2
(Editorial note: The paper was presented using the terminology Semantic dictionaries, but later it was decided by the workshop that the name for these objects should be Content dictionaries. Hence all references to Semantic dictionaries have been updated.)
3
A Content dictionary (CD) should be viewed primarily as a document for humans, even though parts of it will be processed and understood by communicating systems.
GUIDING PRINCIPLES
4
A Content dictionary (CD) contains:5
<CD>
<CD_Name> Basic </CD_Name> 
<CD_URL>http://www.can.nl/OpenMath/Definition/Basic</CD_URL> <CD_Expire> 12/Dec/96 </CD_Expire> <Description> The basic semantic dictionary that every OM compliant implementation should accept. </Description> 
<CD_Definition> <Name> Pi </Name> <Class> Constant </Class> <Type> Pi :: real and Non(rational) and Non(algebraic) </Type> <Description> The mathematical constant Pi, approximately 3.14159 </Description> <CMP> Pi = 3.1415926535897932385, "20digit approximation" </CMP> <CMP> Pi = 4*arctan(1) </CMP> <CMP> Pi = 16*arctan(1/5)4*arctan(1/239), "Machin's formula" </CMP> </CD_Definition> 
<CD_Definition> <Name> + </Name> <Class> Unary_function, Binary_function, Associative, Commutative </Class> <Type> complex+complex :: complex </Type> <Type> real+real :: real </Type> <Type> rational+rational :: rational </Type> <Type> integer+integer :: integer </Type> <Description> The addition operator of any group </Description> <CMP> a+b=b+a, commutativity </CMP> <CMP> a+(b+c)=(a+b)+c, associativity </CMP> <CMP> a+0=0+a=a, identity </CMP> </CD_Definition> 
6
<CD_Definition> <Name> sin </Name> <Class> Unary_function </Class> <Type> sin(real) :: 1..1 </Type> <Description> The circular trigonometric function sine </Description> <Ref> M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, [4.3] </Ref> <CMP> sin(0)=0 </CMP> <CMP> sin(3*x)=4*sin(x)^3+3*sin(x), "triple angle formula", <Ref> ditto, [4.3.27] </Ref> </CMP> </CD_Definition> 
<CMP> sin(x)^2+cos(x)^21=0, "Invariant relation followed by sin and cos", <Ref> M. Abramowitz and I. Stegun, Handbook of Mathematical Functions [4.3.10] </Ref> </CMP> <CMP> sin(Z*Pi)=0, "for any integer Z" </CMP> <CMP> exp(I*Pi) + 1 = 0, "Identity linking I, Pi, 0 and 1", <Ref> ditto, [4.2.26] </CMP> <CMP> sin(2*x) = 2*sin(x)*cos(x), "sine duplicating formula" </CMP> 
</CD>
. . . . <CD_Definition> <Name> sin </Name> <Class> Unary_function </Class> <Replacement_Semantics> Augments </Replacement_Semantics> <Type> sin(complex) :: complex </Type> <Type> sin(symbolic) :: sin(symbolic) </Type> </CD_Definition> . . . . 
712
The transparencies numbered 7 to 12 contain the format definition of the CDs. This is the CD called Meta. Since there has been a lot of activity over this definition, the original ones are no longer interesting.
13
Low Level CDs
Linear Algebra 
Poly nomials 
Special functions 
Power series 
Non commutative  
Inert  
Basic  
Meta^{*} 
14
Other groups have proposed similar layering of dictionaries, see for example the proposal by Roy Pike and his definition of Fields of Mathematics.15


Sept 15, Authors install Basic & Meta CDs as Web pages. Comments and updates follow.
Dec 15, The version at this date is considered the official CD version 1.0.