Refinements and multi-dimensional separation of concerns

Abstract

Step-wise refinement (SWR) asserts that complex programs can be derived from simple programs by progressively adding features. The length of a program specification is the number of features that the program has. Critical to the scalability of SWR are multi-dimensional models that separate orthogonal feature sets. Let n be the dimensionality of a model and k be the number of features along a dimension. We show program specifications that could be O(kn) features long have short and easy-to-understand specifications of length O(kn) when multi-dimensional models are used. We present new examples of multidimensional models: a micro example of a product-line (whose programs are 30 lines of code) and isomorphic macro examples (whose programs exceed 30K lines of code). Our work provides strong evidence that SWR scales to synthesis of large systems.