A Parsing MathML

Overview: Mathematical Markup Language (MathML) Version 3.0
Previous: 8 MathML3 Content Dictionaries
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A Parsing MathML
    A.1 Use of MathML as Well-Formed XML
    A.2 Using the RelaxNG Schema for MathML3
        A.2.1 Full MathML
        A.2.2 The Grammar for Presentation MathML
        A.2.3 The Grammar for Strict Content MathML3
        A.2.4 The Grammar for Pragmatic MathML
        A.2.5 Deprecated Features
        A.2.6 MathML as a module in a RelaxNG Schema
    A.3 Using the MathML DTD
    A.4 Using the MathML XML Schema

A.1 Use of MathML as Well-Formed XML

Issue update_schema wiki (member only)
DTD and W3C XML Schema

DTD and W3C XML Schema need updating to MathML3
Resolution None recorded

A MathML document must be a well-formed XML document using elements in the MathML namespace as defined by this specification, however it is not required that the document refer to any specific Document Type Definition (DTD) or schema that specifies MathML. It is sometimes advantagous not to specify such a language definition as these files are large, often much larger than the MathML expression and unless they have been previously cached by the MathML application, the time taken to fetch the DTD or schema may have an appreciable effect on the processing of the MathML document.

Note also that if no DTD is specified with a DOCTYPE declaration, that entity references (for example to refer to MathML characters by name) may not be used. The document should be encoded in an encoding (for example UTF-8) in which all needed characters may be encoded as character data, or characters may be referenced using numeric character references, for example ∫ rather than ∫

If a MathML fragment is parsed without a DTD, in other words as a well-formed XML fragment, it is the responsibility of the processing application to treat the white space characters occurring outside of token elements as not significant.

However, in many circumstances, especially while producing or editing MathML, it is useful to use a language definition, to constrain the editing process or to check the correctness of generated files. The following section, Section A.2 Using the RelaxNG Schema for MathML3, discusses the RelaxNG Schema for MathML3 [RelaxNG], which forms a normative part of the specification. Following that, Section A.4 Using the MathML XML Schema, and Section A.3 Using the MathML DTD discuss alternative languages definition using the document type definitions (DTD) and the W3C XML schema language, [XMLSchemas], both of which are derived from the normative RelaxNG schema automatically. One should note that the schema definitions of the language is currently stricter than the DTD version. That is, a schema validating processor will declare invalid documents that are declared valid by a (DTD) validating XML parser. This is partly due to the fact that the XML schema language may express additional constraints not expressable in the DTD, and partly due to the fact that for reasons of compatibility with earlier releases, the DTD is intentionally forgiving in some places and does not enforce constraints that are specified in the text of this specification.

A.2 Using the RelaxNG Schema for MathML3

MathML documents should be validated using the RelaxNG Schema for MathML, either in the XML encoding (http://www.w3.org/Math/RelaxNG/mathml3/mathml3.rng) or in compact notation (http://www.w3.org/Math/RelaxNG/mathml3/mathml3.rnc) which is also shown below.

In contrast to DTDs there is no in-document method to associate a RelaxNG schema with a document.

We provide five RelaxNG schemata for sub-languages of MathML3:

we will present them in detail in the next sections below. As the compact notation for RelaxNG grammars is more readable, we will use this format here.

Note that the RelaxNG grammars here are considerably more strict than the MathML2 DTDs (even in strict mode).

A.2.1 Full MathML

The RelaxNG schema for full MathML builds on the schema describing the various arts of teh language which are given in the following sections. It can be found at http://www.w3.org/Math/RelaxNG/mathml3/mathml3.rnc. 

#     This is the Mathematical Markup Language (MathML) 3.0, an XML
#     application for describing mathematical notation and capturing
#     both its structure and content.
#
#     Copyright 1998-2008 W3C (MIT, ERCIM, Keio)
# 
#     Use and distribution of this code are permitted under the terms
#     W3C Software Notice and License
#     http://www.w3.org/Consortium/Legal/2002/copyright-software-20021231
#
#
#     Revision:    mathml3.rnc,v 1.7 2008/11/09 00:24:40 dcarlis Exp $
#
#    Update to MathML3 and Relax NG: David Carlisle and Michael Kohlhase

default namespace m = "http://www.w3.org/1998/Math/MathML"


## the core, strict Content MathML
include "mathml3-strict.rnc"

## Content Expressions now allow pMathML in ci and csymbol
include "mathml3-pragmatic.rnc" {
 
}
 

## Presentation Expressions allow Content Expressions mixed in everywhere
include "mathml3-presentation.rnc"

## include the relevant content dictionaries
include "mathml3-cds-pragmatic.rnc"


## deprecated constucts
include "mathml3-deprecated.rnc"
 {
 
}

 
ContInPres |= ContExp

A.2.2 The Grammar for Presentation MathML 

#     This is the Mathematical Markup Language (MathML) 3.0, an XML
#     application for describing mathematical notation and capturing
#     both its structure and content.
#
#     Copyright 1998-2008 W3C (MIT, ERCIM, Keio)
# 
#     Use and distribution of this code are permitted under the terms
#     W3C Software Notice and License
#     http://www.w3.org/Consortium/Legal/2002/copyright-software-20021231
#
#
#     Revision:    mathml3-presentation.rnc,v 1.8 2008/11/09 11:15:50 mkohlhas2 Exp $
#
#    Update to MathML3 and Relax NG: David Carlisle and Michael Kohlhase

default namespace m = "http://www.w3.org/1998/Math/MathML"


math.content |= ContInPres*

MathML.Common.attrib |= attribute class {xsd:NMTOKENS}?,attribute style {xsd:string}?


Browser-interface.attrib = attribute baseline {xsd:string}?,
                           attribute overflow {"scroll" | "elide" | "truncate" | "scale" | "linebreak"}?,
                           attribute altimg {xsd:anyURI}?,
                           attribute alttext {xsd:string}?,
       			   attribute type {xsd:string}?,
			   attribute name {xsd:string}?,	    
			   attribute height {xsd:string}?,
			   attribute width {xsd:string}?

math.attlist |= Browser-interface.attrib,attribute display {"block" | "inline"}?,
                attribute dir {"ltr" | "rtl"}?,
                linebreak.attrib

simple-size = "small" | "normal" | "big"

centering.values = "left" | "center" | "right"

named-space = "veryverythinmathspace" | "verythinmathspace" | "thinmathspace" | 
              "mediummathspace" | 
              "thickmathspace" | "verythickmathspace" | "veryverythickmathspace"
thickness = "thin" | "medium" | "thick"

# number with units used to specified lengths 

length-with-unit = 
    xsd:string #{pattern="(-?([0-9]+|[0-9]*\.[0-9]+)(em|ex|px|in|cm|mm|pt|pc|%))|0"}
length-with-optional-unit = 
   xsd:string #{pattern="-?([0-9]+|[0-9]*\.[0-9]+)(em|ex|px|in|cm|mm|pt|pc|%)?"}

# This is just "infinity" that can be used as a length 
infinity = "infinity"

# colors defined as RGB 
RGB-color = xsd:string {pattern="#(([0-9]|[a-f]){3}|([0-9]|[a-f]){6})"}

# The mathematics style attributes. These attributes are valid on all
#     presentation token elements except "mspace" and "mglyph", and on no
#     other elements except "mstyle". 

Token-style.attrib = attribute mathvariant
		       {"normal" | "bold" | "italic" | "bold-italic" | "double-struck" | 
                        "bold-fraktur" | "script" | "bold-script" | "fraktur" | 
 			"sans-serif" | "bold-sans-serif" | "sans-serif-italic" | 
			"sans-serif-bold-italic" | "monospace" | 
                        "initial" | "tailed" | "looped" | "stretched"}?,
                     attribute mathsize {simple-size | length-with-unit}?,

                     attribute mathcolor {xsd:string}?,
   		     attribute mathbackground {xsd:string}?

truefalse = "true" | "false"

Operator.attrib = 
# this attribute value is normally inferred from the position of
# the operator in its "<mrow"> 
   attribute form {"prefix" | "infix" | "postfix"}?,
   # set by dictionary, else it is "thickmathspace" 
   attribute lspace {length-with-unit | named-space}?,
   # set by dictionary, else it is "thickmathspace" 
   attribute rspace {length-with-unit | named-space}?,
   # set by dictionnary, else it is "false" 
   attribute fence {truefalse}?,
   # set by dictionnary, else it is "false" 
   attribute separator {truefalse}?,
   # set by dictionnary, else it is "false" 
   attribute stretchy {truefalse}?,
   # set by dictionnary, else it is "true" 
   attribute symmetric {truefalse}?,
   # set by dictionnary, else it is "false" 
   attribute movablelimits {truefalse}?,
   # set by dictionnary, else it is "false" 
   attribute accent {truefalse}?,
   # set by dictionnary, else it is "false" 
   attribute largeop {truefalse}?,
   attribute minsize {length-with-unit | named-space}?,
   attribute maxsize {length-with-unit | named-space | infinity | xsd:float}?


mglyph = element mglyph {MathML.Common.attrib,
                     attribute alt {xsd:string}?,
                     (attribute src {xsd:anyURI}| attribute fontfamily {xsd:string}),
		     attribute width {xsd:string}?,
		     attribute height {xsd:string}?,
		     attribute baseline {xsd:string}?,
		     attribute index {xsd:positiveInteger}?}


linethickness.attrib = attribute linethickness {length-with-optional-unit|thickness}
mline = element mline {MathML.Common.attrib,
      linethickness.attrib?,
      attribute spacing {xsd:string}?,
      attribute length {length-with-unit | named-space}?}

Glyph-alignmark = malignmark|mglyph

mi = element mi {MathML.Common.attrib,Token-style.attrib,(Glyph-alignmark|text)*}

mo = element mo {MathML.Common.attrib,Operator.attrib,Token-style.attrib,
                  linebreak.attrib,
                 (text|Glyph-alignmark)*}

mn = element mn {MathML.Common.attrib,Token-style.attrib,(text|Glyph-alignmark)*}

mtext = element mtext {MathML.Common.attrib,Token-style.attrib,(text|Glyph-alignmark)*}

ms = element ms {MathML.Common.attrib,Token-style.attrib,
                 attribute lquote {xsd:string}?,
		 attribute rquote {xsd:string}?,
		 (text|Glyph-alignmark)*}

# And the group of any token 
Pres-token = mi | mo | mn | mtext | ms

msub = element msub {MathML.Common.attrib,
                  attribute subscriptshift {length-with-unit}?,
                  ContInPres,ContInPres}

msup = element msup {MathML.Common.attrib,
                  attribute supscriptshift {length-with-unit}?, 
                  ContInPres,ContInPres}

msubsup = element msubsup {MathML.Common.attrib,
                     attribute subscriptshift {length-with-unit}?, 
                     attribute supscriptshift {length-with-unit}?, 
                     ContInPres,ContInPres,ContInPres}

munder = element munder {MathML.Common.attrib,
                         attribute accentunder {truefalse}?, 
                         ContInPres,ContInPres}

mover = element mover {MathML.Common.attrib,
                       attribute accent {truefalse}?, 
                       ContInPres,ContInPres}

munderover = element munderover {MathML.Common.attrib,
                                 attribute accentunder {truefalse}?, 
                                 attribute accent {truefalse}?, 
                                 ContInPres,ContInPres,ContInPres}

PresExp-or-none = ContInPres | none
mmultiscripts = element mmultiscripts{MathML.Common.attrib,
	                              ContInPres, 
				      (PresExp-or-none,PresExp-or-none)*,
				      (mprescripts,(PresExp-or-none,PresExp-or-none)*)?}
none = element none {empty}
mprescripts = element mprescripts {empty}

Pres-script = msub|msup|msubsup|munder|mover|munderover|mmultiscripts
linebreak-values = "auto" | "newline" | "indentingnewline" | "nobreak" | "goodbreak" | "badbreak"
mspace = element mspace {MathML.Common.attrib,
                         attribute width {length-with-unit | named-space}?,
	           	 attribute height {length-with-unit}?,
	           	 attribute depth {length-with-unit}?,
attribute spacing {text}?,
                   	 linebreak.attrib}

mrow = element mrow {MathML.Common.attrib,ContInPres*}

mfrac = element mfrac {MathML.Common.attrib,
                       attribute bevelled {truefalse}?,
                       attribute denomalign {centering.values}?,
		       attribute numalign {centering.values}?,
		       linethickness.attrib?,
		       ContInPres,ContInPres}
msqrt = element msqrt {MathML.Common.attrib,ContInPres*}

mroot = element mroot {MathML.Common.attrib,ContInPres,ContInPres}

mpadded-space = xsd:string {pattern="(\+|-)?([0-9]+|[0-9]*\.[0-9]+)(((%?)*(width|lspace|height|depth))|(em|ex|px|in|cm|mm|pt|pc))"}



mpadded-width-space = xsd:string {pattern="((\+|-)?([0-9]+|[0-9]*\.[0-9]+)(((%?) *(width|lspace|height|depth)?)|(width|lspace|height|depth)|(em|ex|px|in|cm|mm|pt|pc)))|((veryverythin|verythin|thin|medium|thick|verythick|veryverythick)mathspace)|0"}

mpadded = element mpadded {MathML.Common.attrib,
	                   attribute width {mpadded-width-space}?,
  			   attribute lspace {mpadded-space}?,
  			   attribute height {mpadded-space}?,
  			   attribute depth {mpadded-space}?,
  			   ContInPres*}

mphantom = element mphantom {MathML.Common.attrib,ContInPres*}

mfenced = element mfenced {MathML.Common.attrib,
                           attribute open {xsd:string}?,
  	                   attribute close {xsd:string}?,
  			   attribute separators {xsd:string}?,
			   ContInPres*}

notation-values = "actuarial"|"longdiv"|"radical"| 
                              "box"|"roundedbox"|"circle"| 
                              "left"|"right"|"top"|"bottom"|
                              "updiagonalstrike"|"downdiagonalstrike"| 
                              "verticalstrike"|"horizontalstrike" | "madruwb"
menclose = element menclose {MathML.Common.attrib,
                          attribute notation {list{notation-values*}}?,
			  ContInPres*}

# And the group of everything 
Pres-layout = mrow|mfrac|msqrt|mroot|mpadded|mphantom|mfenced|menclose

Table-alignment.attrib = attribute rowalign 
 	     {xsd:string {pattern="(top|bottom|center|baseline|axis)(top|bottom|center|baseline|axis)*"}}?,
        attribute columnalign {xsd:string {pattern="(left|center|right)( (left|center|right))*"}}?,
        attribute groupalign {xsd:string}?

mtr.content = mtd
mtr = element mtr {Table-alignment.attrib, MathML.Common.attrib,(mtr.content)+}

mlabeledtr = element mlabeledtr {Table-alignment.attrib,MathML.Common.attrib,(mtr.content)*}

mtd = element mtd {MathML.Common.attrib,
                   Table-alignment.attrib,
                   attribute columnspan {xsd:positiveInteger}?,
  		   attribute rowspan {xsd:positiveInteger}?,
		   ContInPres*}

mtable.content = mtr|mlabeledtr
mtable = element mtable {Table-alignment.attrib,
                         attribute align {xsd:string}?,
			 attribute alignmentscope {xsd:string {pattern="(true|false)( true| false)*"}}?,
			 attribute columnwidth {xsd:string}?,
  			 attribute width {xsd:string}?,
  			 attribute rowspacing {xsd:string}?,
  			 attribute columnspacing {xsd:string}?,
  			 attribute rowlines {xsd:string}?,
  			 attribute columnlines {xsd:string}?,
  			 attribute frame {"none" | "solid" | "dashed"}?,
  			 attribute framespacing {xsd:string}?,
  			 attribute equalrows {truefalse}?,
  			 attribute equalcolumns {truefalse}?,
  			 attribute displaystyle {truefalse}?,
			 attribute side {"left"|"right"|"leftoverlap"|"rightoverlap"}?,
  			 attribute minlabelspacing {length-with-unit}?,
  			 MathML.Common.attrib,
			 (mtable.content)*}

maligngroup = element maligngroup {MathML.Common.attrib,
     attribute groupalign {"left" | "center" | "right" | "decimalpoint"}?}

malignmark = element malignmark {MathML.Common.attrib,attribute edge {"left" | "right"}?}

Pres-table = mtable|maligngroup|malignmark

mcolumn = element mcolumn {MathML.Common.attrib,
     attribute align {"left" | "right"}?,ContInPres*}

mstyle = element mstyle {MathML.Common.attrib,
                         linebreak.attrib,
                         attribute scriptlevel {xsd:integer}?,
                         attribute displaystyle {truefalse}?,
			 attribute scriptsizemultiplier {xsd:decimal}?,
  			 attribute scriptminsize {length-with-unit}?,
  			 attribute background {xsd:string}?,
  			 attribute veryverythinmathspace {length-with-unit}?,
  			 attribute verythinmathspace {length-with-unit}?,
			 attribute thinmathspace {length-with-unit}?,
                         attribute mediummathspace {length-with-unit}?,
                         attribute thickmathspace {length-with-unit}?,
                         attribute verythickmathspace {length-with-unit}?,
                         attribute veryverythickmathspace {length-with-unit}?,
                         linethickness.attrib?,
  			 Operator.attrib,Token-style.attrib,
			 ContInPres*}

merror = element merror {MathML.Common.attrib,ContInPres*}

maction = element maction {MathML.Common.attrib,
			   attribute actiontype {xsd:string}?,
  	                   attribute selection {xsd:positiveInteger}?,
  			   ContInPres*}

semantics-pmml = element semantics {semantics.attribs,PresExp, semantics-annotation*}

PresExp = Pres-token | Pres-layout | Pres-script | Pres-table 
	      |  mspace | mline | mcolumn |  maction | merror | mstyle
	      | semantics-pmml

ContInPres |= PresExp
Issue ednote_rnc_browserinterface_ wiki (member only)

rnc:browserinterface
Resolution None recorded
Issue ednote_rnc_units-patterns_ wiki (member only)

rnc:units-patterns
Resolution None recorded
Issue ednote_rnc_mathvariant_ wiki (member only)

rnc:mathvariant
Resolution None recorded
Issue ednote_mglyph_alt_ wiki (member only)

mglyph_alt
Resolution None recorded
Issue ednote_rnc_leftover-max_ wiki (member only)

rnc:leftover-max
Resolution None recorded
Issue permissive_units wiki (member only)
more permissive lengths/widths

David wrote in an e-mail: length-with-unit doesn't allow white space (anywhere) which (if any) of the following do we want to allow " 2em ", "2 em", "- 2 em". Also it insists on starting with a digit or -, but do we want to allow ".5em" "-.5em"

However we do claim css compatibility here which may suggest some answers to the above http://www.w3.org/TR/CSS21/syndata.html#length-units.

css allows an optional leading + as well +2em css requires number to "immediately" follow any sign and the unit to "immediately" follow the number, which I think means no intervening white space. css <number> are allowed to start with a . so .5em is allowed. css insists on a digit following a . so 5.em is not allowed.

Once we have firm answers to the above it should be easy to drop the regexp back in, and make the text match.

I think we should not allow white space except at beginning and end but allow a leading + (a change from mathml2) and allow no digits before the ., but insist on digits after a . which would be [\-\+]?([0-9]+(\.[0-9]+)?|\.[0-9]+)(em|ex|px|in|cm|mm|pt|pc|%))|0 as written this doesn't allow " 2em " but I think we can set white space trim properties to apply before the regex is checked (I'll check)

Resolution None recorded

A.2.3 The Grammar for Strict Content MathML3

The grammar for Strict Content MathML3 can be found at http://www.w3.org/Math/RelaxNG/mathml3/mathml3-strict.rnc. 

#     This is the Mathematical Markup Language (MathML) 3.0, an XML
#     application for describing mathematical notation and capturing
#     both its structure and content.
#
#     Copyright 1998-2008 W3C (MIT, ERCIM, Keio)
# 
#     Use and distribution of this code are permitted under the terms
#     W3C Software Notice and License
#     http://www.w3.org/Consortium/Legal/2002/copyright-software-20021231
#
#
#     Revision:    mathml3-strict.rnc,v 1.8 2008/11/09 11:15:50 mkohlhas2 Exp $
#
#    Update to MathML3 and Relax NG: David Carlisle and Michael Kohlhase
#
#  This is the RelaxNG schema module for the strict content part of MathML.

default namespace m = "http://www.w3.org/1998/Math/MathML"

include "mathml3-common.rnc"

math.content |= ContExp


opel.content = text

# we want to extend this in pragmatic CMathML, so we introduce abbrevs here.

cn.content = text |(cn,cn)
cn.type.vals  = "integer"|"real"|"double"

cn = element cn {attribute base {text}?,
                 attribute type {cn.type.vals}?,
  		 Definition.attrib,
  		 MathML.Common.attrib,	
		 (cn.content)*}

ci = element ci {attribute type {xsd:string}?,
                 attribute nargs {xsd:string}?,
		 attribute occurrence {xsd:string}?,		
                 Definition.attrib,	
  		 MathML.Common.attrib,
		 opel.content,
		 name.attrib?}

cdname.attrib = attribute cd {xsd:NCName}

csymbol       = element csymbol {MathML.Common.attrib,
	                         Definition.attrib,cdname.attrib?,cdbase.attrib?, 
				 opel.content}

# the content of the apply element, leave it empty and extend it later
apply = element apply {MathML.Common.attrib,cdbase.attrib?,apply.content}
apply-head = apply|bind|ci|csymbol|semantics-apply
apply.content = apply-head,ContExp*
semantics-apply = element semantics {semantics.attribs,apply-head, semantics-annotation*}

qualifier = notAllowed

# the content of the bind element, leave it empty and extend it later
bind = element bind {MathML.Common.attrib,cdbase.attrib?,bind.content}
bind-head = apply|csymbol|semantics-bind
bind.content = bind-head,bvar*,qualifier?,ContExp
semantics-bind   = element semantics {semantics.attribs,bind-head, semantics-annotation*}

bvar = element bvar {MathML.Common.attrib,cdbase.attrib?,bvar-head}
bvar-head = ci|semantics-bvar
semantics-bvar   = element semantics {semantics.attribs,bvar-head, semantics-annotation*}

share = element share {MathML.Common.attrib,attribute href {xsd:anyURI}}

# the content of the cerror element, leave it empty and extend it later
cerror = element cerror {MathML.Common.attrib,cdbase.attrib?,cerror.content}
cerror-head = csymbol|apply|semantics-cerror
cerror.content = cerror-head,ContExp*
semantics-cerror = element semantics {semantics.attribs,cerror-head, semantics-annotation*}

semantics-cmml = element semantics {semantics.attribs,ContExp, semantics-annotation*}

ContExp = cn| ci | csymbol | apply | bind | share | cerror | semantics-cmml
Issue ednote_rnc_opel-content_ wiki (member only)

rnc:opel-content
Resolution None recorded
Issue ednote_rnc_cn-content_ wiki (member only)

rnc:cn-content
Resolution None recorded

A.2.4 The Grammar for Pragmatic MathML

The grammar for pragmatic MathML3 can be found at http://www.w3.org/Math/RelaxNG/mathml3/mathml3-pragmatic.rnc. 

#     This is the Mathematical Markup Language (MathML) 3.0, an XML
#     application for describing mathematical notation and capturing
#     both its structure and content.
#
#     Copyright 1998-2008 W3C (MIT, ERCIM, Keio)
# 
#     Use and distribution of this code are permitted under the terms
#     W3C Software Notice and License
#     http://www.w3.org/Consortium/Legal/2002/copyright-software-20021231
#
#
#     Revision:    mathml3-pragmatic.rnc,v 1.10 2008/11/09 17:55:28 dcarlis Exp $
#
#    Update to MathML3 and Relax NG: David Carlisle and Michael Kohlhase
#
#     This is the RelaxNG schema module for the pragmatic content part of 
#     MathML (but without the presentation in token elements).

default namespace m = "http://www.w3.org/1998/Math/MathML"


## the content of "cn" may have <sep> elements in it
sep = element sep {empty}
cn.content |= (sep|text|Glyph-alignmark)*
cn.type.vals |= "e-notation"|"rational"|"complex-cartesian"|"complex-polar"|"constant" 

## allow degree in bvar
degree = element degree {MathML.Common.attrib,ContExp}
logbase = element logbase {MathML.Common.attrib,ContExp}
momentabout = element momentabout {MathML.Common.attrib,ContExp}
bvar-head |= (degree?,ci)|(ci,degree?)

## allow degree to modify <root/>
apply.content |= root_arith1_elt,degree,ContExp*
apply.content |= moment_s_data1_elt,(degree? & momentabout?),ContInPres*
apply.content |= log_transc1_elt,logbase,ContExp*

##allow apply to act as a binder
apply.content |= bind.content

domainofapplication = element domainofapplication {Definition.attrib,MathML.Common.attrib,cdbase.attrib?,ContExp}

lowlimit = element lowlimit {Definition.attrib,MathML.Common.attrib,cdbase.attrib?,ContExp+}
uplimit = element uplimit {Definition.attrib,MathML.Common.attrib,cdbase.attrib?,ContExp+}

condition = element condition {Definition.attrib,cdbase.attrib?,ContExp}

## allow the non-strict qualifiers
qualifier |= domainofapplication|(uplimit,lowlimit?)|(lowlimit,uplimit?)|degree|condition

## we collect the operator elements by role
opel.constant = notAllowed
opel.binder = notAllowed
opel.application = notAllowed
opel.semantic-attribution = notAllowed
opel.attribution = notAllowed
opel.error = notAllowed

opels = opel.constant | opel.binder | opel.application | 
        opel.semantic-attribution | opel.attribution |
	opel.error
container = notAllowed

## the values of the MathML type attributes;  
MathMLType |= "real" | "complex" | "function" | "algebraic" | "integer"


## we instantiate the strict content model by structure checking
apply-binder-head = semantics-apply-binder|opel.binder
apply.content |= apply-binder-head,bvar*,qualifier?,ContExp*
semantics-apply-binder = element semantics {semantics.attribs,apply-binder-head, semantics-annotation*}

apply-head |= opel.application
bind-head |= opel.binder
cerror-head |= opel.error

## allow all functions, constants, and containers to be content expressions on their own
ContExp |= opel.constant|opel.application|container 


# allow no body
bind.content |= bind-head,bvar*,qualifier?

# not sure what a sequence of things is supposed to map to in strict/OM
# but is definitely allowed in pragmatic
# see Content/SequencesAndSeries/product/rec-product3
math.content |= ContExp*

opel.content |= PresExp|Glyph-alignmark

#     This is the Mathematical Markup Language (MathML) 3.0, an XML
#     application for describing mathematical notation and capturing
#     both its structure and content.
#
#     Copyright 1998-2008 W3C (MIT, ERCIM, Keio)
# 
#     Use and distribution of this code are permitted under the terms
#     W3C Software Notice and License
#     http://www.w3.org/Consortium/Legal/2002/copyright-software-20021231
#
#
#     Revision:    mathml3-pragmatic.rnc,v 1.10 2008/11/09 17:55:28 dcarlis Exp $
#
#    Update to MathML3 and Relax NG: David Carlisle and Michael Kohlhase
#
#     This is the RelaxNG schema module for the pragmatic content part of 
#     MathML (but without the presentation in token elements).

default namespace m = "http://www.w3.org/1998/Math/MathML"


## the content of "cn" may have <sep> elements in it
sep = element sep {empty}
cn.content |= (sep|text|Glyph-alignmark)*
cn.type.vals |= "e-notation"|"rational"|"complex-cartesian"|"complex-polar"|"constant" 

## allow degree in bvar
degree = element degree {MathML.Common.attrib,ContExp}
logbase = element logbase {MathML.Common.attrib,ContExp}
momentabout = element momentabout {MathML.Common.attrib,ContExp}
bvar-head |= (degree?,ci)|(ci,degree?)

## allow degree to modify <root/>
apply.content |= root_arith1_elt,degree,ContExp*
apply.content |= moment_s_data1_elt,(degree? & momentabout?),ContInPres*
apply.content |= log_transc1_elt,logbase,ContExp*

##allow apply to act as a binder
apply.content |= bind.content

domainofapplication = element domainofapplication {Definition.attrib,MathML.Common.attrib,cdbase.attrib?,ContExp}

lowlimit = element lowlimit {Definition.attrib,MathML.Common.attrib,cdbase.attrib?,ContExp+}
uplimit = element uplimit {Definition.attrib,MathML.Common.attrib,cdbase.attrib?,ContExp+}

condition = element condition {Definition.attrib,cdbase.attrib?,ContExp}

## allow the non-strict qualifiers
qualifier |= domainofapplication|(uplimit,lowlimit?)|(lowlimit,uplimit?)|degree|condition

## we collect the operator elements by role
opel.constant = notAllowed
opel.binder = notAllowed
opel.application = notAllowed
opel.semantic-attribution = notAllowed
opel.attribution = notAllowed
opel.error = notAllowed

opels = opel.constant | opel.binder | opel.application | 
        opel.semantic-attribution | opel.attribution |
	opel.error
container = notAllowed

## the values of the MathML type attributes;  
MathMLType |= "real" | "complex" | "function" | "algebraic" | "integer"


## we instantiate the strict content model by structure checking
apply-binder-head = semantics-apply-binder|opel.binder
apply.content |= apply-binder-head,bvar*,qualifier?,ContExp*
semantics-apply-binder = element semantics {semantics.attribs,apply-binder-head, semantics-annotation*}

apply-head |= opel.application
bind-head |= opel.binder
cerror-head |= opel.error

## allow all functions, constants, and containers to be content expressions on their own
ContExp |= opel.constant|opel.application|container 


# allow no body
bind.content |= bind-head,bvar*,qualifier?

# not sure what a sequence of things is supposed to map to in strict/OM
# but is definitely allowed in pragmatic
# see Content/SequencesAndSeries/product/rec-product3
math.content |= ContExp*

opel.content |= PresExp|Glyph-alignmark

This grammar focuses on the pragmatic extensions in , , , , and .

Editorial note: MiKo  
check this again

The pragmatic extensions in , , , , , rely on information that is specified in the MathML content dictionaries. This is handled in the schema http://www.w3.org/Math/RelaxNG/mathml3/mathml3-cds-pragmatic.rnc. 

 Finally, the pragmatic extensions given in  are
                  not covered in this schema, but will be left for full MathML in the next section.
               

            

               
               
A.2.5 Deprecated Features
               

               
The grammar for the deprecated features in MathML3 can be found at http://www.w3.org/Math/RelaxNG/mathml3/mathml3-deprecated.rnc.
               
#     This is the Mathematical Markup Language (MathML) 3.0, an XML
#     application for describing mathematical notation and capturing
#     both its structure and content.
#
#     Copyright 1998-2008 W3C (MIT, ERCIM, Keio)
# 
#     Use and distribution of this code are permitted under the terms
#     W3C Software Notice and License
#     http://www.w3.org/Consortium/Legal/2002/copyright-software-20021231
#
#
#     Revision:    mathml3-deprecated.rnc,v 1.8 2008/11/09 00:24:40 dcarlis Exp $
#
#    Update to MathML3 and Relax NG: David Carlisle and Michael Kohlhase

default namespace m = "http://www.w3.org/1998/Math/MathML"


Token-style.attrib &=
  attribute fontsize {xsd:string}? ,
  attribute fontstyle {xsd:string}? ,
  attribute fontweight {xsd:string}? ,
  attribute color {xsd:string}? ,
  attribute fontfamily {xsd:string}? ,
  attribute fontweight {xsd:string}? 

#Deprecated Content Elements
dep-content = 
  element reln {ContExp*}|
  element fn {ContExp}

ContExp |= dep-content

apply-head |= dep-content

declare = element declare {attribute type {xsd:string}?,
                           attribute scope {xsd:string}?,
                           attribute nargs {xsd:nonNegativeInteger}?,
                           attribute occurrence {"prefix"|"infix"|"function-model"}?,
                           Definition.attrib,cdbase.attrib?, 
                           ContExp+}
ContExp |= declare

mtr.content |= ContInPres


            

               
               
A.2.6 MathML as a module in a RelaxNG Schema
               

               
Normally, a MathML expression does not constitute an entire XML document. MathML is
                  designed to be used as the mathematics fragment of larger markup languages. In
                  particular it is designed to be used as a module in documents marked up
                  with the XHTML family of markup languages. As RelaxNG directly supports modular
                  development, this is usually very easy: an XHTML+MathML schema can be specified as simply as
                  
               
# A RelaxNG Schema for  XHTML+MathML
include "xhtml.rnc"
math = external "mathml3.rnc"
Inline.class |= math
Block.class |= math

                  
                  assuming that we have access to a modular RelaxNG schema for xhtml that uses
                  Inline.class and Block.class to collect the the content models
                  for inline and block-level elements.
               

               

                  

                     Editorial note: Miko
                      
                  

                  

                     check this and reference an external schema
                  

               

               
Specilizing the MathML3 schema so that we can check the content of
                  annotation-xml elements is similarly simple:
                  
                  
               
# A RelaxNG Schema for MathML with OpenMath3 annotations
omobj = external "openmath3.rnc" 
include "mathml3.rnc" {anotation-xml.model = omobj}
For details about RelaxNG grammars and modularization see [RelaxNG] or [RelaxNGBook].
               

               

                  

                     Editorial note: Miko
                      
                  

                  

                     check this and reference an external schema; I think we can even tie the OpenMath model to the value OpenMath in the encoding attribute.
                     
                  

               

            

         

         

            
            
A.3 Using the MathML DTD
            

            

               

                  Editorial note: David
                   
               

               

                  DTD to be generated from Relax NG
               

            

         

         

            
            
A.4 Using the MathML XML Schema
            

            

               

                  Editorial note: David
                   
               

               

                  XSD schema to be generated from Relax NG
               

            

         

      

      

         
         Overview: Mathematical Markup Language (MathML) Version 3.0

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         Next:     B Operator Dictionary