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==Element types==
==Element types==


The following includes descriptions for the various types of MathML elements for the purpose of this document.
The following includes descriptions and examples for the various types of MathML elements for the purpose of this document.
Some examples are pulled from MDN.
Some examples are pulled from MDN.  Information about potential roles and relations will be included alongside the elements they cover.


===Tokens===
===Tokens===
Line 29: Line 29:
ms is used for arbitrary string literals meant to be interpreted by a programming language or other system.
ms is used for arbitrary string literals meant to be interpreted by a programming language or other system.
A special case is mglyph (image), which is used inside other token elements when a Unicode character is unavailable.
A special case is mglyph (image), which is used inside other token elements when a Unicode character is unavailable.
Another special case is the malignmark element, which will be described below in the table and matrix section.
Example markup is listed below.
Example markup is listed below.


<pre>
<pre>
<math>  
<math>
   <mi>y</mi>
   <mi>y</mi>
  <mo>+</mo>
   <mn>10</mn>
   <mn>10</mn>
   <mo>+</mo>
   <mspace width="1em"/>
   <mtext>Arbitrary text</mtext>
   <mtext>Arbitrary text</mtext>
   <mspace width="1em"/>
   <mspace width="1em"/>
   <ms>InterpretedStringLiteral</ms>
   <ms>InterpretedStringLiteral</ms>
  <mspace width="1em"/>
   <mi>
   <mi>
     <mglyph src="an-image" alt="an-image-description"/>
     <mglyph src="x.png" alt="x"/>
   </mi>
   </mi>
</math>
</math>
</pre>
</pre>
[[File:MathML-tokens.png|frame|left|The above describes y + 10, arbitrary text, an interpreted string literal, and a glyph (an image of x).  Rendered using MathJax due to lack of glyph support in Gecko.]]
<br clear=all>
====Potential role mappings====
* mi = MATHML_IDENTIFIER
* mn = MATHML_NUMBER
* mo = MATHML_OPERATOR
* mtext = MATHML_TEXT
* mspace = MATHML_SPACE
* ms = MATHML_STRING_LITERAL
* mglyph = MATHML_GLYPH


===Layout===
===Layout===
These have been split into three groups: layout elements that describe semantic meaning,
These have been split into three groups: layout elements that describe semantic meaning,
layout elements only for formatting and styling, and layout elements for describing elementary math.
layout elements only for formatting and styling, and layout elements for describing elementary math.


Line 80: Line 95:
     </mrow>
     </mrow>
   </mrow>
   </mrow>
  <mspace width="1em"/>
   <mfrac>
   <mfrac>
     <mi>x</mi>
     <mi>x</mi>
     <mn>2</mn>
     <mn>2</mn>
   </mfrac>
   </mfrac>
  <mspace width="1em"/>
   <msqrt>
   <msqrt>
     <mn>2</mn>
     <mn>2</mn>
   </msqrt>
   </msqrt>
  <mspace width="1em"/>
   <mroot>
   <mroot>
     <mi>x</mi>
     <mi>x</mi>
     <mn>5</mn>
     <mn>5</mn>
   </mroot>
   </mroot>
  <mspace width="1em"/>
   <mfenced>
   <mfenced>
     <mi>x</mi>
     <mi>x</mi>
Line 96: Line 115:
     <mi>z</mi>
     <mi>z</mi>
   </mfenced>
   </mfenced>
  <mspace width="1em"/>
   <menclose notation="circle">
   <menclose notation="circle">
     <mi>a</mi>
     <mi>a</mi>
Line 104: Line 124:
</pre>
</pre>


The above describes (x+y) + 2, x/2 as a fraction, the square root of 2, the 5th root of x,  
[[File:MathML-layout-semantics.png|frame|left|The above describes (x+y) + 2, x/2 as a fraction, the square root of 2, the 5th root of x, a 3D vector (x, y, z), and (a + b) circled. Rendered using Gecko.]]
a 3D vector (x, y, z), and (a + b) circled.
<br clear=all>
 
=====Potential role mappings=====
* mrow = MATHML_ROW
* mfrac = MATHML_FRACTION
* msqrt = MATHML_SQUARE_ROOT
* mroot = MATHML_ROOT
* mfenced = MATHML_FENCED
* menclose = MATHML_ENCLOSED
 
=====Potential relations=====
* row to children: MATHML_ROW_FOR
* children to row: MATHML_IN_ROW
* numerator to fraction: MATHML_NUMERATOR_OF
* fraction to numerator: MATHML_NUMERATOR
* denominator to fraction: MATHML_DENOMINATOR_OF
* fraction to denominator: MATHML_DENOMINATOR
* radicand to root: MATHML_RADICAND_OF
* root to radicand: MATHML_RADICAND
* root index to root: MATHML_ROOT_INDEX_OF
* root to root index: MATHML_ROOT_INDEX


====Formatting====
====Formatting====
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* mpadded - adds padding for child elements, containing any number of elements
* mpadded - adds padding for child elements, containing any number of elements
* mphantom - renders child elements invisibly, containing any number of elements
* mphantom - renders child elements invisibly, containing any number of elements
As an mphantom element is visually rendered as an equivalent mrow containing the same elements, but using blank space, it's possible that these sections can be called out explicitly by ATs based on context (e.g. a worksheet for math problems).


Example markup is listed below.
Example markup is listed below.
Line 130: Line 172:
</pre>
</pre>


The above describes the expression "x + y" rendered in blue from right to left,
[[File:MathML-layout-formatting.png|frame|left|The above describes the expression "x + y" rendered in blue from right to left, with extra padding, and with the "+ y" not displayed. Rendered using Gecko.]]
with extra padding, and with the "+ y" not displayed.
<br clear=all>
 
=====Potential role mappings=====
* mstyle = MATHML_STYLE
* mpadded = MATHML_PADDED
* mphantom = MATHML_PHANTOM


====Elementary math====
====Elementary math====
Line 170: Line 217:
     <mn>508</mn>
     <mn>508</mn>
   </mstack>
   </mstack>
  <mspace width="1em"/>
   <mlongdiv>
   <mlongdiv>
     <mn>5</mn>
     <mn>5</mn>
Line 178: Line 226:
</pre>
</pre>


The above describes the subtraction of 15 from 523, with a borrow from the ten's column to the one's column,
[[File:MathML-layout-elementary.png|frame|left|300px|The above describes the subtraction of 15 from 523, with a borrow from the ten's column to the one's column, as well as the division of 5 by 5 resulting in 1. Rendered using the MathML-mml3ff addon with Gecko as elementary math support is not natively available in Gecko.]]
as well as the division of 5 by 5 resulting in 1.
<br clear=all>
 
=====Potential role mappings=====
* mstack = MATHML_STACK
* mlongdiv = MATHML_LONG_DIVISION
* msgroup = MATHML_STACK_GROUP
* msrow = MATHML_STACK_ROW
* mscarries = MATHML_STACK_CARRIES
* mscarry = MATHML_STACK_CARRY
* msline = MATHML_STACK_LINE


===Scripts and limits===
===Scripts and limits===
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* mmultiscripts - multiple scripts, with children described below
* mmultiscripts - multiple scripts, with children described below


mmultiscripts uses a special syntax.  The first child is the base, then a possible subscript and superscript.
mmultiscripts uses a special syntax.  The first child is the base, then any number of pairs of post-subscripts and post-superscripts.
If prescripts are desired, a <mprescripts/> tag is included, then a possible subscript and superscript.
If prescripts are desired, a <mprescripts/> tag is included, then any number of pairs of pre-subscripts and pre-superscripts.
<none/> can be substituted for scripts if no script is desired for each of these cases.
<none/> can be substituted for scripts if no script is desired in a particular pair.
Example markup is listed below.
Example markup is listed below.


<pre>
<pre>
<math>
<math display="block">
   <msubsup>
   <msubsup>
     <mi>b</mi>
     <mi>b</mi>
Line 204: Line 261:
     <mn>2</mn>
     <mn>2</mn>
   </msubsup>
   </msubsup>
  <mspace width="1em"/>
   <munderover>
   <munderover>
     <mo>&sum;</mo>
     <mo>&sum;</mo>
    <mi>5</mi>
     <mrow>
     <mrow>
       <mi>n</mi>
       <mi>n</mi>
Line 212: Line 269:
       <mn>1</mn>
       <mn>1</mn>
     </mrow>
     </mrow>
    <mn>5</mn>
   </munderover>
   </munderover>
   <mi>n</mi>
   <mi>n</mi>
   <mo>=</mo>
   <mo>=</mo>
   <mn>15</mn>
   <mn>15</mn>
  <mspace width="1em"/>
   <mmultiscripts>
   <mmultiscripts>
     <mi>x</mi>
     <mi>x</mi>
Line 227: Line 286:
</pre>
</pre>


The above describes the base b with superscript 1 and subscript 2,
[[File:MathML-scripts-limits.png|frame|left|The above describes the base b with subscript 1 and superscript 2, the summation of n from 1 to 5 being 15, and x with post-superscript a and pre-subscript b. Rendered using Gecko.]]
the summation of n from 1 to 5 being 15, and x with post-superscript a and pre-subscript b.
<br clear=all>
 
====Potential role mappings====
* msub = MATHML_SUB
* msup = MATHML_SUP
* msubsup = MATHML_SUB_SUP
* munder = MATHML_UNDER
* mover = MATHML_OVER
* munderover = MATHML_UNDER_OVER
* mmultiscripts = MATHML_MULTISCRIPTS
 
====Potential relations====
* underscript to parent structure (munder/munderover): MATHML_UNDER_OF
* parent structure to underscript: MATHML_UNDER
* overscript to parent structure (mover/munderover): MATHML_OVER_OF
* parent structure to overscript: MATHML_OVER
* base to parent structure (munder, mover, munderover, msub, msup, msubsup, mmultiscripts): MATHML_BASE_OF
* parent structure to base: MATHML_BASE
* subscript to parent structure (msub, msubsup): MATHML_SUBSCRIPT_OF
* parent structure to subscript: MATHML_SUBSCRIPT
* superscript to parent structure (msup, msubsup): MATHML_SUPERSCRIPT_OF
* parent structure to superscript: MATHML_SUPERSCRIPT
* pre-subscript to parent structure (mmultiscripts): MATHML_PRE_SUBSCRIPT_OF
* parent structure to pre-subscript: MATHML_PRE_SUBSCRIPT
* pre-superscript to parent structure (mmultiscripts): MATHML_PRE_SUPERSCRIPT_OF
* parent structure to pre-superscript: MATHML_PRE_SUPERSCRIPT
* post-subscript to parent structure (mmultiscripts): MATHML_POST_SUBSCRIPT_OF
* parent structure to post-subscript: MATHML_POST_SUBSCRIPT
* post-superscript to parent structure (mmultiscripts): MATHML_POST_SUPERSCRIPT_OF
* parent structure to post-superscript: MATHML_POST_SUPERSCRIPT
 
===Tables/matrices===
These elements describe a table or matrix.  This is also used for layout.
These include the following:
* mtable - the container for a table, contains any number of mtr or mlabeledtr elements
* mtr - a row, containing any number of mtd elements
* mlabeledtr - a labelled row, having a caption on the side, containing any number of mtd elements
* mtd - a table cell, containing any number of elements
 
For mlabeledtr, the first mtd contained inside becomes the caption.
 
In addition, there are two elements used for table formatting:
* maligngroup - denotes a column in a table, used for alignment
* malignmark - denotes an alignment point inside an alignment group
 
malignmark is used inside a token element to set the alignment point.
Example markup is listed below.
 
<pre>
<math>
  <mrow>
    <mo>[</mo>
    <mtable>
      <mtr>
        <mtd>
          <mn>1</mn>
        </mtd>
        <mtd>
          <mn>0</mn>
        </mtd>
      </mtr>
      <mtr>
        <mtd>
          <mn>0</mn>
        </mtd>
        <mtd>
          <mn>1</mn>
        </mtd>
      </mtr>
    </mtable>
    <mo>]</mo>
  </mrow>
  <mspace width="1em"/>
  <mtable>
    <mlabeledtr>
      <mtd>
        <mtext>Volume of a sphere</mtext>
      </mtd>
      <mtd>
        <mi>V</mi>
        <mo>=</mo>
        <mfrac>
          <mn>4</mn>
          <mn>3</mn>
        </mfrac>
        <mo>&InvisibleTimes;</mo>
        <mi>&pi;</mi>
        <mo>&InvisibleTimes;</mo>
        <msup>
          <mi>r</mi>
          <mn>3</mn>
        </msup>
      </mtd>
    </mlabeledtr>
  </mtable>
  <mspace width="1em"/>
  <mtable>
    <mtr>
      <mrow>
        <mn>3</mn>
        <mo>&InvisibleTimes;</mo>
        <maligngroup/>
        <mi>x</mi>
        <maligngroup/>
        <mo>+</mo>
        <maligngroup/>
        <mi>y</mi>
        <maligngroup/>
        <mo>=</mo>
        <maligngroup/>
        <mn>7</mn>
      </mrow>
    </mtr>
    <mtr>
      <mrow>
        <mphantom>
          <mn>0</mn>
          <mo>&InvisibleTimes;</mo>
          <maligngroup/>
          <mi>x</mi>
          <maligngroup/>
          <mo>+</mo>
        </mphantom>
        <maligngroup/>
        <mi>y</mi>
        <maligngroup/>
        <mo>=</mo>
        <maligngroup/>
        <mn>1</mn>
      </mrow>
    </mtr>
  </mtable>
</math>
</pre>
 
[[File:MathML-tables-matrices.png|frame|left|The above describes the two-by-two identity matrix, the equation to determine the volume of a sphere, and two aligned equations.  Rendered using MathJax due to lack of support of mlabeledtr, maligngroup, and malignmark in Gecko.]]
<br clear=all>
 
====Potential role mappings====
* mtable = MATHML_TABLE
* mtr = MATHML_LABELED_ROW
* mlabeledtr = MATHML_TABLE_ROW
* mtd = MATHML_CELL
* maligngroup = MATHML_ALIGNMENT_GROUP
* malignmark = MATHML_ALIGNMENT_MARK
 
===Semantics annotation===
These elements provide explicit annotation for MathML.
These include the following:
* semantics - starts a semantic annotation block, containing MathML and annotations
* annotation - annotation information in non-XML format
* annotation-xml - annotation information in XML format


=Interface=
The first child of semantics is the content being annotated, with the following
annotation elements annotating the content.


==nsIAccessibleMathML==
Example markup is listed below.
Inherit from nsISupports.


<pre>
<pre>
readonly attribute AString tokenValue;
<math>
// Get token value for token MathML elements (mi, mo, mn, mtext, mspace, ms,
  <semantics>
// mglyph).  Returns empty string if not a token element.
    <!-- Presentation MathML -->
    <mrow>
      <msup>
        <mi>x</mi>
        <mn>2</mn>
      </msup>
      <mo>+</mo>
      <mi>y</mi>
    </mrow>
    <!-- Content MathML -->
    <annotation-xml encoding="MathML-Content">
      <apply>
        <plus/>
        <apply>
          <power/>
          <ci>x</ci>
          <cn type="integer">2</cn>
        </apply>
        <ci>y</ci>
      </apply>
    </annotation-xml>
    <!-- annotate TeX -->
    <annotation encoding="application/x-tex">
      x^{2} + y
    </annotation>
  </semantics>
</math>
</pre>
 
[[File:MathML-semantics-annotation.png|frame|left|The above is the square of x added to y, with the content also annotated (invisibly) as Content MathML and TeX markup.  Rendered using Gecko.]]
<br clear=all>
 
====Potential role mappings====
* semantics = MATHML_SEMANTICS
* annotation = MATHML_ANNOTATION
* annotation-xml = MATHML_XML_ANNOTATION
 
===Other===
Other elements not fitting into the above categories.
* maction - binds actions to expressions
* merror - displays content as an error message


readonly attribute boolean isToken;
maction elements allow for interactivity with MathML content.
// Check if this element is a token MathML element.
Example markup is listed below.


readonly attribute nsIPersistentProperties attributes;
<pre>
// Get attributes specific to the MathML element.
<math>
  <merror>
    <mrow>
      <mtext>Division by zero: </mtext>
      <mfrac>
        <mn>1</mn>
        <mn>0</mn>
      </mfrac>
    </mrow>
  </merror>
</math>
</pre>
</pre>


Two options for describing relations between MathML elements:
[[File:MathML-other-error.png|frame|left|The above is a divide by zero error.  Rendered using Gecko.]]
<br clear=all>


Option 1:  Explicit readonly attributes (accessors) for going from parent elements to children and vice versa.  e.g.
<pre>
<pre>
readonly attribute nsIAccessibleMathML radicand;
<math>
readonly attribute nsIAccessibleMathML rootIndex;
  <maction actiontype="toggle">
readonly attribute nsIAccessibleMathML under;
    <mfrac>
...
      <mn>6</mn>
readonly attribute nsIAccessibleMathML parent;
      <mn>8</mn>
    </mfrac>
    <mfrac>
      <mrow>
        <mn>3</mn>
        <mo>&sdot;</mo>
        <mn>2</mn>
      </mrow>
      <mrow>
        <mn>4</mn>
        <mo>&sdot;</mo>
        <mn>2</mn>
      </mrow>
    </mfrac>
    <mfrac>
      <mn>3</mn>
      <mn>4</mn>
    </mfrac>
  </maction>
</math>
</pre>
</pre>


Returns nullptr if the related accessible doesn't exist.
[[File:MathML-other-action.gif|frame|left|The above is a togglable expression displaying 6/8, (3*2)/(4*2), and 3/4 upon each mouse press.  Rendered using Gecko.]]
<br clear=all>
 
====Potential role mappings====
* maction = MATHML_ACTION
* merror = MATHML_ERROR
 
=Interface=
 
==MathMLAccessible==
Inherit from HyperTextAccessibleWrap.


Option 2:  Relations linking accessibles based on role, so we won't have attributes/functions in the interface.  An example would be for a fraction structure, as follows.
* NativeAttributes - Override Accessible, and append MathML specific attributes if the element accepts them.
* RelationByType - Override Accessible, process MathML specific relations.
 
Attributes of interest might include the following:
 
* accent - Boolean value determining if the operator is an accent over the content.
* accentunder - Boolean value determining if the operator is an accent under the content.
* actiontype - String value specifying what an maction should do.
* align - String value specifying the type of alignment to be used for an mtable, munder, mover, munderover, or mstack.  May be useful for determining logical ordering of an equation.
* bevelled - Boolean value determining rendering format of the fraction. May be useful for word choice (e.g. "one over two" vs. "one divided by two").
* close - String value for the closing delimiter of an mfenced element.
* columnlines - String value for the type of line between table columns.  May be useful for determining table purpose.
* crossout - String value specifying the type of crossout to be used in an mscarry, changing the crossout's meaning.
* dir - String value (ltr, rtl) specifying text direction of the content.
* fence - Boolean value specifying whether an mo is a fence element.
* href - String value for hyperlinking to a URI.
* largeop - Boolean value for determining if an mo should be drawn larger.  May be useful in determining semantics.
* linethickness - String or length value determining thickness of an mfrac line.  May be useful in determining fraction's purpose (e.g. displaying binomial coefficients for a linethickness of 0).
* location - String (cardinal direction) value determining location of an mscarry relative to its anchoring element.  May be useful in determining the carry's purpose.
* longdivstyle - String value controlling the appearance of an mlongdiv.  May be useful in determining its usage.
* mathvariant - String value specifying the logical class of a token element.  May be useful in determining a token's usage.
* notation - String value specifying the style to apply to the contents of an menclose.
* open - String value for the opening delimiter of an mfenced element.
* position - Integer value for mstack and mlongdiv child elements determining horizontal positioning.
* rowlines - String value for the type of line between table rows.
* selection - Integer value for determining which child element of an maction is to be used.
* separator - Boolean value specifying whether an mo is a separator.
* separators - String value containing separator values for an mfenced element.
* shift - Integer value for mstack and mlongdiv child elements determining vertical positioning.
* stretchy - Boolean value determining if an mo stretches to its adjacent elements' size.  May be useful in determining operator usage.
 
MathML attributes will be added to/from this tentative list to be displayed under the accessible object attributes based on their usefulness to ATs.
 
Relations will link accessibles based on role.  An example would be for a fraction structure, as follows.


<pre>
<pre>
Line 271: Line 593:
</pre>
</pre>


mfrac would have RELATION_NUMERATOR_IS -> mi and RELATION_DENOMINATOR_IS -> mn or similar.
mfrac would have RELATION_NUMERATOR -> mi and RELATION_DENOMINATOR -> mn.
mi would have RELATION_NUMERATOR_FOR -> mfrac and mn would have RELATION_DENOMINATOR_FOR -> mfrac.
mi would have RELATION_NUMERATOR_OF -> mfrac and mn would have RELATION_DENOMINATOR_OF -> mfrac.
 
A list of relations is as follows:
 
* MATHML_NUMERATOR_OF
* MATHML_NUMERATOR
* MATHML_DENOMINATOR_OF
* MATHML_DENOMINATOR
* MATHML_RADICAND_OF
* MATHML_RADICAND
* MATHML_ROOT_INDEX_OF
* MATHML_ROOT_INDEX
* MATHML_UNDER_OF
* MATHML_UNDER
* MATHML_OVER_OF
* MATHML_OVER
* MATHML_BASE_OF
* MATHML_BASE
* MATHML_SUBSCRIPT_OF
* MATHML_SUBSCRIPT
* MATHML_SUPERSCRIPT_OF
* MATHML_SUPERSCRIPT
* MATHML_PRE_SUBSCRIPT_OF
* MATHML_PRE_SUBSCRIPT
* MATHML_PRE_SUPERSCRIPT_OF
* MATHML_PRE_SUPERSCRIPT
* MATHML_POST_SUBSCRIPT_OF
* MATHML_POST_SUBSCRIPT
* MATHML_POST_SUPERSCRIPT_OF
* MATHML_POST_SUPERSCRIPT
* MATHML_ROW_FOR
* MATHML_IN_ROW


==MathMLAccessible==
==MathMLTableAccessible, MathMLTableRowAccessible, and MathMLTableCellAccessible==
Inherit from AccessibleWrap, and implements nsIAccessibleMathML.
Inherit from HTMLTableAccessible, HTMLTableRowAccessible, and HTMLTableCellAccessible respectively.


* NativeAttributes - Override Accessible, and append MathML specific attributes if the element accepts them.
Override NativeAttributes and RelationByType as with MathMLAccessible.
* GetTokenValue - Sets token value string if applicable.
The table elements can be traversed using the same interface as HTMLTableAccessible (nsIAccessibleTable and nsIAccessibleTableCell).
* GetIsToken - Returns true if element is a token element.


==Roles==
==Roles==
One role for each of the following constructs (41 of them):
One role for each of the following constructs (41 of them), plus the <math> tag itself:


====Tokens====
====Tokens====
Line 342: Line 694:
* maction
* maction
* merror
* merror
* math


===Sample Gecko roles===
===Sample Gecko roles===
* MATHML_MATH
* MATHML_IDENTIFIER
* MATHML_IDENTIFIER
* MATHML_NUMBER
* MATHML_NUMBER
Line 385: Line 739:
* MATHML_STACK_CARRY
* MATHML_STACK_CARRY
* MATHML_STACK_LINE
* MATHML_STACK_LINE
==Comparison with WebKit==
There's a decent mapping between the proposed interface and how WebKit currently implements MathML accessibility.
As an example, the <msup> element will be used.
<pre>
<math>
  <msup>
    <mi>x</mi>
    <mn>2</mn>
  </msup>
</math>
</pre>
MathML elements are of AXRole AXGroup.  In order to determine the type of MathML element, the AXSubrole is checked.  The <msup> element has an AXSubrole of AXMathSubscriptSuperscript.
In order to determine the type of MathML element it is (<msup>, <msub>, or <msubsup>), there are the following three attributes that are added:
* AXMathBase
* AXMathSubscript
* AXMathSuperscript
These attributes point to the element fulfilling each particular role, and have a nil value otherwise.
In this case, since it's a superscript element, AXMathBase points to the <mi> and AXMathSuperscript points to the <mn>.  AXMathSubscript has a nil value.
On the <mi> and <mn> elements, no additional information regarding MathML structure is given, apart from knowing that the sub-roles are AXMathIdentifier and AXMathNumber respectively.
This is an advantage of the proposed interface, as it provides a way for child elements to know what part in their parent structure they are.
<mi> would know it's the base, and <mn> would know it's the superscript in this case.
With regards to mapping the proposed interface back to a WebKit compatible format, the existing AccessibleWrap and RoleMap can be modified so that the same interface is provided on OS X.
Additional information will also be available in the proposed interface (AXMathBaseOf or similar for the above example).
Jwei
29

edits

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