice in the result type of observations is presented. Coalgebraic operations whose result type is structured as a coproduct of basic types are considered, and notions of coterm, covariable and coequation, dual to the algebraic notions of term, variable and equation, are used to specify structures observable through such operations and to constrain their behaviour. A sound and complete deduction calculus for reasoning about observational properties expressed by coequations is then formulated.