Very interesting exposition and comments. I think it shows one of the 'weaknesses' of TAOCP is that it does not formalize or at least make explicit the relation

Very interesting exposition and comments. I think it shows one of the 'weaknesses' of TAOCP is that it does not formalize or at least make explicit the relationship between the available operations and the final functionality of the algorithm. In that sense the TAOCP remains a receipe book and not something that is 'executable' in the sense of being able to generate algorithms tailored to the available operations (and their performance) or at least to be used in a tool that could support the synthesizes or verification of algorithms.