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1.3     ! takayama    1: % $OpenXM: OpenXM/doc/ascm2001p/design-outline.tex,v 1.2 2001/06/20 02:09:45 takayama Exp $
1.1       noro        2:
                      3: \section{Design Outline and OpenXM Request for Comments (OpenXM-RFC)}
                      4:
1.3     ! takayama    5: As Schefstr\"om\cite{schefstrom}, clarified,
1.1       noro        6: integration of tools and software has three dimensions:
                      7: data, control, and user interface.
                      8:
                      9: Data integration concerns with the exchange of data between different
                     10: software or same software.
                     11: OpenMath \cite{OpenMath} and MP (Multi Protocol) \cite{GKW} are,
                     12: for example, general purpose mathematical data protocols.
                     13: They provide standard ways to express mathematical objects.
1.3     ! takayama   14: %For example,
        !            15: %\begin{verbatim}
        !            16: % <OMOBJ>  <OMI> 123 </OMI> </OMOBJ>
        !            17: %\end{verbatim}
        !            18: %means the (OpenMath) integer $123$ in OpenMath/XML expression.
1.1       noro       19:
                     20: Control integration concerns with the establishment and management of
                     21: inter-software communications.
                     22: Control involves, for example, a way to ask computations to other processes
                     23: and a method to interrupt computations on servers from a client.
                     24: RPC, HTTP, MPI, PVM are regarded as a general purpose control protocols or
                     25: infrastructures.
                     26: MCP (Mathematical Communication Protocol)
1.2       takayama   27: by Wang \cite{iamc} and OMEI \cite{omei} are such protocols for mathematics.
1.1       noro       28:
                     29: Although data and control are orthogonal to each other,
                     30: real world requires both.
                     31: NetSolve \cite{netsolve}, OpenMath$+$MCP, MP$+$MCP \cite{iamc},
                     32: and MathLink \cite{mathlink} provide both data and control integration.
                     33: Each integration method has their own features determined by their
                     34: own design goals.
                     35: OpenXM (Open message eXchange protocol for Mathematics)
                     36: is a project aiming to integrate data, control and user interfaces
1.3     ! takayama   37: started by Noro and Takayama.
        !            38:
        !            39: Noro has been involved in the development of
1.1       noro       40: a computer algebra system Risa/Asir \cite{asir}.
                     41: An interface for interactive distributed computations was introduced
1.3     ! takayama   42: to Risa/Asir in 1995.
        !            43: The model of computation was RPC.
1.1       noro       44: A robust interruption protocol was provided
1.3     ! takayama   45: by  two communication channels like ftp.
1.1       noro       46: As an application of this protocol,
                     47: a parallel speed-up was achieved for a Gr\"obner basis computation
                     48: to determine all odd order replicable functions
                     49: (Noro and McKay \cite{noro-mckay}).
1.3     ! takayama   50: Takayama has developed
1.1       noro       51: a special purpose system Kan/sm1 \cite{kan},
1.3     ! takayama   52: which is a Gr\"obner engine for the ring of differential operators $D$
        !            53: and designed as a component of a larger system.
1.1       noro       54:
1.3     ! takayama   55: Noro and Takayama firstly tried to integrate these existing two
        !            56: software systems.
        !            57: We believe that an open integrated system is a future of mathematical
1.1       noro       58: software.
1.3     ! takayama   59: However, we found that it might be just a dream without realizability
        !            60: and that it is an important research subject to
        !            61: build a prototype of such an integrated system. % Project X
1.1       noro       62:
1.3     ! takayama   63: We started the OpenXM project with the following
1.1       noro       64: fundamental architecture, which is currently described in
                     65: OpenXM-RFC 100  proposed standard %% ``draft standard'' and ``standard''
1.3     ! takayama   66: \cite{ox-rfc-100}.
1.1       noro       67: \begin{enumerate}
                     68: \item Communication is an exchange of messages. The messages are classified into
                     69: three types:
                     70: DATA, COMMAND, and SPECIAL.
                     71: They are called OX (OpenXM) messages.
                     72: Among the three types,
                     73: {\it OX data messages} wrap mathematical data.
                     74: We use standards of mathematical data formats such as OpenMath and MP
                     75: as well as our own data format {\it CMO}
                     76: ({\it Common Mathematical Object format}),
                     77: which can be expressed in terms of XML.
                     78: \item Servers, which provide services to other processes, are stack machines.
                     79: The stack machine is called the
                     80: {\it OX stack machine}.
                     81: Existing mathematical software systems are wrapped with this stack machine.
                     82: Minimal requirements for a target software wrapped with the OX stack machine
                     83: are as follows:
                     84: \begin{enumerate}
                     85: \item The target must have a serialized interface such as a character based
                     86: interface.
                     87: \item An output of the target must be understandable for computer programs;
                     88: it should follow a grammar that can be parsed with other software.
                     89: \end{enumerate}
                     90: \item Any server may have a hybrid interface;
                     91: it may accept and execute not only stack machine commands,
                     92: but also its original command sequences.
                     93: For example,
                     94: if we send the following string to the {\tt ox\_asir} server
                     95: (OpenXM server of Risa/Asir) \\
                     96: \verb+        " fctr(x^100-y^100); "      + \\
                     97: and call the stack machine command  \\
                     98: \verb+        SM_executeStringByLocalParser    + \\
                     99: then the server executes the asir command \\
                    100: \verb+ fctr(x^100-y^100); +
                    101: (factorize $x^{100}-y^{100}$ over ${\bf Q}$)
                    102: and pushes the result onto the stack.
                    103: \end{enumerate}
                    104: OpenXM package  implements the OpenXM-RFC 100 \cite{ox-rfc-100}
                    105: and 101 \cite{ox-rfc-101} based on
                    106: the above fundamental architecture.
                    107: In this paper, we discuss mainly on systems implementing
                    108: OpenXM-RFC 100 and 101 on TCP/IP.
                    109: For example, the following is a command sequence to ask $1+1$ from
                    110: the Asir client to the {\tt ox\_sm1} server through TCP/IP:
                    111: \begin{verbatim}
                    112:   P = sm1_start();
                    113:   ox_push_cmo(P,1); ox_push_cmo(P,1);
                    114:   ox_execute_string(P,"add"); ox_pop_cmo(P);
                    115: \end{verbatim}
                    116: Here, {\tt ox\_sm1} is an OpenXM server of Kan/sm1.
                    117:
                    118: Our project of integrating mathematical software
                    119: systems is taking the ``RFC'' approach, which has been
                    120: used to develop internet protocols.
                    121: We think that ``RFC'' approach is an excellent way and
                    122: we hope that other groups, who are working on standard protocols,
                    123: take this ``RFC'' approach, too.
                    124:
                    125: The OpenXM on MPI \cite{MPI} is currently running on Risa/Asir
                    126: as we will see in Section \ref{section:homog}.
                    127: We are now preparing the OpenXM-RFC 102 ``Mathematical communication
                    128: on MPI'' (draft protocol)
                    129: based on our experiments on MPI.
                    130:
                    131: In the rest of the paper, we abbreviate
                    132: OpenXM-RFC 100 and 101 to OpenXM if no confusion arises.
                    133:
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