Title: Toward an Object-Oriented Structure for Mathematical Text

Abstract:
  Computerizing mathematical texts to allow software access to some or
all of the texts' semantic content is a long and tedious process that
currently requires much expertise. We believe it is useful to support
computerization that adds some structural and semantic information,
but does not require jumping directly from the word-processing level
(e.g., LaTeX) to full formalization (e.g., Mizar, Coq, etc.). Although
some existing mathematical languages are aimed at this middle ground
(e.g., MathML, OpenMath, OMDoc), we believe they miss features needed
to capture some important aspects of mathematical texts, especially
the portion written with natural language. For this reason, we have
been developing MathLang, a language for representing mathematical
texts that has weak type checking and support for the special
mathematical use of natural language. MathLang is currently aimed at
only capturing the essential grammatical and binding structure of
mathematical text without requiring full formalization.

  The development of MathLang is directly driven by experience
encoding real mathematical texts. Based on this experience, this paper
presents the changes that yield our latest version of MathLang. We
have restructured and simplified the core of the language, replaced
our old notion of "context" by a new system of blocks and local
scoping, and made other changes. Furthermore, we have enhanced our
support for the mathematical use of nouns and adjectives with
object-oriented features so that nouns now correspond to classes, and
adjectives to mixins.