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Re: Again : Is there a BNF for Mathematica?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg119811] Re: Again : Is there a BNF for Mathematica?
  • From: Richard Fateman <fateman at cs.berkeley.edu>
  • Date: Thu, 23 Jun 2011 07:26:28 -0400 (EDT)
  • References: <irijpq$qf8$1@smc.vnet.net> <itsjm8$8tl$1@smc.vnet.net>

On 6/22/2011 4:29 AM, Szabolcs Horv=E1t wrote:
> If you are looking to implement a Mathematica parser yourself, you might
> want to look at some earlier efforts first:
>
> http://omath.org/w/index.php?title=Main_Page#Developers
> http://stackoverflow.com/questions/1608380/parser-for-the-mathematica-syntax
> http://www.mathics.org/
>
> These pages contain links to several other projects (most dead by now).

I think you may miss the point :)   People who want to write a parser
for Mathematica typically want to write a parser WITHOUT REGARD TO THE
FACT THAT IT HAS ALREADY BEEN DONE.

That is, they subscribe to the belief that two weeks spent writing and
debugging can save five minutes searching on the web. maybe to learn??

And that only their own entirely pre-conceived version of the program in
their own precise framework (Java, C#, Linux, Lisp, Ruby, PHP, ecma, etc
could POSSIBLY be of interest).

A recently revised version of my (Lisp) mathematica parser and evaluator
is in http://www.cs.berkeley.edu/~fateman/lisp/mma4max/.
It was revised in order to read and execute Rubi.  The older and still
working versions 1.6 and 1.7 of mockmma are still around, but the
pattern matcher included there was not as nuanced as required.

If you spend some time writing a parser, you can learn a fair amount,
the first time. This is done by thousands of students in computer
science classes each year.  If you choose to do it on your own, you
should probably choose a language whose syntactic and lexical
description is crystal clear. That excludes Mathematica.

If you intend to write a parser for Mathematica not as a learning
experience, but as a practical tool,   (or as a free alternative to
Mathematica) then it seems to me natural to ask, why?  (I explain why I
wrote MockMMA in a paper published in the SIGSAM Bulletin.  Basically,
people who write Mathematica programs end up having to use some stuff
that I consider broken, like Mathematica arithmetic. Or slow.
Experimenting by using the same "user programs" but different support
might be of interest.  A few experiments by me and by others have used
this code. TILU,  some sourceforge project, some other stuff.)

RJF



>
> On 2011.05.25. 11:57, E. Martin-Serrano wrote:
>> On 2009 Murray Eisenberg posted the article linked below
>>
>>
>>
>> http://forums.wolfram.com/mathgroup/archive/2009/Apr/msg00232.html
>>
>>
>>
>> In which he wrote:
>>
>>
>>
>>>> It's not at all clear to me that a BNF would be of any great
>> use for Mathematica : after all, "everything is an expression" and so if
>> you avoid any of the "special input forms" such as =, :=, /@, {}, =
>> [[]],>>etc., along with prefix, infix, and postfix special forms, then
>> the grammar is utterly simple.
>>
>>
>>
>>>> The complexities arise from (1) Attributes, such as Hold, which do not
>> explicitly appear as part of the syntax one uses in entering expressions
>> but affect the evaluation; and (2) the special input>>forms, where you
>> have to begin worrying about order of precedence.
>>
>>
>>
>> My point now is:
>>
>>
>>
>> Would the Murray's remark be still valid  if  we talk about a
>> BNF grammar whose purpose is to write a parser to make available  just
>> the expressions of the form  ( symbol := expression =E2=94=82 symbol
>> = expression ) after discarding all the stuff on attributes and
>> evaluation order? I am still  concerned, as I posted a year ago o so,
>> with the =E2=80=98data dependency graph=E2=80=99  or =E2=80=98what we
>> could call  =E2=80=98data dependency part of the parsing tree==
E2=80=99.
>>
>>
>>
>> The underlying idea is to extract all the assignments (left and right
>> sides)  in the code preventing the evaluation of the right hand sides.
>> Wrapping the right hand sides in assignments  with
>> =E2=80=98hold=E2=80=99  is unacceptable for my purpose and=
 need.
>>
>>
>>
>> Counting on a BNF (affix)  Grammar, a simple way to extract the data
>> dependency tree/graph would go like this:
>>
>>
>>
>> 1)      Save in plain text format the piece of code (in a notebook) th=
at
>> one needs to parse (all hidden code corresponding to the notebook
>> interface would be dropped).
>>
>>
>>
>> 2)      Perform a first parsing step to drop all the elements mentione=
d
>> or referenced by Murray (Hold and controls of order evaluation), leavi=
ng
>> only the code corresponding to assignments and function definitions.
>>
>>
>>
>> 3)      Perform a second parsing step on the plain text obtained in th=
e
>> previous step, which will produce a set of assignments regardless they
>> are delayed assignments or not.
>>
>>
>>
>> Maybe my ideas were clearer if I compare the above procedure with
>> another, perhaps equivalent (?), method;  consisting in performing a
>> separate (or concurrent) recursive descendent parsing on  all
>> {DownValues, UpValues, OwnValues} for the symbols  in the piece of cod=
e
>> we are interested in. In which case, the parsing trees got in each
>> separate step  {DownValues, UpValues, OwnValues} will defined some val=
id
>> form of data dependency graph for the whole piece of code.
>>
>>
>>
>> Then, with, say, Combinatorica, we would be able to explore and find
>> important properties of the parsed code, easing up the task of: 1)
>> Speeding up complex and tricky dynamic programs,  2) rewriting program=
s
>> written in older (sometimes very old) Mathematica versions, and, 3) no
>> less important, writing the final version of experimental programs
>> written incrementally,  with step by step incremented  functionality,
>> which typically result in something nearly unreadable.
>>
>>
>
>



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