I present an expanded taxonomy of sorting algorithms that is based upon Merritt's inverted taxonomy [1] and Lau's logic-based derivations [2, 3]. The inverted taxonomy was based on a higher level, more abstract, and conceptually simple top-down approach to sorting than the traditional taxonomy such as that given by Knuth [4], Work done in automatic program synthesis suggested the approach. Sorts were divided into two categories, hardsplit/easyjoin and easysplit/hardjoin, of which quicksort and mergesort are the canonical examples, respectively. Lau's [2, 3] logic-based derivations strengthen the inverted taxonomy by deriving comparison-based sorting algorithms that fall into the two categories of hardsplit/easyjoin and easysplit/hardjoin. Moreover, they expand the taxonomy by deriving distributive algorithms in a symmetric way.
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