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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.