OpenMath Content Dictionaries

Content Dictionaries are structured documents used by the

OpenMath

standard [BCC

 + 

04] to codify knowledge about mathematical symbols and concepts used in the representation of mathematical formulae. They differ from the mathematical documents discussed in the last chapter in that they are less geared towards introduction of a particular domain, but act as a reference/glossary document for implementing and specifying mathematical software systems. Content Dictionaries are important for the

OMDoc

format, since the

OMDoc

architecture, and in particular the integration of

OpenMath

builds on the equivalence of

OpenMath

content dictionaries and

OMDoc

theories.

Concretely, we will look at the content dictionary

arith1.ocd

which defines the

OpenMath

symbols

abs

,

divide

,

gcd

,

lcm

,

minus

,

plus

,

power

,

product

,

root

,

sum

,

times

,

unary_minus

(see [OMC] for the original). We will discuss the transformation of the parts listed below into

OMDoc

and see from this process that the

OpenMath

content dictionary format is (isomorphic to) a subset of the

OMDoc

format. In fact, the

OpenMath

2 standard only presents the content dictionary format used here as one of many encodings and specifies abstract conditions on content dictionaries that the

OMDoc

encoding below also meets. Thus

OMDoc

is a valid content dictionary encoding.