MathML-Next Ideas

[AdamSobieski]

Introduction

Some ideas for MathML4 are presented. Comments and discussion are welcomed.

Presentation, Semantics, Metadata and Extensibility

Presentation and Semantics

<math id="eq1">
  <presentation>
    <annotation-xml encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml encoding="application/svg+xml">...</annotation-xml>
    <annotation encoding="image/png" src="data:..." />
    <annotation-xml encoding="MathML-Presentation">...</annotation-xml>
  </presentation>
  <semantics>
    <annotation-xml encoding="application/openmath+xml">...</annotation-xml>
    <annotation-xml encoding="MathML-Content">...</annotation-xml>
  </semantics>
</math>

Metadata

<math id="eq1">
  <presentation>
    <annotation-xml encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml encoding="application/svg+xml">...</annotation-xml>
    <annotation encoding="image/png" src="data:..." />
    <annotation-xml encoding="MathML-Presentation">...</annotation-xml>
  </presentation>
  <semantics>
    <annotation-xml encoding="application/openmath+xml">...</annotation-xml>
    <annotation-xml encoding="MathML-Content">...</annotation-xml>
  </semantics>
  <metadata>
    <annotation-xml encoding="application/rdf+xml">...</annotation-xml>
    <annotation encoding="application/json+ld">...</annotation>
  </metadata>
</math>

Extensibility

Are there any other varieties of content for a mathematical expression beyond “presentation”, “semantics” and “metadata”? Might we want to include “other” for extensibility?

<math id="eq1">
  <presentation>
    <annotation-xml encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml encoding="application/svg+xml">...</annotation-xml>
    <annotation encoding="image/png" src="data:..." />
    <annotation-xml encoding="MathML-Presentation">...</annotation-xml>
  </presentation>
  <semantics>
    <annotation-xml encoding="application/openmath+xml">...</annotation-xml>
    <annotation-xml encoding="MathML-Content">...</annotation-xml>
  </semantics>
  <metadata>
    <annotation-xml encoding="application/rdf+xml">...</annotation-xml>
    <annotation encoding="application/json+ld">...</annotation>
  </metadata>
  <other rel="http://www.example.com/semantic-uri/">
    <annotation-xml encoding="...">...</annotation-xml>
  </other>
</math>

Would content which interrelates mathematical expressions, e.g. for mathematical proofs, be expression “metadata” or “other” content? Would derivations of mathematical expressions be expression “metadata” or “other” content?

Selecting Content from Alternatives and Content Negotiation

Algorithms for selecting “presentation”, “semantic”, “metadata” or “other” content from alternatives may resemble agent-driven or reactive content negotiation.

Together with the encoding attribute, lang, notation, media, and q attributes can facilitate content selection from alternatives in a manner which resembles HTTP-based content negotiation for mathematical content.

See also: MathML3 <annotation> element
See also: MathML3 <annotation-xml> element
See also: HTML5 <source> element

Internationalization

For scenarios where natural language is utilized in the “presentation” annotation content, a BCP47 language attribute can adorn annotation markup and “presentation” annotations can also be described in expression “metadata”.

<math id="eq1">
  <presentation>
    <annotation-xml lang="en" encoding="MathML-Presentation">...</annotation-xml>
    <annotation-xml lang="fr" encoding="MathML-Presentation">...</annotation-xml>
  </presentation>
  <semantics>
    <annotation-xml encoding="MathML-Content">...</annotation-xml>
  </semantics>
  <metadata>
    <annotation-xml encoding="application/rdf+xml">...</annotation-xml>
  </metadata>
</math>

Multimodality

“Presentation” annotations can include content spanning multiple modalities, e.g. SSML or audio, and “presentation” annotations can also be described in expression “metadata”.

<math id="eq1">
  <presentation>
    <annotation-xml lang="en" encoding="MathML-Presentation">...</annotation-xml>
    <annotation-xml lang="fr" encoding="MathML-Presentation">...</annotation-xml>
    <annotation-xml lang="en" encoding="application/ssml+xml">...</annotation-xml>
    <annotation-xml lang="fr" encoding="application/ssml+xml">...</annotation-xml>
    <annotation lang="en" encoding="audio/mpeg" src="..." />
    <annotation lang="fr" encoding="audio/mpeg" src="..." />
  </presentation>
  <semantics>
    <annotation-xml encoding="MathML-Content">...</annotation-xml>
  </semantics>
  <metadata>
    <annotation-xml encoding="application/rdf+xml">...</annotation-xml>
  </metadata>
</math>

Notation

Might the values of a notation attribute be the display names of notations, URI’s, or encoded strings resembling BCP47? Might the values of a notation attribute be, instead, lists of settings and their values resembling the style attribute?

<math id="eq1">
  <presentation>
    <annotation-xml notation="Notation 1" encoding="MathML-Presentation">...</annotation-xml>
    <annotation-xml notation="Notation 2" encoding="MathML-Presentation">...</annotation-xml>
    <annotation-xml notation="Notation 3" encoding="MathML-Presentation">...</annotation-xml>
  </presentation>
  <semantics>
    <annotation-xml encoding="MathML-Content">...</annotation-xml>
  </semantics>
  <metadata>
    <annotation-xml encoding="application/rdf+xml">...</annotation-xml>
  </metadata>
</math>

The following example shows a combination of multiple presentation formats with multiple notations.

<math id="eq1">
  <presentation>
    <annotation-xml notation="Notation 1" encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml notation="Notation 2" encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml notation="Notation 3" encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml notation="Notation 1" encoding="application/svg+xml">...</annotation-xml>
    <annotation-xml notation="Notation 2" encoding="application/svg+xml">...</annotation-xml>
    <annotation-xml notation="Notation 3" encoding="application/svg+xml">...</annotation-xml>
    <annotation notation="Notation 1" encoding="image/png" src="data:..." />
    <annotation notation="Notation 2" encoding="image/png" src="data:..." />
    <annotation notation="Notation 3" encoding="image/png" src="data:..." />
    <annotation-xml notation="Notation 1" encoding="MathML-Presentation">...</annotation-xml>
    <annotation-xml notation="Notation 2" encoding="MathML-Presentation">...</annotation-xml>
    <annotation-xml notation="Notation 3" encoding="MathML-Presentation">...</annotation-xml>
  </presentation>
  <semantics>
    <annotation-xml encoding="application/openmath+xml">...</annotation-xml>
    <annotation-xml encoding="MathML-Content">...</annotation-xml>
  </semantics>
  <metadata>
    <annotation-xml encoding="application/rdf+xml">...</annotation-xml>
  </metadata>
</math>

Media Queries

A media attribute can facilitate the use of media queries. “Presentation” annotations can also be described in expression “metadata”.

<math id="eq1">
  <presentation>
    <annotation-xml encoding="MathML-Presentation">...</annotation-xml>
    <annotation media="(resolution >= 2dppx)" encoding="image/png" src="eq1-high.png" />
    <annotation media="(resolution < 2dppx)" encoding="image/png" src="eq1-low.png" />
    <annotation-xml media="speech" encoding="application/ssml+xml">...</annotation-xml>
    <annotation media="speech" encoding="audio/mpeg" src="..." />
  </presentation>
  <metadata>
    <annotation-xml encoding="application/rdf+xml">...</annotation-xml>
  </metadata>
</math>

Quality Scores

<math id="eq1">
  <presentation>
    <annotation-xml q="0.9" encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml q="0.9" encoding="application/svg+xml">...</annotation-xml>
    <annotation q="0.9" encoding="image/png" src="data:..." />
    <annotation-xml q="1.0" encoding="MathML-Presentation">...</annotation-xml>
  </presentation>
</math>

Remote Content

Remote Resources

<math id="eq1">
  <presentation>
    <annotation-xml encoding="application/xhtml+xml" src="eq1.xhtml" />
    <annotation-xml encoding="application/svg+xml" src="eq1.svg" />
    <annotation encoding="image/png" src="eq1.png" />
    <annotation-xml encoding="MathML-Presentation" src="eq1.mmlp" />
  </presentation>
  <semantics>
    <annotation-xml encoding="application/openmath+xml" src="eq1.om" />
    <annotation-xml encoding="MathML-Content" src="eq1.mmlc" />
  </semantics>
</math>

Remote Components

Perhaps utilizing HTTP-based agent-driven or reactive content negotiation, URL’s could be provided for “presentation”, “semantics” and “metadata” components.

<math id="eq1">
  <presentation src="presentation.php?eq=eq1" />
  <semantics src="semantics.php?eq=eq1" />
  <metadata src="metadata.php?eq=eq1" />
</math>

Alternatively, via a “partial” keyword or Boolean attribute, multiple MathML files could be merged together into mathematical expressions.

URL String Interpolation, Templating and Formatting

Described are uses of a pattern attribute for providing string templates with which string interpolation algorithms can produce values for src attributes on <annotation> and <annotation-xml> elements.

A pattern attribute could be of use for specifying string interpolation placeholders in URL query strings.

<math id="eq1">
  <presentation>
    <annotation-xml pattern="math.php?equation=eq1&amp;type={encoding}&amp;language={lang}" />
  </presentation>
</math>

A pattern attribute could also be of use for specifying string interpolation placeholders in file names and paths.

<math id="eq1">
  <presentation>
    <annotation-xml encoding="application/mathml-presentation+xml" pattern="eq1-{lang}.mmlp" />
  </presentation>
</math>

Media queries could be utilized via a media attribute.

<math id="eq1">
  <presentation>
    <annotation media="(resolution >= 2dppx)" encoding="image/png" pattern="math.php?equation=eq1&amp;type=image%2Fpng&amp;notation={notation}&amp;resolution=high" />
    <annotation media="(resolution < 2dppx)" encoding="image/png" pattern="math.php?equation=eq1&amp;type=image%2Fpng&amp;notation={notation}&amp;resolution=low" />
  </presentation>
</math>

Those <annotation-xml> and <annotation> elements with encoding, lang, notation, media, or q attributes could be described as “more specific” and thus to be utilized first when matching for content selection.

<math id="eq1">
  <presentation>
    <annotation-xml encoding="application/ssml+xml" pattern="math-synthesis.php?equation=eq1&amp;language={lang}" />
    <annotation encoding="audio/mpeg" pattern="math-audio.php?equation=eq1&amp;type=audio%2Fmpeg&amp;language={lang}" />
    <annotation-xml pattern="math.php?equation=eq1&amp;type={encoding}&amp;language={lang}&amp;notation={notation}" />
  </presentation>
</math>

The encoding attribute, the lang attribute and possibly the notation attribute could be utilized with multiple, delimited (e.g. space delimited) values for specifying when a pattern is valid.

<math id="eq1">
  <presentation>
    <annotation-xml encoding="application/mathml-presentation+xml application/xhtml+xml application/svg+xml" lang="en fr es de" pattern="math.php?equation=eq1&amp;type={encoding}&amp;language={lang}&amp;notation={notation}" />
    <annotation encoding="image/png" lang="en fr es de" pattern="math.php?equation=eq1&amp;type={encoding}&amp;language={lang}&amp;notation={notation}" />
  </presentation>
</math>

<math id="eq1">
  <presentation>
    <annotation-xml encoding="application/mathml-presentation+xml" lang="en fr es de" pattern="eq1-{lang}.mmlp" />
  </presentation>
</math>

There is a caveat to delimiting MIME types with spaces in that MIME types can have parameters and spaces could exist between MIME types and their parameters as well as in the quoted string values of their parameters, for instance when specifying codecs.

See: RFC 7231 § 3.1.1.1, RFC 6381

MIME types with spaces can be observed in the HTML5 specification, e.g. HTML5 <source> element § Example 18.

audio/ogg; codecs=speex

If spaces are desired to delimit sets or lists of MIME types, then collapsing spaces in MIME types, including those with complex parameter values, e.g. codecs, would be required.

<math id="eq1">
  <presentation>
    <annotation encoding="audio/ogg;codecs=speex audio/mpeg" pattern="math-audio.php?equation=eq1&amp;type={encoding}&amp;language={lang}" />
  </presentation>
</math>

A fuller set of placeholders can be created for URL string interpolation. For example, a customizable filename {extension} placeholder can be derived from the encoding selected.

<math id="eq1">
  <presentation>
    <annotation-xml encoding="application/mathml-presentation+xml application/xhtml+xml application/svg+xml" lang="en fr es de" pattern="eq1-{lang}.{extension}" />
  </presentation>
</math>

See also: printf format string
See also: String interpolation
See also: Template processing

Remote Mathematical Expressions

Remote mathematical expressions could be facilitated via a src attribute on <math> elements.

<math id="eq1" src="eq1.mml" />

Additionally, HTML5 <img> and <object> elements could be of use.

<img id="eq1" src="eq1.mml" />

<object id="eq1" data="eq1.mml" type="application/mathml+xml" />

See also: HTML5 <img> element
See also: HTML5 <object> element

[davidcarlisle]

This suggestion seems to be a breaking change from all previous versions of MathML, where <semantics> by default displays its first argument. The use cases of supplying alternative presentations and metadata all seem to be covered by the existing <semantics> given suitable annotation-xml labels.

[AdamSobieski]

A simple workaround appears to be to rename <semantics> to <content>. As per:

<math id="eq1">
  <presentation>
    <annotation-xml encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml encoding="application/svg+xml">...</annotation-xml>
    <annotation encoding="image/png" src="data:..." />
    <annotation-xml encoding="application/mathml-presentation+xml">...</annotation-xml>
  </presentation>
  <content>
    <annotation-xml encoding="application/openmath+xml">...</annotation-xml>
    <annotation-xml encoding="application/mathml-content+xml">...</annotation-xml>
  </content>
</math>

We could also map MathML’s <semantics> to <annotations> as per the second example in #80.

Instead of using the first child element or annotation of MathML’s <semantics>, the proposal includes that users’ preferences, e.g. browser settings, would be of use in selecting from alternatives, resembling, perhaps, MathJax's context menu settings.

There is also a proposed q or quality attribute where authors could specify the relative quality of alternatives. As per:

<math id="eq1">
  <presentation>
    <annotation-xml q="0.9" encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml q="0.9" encoding="application/svg+xml">...</annotation-xml>
    <annotation q="0.9" encoding="image/png" src="data:..." />
    <annotation-xml q="1.0" encoding="application/mathml-presentation+xml">...</annotation-xml>
  </presentation>
</math>

These particulars would be detailed in the specification of a content selection algorithm.

[davidcarlisle]

There would be a very high cost to these proposals (changing the HTML5 parser and incompatible with all existing MathML tools) and I haven't yet seen any examples that are not just a re-arrangement of the MathML3 <semantics> markup. If you used the existing <semantics> markup then in some cases you may need to follow some conventions on the attributes on annotation-xml elements to distinguish the cases that you are distinguishing with <presentation but in most cases it would seem to just be a simple re-write unless I am missing something? The example you post above is not understood by any MathML system but

<math id="eq1">
  <semantics>
    <mrow> some default presentation</mrow>
    <annotation-xml encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml encoding="application/svg+xml">...</annotation-xml>
    <annotation encoding="image/png" src="data:..." />
    <annotation-xml encoding="application/mathml-presentation+xml">...</annotation-xml>
    <annotation-xml encoding="application/openmath+xml">...</annotation-xml>
    <annotation-xml encoding="application/mathml-content+xml">...</annotation-xml>
  </semantics>
</math>

Is understood by all MathML systems going back to version 1.0.

In this case I don't see any gain in functionality to compensate for the loss of interoperability.

[AdamSobieski]

Introduction

Beyond purely syntactic topics, the options differ with respect to selecting content from alternatives – with respect to content selection algorithms. Content selection algorithms can be a gain in functionality.

Discussion

There are three syntactic options under discussion. Option 1 is MathML3, option 2 was introduced in this issue (#68) and option 3 was introduced in issue #80.

There are three options for distinguishing between varieties of annotations:

1. MathML3 utilizes cd and name attributes on <annotation> and <annotation-xml> elements to distinguish between varieties of annotations.
2. Option 2 utilizes <presentation>, <semantics> (or <content>), <metadata> and <other> elements to distinguish between varieties of annotations.
3. Option 3 utilizes a kind attribute on <annotation> and/or <annotation-xml> elements to distinguish between varieties of annotations.

There are two options for selecting content from alternatives:

1. MathML3 selects the first child of the <semantics> element as the default presentation content.
2. More advanced content selection algorithms.

There are at least two mental models of mathematical expressions as represented by markup:

1. The first child of <semantics> element is the mathematical expression which is annotated by subsequent <annotation> and <annotation-xml> elements.
2. The <math> element, in its entirety, represents a mathematical expression and it can contain alternatives for presentation, semantics, metadata as well as other types of content.

A tabulation

Option	Distinguishing Varieties of Annotations	Content Selection
MathML3	uses cd and name attributes on <annotation> and <annotation-xml> elements See also: MathML3 Chapter 5, https://www.openmath.org/cd/mathmlkeys	select first child of <semantics> element as presentation
Option 2 (#68)	uses <presentation>, <semantics> (or <content>), <metadata> and <other> elements	a content selection algorithm
Option 3 (#80)	uses kind attribute on <annotation> and <annotation-xml> elements	a content selection algorithm

Option 1: MathML3

<math id="eq1">
  <semantics>
    <mrow>some default presentation</mrow>
    <annotation-xml cd="mathmlkeys" name="alternate-representation" encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml cd="mathmlkeys" name="alternate-representation" encoding="application/svg+xml">...</annotation-xml>
    <annotation cd="mathmlkeys" name="alternate-representation" encoding="image/png" src="data:..." />
    <annotation-xml cd="mathmlkeys" name="contentequiv" encoding="application/openmath+xml">...</annotation-xml>
    <annotation-xml cd="mathmlkeys" name="contentequiv" encoding="application/mathml-content+xml">...</annotation-xml>
  </semantics>
</math>

Question: If a Web browser, EPUB reader, or other software cannot render MathML presentation markup, is it specified what the software should do when provided with presentation alternatives? Is it specified that, for example, the software should iterate through the sequence of presentation alternatives? That is, for the above example, is it specified that a software should consider, in sequence: the MathML presentation content, the XHTML content, the SVG content, then the PNG content, as they occur in the XML-based sequence, until it finds a presentation alternative which it can render?

Option 2: Multiple containing elements

<math id="eq1">
  <presentation>
    <annotation-xml encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml encoding="application/svg+xml">...</annotation-xml>
    <annotation encoding="image/png" src="data:..." />
    <annotation-xml encoding="application/mathml-presentation+xml">...</annotation-xml>
  </presentation>
  <content>
    <annotation-xml encoding="application/openmath+xml">...</annotation-xml>
    <annotation-xml encoding="application/mathml-content+xml">...</annotation-xml>
    <annotation-xml encoding="application/rdf+xml">...</annotation-xml>
  </content>
  <metadata>
    <annotation-xml encoding="application/rdf+xml">...</annotation-xml>
    <annotation encoding="application/json+ld">...</annotation>
  </metadata>
  <other rel="http://www.example.com/semantic-uri/">
    <annotation-xml encoding="...">...</annotation-xml>
  </other>
</math>

Option 3: One containing element with a kind attribute

<math id="eq1">
  <annotations>
    <annotation-xml kind="presentation" encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml kind="presentation" encoding="application/svg+xml">...</annotation-xml>
    <annotation kind="presentation" encoding="image/png" src="data:..." />
    <annotation-xml kind="presentation" encoding="application/mathml-presentation+xml">...</annotation-xml>
    <annotation-xml kind="semantics" encoding="application/openmath+xml">...</annotation-xml>
    <annotation-xml kind="semantics" encoding="application/mathml-content+xml">...</annotation-xml>
    <annotation-xml kind="semantics" encoding="application/rdf+xml">...</annotation-xml>
    <annotation-xml kind="metadata" encoding="application/rdf+xml">...</annotation-xml>
    <annotation kind="metadata" encoding="application/json+ld">...</annotation>
    <annotation-xml kind="other" rel="http://www.example.com/semantic-uri/" encoding="...">...</annotation-xml>
  </annotations>
</math>

Content Selection Algorithms

Content selection algorithms are approaches to selecting resources from multiple alternatives. Examples of content selection algorithms include HTTP content negotiation. In the context of mathematical markup, content selection algorithms can be advantageous to authors and to users.

Content selection algorithms can allow authors to provide alternative presentation, semantics, metadata and other varieties of resources which can facilitate mathematics rendering and utilization. Content selection algorithms can allow users to configure their browsers, EPUB readers or other software to their preferences. Users can, similarly, configure MathJax to select between rendering modes: CommonHTML, MathML, HTML-CSS and SVG.

Should an author provide only one presentation content, then that content is to be selected. When two or more presentation alternatives are provided by an author, instead of automatically selecting the first alternative, we can utilize a content selection algorithm.

<math id="eq1">
  <presentation>
    <annotation-xml encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml encoding="application/mathml-presentation+xml">...</annotation-xml>
  </presentation>
</math>

The encoding, lang, notation, media and q attributes could be utilized on <annotation> and <annotation-xml> elements to describe inline or remote resources so as to facilitate algorithmic approaches to content selection. In the above example, while the MathML presentation content is the second XML child of the <presentation> element, a software may still select it over the XHTML content.

In HTML5, multimedia content selection is facilitated via the <source> element.

In HTTP content negotiation, an example of a content selection algorithm, a number of HTTP request headers are utilized:

Accept-Language: de; q=1.0, en; q=0.5
Accept: text/html; q=1.0, text/*; q=0.8, image/gif; q=0.6, image/jpeg; q=0.6, image/*; q=0.5, */*; q=0.1

These HTTP headers correspond with browser and user settings and configuration. Such settings and configuration could interplay with the content expressible with syntactic options 2 and 3 when selecting content from alternatives.

Furthermore, via a q attribute, authors could specify the relative quality of alternatives or resources.

<math id="eq1">
  <presentation>
    <annotation-xml q="0.9" encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml q="1.0" encoding="application/mathml-presentation+xml">...</annotation-xml>
  </presentation>
</math>

Styling

Custom styling of presentation content in these scenarios is discussed briefly in issue #78. The gist is that a :selected pseudo-class can be utilized to indicate the specific <annotation> or <annotation-xml> element selected by the browser, EPUB reader, or other software.

Option 2 styling ideas:

#eq1 > presentation > annotation-xml:selected >> mrow

Option 3 styling ideas:

#eq1 > annotations > annotation-xml[kind='presentation']:selected >> mrow

Conclusion

Beyond purely syntactic topics, the options differ with respect to selecting content from alternatives – with respect to content selection algorithms. Content selection algorithms can be a gain in functionality.

Content selection algorithms can allow authors to provide alternative presentation, semantics, metadata and other varieties of resources which can facilitate mathematics rendering and utilization. Content selection algorithms can allow users to configure their browsers, EPUB readers or other software to their preferences. Users can, similarly, configure MathJax to select between rendering modes: CommonHTML, MathML, HTML-CSS and SVG.

The content selection algorithms which can accompany syntactic options 2 and 3 are new functionality for MathML and may provide value – may provide benefit – which offsets the cost of breaking changes during the versioning of MathML.

[davidcarlisle]

Sorry I still see no functionality gain in the proposed syntactic changes. With the mathml markup as defined in mathml 1-3 the rendering as first child is only a default, the rendering agent can opt to use an svg or presentation or image annotation instead as the source for the rendering, the suggestion above proposes adding the q attribute to steer that choice, but that attribute could be proposed without the disruptive change to an incompatible syntax. <math id="eq1"> <presentation> <annotation-xml q="0.9" encoding="application/xhtml+xml">...</annotation-xml> <annotation-xml q="1.0" encoding="application/mathml-presentation+xml">...</annotation-xml> </presentation> </math> is the same as the mathml3 below apart from the added q attribute <math id="eq1"> <semantics> <mrow>default</mrow> <annotation-xml q="0.9" encoding="application/xhtml+xml">...</annotation-xml> <annotation-xml q="1.0" encoding="application/mathml-presentation+xml">...</annotation-xml> </semantics> </math>

[AdamSobieski]

Absolutely. The encoding, lang, media and q attributes are drawn from HTML5 multimedia content selection and HTTP content negotiation. The notation attribute is presently theoretical. The encoding, lang, notation, media and q attributes could be utilized on <annotation> and <annotation-xml> elements for each of the indicated syntactic options. Any or all of the aforementioned attributes could adorn <annotation> and <annotation-xml> elements in a MathML3-based syntax, which we could refer to as option 4 – there now being at least four options.

<math id="eq1">
  <semantics>
    <mrow>default</mrow>
    <annotation-xml q="0.9" encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml q="1.0" encoding="application/mathml-presentation+xml">...</annotation-xml>
  </semantics>
</math>

<math id="eq1">
  <semantics>
    <mrow>default</mrow>
    <annotation-xml q="1.0" lang="fr" encoding="application/mathml-presentation+xml">...</annotation-xml>
  </semantics>
</math>

<math id="eq1">
  <semantics>
    <mrow>default</mrow>
    <annotation-xml q="0.9" encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml q="1.0" encoding="application/mathml-presentation+xml">...</annotation-xml>
    <annotation q="0.2" media="(resolution >= 2dppx)" encoding="image/png" src="eq1-hi-res.png" />
    <annotation q="0.2" media="(resolution < 2dppx)" encoding="image/png" src="eq1-lo-res.png" />
  </semantics>
</math>

Furthermore, space-delimited values for encoding and lang could be utilized in MathML3-based syntaxes with a pattern attribute which utilizes string interpolation.

<math id="eq1">
  <semantics>
    <mrow>default</mrow>
    <annotation-xml q="0.9" lang="en fr es de" encoding="application/xhtml+xml" pattern="math.php?language={lang}&amp;encoding=application%2Fxhtml+xml" />
    <annotation-xml q="1.0" lang="en fr es de" encoding="application/mathml-presentation+xml" pattern="math.php?language={lang}&amp;encoding=application%2Fmathml-presentation+xml" />
  </semantics>
</math>

It would, then, be a matter of describing the content selection algorithms with which to select resources from alternatives. One option is to consider utilization of HTTP content negotiation. HTTP request headers could be of use, as per:

Accept-Language: en; q=1.0, fr; q=0.8, es; q=0.8, de; q=0.8
Accept: application/mathml-presentation+xml; q=1.0, application/xhtml+xml; q=0.8, application/svg+xml; q=0.8, image/png; q=0.2, image/*; q=0.2, */*; q=0.1

These HTTP headers, possibly string inputs to content selection algorithms, could be of use for indicating software and user settings and configuration when selecting described resources from alternatives.

[davidcarlisle]

I don't think the other options should be considered. The costs of introducing incompatible element markup which has no fallback in every existing MathML system compared to a functionally equivalent use of some additional attributes which while technically invalid in mathml3 are likely to be silently accepted in all existing systems is simply too high.

[AdamSobieski]

Sounds good. I can make use of backwards-compatible syntaxes for brainstorming and examples. I also updated issue #79.

[AdamSobieski]

Introduction

By adding one attribute to the <semantics> element, default, the above ideas and examples can be expressed in a backwards-compatible syntax. The default attribute has as its possible values: “first” and “none”. The default value of the default attribute is “first”.

The value of “first” for the default attribute indicates that the behavior of the <semantics> element is the MathML3 behavior, where the first child element is the default presentation content. The value of “none” for the default attribute indicates that no child element of the <semantics> element is intended as default content.

Selecting Content from Alternatives and Content Negotiation

Algorithms for selecting “presentation”, “semantic”, “metadata” or “other” content from alternatives may resemble agent-driven or reactive content negotiation.

Together with the encoding attribute, lang, notation, media, and q attributes can facilitate content selection from alternatives in a manner which resembles HTTP-based content negotiation for mathematical content.

See also: MathML3 <annotation> element
See also: MathML3 <annotation-xml> element
See also: HTML5 <source> element

Internationalization

For scenarios where natural language is utilized in the “presentation” annotation content, a BCP47 language attribute can adorn annotation markup and “presentation” annotations can also be described in expression “metadata”.

<math id="eq1">
  <semantics default="none">
    <annotation-xml lang="en" encoding="application/mathml-presentation+xml">...</annotation-xml>
    <annotation-xml lang="fr" encoding="application/mathml-presentation+xml">...</annotation-xml>
  </semantics>
</math>

<math id="eq1">
  <semantics default="none">
    <annotation-xml lang="en" encoding="application/mathml-presentation+xml">...</annotation-xml>
    <annotation-xml lang="fr" encoding="application/mathml-presentation+xml">...</annotation-xml>
    <annotation-xml name="contentequiv" encoding="application/mathml-content+xml">...</annotation-xml>
    <annotation-xml name="metadata" encoding="application/rdf+xml">...</annotation-xml>
  </semantics>
</math>

Multimodality

“Presentation” annotations can include content spanning multiple modalities, e.g. SSML or audio, and “presentation” annotations can also be described in expression “metadata”.

<math id="eq1">
  <semantics default="none">
    <annotation-xml lang="en" encoding="application/mathml-presentation+xml">...</annotation-xml>
    <annotation-xml lang="fr" encoding="application/mathml-presentation+xml">...</annotation-xml>
    <annotation-xml lang="en" encoding="application/ssml+xml">...</annotation-xml>
    <annotation-xml lang="fr" encoding="application/ssml+xml">...</annotation-xml>
    <annotation lang="en" encoding="audio/mpeg" src="..." />
    <annotation lang="fr" encoding="audio/mpeg" src="..." />
    <annotation-xml name="contentequiv" encoding="application/mathml-content+xml">...</annotation-xml>
    <annotation-xml name="metadata" encoding="application/rdf+xml">...</annotation-xml>
  </semantics>
</math>

Notation

Might the values of a notation attribute be the display names of notations, URI’s, or encoded strings resembling BCP47? Might the values of a notation attribute be, instead, lists of settings and their values resembling the style attribute?

<math id="eq1">
  <semantics default="none">
    <annotation-xml notation="Notation 1" encoding="application/mathml-presentation+xml">...</annotation-xml>
    <annotation-xml notation="Notation 2" encoding="application/mathml-presentation+xml">...</annotation-xml>
    <annotation-xml notation="Notation 3" encoding="application/mathml-presentation+xml">...</annotation-xml>
  </semantics>
</math>

The following example shows a combination of multiple presentation formats with multiple notations.

<math id="eq1">
  <semantics default="none">
    <annotation-xml notation="Notation 1" encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml notation="Notation 2" encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml notation="Notation 3" encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml notation="Notation 1" encoding="application/svg+xml">...</annotation-xml>
    <annotation-xml notation="Notation 2" encoding="application/svg+xml">...</annotation-xml>
    <annotation-xml notation="Notation 3" encoding="application/svg+xml">...</annotation-xml>
    <annotation notation="Notation 1" encoding="image/png" src="data:..." />
    <annotation notation="Notation 2" encoding="image/png" src="data:..." />
    <annotation notation="Notation 3" encoding="image/png" src="data:..." />
    <annotation-xml notation="Notation 1" encoding="application/mathml-presentation+xml">...</annotation-xml>
    <annotation-xml notation="Notation 2" encoding="application/mathml-presentation+xml">...</annotation-xml>
    <annotation-xml notation="Notation 3" encoding="application/mathml-presentation+xml">...</annotation-xml>
    <annotation-xml name="contentequiv" encoding="application/openmath+xml">...</annotation-xml>
    <annotation-xml name="contentequiv" encoding="application/mathml-content+xml">...</annotation-xml>
    <annotation-xml name="metadata" encoding="application/rdf+xml">...</annotation-xml>
  </semantics>
</math>

Media Queries

A media attribute can facilitate the use of media queries. “Presentation” annotations can also be described in expression “metadata”.

<math id="eq1">
  <semantics default="none">
    <annotation-xml encoding="application/mathml-presentation+xml">...</annotation-xml>
    <annotation media="(resolution >= 2dppx)" encoding="image/png" src="eq1-high.png" />
    <annotation media="(resolution < 2dppx)" encoding="image/png" src="eq1-low.png" />
    <annotation-xml media="speech" encoding="application/ssml+xml">...</annotation-xml>
    <annotation media="speech" encoding="audio/mpeg" src="..." />
    <annotation-xml name="metadata" encoding="application/rdf+xml">...</annotation-xml>
  </semantics>
</math>

Quality Scores

<math id="eq1">
  <semantics default="none">
    <annotation-xml q="0.9" encoding="application/xhtml+xml">...</annotation-xml>
    <annotation-xml q="0.9" encoding="application/svg+xml">...</annotation-xml>
    <annotation q="0.9" encoding="image/png" src="data:..." />
    <annotation-xml q="1.0" encoding="application/mathml-presentation+xml">...</annotation-xml>
  </semantics>
</math>

Remote Content

Remote Resources

<math id="eq1">
  <semantics default="none">
    <annotation-xml encoding="application/xhtml+xml" src="eq1.xhtml" />
    <annotation-xml encoding="application/svg+xml" src="eq1.svg" />
    <annotation encoding="image/png" src="eq1.png" />
    <annotation-xml encoding="application/mathml-presentation+xml" src="eq1.mmlp" />
    <annotation-xml name="contentequiv" encoding="application/openmath+xml" src="eq1.om" />
    <annotation-xml name="contentequiv" encoding="application/mathml-content+xml" src="eq1.mmlc" />
  </semantics>
</math>

URL String Interpolation, Templating and Formatting

Described are uses of a pattern attribute for providing string templates with which string interpolation algorithms can produce values for src attributes on <annotation> and <annotation-xml> elements.

A pattern attribute could be of use for specifying string interpolation placeholders in URL query strings.

<math id="eq1">
  <semantics default="none">
    <annotation-xml pattern="math.php?equation=eq1&amp;type={encoding}&amp;language={lang}" />
  </semantics>
</math>

A pattern attribute could also be of use for specifying string interpolation placeholders in file names and paths.

<math id="eq1">
  <semantics default="none">
    <annotation-xml encoding="application/mathml-presentation+xml" pattern="eq1-{lang}.mmlp" />
  </semantics>
</math>

Media queries could be utilized via a media attribute.

<math id="eq1">
  <semantics default="none">
    <annotation media="(resolution >= 2dppx)" encoding="image/png" pattern="math.php?equation=eq1&amp;type=image%2Fpng&amp;notation={notation}&amp;resolution=high" />
    <annotation media="(resolution < 2dppx)" encoding="image/png" pattern="math.php?equation=eq1&amp;type=image%2Fpng&amp;notation={notation}&amp;resolution=low" />
  </semantics>
</math>

Those <annotation-xml> and <annotation> elements with encoding, lang, notation, media, or q attributes could be described as “more specific” and thus to be utilized first when matching for content selection.

<math id="eq1">
  <semantics default="none">
    <annotation-xml encoding="application/ssml+xml" pattern="math-synthesis.php?equation=eq1&amp;language={lang}" />
    <annotation encoding="audio/mpeg" pattern="math-audio.php?equation=eq1&amp;type=audio%2Fmpeg&amp;language={lang}" />
    <annotation-xml pattern="math.php?equation=eq1&amp;type={encoding}&amp;language={lang}&amp;notation={notation}" />
  </semantics>
</math>

The encoding attribute, the lang attribute and possibly the notation attribute could be utilized with multiple, delimited (e.g. space delimited) values for specifying when a pattern is valid.

<math id="eq1">
  <semantics default="none">
    <annotation-xml encoding="application/mathml-presentation+xml application/xhtml+xml application/svg+xml" lang="en fr es de" pattern="math.php?equation=eq1&amp;type={encoding}&amp;language={lang}&amp;notation={notation}" />
    <annotation encoding="image/png" lang="en fr es de" pattern="math.php?equation=eq1&amp;type={encoding}&amp;language={lang}&amp;notation={notation}" />
  </semantics>
</math>

<math id="eq1">
  <semantics default="none">
    <annotation-xml encoding="application/mathml-presentation+xml" lang="en fr es de" pattern="eq1-{lang}.mmlp" />
  </semantics>
</math>

There is a caveat to delimiting MIME types with spaces in that MIME types can have parameters and spaces could exist between MIME types and their parameters as well as in the quoted string values of their parameters, for instance when specifying codecs.

See: RFC 7231 § 3.1.1.1, RFC 6381

MIME types with spaces can be observed in the HTML5 specification, e.g. HTML5 <source> element § Example 18.

audio/ogg; codecs=speex

If spaces are desired to delimit sets or lists of MIME types, then collapsing spaces in MIME types, including those with complex parameter values, e.g. codecs, would be required.

<math id="eq1">
  <semantics default="none">
    <annotation encoding="audio/ogg;codecs=speex audio/mpeg" pattern="math-audio.php?equation=eq1&amp;type={encoding}&amp;language={lang}" />
  </semantics>
</math>

A fuller set of placeholders can be created for URL string interpolation. For example, a customizable filename {extension} placeholder can be derived from the encoding selected.

<math id="eq1">
  <semantics default="none">
    <annotation-xml encoding="application/mathml-presentation+xml application/xhtml+xml application/svg+xml" lang="en fr es de" pattern="eq1-{lang}.{extension}" />
  </semantics>
</math>

See also: printf format string
See also: String interpolation
See also: Template processing

Remote Mathematical Expressions

Remote mathematical expressions could be facilitated via a src attribute on <math> elements.

<math id="eq1" src="eq1.mml" />

Additionally, HTML5 <img> and <object> elements could be of use.

<img id="eq1" src="eq1.mml" />

<object id="eq1" data="eq1.mml" type="application/mathml+xml" />

See also: HTML5 <img> element
See also: HTML5 <object> element

[davidcarlisle]

I don't understand the use case for the suggested default attribute. There has to be a default specified somehow. Perhaps you are off line or the servers specified in the annotations are down, presumably the default if no annotation can be used and no default is specified is to act like an empty mrow, so the suggested

<semantics default="none">
<xml-annotation>...

seems to be identical to the existing

<semantics>
<mrow/>
<xml-annotation>...