Correctness-by-construction ∧ taxonomies ⇒ deep comprehension of algorithm families

Correctness-by-construction (CbC) is an approach for developing algorithms inline with rigorous correctness arguments. A high-level specification is evolved into an implementation in a sequence of small, tractable refinement steps guaranteeing the resulting implementation to be correct. CbC facilitates the design of algorithms that are more efficient and more elegant than code that is hacked into correctness. In this paper, we discuss another benefit of CbC, i.e., that it supports the deep comprehension of algorithm families. We organise the different refinements of the algorithms carried out during CbC-based design in a taxonomy. The constructed taxonomy provides a classification of the commonality and variability of the algorithm family and, hence, provides deep insights into their structural relationships. Such taxonomies together with the implementation of the algorithms as toolkits provide an excellent starting point for extractive and proactive software product line engineering.