% $OpenXM: OpenXM/doc/issac2000/design-outline.tex,v 1.7 2000/01/15 03:23:59 takayama Exp $ \section{Design Outline} As Schefstr\"om clarified in \cite{schefstrom}, integration of tools and softwares has three dimensions: data, control, and user interface. Data integration concerns with the exchange of data between different softwares or same softwares. OpenMath \cite{OpenMath} and MP (Multi Protocol) \cite{GKW} are, for example, general purpose mathematical data protocols. They provide standard ways to express mathematical objects. For example, \begin{verbatim} 123 \end{verbatim} means the (OpenMath) integer $123$ in OpenMath/XML expression. Control integration concerns with the establishment and management of inter-software communications. Control involves, for example, a way to ask computations to other processes and a method to interrupt computations on servers from a client. RPC, HTTP, MPI, PVM are regarded as a general purpose control protocols or infrastructures. MCP (Mathematical Communication Protocol) by Wang \cite{iamc} is such a protocol specialized to mathematics. Although, data and control are orthogonal to each other, real world requires both. NetSolve \cite{netsolve}, OpenMath$+$MCP, MP$+$MCP \cite{iamc}, and MathLink \cite{mathlink} provide both data and control integration. Each integration method has their own features due to their own design goals and design motivations. OpenXM (Open message eXchange protocol for Mathematics) is a project aiming to integrate data, control and user interfaces with its own set of design goals. To explain our design outline, we start with a list of our motivations. \begin{enumerate} \item Noro has developed a general purpose computer algebra system Risa/Asir \cite{asir}. An interface for interactive distributed computations was introduced in Risa/Asir version 950831 released in 1995. The model of computation was RPC (remote procedure call) and it had its own serialization. A robust interruption method was provided by having two communication channels like ftp. As an application of this robust and the interactive distributed computation system, speed-up was achieved for a huge Gr\"obner basis computation to determine all odd order replicable functions by Noro and McKay \cite{noro-mckay}. However, the protocol was closed in Asir and we thought that we should design an open protocol. \item Takayama has developed a special purpose computer algebra system Kan/sm1 \cite{kan}, which is a Gr\"obner engine for the ring of differential operators $D$. In order to implement algorithms in D-modules due to Oaku (see, e.g., \cite{sst-book}), factorizations and primary ideal decompositions were necessary. Kan/sm1 does not have an implementation for these and called Risa/Asir as a C library or a UNIX external program. This approach was not satisfactory. Especially, we could not write a clean interface code between these two systems. We thought that it is necessary to provide a data and control protocol for Risa/Asir to work as a server of factorization and primary ideal decomposition. \item The number of mathematical softwares is increasing rapidly in the last decade of the 20th century. These are usually ``expert'' systems in one area of mathematics such as ideals, groups, numbers, polytopes, and so on. They have their own interfaces and data formats. Interfaces are sometimes specialized to a specific field of mathematics or poor. It is fine for intensive and serious users of these systems. However, for users who want to explore a new area of mathematics with these softwares or users who need these systems only occasionally, a unified system will be more convenient. \item We believe that an open integrated system is a future of mathematical softwares. However, it might be just a dream without realizability. We want to build a prototype system of such an open system by using existing standards, technologies and several mathematical softwares. We want to see how far we can go with this approach. \end{enumerate} Motivated with these, we started the OpenXM project with the following fundamental architecture. \begin{enumerate} \item Communication is an exchange of messages. The messages are classified into three types: DATA, COMMAND, and others. The messages are called OX (OpenXM) messages. Mathematical data are wrapped with {\it OX messages}. We use standards of mathematical data formats such as OpenMath and MP and our own data format ({\it CMO --- Common Mathematical Object format}) as data expressions. \item Servers, which provide services to other processes, are stack machines. The stack machine is called the {\it OX stack machine}. Existing mathematical softwares are wrapped with this stack machine. Minimal requirements for a target software wrapped with the OX stack machine are as follows: \begin{enumerate} \item The target must have a serialized interface such as a character based interface. \item An output of the target must be understandable for computer programs; it should follow a grammar that can be parsed with other softwares. \end{enumerate} \item Any server may have a hybrid interface; it may accept and execute its original command sequences. For example, if we send the following string to ox\_asir server {\footnotesize \begin{verbatim} " fctr(x^10-y^10); " \end{verbatim} } and call the stanck machine command SM\_executeStringByLocalParser, then the server executes the asir command \verb+ fctr(x^10-y^10); + (factorize $x^10-y^10$ over ${\bf Q}$) and push the result on the stack. \end{enumerate} We are implementing a package, OpenXM package. It is based on above fundamental architecture. For example, the following is a command sequence to ask $1+1$ from the Asir client to the OX sm1 server: \begin{verbatim} P = sm1_start(); ox_push_cmo(P,1); ox_push_cmo(P,1); ox_execute_string(P,"add"); ox_pop_cmo(P); \end{verbatim} The current system, OpenXM on TCP/IP, uses client-server model and the TCP/IP is used for interprocess communications. The OpenXM on MPI \cite{MPI} is currently running on Risa/Asir as we will see in Section \ref{section:homog}. However, we focus only on the system based on TCP/IP in this paper.