Representing Object Models as Theories

Although techniques for using formal speci cations have been progressing, methods for developing formal speci cations themselves have improved little. To alleviate this problem, we propose a parallel re nement approach to speci cation acquisition where the designer uses an object-oriented speci cation representation while an underlying speci cation composition system manipulates an equivalent theory-based specication. This paper presents the key to such a system { a theory-based object model. Our theory-based object model formally de nes object-oriented concepts in terms of algebraic theories and category theory operations. The theory-based object model provides the basis for the translation of the speci cation from a semi-formal, object-oriented representation to a formal theory-based speci cation suitable for input to semi-automated software synthesis systems.