A new modular mathematical programming language M2001 is introduced. I
t is designed to serve as an expository/pedagogical language, used for
the development and the presentation of algorithmic processes, as fou
nd in the full range of mathematical discourse - from the modern discr
ete to the classical continuous mathematics. Built on a semantical fra
mework based in the theory of categories, the M2001 language has a Pas
cal/Modula-like syntax, but uses the class concept only as a fully-enc
apsulated, built-in apparatus for handling the traditional mathematica
l structures and classical computer science (abstract) data types, as
found in the elementary applications of the early undergraduate mathem
atics curriculum. The (categorical) semantic interpretation of the lan
guage is outlined, and a complete set of syntax diagrams is presented
in an accompanying Appendix.