Step-wise refinement is a powerful paradigm for developing a complex program from a simple program by adding features incrementally. We present the AHEAD (algebraic hierarchical equations for application design) model that shows how step-wise refinement scales to synthesize multiple programs and multiple noncode representations. AHEAD shows that software can have an elegant, hierarchical mathematical structure that is expressible as nested sets of equations. We review a tool set that supports AHEAD. As a demonstration of its viability, we have bootstrapped AHEAD tools from equational specifications, refining Java and nonJava artifacts automatically; a task that was accomplished only by ad hoc means previously.

Step-wise refinement is a powerful paradigm for developing a complex program from a simple program by adding features incrementally. We present the AHEAD (Algebraic Hierarchical Equations for Application Design) model that shows how step-wise refinement scales to synthesize multiple programs and multiple non-code representations. AHEAD shows that software can have an elegant, hierarchical mathematical structure that is expressible as nested sets of equations. We review a tool set that supports AHEAD. As a demonstration of its viability, we have bootstrapped AHEAD tools solely from equational specifications, generating Java and non-Java artifacts automatically, a task that was accomplished only by ad hoc means previously.

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.