The proofs may be mechanised by systems such as OBJ , designed by Prof. Joseph Goguen , at Oxford 1988-1996, who undertook much of the theoretical underpinning in the area of initial algebras and order sorted algebra. Modelling is an important aspect of computer science. However many algebraic properties may be derived from models. A particular process is modelled as the subset of observations to which it can give rise. Process composition is modelled by relating observations of a composite process to those of its components.
Indirect observations play an essential role is such compositions.
Algebraic properties of the composition operators are derived with the aid of the simple theory of sets and relations. The viability of such approaches has yet to be seen in widespread industrial practice. But neither of these achievements is enough. We need to build up a large collection of models and algebras, covering a wide range of computational paradigms, appropriate for implementation either in hardware or in software, either of the present day or of some possible future. However the prospects for the use of algebraic techniques in the design and verification of computer based systems are promising if the techniques can become as familiar to engineers as school algebra is to many today.