  The words ``Programming is the second literacy'' were coined more than 40
years ago but never came to life. This paper is one in the series of papers
aimed at the analysis of mathematical requirements for a merge of school
mathematics with computer science and computer programming. First indications
are this demands development of quite serious mathematical tools most of which,
hopefully, will be hidden "under the hood'' of software systems used in the
process, but many will feature prominently in the Domain Specific Language
needed for support of mathematical exchanges between Learner, Teacher, and
Computer. We focus on "hardcore" mathematical aspects of this development.
