Representing Object Models as Theories

Although techniques for using formal specifications have been progressing, methods for developing formal specifications themselves have improved little. To alleviate this problem, we propose a parallel refinement approach to specification acquisition wherethe designer uses an object-orientedspecification representation while an underlying specification composition system manipulates an equivalent theory-basedspecification. This paper presents the key to such a system --atheory-based object model. Our theory-based object model formally defines object-orientedconcepts in terms of algebraic theories and category theory operations. The theory-based object model provides the basis for the translation of the specification from a semi-formal, object-orientedrepresentation to a formal theory-based specification suitable for input to semi-automated software synthesis systems. 1