Towards Specifying with Inclusions

Abstract

In this article we present a functional specification language based on inclusions between set expressions.

Instead of computing with data individuals we deal with their classification into sets.

The specification of functions and relations by means of inclusions can be considered as a generalization of the conventional algebraic specification by means of equations.

The main aim of this generalization is to facilitate the incremental refinement of specifications.

Furthermore, inclusional specifications admit a natural visual syntax which can also be used to visualize the reasoning process.

We show that reasoning with inclusions is well captured by bi-rewriting, a rewriting technique introduced by Levy and Agustí [15].

However, there are still key problems to be solved in order to have executable inclusional specifications, necessary for rapid prototyping purposes.

The article mainly points to the potentialities and difficulties of specifying with inclusions.