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+Network Working Group                                         A. Bhushan
+Request for Comments: 578                                        N. Ryan
+NIC: 19501                                                 MIT-PTD (DMS)
+                                                            October 1973
+
+
+             USING MIT-MATHLAB MACSYMA FROM MIT-DMS MUDDLE
+              An Experiment in Automated Resource Sharing
+
+I.  INTRODUCTION
+
+   This paper describes an experiment in non-trivial automated resource
+   sharing between dissimilar systems.  The goal of the experiment was
+   to interface the MUDDLE system at MIT-DMS (Host 70.) to the MACSYMA
+   system at MIT-Mathlab (Host 198.), in such a manner that the MUDDLE-
+   user at MIT-DMS is not required to know anything about the ARPANET,
+   Mathlab, or even MACSYMA.  In fact, the user need not be aware that
+   part of the computation is performed by MACSYMA on the Mathlab
+   computer.
+
+   This experiment differs from the MATHLAB-UCSB/OLS experiment (ref.
+   NWG/RFC 525, NIC 17161 "MIT-MATHLAB Meets UCSB-OLS" by Parrish and
+   Pickens) in several important respects.  First, the use of the remote
+   network resource is *completely automated*.  The human user does
+   nothing more than use a function in MUDDLE such as "INTEGRATE" which
+   requires the remote MACSYMA resource for computation.  The program
+   performs all the required tasks of connecting to Mathlab, log in, and
+   using MACSYMA.  (In the UCSB-OLS experiment, the user had to manually
+   connect to Mathlab, login, use MACSYMA, type the input in a form
+   suitable for MACSYMA, save the results in a file at Mathlab,
+   disconnect from Mathlab, start a retrieval job at UCSB to retrieve
+   the "saved" results, and finally submit the results to a local
+   program.)  Second, the use of the remote resource is *completely
+   integrated* into the local MUDDLE system.  The user can specify the
+   computations in a form that MUDDLE understands.  The resource-sharing
+   program (whose existence the user need not be aware of) does the
+   translation from the MUDDLE "prefix" form to the MACSYMA "infix" form
+   on input, and vice-versa on output.  This ability allows the MACSYMA
+   resources to be completely integrated into MUDDLE to the extent that
+   parts of the same computation can be performed by MACSYMA and others
+   by MUDDLE.
+
+II.  THE MACSYMA AND MUDDLE RESOURCES
+
+   Before proceeding to describe the resource sharing facility a
+   description of the two resources, MACSYMA and MUDDLE, is in order.
+   The MACSYMA system at Mathlab is a powerful resource for symbolic
+   manipulation of algebraic functions.  It can, among other things,
+
+
+
+Bhushan & Ryan                                                  [Page 1]
+
+RFC 578      Using MIT-MATHLAB MACSYMA from MIT-DMS MUDDLE  October 1973
+
+
+   perform symbolic integration and differentiation, expand series,
+   perform Laplace and inverse-Laplace transforms, solve equations and
+   systems of equations, and simplify rational functions.  (A
+   description of MACSYMA's capabilities is given in "The MACSYMA Users'
+   Manual" available from the MIT-Mathlab group at Project MAC.)
+
+   The MUDDLE system provides a general-purpose environment suitable for
+   automatic programming, graphics, data management, "networking", and
+   mathematical computations.  The MUDDLE language represents a powerful
+   extension of the list processing language LISP in the area of data
+   types such as strings, vectors, uniform vectors, and user definable
+   types.  (MUDDLE is described in some detail in "The MUDDLE Primer"
+   (SYS.11.01) by Greg Pfister, available from the Programming
+   Technology Division at Project MAC.)
+
+   MUDDLE has extensive graphical and numerical computation facilities.
+   The user can display graphs on ARDS and IMLAC type consoles, and on
+   the Evans and Sutherland (E&S) display system.  The MUDDLE console
+   graphics provide a facility to view graphical representation of
+   functions with overlay capability and automatic scaling that can be
+   controlled by the user.  The E&S provides the user with a versatile
+   tool for studying the dynamic characteristics of graphs, curved
+   surfaces, and other three-dimensional objects.  The combination of
+   MACSYMA, MUDDLE, and the E&S graphics capabilities represents a very
+   powerful resource for problem solving that is integrated and made
+   easily usable by the resource sharing facility.
+
+III.  THE AUTOMATED RESOURCE-SHARING FACILITY
+
+   The resource-sharing facility described herein uses the most easily
+   accessible communication path to MACSYMA, the TELNET connection to
+   the logger service on socket 1.  No modifications were made to
+   MACSYMA, nor were any special programs created on the Mathlab
+   computer.  The entire task of resource sharing is performed by
+   programs in MUDDLE.  Let us say on the outset that we are not
+   advocating this mode of usage for automated resource sharing.  A
+   resource-sharing protocol that allows convenient use of remote
+   resources via programs is a far more reliable and efficient way, but
+   that requires work on the part of server sites.  The existing
+   protocols and systems FTP, RJE, RSEXEC, and the Datacomputer cater to
+   a limited subset of easily managed resources.  We register here our
+   desire for uniformity (which alas is lacking) in the current systems,
+   and work along the direction of general-purpose resource sharing.  In
+   the absence of a general resource-sharing protocol and a MACSYMA
+   server to go along with it at Mathlab, the TELNET connection is the
+   best a user can do.
+
+
+
+
+
+Bhushan & Ryan                                                  [Page 2]
+
+RFC 578      Using MIT-MATHLAB MACSYMA from MIT-DMS MUDDLE  October 1973
+
+
+   The resource sharing facility comprises of several independent but
+   integrated parts.  These are:
+
+   1) Connecting to Mathlab, login, and invoking MACSYMA.
+   2) Conversion of MUDDLE's prefix to MACSYMA's infix form.
+   3) Generation of MACSYMA input.
+   4) Interpreting MACSYMA's results including errors and comments.
+   5) MACSYMA infix to MUDDLE prefix conversion.
+   6) Plotting graphs for the functions.
+   7) Allowing human intervention if desired.
+   8) Disconnect from MACSYMA.
+
+   The user (assuming that he has loaded the necessary programs in
+   MUDDLE) to integrate the function "3*X" has only to type:
+
+                        <INTEGRATE '<* .X 3>>$
+
+   where '$' represents the ASCII character <ESC> (or <ALT-MODE>).
+   MUDDLE will then return the following result:
+
+                        </ <* 3 <^ .X 2>> 2>
+
+   Alternatively, if the user wishes to use the infix form, he can type:
+
+                        <INTEGRATE "3*X">$
+
+   and the corresponding answer returned by MUDDLE would be
+
+                        "3*X^2/2"
+
+   The following sequence of events takes place when integrate (or any
+   other function that uses MACSYMA) is used.  If the user isn't already
+   communicating with a MACSYMA (the program keeps track of the
+   connection), a connection is established to MIT-Mathlab, the user is
+   logged in (automatically by program, using the user's
+   identification), and a MACSYMA is initiated.  A prefix to infix
+   conversion is performed and the following input is sent to MACSYMA
+   (using the above example):
+
+                        STRING (INTEGRATE (3*X,X));
+
+   The program then interprets MACSYMA's output recognizing error
+   responses and comments and extracts the result if no error is
+   encountered.  The result which is in infix form is then converted to
+   the prefix form which is returned by the MUDDLE function INTEGRATE.
+
+
+
+
+
+
+Bhushan & Ryan                                                  [Page 3]
+
+RFC 578      Using MIT-MATHLAB MACSYMA from MIT-DMS MUDDLE  October 1973
+
+
+   The INTEGRATE function takes an optional argument, the variable with
+   respect to which the integration is be performed.  The syntax for the
+   function is:
+
+                        <INTEGRATE {EXPR} ["{VAR}"]>
+
+   where EXPR is any expression of the type STRING or QUOTED FORM.  The
+   optional argument (in square brackets) VAR must be of the type STRING
+   (enclosed by double-quotes).  The syntax of other functions is:
+
+                                 <SIMPLIFY {EXPR}>
+                         <DIFF {EXPR} ["{VAR}" "{TIMES}"]>
+                    <EXPAND {EXPR} ["{MAXPOSEX}" "{MAXNEGEX}"]>
+
+   where TIMES is the number of times the EXPR is to be differentiated
+   and MAXPOSEX and MAXNEGEX control the maximum positive and negative
+   integer exponent to be used in expansion.  The default value for VAR
+   is "X", for times is "1", and for MAXPOSEX and MAXNEGEX is "6" each.
+
+   The user can use the result returned by MUDDLE in any of his
+   computations, including drawing a graph.  For example, typing:
+
+                        <GRAPH <DIFF '<^ X. 3>> X -5 5>$
+
+   to MUDDLE will draw the graph "Y = 3*X^2" on the IMLAC or ARDS screen
+   with values of X from -5 to +5 (assuming the user has the graphics
+   package and the right IMLAC program loaded).  The same graph would be
+   drawn if the user typed:
+
+                        <GRAPH <IPARSE <DIFF "X^3">> X -5 5>$
+
+   where IPARSE is the MUDDLE function that converts infix to prefix
+   form.  The corresponding function for prefix to infix conversion is
+   UNIPARSE.
+
+   The details of using the MACSYMA resource sharing facility may be
+   gathered from the annotated script of the example given in Section V
+   of this paper.
+
+IV.  CAPABILITIES AND LIMITATIONS
+
+   The program tries to be helpful to the user as much as possible.  For
+   example, if for some reason the MIT-Mathlab computer is not
+   available, the MACSYMA service at the MIT-AI computer is procured.
+
+   It should be mentioned that though the program is fairly capable in
+   retrieving results, recognizing error messages, and separating
+   comments, its recognition is not fool-proof.  The program only makes
+
+
+
+Bhushan & Ryan                                                  [Page 4]
+
+RFC 578      Using MIT-MATHLAB MACSYMA from MIT-DMS MUDDLE  October 1973
+
+
+   an educated guess as to where the answer lies: it is not as clever as
+   a human user sitting at a console, who can filter out such messages
+   as "System going down" and communication from another user (console-
+   link) if they were to appear in the middle of the result.  This
+   points to one of the pitfalls of using a facility via a program that
+   is basically designed for use by human users.
+
+   The program reliability can be marginally improved by asking MACSYMA
+   to print special characters before and after the results it sends
+   (but again this is not fool-proof).  For example, the following input
+   to MACSYMA:
+
+           Block ([ans],
+           print (/(),
+           ans: diff (X^2,X),
+           print (string (ans))
+           print (/)),
+           return (ans));
+
+   will cause MACSYMA to generate the following output:
+
+           (
+           2*X
+           )
+           (D**)           2X
+
+   From the above output, the answer "2*X" can be easily extracted.
+
+   The resource sharing program does however recognize the so-called
+   "unintegratable" functions such as "EXP (X^2)" -- and gives the
+   correct error response.  Normally, the user is in "TERSE" mode, and
+   does not see the interaction between MACSYMA and MUDDLE.  To see the
+   interaction the user must enter "VERBOSE" mode by typing:
+
+                        <VERBOSE>$
+
+   to MUDDLE.  To return to "TERSE" mode the user types:
+
+                        <TERSE>$
+
+   The user can also, if he is proficient in use of MACSYMA, communicate
+   directly with MACSYMA at any point by typing:
+
+                        <TELCOM 1>$
+
+
+
+
+
+
+
+Bhushan & Ryan                                                  [Page 5]
+
+RFC 578      Using MIT-MATHLAB MACSYMA from MIT-DMS MUDDLE  October 1973
+
+
+   to MUDDLE.  The TELCOM feature may be useful if the user wishes to
+   see what is going on, or wants to examine the MACSYMA computations by
+   entering the LISP environment (typing <Control-G> to MACSYMA).  To
+   return to MUDDLE and the automated environment, the user first
+   escapes to MUDDLE by typing <Control-E>, and then types:
+
+                        <AUTO>$
+
+   to MUDDLE.  If the user types "<ERRET 1>$" after escaping to MUDDLE
+   from "TELCOM" mode, he will be returned in direct communication with
+   MACSYMA.  If the user discovers that his "MACSYMA" is hopelessly
+   confused or if he wishes to start a new version of MACSYMA, he must
+   type:
+
+                        <DIS>$
+
+   to MUDDLE, which will disconnect him.  Typing "<MACSYMA>$" or using
+   any of the functions that use MACSYMA will connect him to MACSYMA
+   again.
+
+   Currently, MUDDLE recognizes and takes action as described above
+   whenever differentiate, integrate, expand, simplify, and
+   integrate.simplify (integrate and simplify) functions are
+   encountered.  But it is quite easy to generate programs for other
+   operations such as Laplace transforms and solving equations.  The
+   prefix-to-infix conversion and vice-versa works for all mathematical
+   forms we have encountered so far in our short experiment.
+
+   An alternate way to utilize MACSYMA's capabilities would have been to
+   use it in the LISP environment by constructing a suitable interface
+   between LISP and MUDDLE.  Such an approach would avoid the multiple
+   conversions from prefix to infix form and vice-versa, but other,
+   perhaps more difficult, conversions would be required.
+
+V.  EXAMPLE
+
+   The following scenario describes the use of the resource-sharing
+   facility.  The facility is accessible in the MUDDLE system at MIT-
+   DMS.  The interaction between MUDDLE and MACSYMA, normally not
+   visible to the user, is also shown here (in VERBOSE mode) so that the
+   reader may gain a better understanding of how the program operates.
+   It should be noted that the graphs will be plotted only if the user
+   has loaded the "graphics package" and is on an IMLAC or ARDS console.
+   We would also like to stress that this scenario is not intended to
+   demonstrate the full capabilities of MACSYMA, or of MUDDLE, but only
+   to illustrate the resource sharing facility.
+
+           SCENARIO FOR USING THE MUDDLE-MACSYMA FACILITY
+
+
+
+Bhushan & Ryan                                                  [Page 6]
+
+RFC 578      Using MIT-MATHLAB MACSYMA from MIT-DMS MUDDLE  October 1973
+
+
+   (In the following scenario, user input is underlined and our comments
+   are preceded with a semicolon.  <CR> represents a carriage return and
+   $ represents <ESC> or alt-mode.  The user is assumed to be logged in
+   at MIT-DMS (Host 70).  Note that the input should be typed exactly as
+   shown, as MUDDLE distinguishes between upper and lower case
+   characters.  Please refer to "THE MUDDLE PRIMER" (SYS.11.01) by Greg
+   Pfister for a description of the MUDDLE system and to "MUDDLE CONSOLE
+   GRAPHICS USER GUIDE" (SYS.11.11) by Neal Ryan for a description of
+   the graphics package.  Both documents are available from the
+   Programming Technology Division at Project MAC.)
+
+[;]MUDDLE<CR>                   ; Get a MUDDLE, ';' is MONIT prompt.
+   ----------
+MUDDLE 42 IN OPERATION.
+LISTENING-AT-LEVEL 1 PROCESS 1
+<FLOAD "MUDDLE;MACSYM">$        ; Load the program from MUDDLE
+------------------------        ; directory.
+/METMUDGIN GOUT
+GIN GOUT                        ; Harmless comments from MUDDLE.
+"DONE"
+<DIFF '<- <* .X <LOG .X>> .X>>$
+-------------------------------
+PLEASE BE PATIENT, MACSYMA LOADING MAY TAKE TIME
+MACSYMA AT MIT-MATHLAB          ; Comments from the program.
+<LOG .X>                        ; The result is a MUDDLE form.
+<INTEGRATE '<LOG .X>>$
+----------------------
+SIN FASL DSK MACSYM BEING LOADED
+LOADING DONE                    ; Comments from MACSYMA.
+SCHATC FASL DSK MACSYM BEING LOADED
+LOADING DONE
+<- <* .X <LOG .X>> .X>          ; The answer again.
+<SET A <INTEGRATE "X/(X^3+1)">>$; The input is in infix form.
+--------------------------------
+"LOG(X^2-X+1)/6+ATAN((2*X-1)/SQRT(3))/SQRT(3)-LOG(X+1)/3"
+                                ; The answer now is in infix form.
+<SET B <DIFF .A>>$
+------------------
+"2/(3*((2*X-1)^2/3+1))+(2*X-1)/(6*(X^2-X+1))-1/(3*(X+1))"
+<SIMPLIFY .B>$
+--------------
+"X/(X^3+1)"                     ; We get back the original expression.
+<EXPAND '<^ <+ .X 2> 5>>$
+-------------------------
+<+ <+ <+ <+ <+ <^ .X 5> <* 10 <^ .X 4>>> <* 40 <^ .X 3>>>
+<* 80 <^ .X 2>>> <* 80 .X>> 32>
+<INTEGRATE '<EXP <^ .X 2>>>$
+----------------------------
+
+
+
+Bhushan & Ryan                                                  [Page 7]
+
+RFC 578      Using MIT-MATHLAB MACSYMA from MIT-DMS MUDDLE  October 1973
+
+
+RISCH FASL DSK MACSYM BEING LOADED
+LOADING DONE
+*ERROR*                         ; Program recognizes that MACSYMA
+CANT-INTEGRATE                  ; couldn't integrate.
+LISTENING-AT-LEVEL 2 PROCESS 1
+<ERRET>$                        ; To get back to level 1.
+--------
+LISTENING-AT-LEVEL 1 PROCESS 1
+<DIS>$          ; We disconnect here to show the verbose mode,
+------          ; the program disconnects automatically on quitting.
+"CONNECTIONS CLOSED NOW"
+<VERBOSE>$
+----------
+"YOU WILL BE ABLE TO OBSERVE MUDDLE-MACSYMA INTERACTION NOW"
+<DIFF '<^ .X 3>>$
+-----------------
+PLEASE BE PATIENT, MACSYMA LOADING MAY TAKE TIME
+MIT MATHLAB PDP-10 STELNT.59
+ML ITS.1. DDT.516.
+10. USERS
+:LOGIN 70GUEST          ; The program uses User's SNAME (GUEST here).
+:MACSYMA
+THIS IS MACSYMA 226
+SEE UPDATE > MACSYM; FOR CHANGES
+FIX 226 DSK MACSYM BEING LOADED
+LOADING DONE
+(C1)
+MACSYMA AT MIT-MATHLAB          ; The program announces MACSYMA,
+ STRING (DIFF ((X^3),X,1));     ; and sends input in infix form.
+(D1)                                   3*X^2
+<* 3 <^ .X 2>>                  ; The output is in MUDDLE prefix form.
+<INTEGRATE '</ .X <+ .X 1>>>$
+-----------------------------
+C2) STRING (INTEGRATE ((X/(X+1)),X));
+SIN FASL DSK MACSYM BEING LOADED
+LOADING DONE
+SCHATC FASL DSK MACSYM BEING LOADED
+LOADING DONE
+(D2)                                 X-LOG(X+1)
+<- .X <LOG <+ .X 1>>>           ; The output again.
+<TERSE>$
+--------
+"OK"                            ; Back in TERSE mode now.
+
+<FLOAD "MUDDLE;UGRF">$          ; To load graphics program
+----------------------
+IMLAC? (ANSWER Y OR N) Y        ; for graphics on an IMLAC.
+                       -
+
+
+
+Bhushan & Ryan                                                  [Page 8]
+
+RFC 578      Using MIT-MATHLAB MACSYMA from MIT-DMS MUDDLE  October 1973
+
+
+"DONE"
+<GRAPH <SLT A '<^ <SIN .X> 2>> X -3 3>$
+---------------------------------------
+        ; To graph function sin(X)^2 (graph 1 on Figure 1).
+<GRAPH  <DIFF .A>>$
+-------------------
+        ; To graph diff of sin(X)^2 (see graph 2, Figure 1).
+<GRAPH <INTEGRATE .A>>$
+-----------------------
+        ; To graph integral of sin(X)^2 (see graph 3, Figure 1).
+<QUIT>$                         ; To quit from program and MUDDLE.
+-------
+KILL
+[;]                     ; semicolon prompt from MONIT.
+
+
+
+
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+Bhushan & Ryan                                                  [Page 9]
+
+RFC 578      Using MIT-MATHLAB MACSYMA from MIT-DMS MUDDLE  October 1973
+
+
+     FIG 1.  GRAPH FOR SIN(X)^2, DIFF(SIN(X)^2), AND INTEGRATE(SIN(X)^2)
+
+
+                                --+--2.0
+                                  |
+                                  |
+                                  |                        +++ (3)
+                                  |                    ++++
+                                  |                  ++
+                                  |                 +
+                                  |               ++
+             ooo   ****         --+--   ooo   ***+
+            o   o**    **         |    o   o**  + **
+           o    *o       *        |   o    *o  +    *
+          o    *          *       |  o    *   +      *
+         o    *   o        *      | o    *   o        *
+             *     o        *     |     *   + o        *
+        o  **                **   |o  **  ++            **
+|         *      |  o          *  |  *  ++     o   |      *   (1)   |
+|-------**-------+-----------+++++o+++++-----------+-------**-------|
+|-4.0            |   o     ++     |             o  |          (2)   |4.0
+                         ++      o|                         o
+                      o +         |              o
+                       o        o |               o        o
+                      +        o  |                       o
+                     +  o     o   |                o     o
+                    +    o   o    |                 o   o
+                   +      ooo   --+-- -1.0           ooo
+                 ++               |
+                +                 |
+              ++                  |
+          ++++                    |
+       +++                        |
+                                  |
+                                  |
+                                --+-- -2.0
+
+
+     [ This RFC was put into machine readable form for entry ]
+      [ into the online RFC archives by Graeme Hewson 3/98 ]
+
+
+
+
+
+
+
+
+
+
+
+Bhushan & Ryan                                                 [Page 10]
+