## Object Oriented Mathematics

PDF.

### Abstract

Computers demand unambiguous notation, programmers want brevity and
maintainers of software want clarity. Users of mathematical notation demand
brevity and clarity, but the demand for unambiguous notation is less pressing in
mathematics. Hence, development of unambiguous notation has mainly occurred in
the fields of mathematical logic and computer science, with computer science as
the place where unambiguity is most needed. It is therefore no surprise that
computer science has developed a number of formalisms (i.e. programming
languages) that are completely unambiguous.

In many respects, mathematical notation is superior to computer science ditto.
This is so because mathematics has had longer time to develop its notation and
because computer science has been restricted to a character set with 96
characters and typewriters that could merely arrange those characters as
simple, linear strings. The present paper aims at combining the best from the
two worlds.

Such a combination of notation from two worlds will necessarily offend both
worlds as not all properties of each world will be included or even
appreciated.

Section 2 will present a number of ambiguities that appear in
contemporary mathematical notation. Section 3 will present the
choices that were made in the development of the notation. Section
4 develops the notation itself.

Klaus Grue, August 27, 1996