# Design Thoughts on Semantic Latex (SELATEX)

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## Design Thoughts on Semantic Latex (SELATEX)

 Fateman [0] raised a set of issues with the OpenMathapproach. We are not trying to be cross-platform in thiseffort. Axiom does provide an algebraic scaffold so it ispossible that the selatex markup might be useful elsewherebut that is not a design criterion.Fateman[1] also raises some difficult cross-platform issuesthat are not part of this design.Fateman[2] shows that parsing tex with only syntactic markupsucceeded on only 43% of 10740 inputs. It ought to be posibleto increase this percentage given proper semantic markup.(Perhaps there should be a competition similar to the deeplearning groups? PhDs have been awarded on incrementalimprovements of the percentage)This is a design-by-crawl approach to the semantic markupidea. The hope is to get something running this week that'works' but giving due consideration to global and long-termissues. A first glance at CRC/NIST raises more questionsthan answers as is usual with any research.It IS a design goal to support a Computer Algebra Test Suite(http://axiom-developer.org/axiom-website/CATS). It is verytedious to hand construct test suites. It will be even moretedious to construct them "second-level" by doing semanticmarkup and then trying to use them as input, but the hope isthat eventually the CRC/NIST/G&R, etc will eventually bepublished with semantics so computational mathematics canstop working from syntax.===========Consideration 4: I/O transparency Assume for the moment that we take a latex file containingonly formulas. We would like to be able to read this file so it has computational mathematics (CM) semantics.It is clear that there needs to be semantic tags that carry theinformation but these tags have to be carefully designed NOTto change the syntactic display. They may, as noted before,require multiple semantic versions for a single syntax.It is also clear that we would like to be able to output formulaswith CM semantics where currently we only output syntax.===========Consideration 5: I/O isomorphismAn important property of selatex is an isomorphism withinput/output. Axiom allows output forms to be defined for avariety of targets so this does not seem to be a problem. Forinput, however, this means that the reader has to know howto expand \INT{3} into the correct domain. This could be donewith a stand-alone pre-processor from selatex->inputform.It should be possible to read-then-write an selatex formula,or write-then-read an selatex formula with identical semantics.That might not mean that the I/O is identical though due to things like variable ordering, etc. ===========Consideration 6: Latex semantic macrosSemantic markup would be greatly simplified if selatex provideda mechanism similar to Axiom's ability to define types "on the fly"using either assignment   TYP:=FRAC(POLY(INT))or macro form   TYP ==> FRAC(POLY(INT))Latex is capable of doing this and selatex should probably includea set of pre-defined common markups, such as  \FRINT ==> \FRAC\INT===========Consideration 7: selatex \begin{semantic} environment?Currently Axiom provides a 'chunk' environment which surroundssource code. The chunks are named so they can be extractedindividually or in groups   \begin{chunk}{a name for the chunk}      anything   \end{chunk}We could provide a similar environment for semantics such as  \begin{semantics}{a name for the block}  \end{semantics}which would provide a way to encapsulate markup and also allowa particular block to be extracted in literate programming style.===========Consideration 8: Latex-time processingAxiom currently creates specific files using \write to createintermediate files (e.g. for tables). This technique can be usedto enhance latex-time debugging (where did it fail?). It can be used to create Axiom files which pre-construct domains needed when the input file with semantic markup is read.This would help a stand-alone selatex->inputform preprocessor.===========Consideration 9: Design sketchesIt is all well-and-good to hand-wave at this idea but a largeamount of this machinery already exists. It would seem useful to develop an incremental test suite thatstarts with "primitive" domains (e.g. INT), creating selatex I/O.Once these are in place we could work on "type tower" markupsuch as \FRAC\INT or \POLY\COMPLEX\FLOAT.Following that might be pre-existing latex functions like \int, \sum,\cos, etc. To validate these ideas Axiom will include an selatex.sty file andsome unit tests files on primitive domain markup. That should be enough to start the bikeshed discussions.Ideas? Considerations? Suggestions?Tim[0] Fateman, Richard J."A Critique of OpenMath and Thoughts onEncoding Mathematics, January, 2001"https://people.eecs.berkeley.edu/~fateman/papers/openmathcrit.pdf[1] Fateman, Richard J."Verbs, Nouns, and Computer Algebra, or What's Grammar Got todo with Math? ", December 18, 2008https://people.eecs.berkeley.edu/~fateman/papers/nounverbmac.pdf[2] Fateman, Richard J."Parsing TeX into Mathematics",https://people.eecs.berkeley.edu/~fateman/papers/parsing_tex.pdf _______________________________________________ Axiom-developer mailing list [hidden email] https://lists.nongnu.org/mailman/listinfo/axiom-developer
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## Re: Design Thoughts on Semantic Latex (SELATEX)

 I agree that this is doable and would be useful; but I would include a built-in (or separate) lint that gives a context for troubleshooting when the 57% (or whatever) occurs.  Ray On 08/18/2016 02:45 PM, Tim Daly wrote: Fateman [0] raised a set of issues with the OpenMath approach. We are not trying to be cross-platform in this effort. Axiom does provide an algebraic scaffold so it is possible that the selatex markup might be useful elsewhere but that is not a design criterion. Fateman[1] also raises some difficult cross-platform issues that are not part of this design. Fateman[2] shows that parsing tex with only syntactic markup succeeded on only 43% of 10740 inputs. It ought to be posible to increase this percentage given proper semantic markup. (Perhaps there should be a competition similar to the deep learning groups? PhDs have been awarded on incremental improvements of the percentage) This is a design-by-crawl approach to the semantic markup idea. The hope is to get something running this week that 'works' but giving due consideration to global and long-term issues. A first glance at CRC/NIST raises more questions than answers as is usual with any research. It IS a design goal to support a Computer Algebra Test Suite (http://axiom-developer.org/axiom-website/CATS). It is very tedious to hand construct test suites. It will be even more tedious to construct them "second-level" by doing semantic markup and then trying to use them as input, but the hope is that eventually the CRC/NIST/G&R, etc will eventually be published with semantics so computational mathematics can stop working from syntax. =========== Consideration 4: I/O transparency Assume for the moment that we take a latex file containing only formulas. We would like to be able to read this file so it has computational mathematics (CM) semantics. It is clear that there needs to be semantic tags that carry the information but these tags have to be carefully designed NOT to change the syntactic display. They may, as noted before, require multiple semantic versions for a single syntax. It is also clear that we would like to be able to output formulas with CM semantics where currently we only output syntax. =========== Consideration 5: I/O isomorphism An important property of selatex is an isomorphism with input/output. Axiom allows output forms to be defined for a variety of targets so this does not seem to be a problem. For input, however, this means that the reader has to know how to expand \INT{3} into the correct domain. This could be done with a stand-alone pre-processor from selatex->inputform. It should be possible to read-then-write an selatex formula, or write-then-read an selatex formula with identical semantics. That might not mean that the I/O is identical though due to things like variable ordering, etc. =========== Consideration 6: Latex semantic macros Semantic markup would be greatly simplified if selatex provided a mechanism similar to Axiom's ability to define types "on the fly" using either assignment    TYP:=FRAC(POLY(INT)) or macro form    TYP ==> FRAC(POLY(INT)) Latex is capable of doing this and selatex should probably include a set of pre-defined common markups, such as   \FRINT ==> \FRAC\INT =========== Consideration 7: selatex \begin{semantic} environment? Currently Axiom provides a 'chunk' environment which surrounds source code. The chunks are named so they can be extracted individually or in groups    \begin{chunk}{a name for the chunk}       anything    \end{chunk} We could provide a similar environment for semantics such as   \begin{semantics}{a name for the block}   \end{semantics} which would provide a way to encapsulate markup and also allow a particular block to be extracted in literate programming style. =========== Consideration 8: Latex-time processing Axiom currently creates specific files using \write to create intermediate files (e.g. for tables). This technique can be used to enhance latex-time debugging (where did it fail?). It can be used to create Axiom files which pre-construct domains needed when the input file with semantic markup is read. This would help a stand-alone selatex->inputform preprocessor. =========== Consideration 9: Design sketches It is all well-and-good to hand-wave at this idea but a large amount of this machinery already exists. It would seem useful to develop an incremental test suite that starts with "primitive" domains (e.g. INT), creating selatex I/O. Once these are in place we could work on "type tower" markup such as \FRAC\INT or \POLY\COMPLEX\FLOAT. Following that might be pre-existing latex functions like \int, \sum, \cos, etc. To validate these ideas Axiom will include an selatex.sty file and some unit tests files on primitive domain markup. That should be enough to start the bikeshed discussions. Ideas? Considerations? Suggestions? Tim [0] Fateman, Richard J. "A Critique of OpenMath and Thoughts on Encoding Mathematics, January, 2001" https://people.eecs.berkeley.edu/~fateman/papers/openmathcrit.pdf [1] Fateman, Richard J. "Verbs, Nouns, and Computer Algebra, or What's Grammar Got to do with Math? ", December 18, 2008 https://people.eecs.berkeley.edu/~fateman/papers/nounverbmac.pdf [2] Fateman, Richard J. "Parsing TeX into Mathematics", https://people.eecs.berkeley.edu/~fateman/papers/parsing_tex.pdf _______________________________________________ Axiom-developer mailing list [hidden email] https://lists.nongnu.org/mailman/listinfo/axiom-developer  -- Two views on life: life is an art not to be learned by observation. George Santayana:Interpretations of Poetry and Religion It's kinda nice to participate in your life Raymond Rogers  _______________________________________________ Axiom-developer mailing list [hidden email] https://lists.nongnu.org/mailman/listinfo/axiom-developer
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## Re: Design Thoughts on Semantic Latex (SELATEX)

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## Re: Design Thoughts on Semantic Latex (SELATEX)

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