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1.3     ! takayama    1: % $OpenXM: OpenXM/doc/issac2000/design-outline.tex,v 1.2 2000/01/02 07:32:11 takayama Exp $
1.2       takayama    2:
                      3: \section{Design Outline}
                      4:
                      5: As Schefstr\"om clarified in \cite{schefstrom},
                      6: integration of tools and softwares has three dimensions:
                      7: data, control, and user interface.
                      8:
                      9: Data integration concerns with the exchange of data between different
                     10: softwares or same softwares.
                     11: OpenMath \cite{OpenMath} and MP (Multi Protocol) \cite{GKW} are,
                     12: for example, general purpose mathematical data protocols.
1.3     ! takayama   13: They provide a standard way to express mathematical objects.
1.2       takayama   14: For example,
                     15: \begin{verbatim}
                     16:  <OMOBJ>  <OMI> 123 </OMI> </OMOBJ>
                     17: \end{verbatim}
1.3     ! takayama   18: means the (OpenMath) integer $123$ in OpenMath/XML expression.
1.2       takayama   19:
                     20: Control integration concerns with the establishment and management of
1.3     ! takayama   21: inter-software communications.
1.2       takayama   22: Control involves, for example, a way to ask computation to other processes
1.3     ! takayama   23: and a method to interrupt computations on servers from a client.
1.2       takayama   24: RPC, HTTP, MPI, PVM are regarded as a general purpose control protocols or
1.3     ! takayama   25: infrastructures.
1.2       takayama   26: MCP (Mathematical Communication Protocol)
                     27: by Wang \cite{iamc} is such a protocol specialized to mathematics.
                     28:
                     29: Although, data and control are orthogonal to each other,
                     30: real world requires both.
                     31: NetSolv \cite{netsolve}, OpenMath$+$MCP, MP$+$MCP \cite{iamc},
                     32: and MathLink of Mathematica provide both data and control integration.
                     33: These are currently studied ways of data and control integration.
                     34: Each integration method has their own special features due to their
                     35: own design goals and design motivations.
                     36: OpenXM is a project aiming to integrate data, control and user interfaces
                     37: from a different emphasis of a set of design goals with other projects.
                     38: To explain our design outline, we start with a list of
                     39: our motivations.
                     40: \begin{enumerate}
                     41: \item Noro,  who is one of the authors of OpenXM, has developed a general
                     42: purpose computer algebra system Risa/Asir \cite{asir}.
                     43: A set of functions for interative distributed computations were introduced
1.3     ! takayama   44: in Risa/Asir version 950831 released in 1995.
1.2       takayama   45: The model of computation was RPC (remote procedure call)
                     46: and it had its own serialization method for objects.
                     47: A robust interruption method was provided by having two communication channels
                     48: like ftp, which implements the simple network management protocol.
1.3     ! takayama   49: As an application of this robust and interractive distributed computation
        !            50: system,
1.2       takayama   51: a huge Gr\"obner basis was computed
                     52: to determine all replicable functions by Noro and McKay \cite{noro-mckay}.
                     53: However, the protocol was closed in asir and we thought that we should
                     54: design an open protocol.
                     55: \item Takayama, who is also one of the authors of OpenXM, has developed
                     56: a special purpose computer algebra system Kan/sm1 \cite{kan},
1.3     ! takayama   57: which is a Gr\"obner engine for the ring of differential operators $D$ and
1.2       takayama   58: a package for computational algebraic geometry via D-module computations.
                     59: In order to implement algorithms in D-modules due to Oaku
                     60: (see, e.g., \cite{sst-book}),
                     61: factorizations and primary ideal decompositions were necessary.
1.3     ! takayama   62: Kan/sm1 does not have an implementation for these and called
1.2       takayama   63: Risa/asir as a C library or a unix external program.
                     64: This approach was not satisfactory.
                     65: Especially, we could not write a clean interface code between these
                     66: two systems.
                     67: We thought that it is necessary to provide a data and control protocol
                     68: for Risa/asir to work as a server of factorization and primary ideal
                     69: decomposition.
                     70: \item The number of mathematical softwares is increasing rapidly in the last
1.3     ! takayama   71: decade of the 20th century.
1.2       takayama   72: These are usually ``expert'' systems for one area of mathematics
                     73: such as ideals, groups, numbers, polytopes, and so on.
1.3     ! takayama   74: They have their own interfaces and data formats.
        !            75: Interfaces are usually specialied to a specific field of mathematics
1.2       takayama   76: or poor because developers do not have time for designing user interface
                     77: languages.
                     78: It is fine for intensive and serious users of these systems.
                     79: %% x2 stands for x^2, specialized for polynomial ring.
                     80: However, for users who want to explore a new area of mathematics with these
1.3     ! takayama   81: softwares or users who need these systems only occasionally,
1.2       takayama   82: a unified system will be more convinient.
                     83: For example, if we can call and use mathematical softwares
                     84: like CoCoa, GAP, Macaulay2, Porta, Singular, Snapea, $\ldots$
                     85: from Asir, Axion, Maple, muPAD, Mathematica, and so on,
                     86: it will be wonderful in research and education
                     87: of mathematics. This is an unification of user interfaces of mathematical
                     88: softwares.
                     89: \item  We believe that open integrated systems is a future of mathematical
                     90: softwares.
1.3     ! takayama   91: However, it might be just a dream without realizability.
1.2       takayama   92: We wanted to build a prototype system of such an open system by using
                     93: existing standards, technologies and several mathematical softwares.
                     94: We want to see how far we can go with this approach.
                     95: \end{enumerate}
                     96:
                     97: Motivated with these, we started the OpenXM project with the following
                     98: fundamental architecture.
                     99: \begin{enumerate}
                    100: \item Communication is an exchange of messages. The messages are classifed into
                    101: three types:
                    102: DATA, COMMAND, and others.
                    103: The messages are called OX (OpenXM) messages.
1.3     ! takayama  104: Mathematical data are wrapped with {\it OX messages}.
        !           105: We use standards of mathematical data formats such as OpenMath and MP
        !           106: and our own data format ({\it CMO --- Common Mathematical Object format})
1.2       takayama  107: as data expressions.
                    108: \item Servers, which provide services to other processes, are stackmachines.
                    109: The stackmachine is called the
1.3     ! takayama  110: {\it OX stackmachine}.
1.2       takayama  111: Existing mathematical softwares are wrapped with this stackmachine.
1.3     ! takayama  112: Minimal requirements for a target software wrapped with the OX stackmachine
1.2       takayama  113: are as follows:
                    114: \begin{enumerate}
                    115: \item The target must have a seriealized interface such as a character based
                    116: interface.
1.3     ! takayama  117: \item An output of the target must be understandable for computer programs;
        !           118: it should follow a grammer that can be parsed with other softwares.
1.2       takayama  119: \end{enumerate}
                    120: \end{enumerate}
1.3     ! takayama  121: We are implementing a package, OpenXM package,
        !           122: which aims to realize our wishes stated as motivations.
1.2       takayama  123: It is based on above fundamental architecture.
                    124: For example, the following is a command sequence to ask $1+1$ from
                    125: the asir client to the OX sm1 server:
                    126: \begin{verbatim}
                    127:   P = sm1_start();
                    128:   ox_push_cmo(P,1); ox_push_cmo(P,1);
                    129:   ox_execute_string(P,"add"); ox_pop_cmo(P);
                    130: \end{verbatim}
                    131: The current system, OpenXM on TCP/IP,
1.3     ! takayama  132: uses client-server model and the TCP/IP is used for interprocess
1.2       takayama  133: communications.
1.3     ! takayama  134: A prototype OpenXM system on MPI \cite{MPI} already exists for Risa/asir and
        !           135: a general OpenXM on MPI is a work in progress.
        !           136: However, we focus only on the system based on TCP/IP in this paper.
1.2       takayama  137:
                    138:
1.1       takayama  139: