Towards an algebraic semantics for the object paradigm (abstract)
This paper surveys our current state of knowledge (and ignorance) on
the use of hidden sorted algebra as a foundation for the object paradigm.
Our main goal is to support equational reasoning about properties of concurrent
systems of objects, because of its simple and efficient mechanisation.
We show how equational specifications can describe objects, inheritance
and modules; our treatment of the latter topic emphasises the importance
of reuse, and the role of the so-called Satisfaction Condition. We then
consider how to prove things about objects, how to unify the object and
logic paradigms by using logical variables that range over objects, and
how to connect objects into concurrent systems. We provide a universal
characterisation of parallel connection, and more generally, of parallel
connection with synchronisation, and show how the former construction gives
a class manager that provides unique identifiers for its objects. The paper
concludes with some topics for further research.
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