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% $OpenXM: OpenXM/doc/issac2000/data-format.tex,v 1.4 2000/01/11 05:35:48 noro Exp $

% $OpenXM: OpenXM/doc/issac2000/data-format.tex,v 1.7 2000/01/15 12:18:42 takayama Exp $

\section{Data Format} (Ohara)

\section{Data Format}

OpenXM admits multiple mathematical encodings such as OpenMath, MP, CMO

(Common Mathematical Object format).

OpenXM itself does not exhibit a bias towards a particular encodings

as a main mathematical data carrier and an OpenXM compliant system do not need to

implement all possible data formats.

A server or a client does not necessarily implement full specifications

However they should at least implement seven primitive

of OpenXM.

data types of the CMO, which are necessary to

However, if a program sends an OX data or an OX command unknown to its peer,

carry several control informations such as a {\it mathcap}.

Mathcap is a list of supported CMO's, OpenXM stack machine codes,

and necessary extra informations.

If a program sends an OX messages unknown to its peer,

an unrecoverable error may occur.

To avoid such a case OpenXM provides a scheme not

By exchanging mathcaps a program knows its peer's capability

to send an OX message unknown to peers.

and such an error can be avoided.

It is realized by exchanging a list of

Mathcap is also defined as a CMO.

supported CMO's, OpenXM stack machine codes, and necessary extra informations.

See \cite{noro-takayama} for the details.

The list is called {\it mathcap}.

% Mathcap is also defined as a CMO and its elements are 32bit integers

% or strings.

Mathcap is also defined as a CMO and the CMO has a structure of a nest

of lists. its leafs of the end are also a CMO which tags with

CMO\_INT32 or CMO\_STRING.

Mathematical encoding types of OX data are distinguished with tags

Encoding types of OX data are distinguished with tags

of OX messages.

For example,

an OX message with the tag

OX\_DATA is followed by a CMO packet.

{\tt OX\_DATA} is followed by a CMO packet.

An OX message with the tag

OX\_DATA\_OPENMATH\_XML is followed by

{\tt OX\_DATA\_OPENMATH\_XML} is followed by

an OpenMath XML string and its length.

an OpenMath XML string.

All OpenXM compliant systems should implement seven primitive data types

of the CMO.

These are used not only to express mathematical objects, but also

indispensable to carry control informations such as mathcap.

CMO is an original mathematical data encoding system of the OpenXM project.

Let us explain the data format of CMO.

Any CMO packet consists of a header and a body.

The size of the header is 4 bytes that tags the data type of the body.

Data type tags are signed 32 bit integers which is called {\sl int32} in this

paper.

Following tags are registered in the OpenXM for now.

Following tags are registered in the OpenXM.

\begin{verbatim}

#define CMO_ERROR2 0x7f000002

#define CMO_NULL 1

Line 66 Following tags are registered in the OpenXM for now.

Line 58 Following tags are registered in the OpenXM for now.

#define CMO_RATIONAL 34

#define CMO_64BIT_MACHINE_DOUBLE 40

#define CMO_ARRAY_OF_64BIT_MACHINE_DOUBLE 41

#define CMO_128BIT_MACHINE_DOUBLE 42

#define CMO_ARRAY_OF_128BIT_MACHINE_DOUBLE 43

#define CMO_BIGFLOAT 50

#define CMO_IEEE_DOUBLE_FLOAT 51

#define CMO_INDETERMINATE 60

#define CMO_TREE 61

#define CMO_LAMBDA 62

\end{verbatim}

The first seven types should be implemented on all OpenXM compliant systems.

The first seven primitive types should be implemented

The format of the first seven CMO's are as follows. \\

on all OpenXM compliant systems.

The formats are as follows. \\

\begin{tabular}{|c|c|}

\hline

{\sl int32} {\tt CMO\_ERROR2} & {\sl CMObject} {\rm ob} \\

Line 118 $\cdots$ & {\sl CMObject} {\rm ob[n-1]} \\

Line 109 $\cdots$ & {\sl CMObject} {\rm ob[n-1]} \\

\cline{1-2}

\end{tabular} \\

A mathematical programmer who wants to implement CMO on a server proceeds

As to the formats of other CMO's, see \cite{noro-takayama}.

When one wants to implement CMO on a server, the person proceeds

as follows.

\begin{enumerate}

\item Look for the CMO list at the web cite \cite{openxm-web}.

If there is a CMO that fits to her or his requirement, then use this CMO.

If there is a CMO that fits to one's requirement, then use this CMO.

\item If there is no suitable CMO, design a new CMO and register

the new CMO to \cite{openxm-web} with a description and examples.

\end{enumerate}

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