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1.2     ! noro        1: % $OpenXM: OpenXM/doc/calc2000/openxm-stackmachines.tex,v 1.1.1.1 2000/04/24 04:20:11 noro Exp $
1.1       noro        2:
                      3: \section{OpenXM Stack machines}\label{sec:ox-stackmachines}
                      4:
                      5: In OpenXM specification, all servers are stack machines.
                      6: %These are called OpenXM stack machines.
                      7: When a server ox\_xyz gets an OX data message,
                      8: it translates the data into a local object of ox\_xyz
                      9: and pushes the object onto the stack.
                     10: The translation scheme
                     11: %% together with definitions of mathematical operations
                     12: %% of the system ox\_xyz
                     13: is called the {\it PhraseBook} of ox\_xyz (cf. OpenMath \cite{OpenMath}).
                     14: For example, the Asir command {\tt ox\_push\_cmo(P,1)}
                     15: (push integer $1$ onto the server $P$)
                     16: sends an OX data message
                     17: {\tt (OX\_DATA,(CMO\_ZZ,1))} to the server $P$.
                     18: Here,
                     19: {\tt OX\_DATA} stands for {\tt OX\_DATA} header and
                     20: {\tt (CMO\_ZZ,1)} is a body standing for $1$ expressed
                     21: by the CMO.
                     22: The server translates {\tt (CMO\_ZZ, 1)} to its internal object of
                     23: the integer  $1$
                     24: and pushes the object onto the stack.
                     25:
                     26: If the server gets an {\it OX command} message, then the server
                     27: executes the command.
1.2     ! noro       28: Any OX command message starts with the int32 tag {\tt OX\_COMMAND}.
1.1       noro       29: The body is a stack machine operation code expressed by int32.
                     30: The codes are listed below \cite{noro-takayama}.
                     31: \begin{verbatim}
                     32: SM_popSerializedLocalObject, SM_popCMO, SM_popString,
                     33: SM_mathcap, SM_pops, SM_setName, SM_evalName,
                     34: SM_executeStringByLocalParser, SM_executeFunction,
                     35: SM_beginBlock, SM_endBlock, SM_shutdown, SM_setMathCap,
                     36: SM_executeStringByLocalParserInBatchMode, SM_getsp,
                     37: SM_dupErrors, SM_control_kill, SM_control_to_debug_mode,
                     38: SM_control_exit_debug_mode, SM_control_reset_connection
                     39: \end{verbatim}
                     40:
                     41: OpenXM does not have a standard for mathematical operation sets
                     42: while it is a work in progress in the GAP group \cite{gap}.
                     43: Each OpenXM server has its own set of mathematical operations,
                     44: which are performed as follows.
                     45: First, arguments for a mathematical operation
                     46: and the number of the arguments are pushed.
                     47: Second,
                     48: the mathematical operator name,
                     49: such as {\tt fctr} (the factorization command of Asir),
                     50: is pushed as a string.
                     51: Finally, the stack machine command
                     52: {\tt SM\_executeFunction} (269) evaluates the operator and
                     53: pushes the result onto the stack
                     54: after poping the operator name, the number of arguments
                     55: and arguments.
                     56: For example, the following code factorizes $x^{100}-1$ by calling
                     57: {\tt ox\_asir} from Asir.
                     58: \begin{verbatim}
                     59: P = ox_launch();
                     60: ox_push_cmo(P,x^100-1); ox_push_cmo(P,ntoint32(1));
                     61: ox_push_cmo(P,"fctr");  ox_push_cmd(P,269);
                     62: Ans = ox_pop_cmo(P);
                     63: \end{verbatim}
                     64:
                     65: When an error has occurred on an OpenXM server,
                     66: an error object is pushed onto the stack
                     67: instead of a result of the computation.
                     68: The error object consists of the serial number of the OX message
                     69: which caused the error, and an error message.
                     70: \begin{verbatim}
                     71: [340] P = ox_launch()$
                     72: [341] ox_rpc(P,"fctr",1.2*x)$
                     73: [342] ox_pop_cmo(P);
                     74: error([8,fctr : invalid argument])
                     75: \end{verbatim}
                     76:
                     77: OpenXM server won't send error messages to the client
                     78: except when it receives a {\tt SM\_pop*} command.
                     79: OX stack machines work in the asynchronous mode which is similar
                     80: to X servers.
                     81: For servers of graphic and sound applications,
                     82: it may be an advantageous feature.
                     83: It is also possible to emulate RPC and a web server for MCP \cite{iamc}
                     84: on our asynchronous OX stack machines.
                     85:
                     86:
                     87:
                     88:
                     89: