gmane.comp.web.mathematics

Deadline Extended to 1 June: OpenMath workshop at CICM (11 July, Bremen, Germany)

Christoph LANGE — 2012-05-24T19:34:10

24th OpenMath Workshop
Bremen, Germany
11 July 2012
co-located with CICM 2012
Submission deadline (EXTENDED) 1 June

http://www.informatik.uni-bremen.de/cicm2012/cicm.php?event=openmath

OBJECTIVES

OpenMath (http://www.openmath.org) is a language for exchanging
mathematical formulae across applications (such as computer algebra
systems).  From 2010 its importance has increased in that OpenMath
Content Dictionaries were adopted as a foundation of the MathML 3 W3C
recommendation (http://www.w3.org/TR/MathML), the standard for
mathematical formulae on the Web.

Topics we expect to see at the workshop include

    * Feature Requests (Standard Enhancement Proposals) and Discussions
      for going beyond OpenMath 2;
    * Further convergence of OpenMath and MathML 3;
    * Reasoning with OpenMath;
    * Software using or processing OpenMath;
    * New OpenMath Content Dictionaries;

Contributions can be either full research papers, Standard Enhancement
Proposals, or a description of new Content Dictionaries, particularly
ones that are suggested for formal adoption by the OpenMath Society.

IMPORTANT DATES (all times are "anywhere on earth")

    * 1 June: Submission (EXTENDED)
    * 20 June: Notification of acceptance or rejection
    * 04 July: Final revised papers due
    * 11 July: Workshop

SUBMISSIONS

Submission is via EasyChair
(http://www.easychair.org/conferences?conf=om20120).  Final papers
must conform to the EasyChair LaTeX style.  Initial submissions in
this format are welcome but not mandatory – but they should be in PDF
and within the given limit of pages/words.

Submission categories:

    * Full paper: 5–10 EasyChair pages
    * Short paper: 1–4 EasyChair pages
    * CD description: 1-6 EasyChair pages; a .zip or .tgz file of the
      CDs must be attached, or a link to the CD provided.
    * Standard Enhancement Proposal: 1-10 EasyChair pages (as
      appropriate w.r.t. the background knowledge required); a .zip or
      .tgz file of any related implementation (e.g. a Relax NG schema)
      should be attached.

If not in EasyChair format, 500 words count as one page.

PROCEEDINGS

Electronic proceedings will be published with CEUR-WS.org in time for
the conference.

ORGANISATION COMMITTEE

    * Christoph Lange (University of Bremen and Jacobs University
      Bremen, Germany)
    * James Davenport (University of Bath, UK)

Comments/questions/enquiries: to be sent to om2012-0< at >easychair.org

unitless lengths in mpadded attributes

Karl Tomlinson — 2012-05-21T21:54:03

Can get clarification of these questions in the context of mpadded
attributes, please?

1. Are unitless lengths valid attribute values?
2. Is "0" a special case where no unit is valid?

In the attribute table, the description
'( "+" | "-" )? unsigned-number (("%" pseudo-unit?) | pseudo-unit | unit | namedspace )'
has no "?" following the second set of parentheses, indicating
that there must be something following the unsigned-number.

That seems reasonably clear that the answer to both my questions
is "no", but there are some possible hints elsewhere in the spec
that unitless values might be valid, so I want to check that I am
not missing something.

The default for both lspace and voffset is "0".
I guess it's quite feasible to have a default that is not a string
that can be specified as a valid value, but it feels a little odd.

Would it be clearer to specify the default value as "0em", as it
was in MathML2?

In the text "Each format begins with an unsigned-number, which may
be followed by a % sign (effectively scaling the number) and an
optional pseudo-unit, by a pseudo-unit alone, or by a unit
(excepting %)", would it be clearer to replace "which may be followed" 
with "followed"?

In the text "the resulting length is the product of the number
(possibly including the %) and the following pseudo-unit, unit,
namedspace or the default value for the attribute if no such unit
or space is given", would it be clearer to replace "if no such unit
or space is given" with "if % is specified with no pseudo-unit"? 

http://www.w3.org/Math/draft-spec/chapter3.html#presm.mpadded

minor suggestions on Public Editor's draft of MathML

Joe Java — 2012-05-16T19:34:04

Nit-picking at the latest MATHML editors draft


1.  Some of the examples appear to use theHyphen-minus (&#x002D;) instead of the &minus; (&#x2212;) character
to represent the minus sign.  For an example see "3.5.5.8 MathML representation of an alignment example" in the editors draft.  

Section "7.7.1.1 Minus" does say that MathML renderers should treat Hyphen-minus as a minus sign, 

but perhaps the defining document of MathML should use the correct character defined as the minus sign.

2. The examples use the Unicode number followed by a commented out long Unicode name for non-ASCII characters.
Now that the "XML Entity Definitions for Characters" is out and the latest HTML5 draft has a table of all the character entity names,
it might be better to only have the entity names used rather than the Unicode number of the non-ASCII characters/entities.

3.  The document HTML5 + MATHML (http://www.w3.org/Math/draft-spec/mathml.html) does not validate with the W3C validator.  

It would be easy to fix this problem, but the documents' HTML code is very poorly indented and spaced.  

For example see line 24605 of the HTML5 + MATHML document 

Any decent code editor can easily assist in proper indentation and line spacing.   

     Joe

Public Editor's draft of MathML

David Carlisle — 2012-05-16T08:22:03



I'm pleased to announce that we now have a copy of the editor's draft of
MathML available. Previously it was only available to W3C members (or as
copies from other locations).

http://www.w3.org/Math/draft-spec/

This is a draft "2nd Edition" of MathML 3.0. It incorporates a number of
errata that have been reported over the last year. We will continue to
gather and correct mistakes in the MathML 3.0 spec and update this draft
accordingly. At the present time we have no plans to issue a actual
second edition as an official W3C Recommendation.


Many but not all issues raised have been addressed, and some editorial
notes have been added for still open issues. Please see the change log
in the diff marked version:

http://www.w3.org/Math/draft-spec/appendixf-d.html#changes.mathml3.02e-3.0

(some of the change log entries are not fully described at present but
the list should link to all sections that have changes.)



The draft is available in several formats

* HTML(4):
http://www.w3.org/Math/draft-spec/


* Diff Marked HTML(4)
Showing any changes from the 1st edition of MathML 3.0.
http://www.w3.org/Math/draft-spec/Overview-d.html



* XHTML + MathML Version
XHTML including MathML examples to be displayed in the browser:
http://www.w3.org/Math/draft-spec/Overview.xml


* Single file HTML(5) + MathML Version
NEW! The spec as a single HTML page (rather than a page per chapter)
with inline MathML examples. This version also includes the option of
applying JavaScript to affect the display of MathML, Converting Content
MathML to Presentation and optionally invoking the MathJax system to
render the MathML.
http://www.w3.org/Math/draft-spec/mathml.html


* PDF version.
Version of the document typeset with LaTeX.
http://www.w3.org/Math/draft-spec/mathml.pdf

David

________________________________________________________________________
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Wilkinson House, Jordan Hill Road, Oxford OX2 8DR, United Kingdom.

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________________________________________________________________________

Mathematical and Scientific Notations

Adam Sobieski — 2012-05-11T08:25:37

1. Introduction
Described are some ideas about extending MathML to include XSLT functionality for transforming input semantic content into output presentational content.  An element, <notation>, is described and illustrations and examples are provided.  The functionality described herein can accompany the current version of the mathematical markup language or can supplement a next version.  Additionally, a sketch of an XSLT-enhanced XInclude is provided (see Appendix A).
1.1 XSL Transforms
XSLT describes transformations, rules for transforming source trees into resultant trees [XSLT10, XSLT20, XSLT21].  XSLT utilizes the syntax of its target language, XML, and can be viewed as a Turing-complete template processor.  For processing semantic content into presentational content, including from  mathematical semantic content to MathML presentational content, XSLT is often utilized.  XSLT-based approaches can facilitate modularity, configurability, notational conventions and the specialized notational practices of mathematical and scientific subfields.
1.2 XInclude
The XInclude specification describes a mechanism for merging XML documents, facilitating modularity [XINCLUDE10].
2. Syntax
2.1 The <notation> Element
2.1.1 Attributes
The class Attribute
The syntax of this attribute's value is a set of space-separated tokens.
The style Attribute
The syntax of this attribute's value is as defined by the CSS Styling Attribute Syntax specification [CSSATTR].
The present Attribute
The syntax of this attribute's value is as per that of the HTTP request header Accept [HTTP11, RFC4229].
The src Attribute
The syntax of this attribute's value is as per a URI [RFC3986].
The type Attribute
The syntax of this attribute's value is as per a MIME type [RFC2046].
The charset Attribute
The value must be a valid character encoding name [IANACHARSET].
The lang Attribute
The syntax of this attribute's value must be a valid BCP 47 language tag [BCP47].
The media Attribute
The syntax of this attribute's value is as per a valid media query [MQ].
The transform Attribute
The syntax of this attribute's value is as per a URI [RFC3986].
2.2 The <presentation> Element
2.3 The <data> Element
The <data> element combines aspects of MathML's <annotation> and <annotation-xml> elements [MATHML3] with HTML's <link> and <source> elements [HTML5].  The <data> element has two contexts, semantic and presentational; a <data> element in in a <notation> element is in a semantic context unless within a <presentation> element.
2.3.1 Attributes
The src Attribute
The syntax of this attribute's value is as per a URI [RFC3986].
The type Attribute
The syntax of this attribute's value is as per a MIME type [RFC2046].
The charset Attribute
The syntax of this attributes' value must be a valid character encoding name [IANACHARSET].
The lang Attribute
The syntax of this attribute's value must be a valid BCP 47 language tag [BCP47].
The media Attribute
The syntax of this attribute's value is as per a valid media query [MQ].
The q Attribute
The syntax of this attribute's value is a floating-point number ranging from 0 to 1.  The default value is q=1.  The attribute is valid on <data> elements in a presentational context [HTTP11, RFC4229].
The transform Attribute
The syntax of this attribute's value is as per a URI [RFC3986].
The input Attribute
The input attribute can reference semantic context <data> elements by id.
2.4 The <with-param> Element
Resembles XSLT's <with-param> element [XSLT10, XSLT20, XSLT21].
2.4.1 Attributes
The name Attribute
The syntax of this attribute's value is an XML qualified name [XMLNS].
The as Attribute
The syntax of this attribute's value is an XPath sequence type [XPATH10, XPATH20, XPATH30].
The tunnel Attribute
The syntax of this attribute's value is "yes" or "no" with a default value of "no".
The src Attribute
The syntax of this attribute's value is a URI [RFC3986].
2.5 The <with-extension> Element
2.5.1 Attributes
The name Attribute
The syntax of this attribute's value is an XML qualified name [XMLNS].
The as Attribute
The syntax of this attribute's value is an XPath sequence type [XPATH10, XPATH20, XPATH30].
The oncall Attribute
The syntax of this attribute's value is that of an event handler.
2.6 The <param> Element
Resembles XSLT's <param> element [XSLT10, XSLT20, XSLT21].
2.6.1 Attributes
The name Attribute
The syntax of this attribute's value is an XML qualified name [XMLNS].
The as Attribute
The syntax of this attribute's value is an XPath sequence type [XPATH10, XPATH20, XPATH30].
The required Attribute
The syntax of this attribute's value is "yes" or "no" with a default value of "no".
The tunnel Attribute
The syntax of this attribute's value is "yes" or "no" with a default value of "no".
The src Attribute
The syntax of this attribute's value is a URI [RFC3986].
3. Discussion
3.1 Client-Side XSL Transformations
In a presentational context, <data> elements can reference XSLT resources by means of their transform attributes.  The described <notation> system utilizes XSLT to transform mathematical and scientific semantic content into presentational content to be rendered by UA's.
While processing models resembling an XSLT-enhanced XInclude [XINCLUDE10] are possible (see Appendix A), the processing model described herein is one where <data> elements in both presentational and semantic contexts, their attribute values, contained text, XML content or referenced resources are utilized to arrive at resultant content which, in the output <notation> element, is rendered by a UA.
3.2 The Document Object Model and Cascading Stylesheets
The utilized, obtained, processed or otherwise resultant content, in the output <notation> element, is a part of the DOM structure of the resultant document and can be styled accordingly.  Attributes such as id, class and style are preserved between input and output <notation> elements.  An extension to the DOM is possible for traversing from the resultant or output <notation> node to the input <notation> node's XML DOM contents.
3.3 Multimedia Content
When multimedia resources are referenced in input <notation> elements in HTML5 scenarios [HTML5], for resultant <notation> elements, "image/svg+xml" can map to an <svg> element, other "image/..." types can map to an an <img> element, "audio/..." types can map to an <audio> element, and "video/..." types can map to a <video> element.
3.4 UA Tables
Two UA Tables are described herein.  The following two tables provide for convenient and succinct syntax for document authors by providing situational default attribute values.
3.4.1. UA Table 1: Default Output Content Type for Input Content Types
UA Table 1 describes for content-related MIME types, default output or presentational MIME types.  For example, for mathematics-related content types (e.g. "application/mathml-content+xml", "application/openmath+xml") the default output MIME type could be "application/mathml-presentation+xml", which facilitates layout scenarios including mathematics in sentences while interoperable with cascading stylesheets.  Table 1 describes default output content types for various input content types.
3.4.2. UA Table 2: UA Default XSLT Resources for Input and Output Content Type Pairs
UA Table 2 maps pairs of content types map to UA default XSLT resources.  While the transform attribute on the <data> element allows authors to specify XSLT resources, UA's can include default XSLT resources for pairs of input and output content types.
3.5 Client-Side XSL Transformations, Tunneling Parameters and HTTP Semantics
When processing XSLT for <notation> elements, and possibly for other XSLT from HTML scenarios, tunneling parameters can be passed to XSLT processing utilizing HTTP semantics [HTTP11] with HTTP vocabulary in RDF 1.0 [HTTP-RDF].
A <notation> element's present attribute value or otherwise a string assembled from presentational context <data> elements' type and q attributes (see Illustration B.4) can be passed to XSLT as a tunneling parameter named http://www.w3.org/2011/http-headers#accept .
Similarly, the charset attribute or the text encoding of the document containing the <notation> element can be passed as a tunneling parameter named http://www.w3.org/2011/http-headers#accept-charset .
The values from lang attributes [BCP47] on, or from the document context of, presentational context <data> elements can be combined into a string value for a tunneling parameter named http://www.w3.org/2011/http-headers#accept-language .  The language value of the document context of the <notation> element can also be utilized to provide the http://www.w3.org/2011/http-headers#accept-language parameter value to XSLT.
The values from the media attributes, media queries [MQ], on <data> elements in a presentational context, or from the UA context, can be assembled together and passed as a tunneling parameter named http://www.w3.org/2011/http-headers#accept-features [RFC2295, RFC4229].
Media types [RFC2046], character sets [IANACHARSET], languages [BCP47], and features (including media query related [MQ]) are described as the four dimensions of HTTP content negotiation [RFC2295].
3.6 Content Negotiation
3.6.1 The <data> Element and Content Negotiation
The attributes type, charset, lang, and media correspond with the four dimensions of HTTP content negotiation.  Multiple <data> elements, in a presentational context, resemble the contents of an HTTP Alternates response header [RFC2295] (http://www.w3.org/2011/http-headers#alternates).  However, the <data> elements described herein have the additional expressiveness for inline text or XML content and, in presentational contexts, can describe XSLT transformations upon the contents of semantic context <data> elements by means of the transform and input attributes.  While media queries are a subset of feature-based content negotiation, an attribute features can also extend the <notation> and <data> elements.
3.6.2 Client-Side XSL Transformations and Content Negotiation
Content negotiation topics include scenarios between UA's and external resources, UA's and XSLT processors, between XSLT processors, and possibly between XSLT processors and external resources.
3.7 Client-Side XSL Transformations, Scripting and Extension Functions
The <with-extension> and <param> elements describe a means of providing JavaScript functions to XSLT.   With regard to to XSLT processors, the availability of and interoperability with UA API's such as DOM, CSSOM, and XMLHttpRequest is topical.
3.8 JavaScript API
A JavaScript API can exist to provide functionality resembling XSLTHttpRequest, resembling and encapsulating the XMLHttpRequest API.  The XSLTProcessor API could version to include indicating JavaScript-interoperable extension objects.
3.9 The HTML <link> Element
With a link relation type, e.g. "notation", XSLT can be referenced by <link> elements [HTML5] into the processing context of document <notation> elements (see Example C.10).
Furthermore, alternate notations can be indicated with <link> elements having a rel attribute value such as "alternate notation" (see Example C.11).
3.10 Parallel Markup
3.10.1 Parallel Markup and XML Elements
MathML3 includes an annotational parallel markup system [MATHML3].  In the system described herein, parallel markup can be achieved and a means of navigating from resultant presentational DOM nodes to input content nodes is described in Section 3.2 .
3.10.2 Parallel Markup and Multiple XML Elements
While notational elements, in general, are expressive, it often occurs that semantic structures can interrelate sets of such elements.  Examples include mathematical proofs in hypertext documents.  To indicate such semantic structures in documents, some existing techniques include RDFa [RDFA-CORE], the use of xref attributes between resources, and solutions where external XML resources can relate XML elements from multiple resources, for example SMIL [SMIL30].
3.10.3 Multipart MIME
Regarding parallel markup and content types of various simultaneous formats, the MIME type "multipart/alternative" describes where contents are multiple versions or variants of the same data [RFC2046].
3.11 Clipboarding, Drag and Drop and Interprocess Communication
As the input <notation> element contents are available to JavaScript (see Section 3.2), by means of that content, the rows of Table 2 (see Section 3.4), and custom notations (see Section 3.9), a UA can determine which formats it can place onto a DataTransfer for a <notation> item.  By adding a function, setDataProvider, to DataTransfer, computation can be deferred until paste or drop recipients request the data in particular data formats.  With such techniques, UA's can place all possible formats onto a DataTransfer for clipboarding, drag and drop and interprocess communication.
Client-side XSLT functionality with XML document fragments is topical as are client-side XSLT and DOM selections and ranges (see also Section 3.10.2).
3.12 Advanced Mathematical and Scientific Presentational Markup Scenarios
With the XSLT processing of semantic content into presentational content as a supported scenario, it is possible that presentational markup can come to include even more advanced features and CSS interoperability that might have been otherwise cumbersome for manual markup authoring scenarios.
3.13 Multimodal Mathematical and Scientific Input
Means can be devised to obtain InkML [INKML] and SRGS/SISR [SRGS10, SISR10] content from notational contexts (see Sections 3.4 and 3.9) and/or semantic content; document authors should be able to include and users to make use of such content.
3.14 Natural Language Generation and Synthesis
Synthesis processors can utilize the MIME type "application/ssml+xml" and/or the media query of "speech" to obtain SSML [SSML] from <notation> elements (see Sections 3.4 and 3.9 and Examples C.7 and C.8).
4. Conclusion
The current version of the MathML syntax [MATHML3] utilizes an annotational system for parallel markup for both presentational and semantic content (see Section 3.10).  Adding XSLT interoperability to such a syntax enhances the difference between semantics and presentation, input and output, and effectively charts a course through the Pillars of Hercules.  While a <notation> syntax as described herein could accompany the current version of MathML's <math>, <semantics>, <annotation> and <annotation-xml> elements, if the MathML syntax were to version to include an element such as the <data> element, and did so in a manner so as to replace the <annotation> and <annotation-xml> elements, and, as the <math> element has thus far had a default presentational context, if the MathML <semantics> element were reinterpreted so as to create a semantic context inside of a <math> element, syntactic possibilities could resemble:

<notation>
  <presentation>
    <data type="application/mathml-presentation+xml">...</data>
  </presentation>
  <data type="application/mathml-content+xml">...</data>
</notation>


<math>
  <data type="application/mathml-presentation+xml">...</data>
  <semantics>
    <data type="application/mathml-content+xml">...</data>
  </semantics>
</math>

Furthermore, with the default content type for such a <math> element as "application/mathml-presentation+xml", such a syntax would be backwards compatible with traditional mathematical presentational markup scenarios.
5. References
5.1 Normative References

[BCP47] Tags for Identifying Languages; Matching of Language Tags. A. Phillips, M. Davis. IETF.
[CSSATTR] CSS Styling Attribute Syntax. T. Çelik, E. Etemad. W3C.
[HTML5] HTML5. Ian Hickson, David Hyatt. W3C.
[HTTP11] Hypertext Transfer Protocol — HTTP/1.1. R. Fielding, J. Gettys, J. Mogul, H. Frystyk, L. Masinter, P. Leach, T. Berners-Lee. IETF.
[HTTP-RDF] HTTP Vocabulary in RDF 1.0. J. Koch, C. Velasco, P. Ackermann. W3C.
[IANACHARSET] Character Sets.  IANA.
[MATHML3] Mathematical Markup Language (MathML). D. Carlisle, P. Ion, R. Miner, N. Poppelier. W3C.
[MIMESNIFF] MIME Sniffing. A. Barth, I. Hickson. WHATWG.
[MQ] Media Queries. H. Lie, T. Çelik, D. Glazman, A. van Kesteren. W3C.
[RFC2046] Multipurpose Internet Mail Extensions (MIME) Part Two: Media Types. N. Freed, N. Borenstein. IETF.
[RFC2295] Transparent Content Negotiation in HTTP. K. Holtman, A. Mutz. IETF.
[RFC3986] Uniform Resource Identifier (URI): Generic Syntax. T. Berners-Lee, R. Fielding, L. Masinter. IETF.
[RFC4229] HTTP Header Field Registrations. M. Nottingham, J. Mogul. IETF.
[XML10] Extensible Markup Language (XML) 1.0 (Fifth Edition). T. Bray, J. Paoli, C. Sperberg-McQueen. W3C.
[XML11] Extensible Markup Language (XML) 1.1 (Second Edition). T. Bray, J. Paoli, C. Sperberg-McQueen. W3C.
[XMLNS] Namespaces in XML. T. Bray, D. Hollander, A. Layman, R. Tobin. W3C.
[XPATH10] XML Path Language (XPath) 1.0. J. Clark, S. DeRose. W3C.
[XPATH20] XML Path Language (XPath) 2.0. D. Chamberlin, A. Berglund, S. Boag. W3C.
[XPATH30] XML Path Language (XPath) 3.0. J. Robie, D. Chamberlin, M. Dyck, J. Snelson. W3C.
[XSLT10] XSL Transformations (XSLT) Version 1.0. J. Clark. W3C.
[XSLT20] XSL Transformations (XSLT) Version 2.0. M. Kay. W3C.
[XSLT21] XSL Transformations (XSLT) Version 2.1. M. Kay. W3C.

5.2 Informative References

[CLIPAPI] Clipboard API and Events. H. Steen. W3C.
[DOM4] DOM4. A. van Kesteren, A. Gregor, et al. W3C. 
[INKML] Ink Markup Language (InkML). Y. Chee, M. Froumentin, S. Watt. W3C.
[OPENMATH20] The OpenMath Standard Version 2.0. S. Buswell, O. Caprotti, D. Carlisle, M. Dewar, M. Gaëtano and M. Kohlhase. The OpenMath Society.
[OMDOC12] OMDoc - An Open Markup Format for Mathematical Documents Version 1.2. Michael Kohlhase.
[RDFA-CORE] RDFa Core 1.1: Syntax and Processing Rules for Embedding RDF through Attributes. B. Adida, M. Birbeck, S. McCarron, I. Herman. W3C. 
[SISR10] Semantic Interpretation for Speech Recognition. L. Van Tichelen, D. Burke. W3C.
[SMIL30] Synchronized Multimedia Integration Language (SMIL 3.0). D. Bulterman, J. Jansen, P. Cesar, et al. W3C.
[SRGS10] Speech Recognition Grammar Specification 1.0. A. Hunt, S. McGlashan. W3C.
[SSML11] Speech Synthesis Markup Language (SSML) 1.1. D.  Burnett, Z. Shuang. W3C.
[XHR2] XMLHttpRequest Level 2. A. van Kesteren. W3C.
[XINCLUDE10] XML Inclusions (XInclude) Version 1.0 (Second Edition). J. Marsh, D. Orchard, D. Veillard. W3C.

Appendix A. An XSLT-Enhanced XInclude
As described in Section 3.1, one of several approaches for an XSLT-Enhanced XInclude [XINCLUDE10] is sketched.
A.1 The <include> element
A.1.1 Attributes
The src Attribute
The href attribute is refactored to src to resemble the syntactic conventions above.  The syntax of this attribute's value is as per a URI [RFC3986].
The type Attribute
The syntax of this attribute's value is as per a MIME type [RFC2046].
The transform Attribute
The syntax of this attribute's value is as per a URI [RFC3986].
The xpath Attribute
The syntax of this attribute's value is an XPath expression [XPATH10, XPATH20, XPATH30].
A.2 The <fallback> Element
A.3 The <with-param> Element
See Section 2.4
A.4 The <with-extension> Element
See Section 2.5
A.5 The <param> Element
See Section 2.6
A.6. Discussion
Syntactic possibilities for an XSLT-enhanced XInclude also include the use of elements resembling <data> elements as described herein.
Appendix B. Illustrations
Utilizing UA Tables 1 and 2 (see Section 3.4) for the default values of some attributes, and UA default XSLT resources, the expressiveness of the <notation> system is illustrated.
In the following illustrations, the syntax "ua/default" intends to indicate the value in UA Table 1 for the corresponding input content type.  The syntax "uadefault.xslt", "uadefault1.xslt" and "uadefault2.xslt" intends to indicate the UA default XSLT resources, contextually, from UA Table 2.
In the following illustrations, an example HTTP server returns, in its HTTP response content type headers, "application/mathml-content+xml" for files of type ".mmlc" and "application/openmath+xml" for files of type ".om".
Illustration B.1


<notation>
  <presentation>
    <data type="ua/default" transform="uadefault.xslt" input="#content1" />
  </presentation>
  <data id="content1" type="application/mathml-content+xml">...</data>
</notation>


<notation>
  <presentation>
    <data type="ua/default" transform="uadefault.xslt" />
  </presentation>
  <data type="application/mathml-content+xml">...</data>
</notation>


<notation>
  <data type="application/mathml-content+xml">...</data>
</notation>


<notation type="application/mathml-content+xml">...</notation>


<notation>...</notation>


Illustration B.2


<notation>
  <presentation>
    <data type="ua/default" transform="uadefault.xslt" input="#content1" />
  </presentation>
  <data id="content1" type="application/mathml-content+xml" src="file.mmlc"/>
</notation>


<notation>
  <presentation>
    <data type="ua/default" transform="uadefault.xslt" />
  </presentation>
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation>
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation type="application/mathml-content+xml" src="file.mmlc" />


<notation src="file.mmlc" />


Illustration B.3


<notation>
  <presentation>
    <data type="ua/default" transform="custom.xslt" input="#content1" />
  </presentation>
  <data id="content1" type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation>
  <presentation>
    <data type="ua/default" transform="custom.xslt" />
  </presentation>
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation present="ua/default" transform="custom.xslt">
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation present="ua/default" transform="custom.xslt" type="application/mathml-content+xml" src="file.mmlc" />


<notation present="ua/default" transform="custom.xslt" src="file.mmlc" />


<notation transform="custom.xslt" src="file.mmlc" />


Illustration B.4


<notation>
  <presentation>
    <data type="application/mathml-presentation+xml" q="0.9" transform="uadefault1.xslt" input="#content1"/>
    <data type="image/svg+xml" q="0.2" transform="uadefault2.xslt" input="#content1" />
  </presentation>
  <data id="content1" type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation>
  <presentation>
    <data type="application/mathml-presentation+xml" q="0.9" transform="uadefault1.xslt" />
    <data type="image/svg+xml" q="0.2" transform="uadefault2.xslt" />
  </presentation>
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation>
  <presentation>
    <data type="application/mathml-presentation+xml" q="0.9" />
    <data type="image/svg+xml" q="0.2" />
  </presentation>
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation present="application/mathml-presentation+xml;q=0.9, image/svg+xml;q=0.2">
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation present="application/mathml-presentation+xml;q=0.9, image/svg+xml;q=0.2" type="application/mathml-content+xml" src="file.mmlc" />


<notation present="application/mathml-presentation+xml;q=0.9, image/svg+xml;q=0.2" src="file.mmlc" />


Illustration B.5


<notation>
  <presentation>
    <data type="ua/default" transform="custom.xslt" input="#content1">
      <with-param name="namespace:param1" as="xs:string">text</with-param>
      <with-param name="namespace:param2" as="schema:type">
        <xml>
          <xml />
        </xml>
      </with-param>
    </data>
  </presentation>
  <data id="content1" type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation>
  <presentation>
    <data type="ua/default" transform="custom.xslt">
      <with-param name="namespace:param1" as="xs:string">text</with-param>
      <with-param name="namespace:param2" as="schema:type">
        <xml>
          <xml />
        </xml>
      </with-param>
    </data>
  </presentation>
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation>
  <presentation>
    <data transform="custom.xslt">
      <with-param name="namespace:param1" as="xs:string">text</with-param>
      <with-param name="namespace:param2" as="schema:type">
        <xml>
          <xml />
        </xml>
      </with-param>
    </data>
  </presentation>
  <data src="file.mmlc" />
</notation>


<notation transform="custom.xslt" src="file.mmlc">
  <with-param name="namespace:param1" as="xs:string">text</with-param>
  <with-param name="namespace:param2" as="schema:type">
    <xml>
      <xml />
    </xml>
  </with-param>
</notation>


Appendix C. Examples
Example C.1
<notation src="file.om" />
Example C.2
<notation transform="custom.xslt" src="file.om" />
Example C.3

<notation>
  <presentation>
    <data type="application/mathml-presentation+xml" src="file.mmlp" />
  </presentation>
</notation>

Example C.4

<notation>
  <presentation>
    <data type="model/x3d+xml" src="file.x3d" media="screen" />
    <data type="image/png" src="file.png" media="print" />
  </presentation>
</notation>

Example C.5

<notation>
  <presentation>
    <data type="model/x3d+xml" transform="3d.xslt" media="screen" />
    <data type="image/svg+xml" transform="svg.xslt" media="print" />
  </presentation>
  <data type="application/...+xml" src="..." />
</notation>

Example C.6

<notation>
  <presentation>
    <data type="image/svg+xml" q="0.9" transform="feynman-diagram.xslt" />
    <data type="image/png" q="0.2" src="file.png" />
  </presentation>
  <data type="application/...+xml">...</data>
</notation>

Example C.7

<notation>
  <presentation>
    <data type="application/mathml-presentation+xml" media="screen, print" />
    <data type="application/ssml+xml" transform="synthesize.xslt" lang="en" media="speech">
      <with-param name="namespace:param1" as="xs:string">text</with-param>
    </data>
  </presentation>
  <data type="application/openmath+xml">...</data>
</notation>

Example C.8

<notation>
  <presentation>
    <data type="application/mathml-presentation+xml" media="screen, print" />
    <data type="application/ssml+xml" transform="synthesize.xslt" lang="en" media="speech">
      <with-param name="namespace:param1" as="xs:string">text</with-param>
      <with-extension name="namespace:function" as="xs:string" oncall="jsfun(event)">
        <param name="namespace:functionparam1" as="xs:string" required="yes" />
      </extension>
    </data>
  </presentation>
  <data type="application/openmath+xml">...</data>
</notation>

Example C.9

<html>
  <head>
    <xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform" id="x1"> 
      ...
    </xsl:stylesheet>
  </head>
  <body>
    <notation transform="#x1" src="file.om" />
  </body>
</html>

Example C.10

<html>
  <head>
    <link rel="notation" type="application/xslt+xml" href="custom.xslt" />
  </head>
  <body>
    <notation src="file.om" />
  </body>
</html>

Example C.11

<html>
  <head>
    <link rel="notation" type="application/xslt+xml" href="custom1.xslt" title="title1" />
    <link rel="alternate notation" type="application/xslt+xml" href="custom2.xslt" title="title2" />
  </head>
  <body>
    <notation src="file.om" />
  </body>
</html>

Mathematical and Scientific Notations

Adam Sobieski — 2012-05-09T03:42:51

1. Introduction
Described are some ideas about extending MathML to include XSLT functionality for transforming input semantic content into output presentational content.  An element, <notation>, is described and illustrations and examples are provided.  The functionality described herein can accompany the current version of the mathematical markup language or can supplement a next version.  Additionally, a sketch of an XSLT-enhanced XInclude is provided (see Appendix A).
1.1 XSL Transforms
XSLT describes transformations, rules for transforming a source tree into a resultant tree [XSLT10, XSLT20, XSLT21].  XSLT utilizes the syntax of its target language, XML, and can be viewed as a Turing-complete template processor.  For processing semantic content into presentational content, including from  mathematical semantic content to MathML presentational content, XSLT is often utilized.  XSLT-based approaches can facilitate modularity, configurability, notational conventions and the specialized notational practices of mathematical and scientific subfields.
1.2 XInclude
The XInclude specification describes a mechanism for merging XML documents to facilitate modularity [XINCLUDE10].
2. Syntax
2.1 The <notation> Element
2.1.1 Attributes
The class Attribute
The syntax of this attribute's value is a set of space-separated tokens.
The style Attribute
The syntax of this attribute's value is as defined by the CSS Styling Attribute Syntax specification [CSSATTR].
The present Attribute
The syntax of this attribute's value is as per that of the HTTP request header Accept [HTTP11, RFC4229].
The type Attribute
The syntax of this attribute's value is as per a MIME type [RFC2046].
The src Attribute
The syntax of this attribute's value is as per a URI [RFC3986].
The transform Attribute
The syntax of this attribute's value is as per a URI [RFC3986].
2.2 The <presentation> Element
2.3 The <data> Element
The <data> element combines aspects of MathML's <annotation> and <annotation-xml> elements [MATHML3] with HTML's <link> element [HTML5].  The <data> element has two contexts, semantic and presentational; a <data> element in in a <notation> element is in a semantic context unless within a <presentation> element.
2.3.1 Attributes
The type Attribute
The syntax of this attribute's value is as per a MIME type [RFC2046].
The q Attribute
The syntax of this attribute's value is a floating-point number ranging from 0 to 1.  The default value is q=1.  The attribute is valid on <data> elements in a presentational context [HTTP11, RFC4229].
The media Attribute
The syntax of this attribute's value is as per a valid media query [MQ].
The src Attribute
The syntax of this attribute's value is as per a URI [RFC3986].
The transform Attribute
The syntax of this attribute's value is as per a URI [RFC3986].
The input Attribute
The input attribute can reference semantic context <data> elements by id.
2.4 The <with-param> Element
Resembles XSLT's <with-param> element [XSLT10, XSLT20, XSLT21].
2.4.1 Attributes
The name Attribute
The syntax of this attribute's value is an XML qualified name [XMLNS].
The as Attribute
The syntax of this attribute's value is an XPath sequence type [XPATH10, XPATH20, XPATH30].
The tunnel Attribute
The syntax of this attribute's value is "yes" or "no" with a default value of "no".
The src Attribute
The syntax of this attribute's value is a URI [RFC3986].
2.5 The <extension> Element
2.5.1 Attributes
The name Attribute
The syntax of this attribute's value is an XML qualified name [XMLNS].
The as Attribute
The syntax of this attribute's value is an XPath sequence type [XPATH10, XPATH20, XPATH30].
The oncall Attribute
The syntax of this attribute's value is that of an event handler.
2.6 The <param> Element
Resembles XSLT's <param> element [XSLT10, XSLT20, XSLT21].
2.6.1 Attributes
The name Attribute
The syntax of this attribute's value is an XML qualified name [XMLNS].
The as Attribute
The syntax of this attribute's value is an XPath sequence type [XPATH10, XPATH20, XPATH30].
The required Attribute
The syntax of this attribute's value is "yes" or "no" with a default value of "no".
The tunnel Attribute
The syntax of this attribute's value is "yes" or "no" with a default value of "no".
The src Attribute
The syntax of this attribute's value is a URI [RFC3986].
3. Discussion
3.1 Client-Side XSL Transformations
In a presentational context, <data> elements can reference XSLT resources by means of their transform attributes.  The described <notation> system utilizes XSLT to transform mathematical and scientific semantic content into presentational content to be rendered by UA's.
While processing models resembling an XSLT-enhanced XInclude [XINCLUDE10] are possible (see Appendix A), the processing model described herein is one where <data> elements in both presentational and semantic contexts, their attribute values, contained text, XML content or referenced resources are utilized to arrive at resultant content which, in the output <notation> element, is rendered by a UA.
3.2 The Document Object Model and Cascading Stylesheets
The utilized, obtained, processed or otherwise resultant content, in the output <notation> element, is a part of the DOM structure of the resultant document and can be styled accordingly.  Attributes such as id, class and style are preserved between input and output <notation> elements.  An extension to the DOM is possible for traversing from the resultant or output <notation> node to the input <notation> node's XML DOM contents.
3.3 Multimedia Content
When resources are referenced with MIME types which describe neither text nor XML content, with regard to the content in resultant <notation> elements, for HTML5 scenarios [HTML5], "image/..." content can map to an an <img> element, "audio/..." can map to an <audio> element, and "video/..." can map to a <video> element.
3.4 UA Tables
Two UA Tables are described herein.  The following two tables provide for convenient and succinct syntax for document authors by providing situational default attribute values.
3.4.1. UA Table 1: Default Output Content Type for Input Content Types
UA Table 1 describes for content-related MIME types, default output or presentational MIME types.  For example, for mathematics-related content types (e.g. application/mathml-content+xml, application/openmath+xml) the default output MIME type could be application/mathml-presentation+xml, which facilitates layout scenarios including mathematics in sentences while interoperable with cascading stylesheets.  Table 1 describes default output content types for various input content types.
3.4.2. UA Table 2: UA Default XSLT Resources for Input and Output Content Type Pairs
UA Table 2 maps pairs of content types map to UA default XSLT resources.  While the transform attribute on the <data> element allows authors to specify XSLT resources, UA's can include default XSLT resources for pairs of input and output content types.
3.5 Client-Side XSL Transformations, Tunneling Parameters and HTTP Semantics
When processing XSLT for <notation> elements, and possibly for other XSLT from HTML scenarios, tunneling parameters can be passed to XSLT processing utilizing HTTP semantics [HTTP11] with HTTP vocabulary in RDF 1.0 [HTTP-RDF].
A <notation> element's present attribute value or otherwise a string assembled from presentational context <data> elements' type and q attributes (see Illustration B.4) can be passed to XSLT as a tunneling parameter named http://www.w3.org/2011/http-headers#accept .
Similarly, the values from lang attributes [BCP47] on, or from the document context of, presentational context <data> elements can be combined into a string value for a tunneling parameter named http://www.w3.org/2011/http-headers#accept-language .  The language value of the document context of the <notation> element can also be utilized to provide the http://www.w3.org/2011/http-headers#accept-language parameter value to XSLT.
The values from the media attributes, media queries [MQ], on <data> elements in a presentational context, or from the UA context, can be assembled together and passed as a tunneling parameter named http://www.w3.org/2011/http-headers#accept-features [RFC4229].
The text encoding of the document containing the <notation> element can be passed as a tunneling parameter named http://www.w3.org/2011/http-headers#accept-charset .
3.6 Client-Side XSL Transformations and Content Negotiation
Content negotiation topics include content negotiation between the UA and XSLT processors, between the UA and indicated input resources to XSLT processors, between XSLT processors, and HTTP content negotiation that may occur when XSLT processors request external resources.
3.7 Client-Side XSL Transformations, Scripting and Extension Functions
The <extension> and <param> elements describe a means of providing JavaScript functions to XSLT.   With regard to to XSLT processors, the availability of and interoperability with UA API's such as DOM, CSSOM, and XMLHttpRequest is topical.
3.8 JavaScript API
A JavaScript API can exist to provide functionality resembling XSLTHttpRequest, resembling and encapsulating the XMLHttpRequest API.  The XSLTProcessor API could version to include indicating JavaScript-interoperable extension objects.
3.9 The HTML <link> Element
With a link relation type, e.g. "notation", XSLT can be referenced by <link> elements [HTML5] into the processing context of document <notation> elements (see Example C.10).
Furthermore, alternate notations can be indicated with <link> elements having a rel attribute value such as "alternate notation" (see Example C.11).
3.10 Parallel Markup
MathML3 includes an annotational parallel markup system [MATHML3].  In the system described herein, parallel markup can be achieved and a means of navigating from resultant presentational DOM nodes to input content nodes is described in Section 3.2 .
While notational elements, in general, in documents are expressive, it often occurs that sets of such elements can be interrelated in semantic structures.  To indicate such semantic structures in documents, some existing techniques include RDFa [RDFA-CORE], the use of xref attributes between resources, and solutions where external XML resources can relate XML elements from multiple resources, for example SMIL [SMIL30].
3.11 Clipboarding, Drag and Drop and Interprocess Communication
As the input <notation> element contents are available to JavaScript (see Section 3.2), by means of that content, the rows of Table 2 (see Section 3.4), and custom notations (see Section 3.9), a UA can determine which formats it can place onto a DataTransfer for a <notation> item.  By adding a function, setDataProvider, to DataTransfer, computation can be deferred until paste or drop recipients request the data in particular data formats.  With such techniques, UA's can place all possible formats onto a DataTransfer for clipboarding, drag and drop and interprocess communication.
3.12 Advanced Mathematical and Scientific Presentational Markup Scenarios
With the XSLT processing of semantic content into presentational content as a supported scenario, it is possible that presentational markup can come to include even more advanced features and CSS interoperability that might have been otherwise cumbersome for manual markup authoring scenarios.
3.13 Multimodal Mathematical and Scientific Input
Means can be devised to obtain InkML [INKML] and SRGS/SISR [SRGS10, SISR10] content from notational contexts (see Sections 3.4 and 3.9) and/or semantic content; document authors should be able to include and users to make use of such content.
3.14 Natural Language Generation and Synthesis
Synthesis processors can utilize the MIME type "application/ssml+xml" and/or the media query of "speech" to obtain SSML [SSML] from <notation> elements (see Sections 3.4 and 3.9 and Examples C.7 and C.8).
4. Conclusion
The current version of the MathML syntax [MATHML3] utilizes an annotational system for parallel markup for both presentational and semantic content (see Section 3.10).  Adding XSLT interoperability to such a syntax exacerbates the dichotomy between input and output content, semantics and presentation.  While a <notation> syntax as described herein can accompany the current version of MathML's <math>, <semantics>, <annotation> and <annotation-xml> elements, if the MathML syntax were to version to include an element such as the <data> element, and did so in a manner so as to replace the <annotation> and <annotation-xml> elements, and, as the <math> element has thus far had a default presentational context, if the MathML <semantics> element were reinterpreted so as to create a semantic context inside of a <math> element, syntactic possibilities could resemble:

<notation>
  <presentation>
    <data type="application/mathml-presentation+xml">...</data>
  </presentation>
  <data type="application/mathml-content+xml">...</data>
</notation>


<math>
  <data type="application/mathml-presentation+xml">...</data>
  <semantics>
    <data type="application/mathml-content+xml">...</data>
  </semantics>
</math>

Furthermore, with the default content type for such a <math> element as "application/mathml-presentation+xml", such a syntax would be backwards compatible with traditional mathematical presentational markup scenarios.
5. References
5.1 Normative References

[BCP47] Tags for Identifying Languages; Matching of Language Tags. A. Phillips, M. Davis. IETF.
[CSSATTR] CSS Styling Attribute Syntax. T. Çelik, E. Etemad. W3C.
[HTML5] HTML5. Ian Hickson, David Hyatt. W3C.
[HTTP11] Hypertext Transfer Protocol — HTTP/1.1. R. Fielding, J. Gettys, J. Mogul, H. Frystyk, L. Masinter, P. Leach, T. Berners-Lee. IETF.
[HTTP-RDF] HTTP Vocabulary in RDF 1.0. J. Koch, C. Velasco, P. Ackermann. W3C.
[MATHML3] Mathematical Markup Language (MathML). D. Carlisle, P. Ion, R. Miner, N. Poppelier. W3C.
[MIMESNIFF] MIME Sniffing. A. Barth, I. Hickson. WHATWG.
[MQ] Media Queries. H. Lie, T. Çelik, D. Glazman, A. van Kesteren. W3C.
[RFC2046] Multipurpose Internet Mail Extensions (MIME) Part Two: Media Types. N. Freed, N. Borenstein. IETF.
[RFC3986] Uniform Resource Identifier (URI): Generic Syntax. T. Berners-Lee, R. Fielding, L. Masinter. IETF.
[RFC4229] HTTP Header Field Registrations. M. Nottingham, J. Mogul. IETF.
[XML10] Extensible Markup Language (XML) 1.0 (Fifth Edition). T. Bray, J. Paoli, C. Sperberg-McQueen. W3C.
[XML11] Extensible Markup Language (XML) 1.1 (Second Edition). T. Bray, J. Paoli, C. Sperberg-McQueen. W3C.
[XMLNS] Namespaces in XML. T. Bray, D. Hollander, A. Layman, R. Tobin. W3C.
[XPATH10] XML Path Language (XPath) 1.0. J. Clark, S. DeRose. W3C.
[XPATH20] XML Path Language (XPath) 2.0. D. Chamberlin, A. Berglund, S. Boag. W3C.
[XPATH30] XML Path Language (XPath) 3.0. J. Robie, D. Chamberlin, M. Dyck, J. Snelson. W3C.
[XSLT10] XSL Transformations (XSLT) Version 1.0. J. Clark. W3C.
[XSLT20] XSL Transformations (XSLT) Version 2.0. M. Kay. W3C.
[XSLT21] XSL Transformations (XSLT) Version 2.1. M. Kay. W3C.

5.2 Informative References

[INKML] Ink Markup Language (InkML). Y. Chee, M. Froumentin, S. Watt. W3C.
[OPENMATH20] The OpenMath Standard Version 2.0. S. Buswell, O. Caprotti, D. Carlisle, M. Dewar, M. Gaëtano and M. Kohlhase. The OpenMath Society.
[OMDOC12] OMDoc - An Open Markup Format for Mathematical Documents Version 1.2. Michael Kohlhase.
[RDFA-CORE] RDFa Core 1.1: Syntax and Processing Rules for Embedding RDF through Attributes. B. Adida, M. Birbeck, S. McCarron, I. Herman. W3C. 
[SISR10] Semantic Interpretation for Speech Recognition. L. Van Tichelen, D. Burke. W3C.
[SMIL30] Synchronized Multimedia Integration Language (SMIL 3.0). D. Bulterman, J. Jansen, P. Cesar, et al. W3C.
[SRGS10] Speech Recognition Grammar Specification 1.0. A. Hunt, S. McGlashan. W3C.
[SSML11] Speech Synthesis Markup Language (SSML) 1.1. D.  Burnett, Z. Shuang. W3C.
[XINCLUDE10] XML Inclusions (XInclude) Version 1.0 (Second Edition). J. Marsh, D. Orchard, D. Veillard. W3C.

Appendix A. An XSLT-Enhanced XInclude
As described in Section 3.1, one of several approaches for an XSLT-Enhanced XInclude [XINCLUDE10] is sketched.
A.1 The <include> element
A.1.1 Attributes
The src Attribute
The href attribute is refactored to src to resemble the syntactic conventions above.  The syntax of this attribute's value is as per a URI [RFC3986].
The type Attribute
The syntax of this attribute's value is as per a MIME type [RFC2046].
The transform Attribute
The syntax of this attribute's value is as per a URI [RFC3986].
The xpath Attribute
The syntax of this attribute's value is an XPath expression [XPATH10, XPATH20, XPATH30].
A.2 The <fallback> Element
A.3 The <with-param> Element
See Section 2.4
A.4 The <extension> Element
See Section 2.5
A.5 The <param> Element
See Section 2.6
Appendix B. Illustrations
Utilizing UA Tables 1 and 2 (see Section 3.4) for the default values of some attributes, and UA default XSLT resources, the expressiveness of the <notation> system is illustrated.
In the following illustrations, the syntax "ua/default" intends to indicate the value in UA Table 1 for the corresponding input content type.  The syntax "uadefault.xslt", "uadefault1.xslt" and "uadefault2.xslt" intends to indicate the UA default XSLT resources, contextually, from UA Table 2.
In the following illustrations, an example HTTP server returns, in its HTTP response content type headers, "application/mathml-content+xml" for files of type ".mmlc" and "application/openmath+xml" for files of type ".om".
Illustration B.1


<notation>
  <presentation>
    <data type="ua/default" transform="uadefault.xslt" input="#content1" />
  </presentation>
  <data id="content1" type="application/mathml-content+xml">...</data>
</notation>


<notation>
  <presentation>
    <data type="ua/default" transform="uadefault.xslt" />
  </presentation>
  <data type="application/mathml-content+xml">...</data>
</notation>


<notation>
  <data type="application/mathml-content+xml">...</data>
</notation>


<notation type="application/mathml-content+xml">...</notation>


<notation>...</notation>


Illustration B.2


<notation>
  <presentation>
    <data type="ua/default" transform="uadefault.xslt" input="#content1" />
  </presentation>
  <data id="content1" type="application/mathml-content+xml" src="file.mmlc"/>
</notation>


<notation>
  <presentation>
    <data type="ua/default" transform="uadefault.xslt" />
  </presentation>
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation>
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation type="application/mathml-content+xml" src="file.mmlc" />


<notation src="file.mmlc" />


Illustration B.3


<notation>
  <presentation>
    <data type="ua/default" transform="custom.xslt" input="#content1" />
  </presentation>
  <data id="content1" type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation>
  <presentation>
    <data type="ua/default" transform="custom.xslt" />
  </presentation>
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation present="ua/default" transform="custom.xslt">
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation present="ua/default" transform="custom.xslt" type="application/mathml-content+xml" src="file.mmlc" />


<notation present="ua/default" transform="custom.xslt" src="file.mmlc" />


<notation transform="custom.xslt" src="file.mmlc" />


Illustration B.4


<notation>
  <presentation>
    <data type="application/mathml-presentation+xml" q="0.9" transform="uadefault1.xslt" input="#content1"/>
    <data type="image/svg+xml" q="0.2" transform="uadefault2.xslt" input="#content1" />
  </presentation>
  <data id="content1" type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation>
  <presentation>
    <data type="application/mathml-presentation+xml" q="0.9" transform="uadefault1.xslt" />
    <data type="image/svg+xml" q="0.2" transform="uadefault2.xslt" />
  </presentation>
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation>
  <presentation>
    <data type="application/mathml-presentation+xml" q="0.9" />
    <data type="image/svg+xml" q="0.2" />
  </presentation>
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation present="application/mathml-presentation+xml;q=0.9, image/svg+xml;q=0.2">
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation present="application/mathml-presentation+xml;q=0.9, image/svg+xml;q=0.2" type="application/mathml-content+xml" src="file.mmlc" />


<notation present="application/mathml-presentation+xml;q=0.9, image/svg+xml;q=0.2" src="file.mmlc" />


Illustration B.5


<notation>
  <presentation>
    <data type="ua/default" transform="custom.xslt" input="#content1">
      <with-param name="namespace:param1" as="xs:string">text</with-param>
      <with-param name="namespace:param2" as="schema:type">
        <xml>
          <xml />
        </xml>
      </with-param>
    </data>
  </presentation>
  <data id="content1" type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation>
  <presentation>
    <data type="ua/default" transform="custom.xslt">
      <with-param name="namespace:param1" as="xs:string">text</with-param>
      <with-param name="namespace:param2" as="schema:type">
        <xml>
          <xml />
        </xml>
      </with-param>
    </data>
  </presentation>
  <data type="application/mathml-content+xml" src="file.mmlc" />
</notation>


<notation>
  <presentation>
    <data transform="custom.xslt">
      <with-param name="namespace:param1" as="xs:string">text</with-param>
      <with-param name="namespace:param2" as="schema:type">
        <xml>
          <xml />
        </xml>
      </with-param>
    </data>
  </presentation>
  <data src="file.mmlc" />
</notation>


<notation transform="custom.xslt" src="file.mmlc">
  <with-param name="namespace:param1" as="xs:string">text</with-param>
  <with-param name="namespace:param2" as="schema:type">
    <xml>
      <xml />
    </xml>
  </with-param>
</notation>


Appendix C. Examples
Example C.1
<notation src="file.om" />
Example C.2
<notation transform="custom.xslt" src="file.om" />
Example C.3

<notation>
  <presentation>
    <data type="application/mathml-presentation+xml" src="file.mmlp" />
  </presentation>
</notation>

Example C.4

<notation>
  <presentation>
    <data type="model/x3d+xml" src="file.x3d" media="screen" />
    <data type="image/png" src="file.png" media="print" />
  </presentation>
</notation>

Example C.5

<notation>
  <presentation>
    <data type="model/x3d+xml" transform="3d.xslt" media="screen" />
    <data type="image/svg+xml" transform="svg.xslt" media="print" />
  </presentation>
  <data type="application/...+xml" src="..." />
</notation>

Example C.6

<notation>
  <presentation>
    <data type="image/svg+xml" q="0.9" transform="feynman-diagram.xslt" />
    <data type="image/png" q="0.2" src="file.png" />
  </presentation>
  <data type="application/...+xml">...</data>
</notation>

Example C.7

<notation>
  <presentation>
    <data type="application/mathml-presentation+xml" media="screen, print" />
    <data type="application/ssml+xml" transform="synthesize.xslt" xml:lang="en" media="speech">
      <with-param name="namespace:param1" as="xs:string">text</with-param>
    </data>
  </presentation>
  <data type="application/openmath+xml">...</data>
</notation>

Example C.8

<notation>
  <presentation>
    <data type="application/mathml-presentation+xml" media="screen, print" />
    <data type="application/ssml+xml" transform="synthesize.xslt" xml:lang="en" media="speech">
      <with-param name="namespace:param1" as="xs:string">text</with-param>
      <extension name="namespace:function" as="xs:string" oncall="jsfun(event)">
        <param name="namespace:functionparam1" as="xs:string" required="yes" />
      </extension>
    </data>
  </presentation>
  <data type="application/openmath+xml">...</data>
</notation>

Example C.9

<html>
  <head>
    <xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform" id="x1"> 
      ...
    </xsl:stylesheet>
  </head>
  <body>
    <notation transform="#x1" src="file.om" />
  </body>
</html>

Example C.10

<html>
  <head>
    <link rel="notation" type="application/xslt+xml" href="custom.xslt" />
  </head>
  <body>
    <notation src="file.om" />
  </body>
</html>

Example C.11

<html>
  <head>
    <link rel="notation" type="application/xslt+xml" href="custom1.xslt" title="title1" />
    <link rel="alternate notation" type="application/xslt+xml" href="custom2.xslt" title="title2" />
  </head>
  <body>
    <notation src="file.om" />
  </body>
</html>

Japanese Completed translation of A MathML for CSS Profile

Yoshikazu Takamura — 2012-04-30T14:05:16

Dear Translators
And Dear W3C Math mailing list Members

I have completed the translation into Japanese of the following document:

MathML for CSS
Profile(http://www.w3.org/TR/2011/REC-mathml-for-css-20110607/)
CSSに対応するMathMLの概要書(http://www3.fctv.ne.jp/~takamu/mathml-for-
css-ja.html)

I confirm that, in compliance with the W3C Intellectual Property FAQ
(http://www.w3.org/Consortium/Legal/IPR-FAQ-20000620#translate), I have
placed a prominent disclaimer in my translation in which I disclose, (1)
the title of and link to the original English document, (2) that my
document is a translation which may contain errors, and (3) that the
original English document on the W3C website is the one that is
official. (Items (2) and (3) are in the target language.)

I confirm that the links within my translation are valid and I have
endeavoured to provide valid markup and CSS (validation tools are at
http://validator.w3.org/).

Sincerely

30.Apr.2012

高村 吉一(Yoshikazu Takamura)
MailAdress : takamu< at >mx3.fctv.ne.jp

Looking for examples

Mitchell Amiano — 2012-04-23T14:00:19

Hello,

I am assisting a math education research project at North Carolina State University, and doing an informal search for exemplars where rich internet interfaces were used to author, and interact with, course materials. 

Backstory and Motivation: The materials we presently are considering come from systems engineering and operations research. Although it uses mathematics, the approach is to use tools to explain algorithms, rather than a focus on presenting math formulas. It does however make use of spreadsheets (and solvers), and contains a considerable amount of content on linear programming and probability. The materials are meant to be very hands-on, with worksheets based on procedures coming from operations research. There is a strong interest in mobile delivery and use of standards-based approaches to managing and delivering/interacting with the content. 

To sum up: are there good exemplars of interactive curricula aimed at interacting with students, based upon MathML, HTML, ePub... ? 
 
Regards,

Mitch Amiano

Firefox 12 Release Notes

Frédéric WANG — 2012-04-25T15:33:54

Dear all,

Michael Kohlhase asked me to give regular notifications about 
improvements in Firefox's MathML implementation. I'm afraid that it 
could look like spamming but I also agree that it makes sense to inform 
the Math WG about the evolution of this implementation and it may also 
be of interest to the subscribers of math< at >w3.org. I'm just going to copy 
and paste "Firefox for developers" notes but if you need more 
information, do not hesitate to ask. I also try to give more details on 
my blog.

Firefox 12 (Release)

  * To control the directionality of MathML formulas, the |dir|
    attribute is now supported on the |<math>
    <https://developer.mozilla.org/en/MathML/Element/math>| , |<mrow>
    <https://developer.mozilla.org/en/MathML/Element/mrow>| , and
    |<mstyle> <https://developer.mozilla.org/en/MathML/Element/mstyle>|
    elements as well as on MathML Token Elements
    <https://developer.mozilla.org/Special:Tags?tag=MathML:Token+Elements>.
    This is particularly important for some Arabic mathematical
    notations <http://www.w3.org/TR/arabic-math/>.
  * The alignment attribute |align| defined in MathML3 has been
    implemented for |<munder>
    <https://developer.mozilla.org/en/MathML/Element/munder>| , |<mover>
    <https://developer.mozilla.org/en/MathML/Element/mover>| , and
    |<munderover>
    <https://developer.mozilla.org/en/MathML/Element/munderover>| .

Firefox 13 (Beta)

  * Support for the |width| attribute on |<mtable>
    <https://developer.mozilla.org/en/MathML/Element/mtable>| elements
    has been added (bug 722880
    <https://bugzilla.mozilla.org/show_bug.cgi?id=722880> ).
  * MathJax fonts
    <http://cdn.mathjax.org/mathjax/latest/fonts/HTML-CSS/TeX/otf/> are
    now used as the default fonts for mathematical text. See Fonts for
    Mozilla's MathML engine
    <https://developer.mozilla.org/en/Mozilla_MathML_Project/Fonts> for
    more information.

Firefox 14 (Aurora)

  * The syntax of the |statusline| action type on |<maction>
    <https://developer.mozilla.org/en/MathML/Element/maction>| elements
    has been adjusted to follow the MathML specification.


BTW, I'm glad to announce that Andrii Zui has been accepted to Google 
Summer of Code 2012 and is going to work on Firefox's MathML implementation:

http://www.google-melange.com/gsoc/project/google/gsoc2012/prazuber/19001
https://bugzilla.mozilla.org/show_bug.cgi?id=544036
https://bugzilla.mozilla.org/show_bug.cgi?id=744783

Speech Synthesis and Recognition of Mathematical and Scientific Content

Adam Sobieski — 2012-04-16T14:15:15


















































































Math Working Group, Greetings.  In the new Speech API Community Group, I indicated some synthesis and recognition topics pertaining to mathematical and scientific notation (http://lists.w3.org/Archives/Public/public-speech-api/2012Apr/0004.html): EPUB3-style (http://idpf.org/epub/30/spec/epub30-contentdocs.html#sec-xhtml-ssml-attrib) SSML attributes: <math ssml:ph="..."> ... </math> SSML in <annotation-xml>:
 
<math>
<semantics>
...
<annotation-xml encoding="application/ssml+xml"> ... </annotation-xml>
</semantics>
</math> Some other related topics include referencing audio in <annotation>, interoperability with media fragment URI: <math>
<semantics>
...
<annotation encoding="audio/..." src="..." /></semantics>
</math> and speech synthesis interoperability with SMIL-based scenarios. An interesting speech synthesis feature is the automatic synthesis of mathematical and scientific content.  The MathAudio project (http://lpf-esi.fe.up.pt/~audiomath/index_en.html) illustrates processing the MathML presentation layer into Portuguese (http://lpf-esi.fe.up.pt/~hfilipe/projecto/mathml.html) (http://lpf-esi.fe.up.pt/~audiomath/links_en.html). Semantic content can additionally be of use as input for such processing and related topics include somehow extending or annotating content dictionaries with linguistic data or extending or annotating linguistic data formats with content dictionary data for extensibility in that regard. I also indicated the possibility of extending or more fully utilizing speech recognition grammar techniques (SRGS/SISR) for recognition output scenarios including XML, hypertext, and/or MathML. I wanted to apprise the Math Working Group about those new developments and to welcome discussion and any comments and suggestions about the synthesis of and recognition of speech containing mathematical and scientific formulas.    Kind regards, Adam Sobieski

HostMath - Online LaTeX formula editor and math equation editor

webmaster — 2012-04-12T11:08:09

Dear support,

HostMath is a powerful interactive mathematical expressions editor. It uses WYSIWYG-style editing and allows creating mathematical equations through simple point-and-click techniques.

1. Many pre-defined Templates and Symbols in well-organized palettes that cover Mathematics, Physics, Electronics, and many other higher educations 
2. Fine adjustment for Template shapes, gaps, and thicknesses with visual interface
3. Multiple Undo and Redo 
4. Can generate equations as MathML. MathML will allow you to copy and paste math into many applications that understand MathML. 

URL: http://www.hostmath.com/



Best regards,

webmaster
webmaster< at >hostmath.com
2012-04-12

Mathematical Proofs in HTML5 Documents

Adam Sobieski — 2012-04-02T22:54:17

Math Working Group,

Greetings. I would like to describe some ideas about the representation of, the clipboarding of, and the dragging and dropping of <math> objects as well as other mathematical document objects that can each contain multiple <math> element instances along with other hypertext. Such mathematical document objects can include representations of mathematical proofs.

MathML3 includes <annotation> and <annotation-xml> elements which can provide parallel representations of mathematical semantics (http://www.w3.org/TR/MathML3/chapter5.html). The versatile clipboarding and dragging and dropping of mathematics could, then, be a JavaScript topic so as to provide at least as many data formats as are expressed in a contextual document region or selection. Relevant JavaScript API's topics include: clipboarding (http://dev.w3.org/2006/webapi/clipops/clipops.html), drag and drop (http://dev.w3.org/html5/spec/dnd.html), DataTransferItem (http://dev.w3.org/html5/spec/dnd.html#datatransferitem), and DataTransferItemList (http://dev.w3.org/html5/spec/dnd.html#datatransferitemlist). In mathematical articles and textbooks, where hypertext sections or selections may contain or be related to one or more mathematical objects, such as mathematical proof structures or substructures, combinations of structured knowledge and JavaScript can deliver new functionalities. Structured knowledge, such as representations of mathematical proofs, can be included in HTML5 documents and can be attached to or referenced by HTML5 documents. Some techniques include:
1. Having entire proofs in <math> elements. Proof formats could then express semantics in <annotation> or <annotation-xml> elements. OpenMath content dictionaries could come to exist for mathematical proof structures.

2. Having proofs in HTML5 document structure, possibly containing one or more <math> element instances, while utilizing XML attributes from other XMLNS. Proof structure and semantics can overlay the HTML5 and/or the XML can relate elements to referenced external resources. 3. Having proofs in HTML5 document structure, possibly containing one or more <math> element instances, while utilizing RDFA (http://dev.w3.org/html5/rdfa/). Proof structure and semantics can overlay the HTML5 and/or the RDFA can relate elements to referenced external resources.
4. An element from an XMLNS, resembling <semantics>, which can include <annotation>- and <annotation-xml>-like elements, and which can appear in HTML5 documents in the <head> section, or alternatively on any element, while referencing HTML5 document elements by id.

5. The use of SMIL3, SMIL timesheets, for example with timesheets.js, to align two or more XML-based documents referring to documents' elements by id's.
Kind regards, Adam Sobieski

CfP: Math Information Retrieval Worksohp 14. July 2012

2012-03-29T16:20:46

[apologies for multiple copies]

             MIR 2012 Workshop (Mathematics Information Retrieval)
             July 14. 2011 
             at CICM 2012, Bremen Germany
     http://cicm2012.cicm-conference.org/cicm.php?event=mir

The MIR Workshop brings together researchers working on information retrieval for
mathematical document collections for discussions and friendly systems
competition.

Workshop format:
===========

The MIR Workshop will consist of a traditional-style scientific program with
presentations of submitted papers in the half-day Math IR Symposium together
with the Math IR happening, where workshop participants competitively or jointly
solve a set of Math IR challenges and submit their solutions to a panel of
mathematician judges.

Important dates:
- Symposium:
   Paper Submission:        May 20. 2012
   Notification:                 May 28. 2012
   Final Versions:June 15. 2012

- Happening:
   Dataset available:         now    
   System Registration:    May 20. 2012

Organizers:
Michael Kohlhase, Jacobs University (PC co-chair)
Petr Sojka, Brno University  (PC co-chair)

Math IR Symposium at MIR 2012 
====================
http://cicm2012.cicm-conference.org/cicm.php?event=mir&menu=symposium

The Math IR Symposium is a traditional-style workshop with scientific
contributions about mathematics information retrieval. Topics include but not
limited to:

-  requirements for mathematics information retrieval: use cases and typical queries
-  formula search algorithms
-  semantically enhancing mathematical corpora for IR
-  extracting semantic relations from corpora.
-   evaluation of MIR (methods and test corpora)

 
Math IR Happening at MIR 2012 
====================
http://cicm2012.cicm-conference.org/cicm.php?event=mir&menu=happening

A friendly competition for the systems presented at the workshop. Since math
information retrieval is still quite young and developing, we will not make this
an official competition, but a happening, where we get together and test our
system on a common set of problems.  We expect the happening to transcend the
workshop proper.

Section 4.3.4.1.2 - type attribute on nary-set.class members

Andrew Miller — 2012-03-26T20:25:35

Section 4.3.4.1.2 includes the following text:

'The above rule applies to all symbols in the listed classes. In the 
case of *nary-set.class* the choice of Content Dictionary to use depends 
on the |type| attribute on the symbol, defaulting to set1 
<http://www.openmath.org/cd/set1.xhtml>, but multiset1 
<http://www.openmath.org/cd/multiset1.xhtml> should be used if 
|type|="multiset"'.

However, according to Appendix A...

*nary-set.class*  =union  <http://www.w3.org/TR/MathML/appendixa.html#parsing_union>  |intersect  <http://www.w3.org/TR/MathML/appendixa.html#parsing_intersect>  |cartesianproduct  <http://www.w3.org/TR/MathML/appendixa.html#parsing_cartesianproduct>
*union*  =*element*  |union|  {CommonAtt  <http://www.w3.org/TR/MathML/appendixa.html#parsing_CommonAtt>,DefEncAtt  <http://www.w3.org/TR/MathML/appendixa.html#parsing_DefEncAtt>, empty}
*intersect*  =*element*  |intersect|  {CommonAtt  <http://www.w3.org/TR/MathML/appendixa.html#parsing_CommonAtt>,DefEncAtt  <http://www.w3.org/TR/MathML/appendixa.html#parsing_DefEncAtt>, empty}
*cartesianproduct*  =*element*  |cartesianproduct|  {CommonAtt  <http://www.w3.org/TR/MathML/appendixa.html#parsing_CommonAtt>,DefEncAtt  <http://www.w3.org/TR/MathML/appendixa.html#parsing_DefEncAtt>, empty}
*DefEncAtt*  =*attribute*  |encoding|  {xsd:string}?,
             *attribute*  |definitionURL|  {xsd:anyURI}?
*CommonAtt*  =*attribute*  |id|  {xsd:ID}?,
             *attribute*  |xref|  {text}?,
             *attribute*  |class|  {xsd:NMTOKENS}?,
             *attribute*  |style|  {xsd:string}?,
             *attribute*  |href|  {xsd:anyURI}?,
             CommonDeprecatedAtt  <http://www.w3.org/TR/MathML/appendixa.html#parsing_CommonDeprecatedAtt>,
             NonMathMLAtt  <http://www.w3.org/TR/MathML/appendixa.html#parsing_NonMathMLAtt>*
*CommonDeprecatedAtt*  =*attribute*  |other|  {text}?
*NonMathMLAtt*  =*attribute*  |(* - (local:*|m:*)|) {xsd:string}

... it is not legal for any member of nary-set.class to have a type="multiset" attribute.

It therefore is pointless and confusing to include the text about what to do if the type="multiset" is present, if it is never legal for it to be present.

Best wishes,
Andrew

MathPlayer 2.2 stretches parentheses to the size of the integral symbol.

saf sied — 2012-03-26T03:39:20

Without using mrow tag around the parentheses, the above happens. This behavior does not happen with the summation symbol for example. Also, this is not an issue with Firefox (XHTML or HTML5). Is there any way we can get it to work for integrals without using mrow tag around the parentheses?

To understand the problem, please copy the following and save as a “.htm” file. Thank you, Saf:

/////////Begin: HTML file source view//////////

<html xmlns:m="http://www.w3.org/1998/Math/MathML" >
 
<head><object id="mathplayer" classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987"></object>
<?import namespace="m" implementation="#mathplayer"?>
</head>
 
<body>
<div>
<p>Without using mrow tag around parenthesis</p>
<br/>
<m:math><m:mo>&#8747;</m:mo><m:mi>f</m:mi><m:mo>(</m:mo><m:mi>t</m:mi><m:mo>)</m:mo><m:mi>d</m:mi><m:mi>t</m:mi></m:math>
<br/>

<p>After using mrow tag around parenthesis</p>
<m:math><m:mo>&#8747;</m:mo><m:mi>f</m:mi><m:mrow><m:mo>(</m:mo><m:mi>t</m:mi><m:mo>)</m:mo></m:mrow><m:mi>d</m:mi><m:mi>t</m:mi></m:math>
<br/>
<p>Without using mrow tag around parenthesis. Works ok with summation symbol</p>
<br/>
<m:math><m:mo>&#8721;</m:mo><m:mi>f</m:mi><m:mo>(</m:mo><m:mi>t</m:mi><m:mo>)</m:mo><m:mi>d</m:mi><m:mi>t</m:mi></m:math>
</div>
</body>
 
</html>

/////////End: HTML file source view//////////

MathML 3 - section 4.6 "The Strict Content MathML Transformation"

Andrew Miller — 2012-03-25T18:57:00

Hi all,

Section 4.6 includes the following text under point 4b:

"Rewrite interval, vectors, matrices, and matrix rows as described in 
Section 4.4.1.1 Interval |<interval>| 
<http://www.w3.org/TR/MathML/chapter4.html#contm.interval>, 
Section 4.4.9.1 Vector |<vector>| 
<http://www.w3.org/TR/MathML/chapter4.html#contm.vector>, 
Section 4.4.9.2 Matrix |<matrix>| 
<http://www.w3.org/TR/MathML/chapter4.html#contm.matrix> and 
Section 4.4.9.3 Matrix row |<matrixrow>| 
<http://www.w3.org/TR/MathML/chapter4.html#contm.matrixrow>".

However, sections 4.4.9.1, 4.4.9.2, and 4.4.9.3 do not describe any 
rules on how to rewrite vector, matrix, and matrixrow elements.

Given that vectors (and matrices, and matrixrows) can have domain 
qualifiers, I presume that there is supposed to be a transformation like 
the one for sets, although it is not clear what OpenMath the following 
is supposed to map into:
<vector>
<bvar><ci>x</ci></bvar>
<domainofapplication><set><cn>1</cn><cn>2</cn><cn>3</cn></set></domainofapplication>
<apply><plus/>
<ci>x</ci>
<cn>1</cn>
</apply>
</vector>

The OpenMath linalg7 CD has a list_to_vector symbol, but it is a binary 
function that requires the ring of the vector to be specified explicitly.

AW: Re: Using content-MathML for computation and analysis in Science and Engineering

Andreas.strotmann — 2012-03-21T00:16:06

I did not actually intend to detract from the previous discussion on assignment operators. I just noticed that a piece of common knowledge would have been important to know for newcomers to MathML Content. 

That said, I'm afraid that I need to burst a little bubble here. MathML Content brings with it what you need to describe (the semantics of) side effect free algorithms. 

Any clean Content markup language would need to add a language primitive for something that has a semantics that falls outside of the range of its existing semantic constructors. Since assignments are not context free, you would probably have some serious trouble to define an OpenMath dictionary with a clean semantics for an assignment operator.

In my 2003 dissertation I argued that this compositionality principle for content markup languages implies, in a similar logic, that typing is another semantic primitive missing from OpenMath (and by implication, MathML 3).

Now as we all know implementations are free to ignore this, as is Peter. As always, my comments are just for the language purists. 

-Andreas null

AW: Re: Using content-MathML for computation and analysis in Science and Engineering

Andreas.strotmann — 2012-03-20T23:43:15

As I pointed out to Peter offline, bindings become very intuitive when used in a syntax like 

Let x =... . Then. ...

Or

… where x=…

A fundamental property of MathML is that nobody writes it by hand. For most forms of lambda, syntactic sugar removes all the dread, as we demonstrated amply in the WebALT project.

-------- Original message --------
Subject: Re: Using content-MathML for computation and analysis in Science and Engineering 
From: Paul Libbrecht <paul< at >hoplahup.net> 
To: Andreas Strotmann <andreas.strotmann< at >gmail.com> 
CC: Bruce Miller <bruce.miller< at >nist.gov>,"www-math< at >w3.org" <www-math< at >w3.org>,Daniel Marques <dani< at >wiris.com>,Peter Murray-Rust <pm286< at >cam.ac.uk> 


Le 20 mars 2012 à 08:12, Andreas Strotmann a écrit :
More to the point, a sequence of assignments would therefore 'naturally' be expressed as nested lambda expressions in MathML to preserve semantics.


My personal opinion, as a mathematician, is that this way of writing might be well-founded in terms of expressivity or logic, it remains fully opaque to most mathematicians except logicians.

The concept of binding is understandable, and even that of mapping, but having to enter everything within lambda terms tends to be a real readability problem.

paul

AW: Re: Using content-MathML for computation and analysis in Science and Engineering

Andreas.strotmann — 2012-03-20T09:42:41

Peter,

You make an excellent suggestion here. I recently talked to people involved heavily in developing the DDI standard for social science data sets. They too are considering a MathML Content based extension to document data cleaning operations that were performed on the data. Algorithm specifications are a fairly common need, I agree.

-Andreas

-------- Original message --------
Subject: Re: Using content-MathML for computation and analysis in Science and Engineering 
From: Peter Murray-Rust <pm286< at >cam.ac.uk> 
To: Andreas Strotmann <andreas.strotmann< at >gmail.com> 
CC: Bruce Miller <bruce.miller< at >nist.gov>,"www-math< at >w3.org" <www-math< at >w3.org>,Paul Libbrecht <paul< at >hoplahup.net>,Daniel Marques <dani< at >wiris.com> 

null

MathML3 specification is inconsistent about qualifier content of non-strict constructors

Andrew Miller — 2012-03-20T02:34:10

Hi all,

In most of the MathML 3 specification, the content model is described 
using the 'content' field, and if qualifiers are allowed in the content, 
this is mentioned in the 'Content' row of the table.

Throughout most of the specification, mentioning something in the 
'Qualifiers' row for an element doesn't imply that the qualifier can be 
a child element of that element, and instead implies that the qualifier 
is used with the parent apply element - this is explicitly stated in the 
last paragraph of 4.1.5.

However, when constructor elements are defined (for example, in section 
4.4.5.1), qualifiers are listed in the Qualifier row, but not in the 
Content row. The examples (and the 'Parsing MathML' appendix, and the 
transformation rule in 4.3.4.2.2), however, contradict the lack of the 
qualifiers in the element content, so it seems that the omission of the 
qualifiers from the 'Content' rows of the constructors must have been 
accidental.

Best wishes,
Andrew

Minor problems found in MathML 3 specification

Andrew Miller — 2012-03-19T21:35:23

Hi all,

I've found a few (primarily editorial) issues with Chapter 4 of the 
MathML 3 specification; I can't find the link for a bug tracker for 
specification issues, so I presume this list is the correct place to 
send things like that?

1. Rewrite: partialdiffdegree
      This rule refers to the expression as 'expression-in-x1-xk' in the 
match rule, but as 'A' in what it is supposed to be transformed into.

2. Section 4.2.2.1 Strict uses of|<ci>
      This section neglects to specify how ci elements with type 
'complex' are transformed into strict form, given that there is no 
complex in the mathmltypes CD.

Best wishes,
Andrew

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