On Feb 26, 5:37 am, David Kirkby <david.kir...@onetel.net> wrote:
> > I was hoping someone might have done it, [Write a grammar for Mathematica] as the task seems > non-trivial. Did you write one for MockMMA, and if so are you willing > to share it? 1. I (with a student) looked at the task and wrote a partial grammar, but despaired of completing it as we found too many ad hoc patches. Now it may be that someone has devised a complete and accurate grammar, especially one suited to some automated parser generator, e.g. LALR(1) or LL(1) or GLR but we were not clever enough to find a neat one. I believe, and this is a contentious point, it is likely for someone to think he has a complete and accurate grammar, even if it is not complete or accurate. People found errors in my parser (since corrected), after several years. There may still be errors. And now there are deliberate differences because I found more convenient notation, e.g. for comparisons. 2. The material in the file http://www.cs.berkeley.edu/~fateman/lisp/mma4max/parser.lisp is source code for a parser. The parser is a recursive descent parser with programs named in a fairly uniform fashion from which one can generate a grammar. e.g. parse-dot, parse-power, .... But the actions associated with some of these reduction routines are nasty, and in some cases depend critically on material which should have been abstracted out of the grammar into the lexical phase. You (or anyone) is welcome to read up on recursive descent parsing and run the algorithm for generating a R.D. parser in reverse, and generate a grammar. But it won't be complete and accurate because the component subroutines do screwy things, like looking ahead for the occasional odd character, -- not token, but character. Now it may be possible to do all this with a parser; indeed it most assuredly IS possible, but the obvious grammar might be quite huge. A cleverly-encoded grammar might be smaller, but I think it would not be trivial to do that. Among other things it would have to take into account that blank space is sometimes a token, but sometimes not. 3. I am of course perfectly willing to share the code. It has, in fact, even been used in a proposal to the NSF under some small business initiation grant. I had nothing to do with the proposal, and the proposers did not seek my permission (not that they needed it). I'm sure that this discussion of the Mathematica syntax could be placed in a more accessible location, but who knows. Here's a puzzle. a.b.c is parsed as Dot[a,b,c] or in Lisp, (Dot a b c). 1 . 2 . 3 is parsed as Dot[1,2,3], and is displayed by Mathematica as 1.2.3 ... Observe the white-space or the lack of it around the dots. But if you type in 1.2.3 what do you think you get? And what about 1. 2.3 ? For those who do not have Mathematica handy 1.2.3 comes out as 0.36 And if you type it in to WolframAlpha you get 6. If you type it in to MockMMa, you get 6/5.3 (that is, (Dot 6/5 3). Note that 1.2 is converted to 6/5. What do you suppose Ira's parser produces? It is not the first case in which the person who wrote the display for Mathematica gives a result which is apparently at odds with the input syntax. [the C grammar] > I overlooked that. Thank you for the correction. You are welcome. I think the important point I might re-emphasize is this: Parsing Mathematica syntax with a Sage back end does not get you very far. Any non-trivial piece of Mathematica will require a mathematica evaluator with matching, binding of variables, etc. while parsing Sin[x] to get sin(x) is trivial, it is mostly pointless. You might think that converting Integrate[f,x] into integrate(f,x) gets you somewhere, but the accessible syntax for translating f into Sage (or Maxima) consists of +,*,/, [,], and the typical functions like sin, cos, tan. Why would someone write in Mathematica syntax in the first place? Wolfram Alpha seems to not expect Mathematica syntax -- its parser seems to disagree. RJF -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
