This presents an informal EBNF grammar that can be used to validate the structure of Content Markup.
#PCDATA denotes XML parsed character data.Presentation_tags ::= "presentation" /* placeholder */ [2] Space ::= #x09 | #x0A | #x0D | #x20 /* tab, lf, cr, space characters */ [3] S ::= (Space | Presentation_tags")* /* treat presentation as space */ Characters, only for content validation characters [4] Char ::= #x9 | #xA | #xD | [#x20-#xD7FF] | [#xE000-#xFFFD] | [#x10000-#x10FFFF] /* valid XML chars */
start(ci) ::= "<ci>" end(cn) ::= "</cn>" empty(plus) ::= "<plus/>"
The reason for doing this is to avoid writing a grammar for all the attributes. The model below is not complete for all possible attribute values.
start and end tag functions [5]_start(\%x) ::= "<\%x" (Char - '>')* ">" /* returns a valid start tag for the element \%x */ [6] _end(\%x) ::= "<\%x" Space* ">" /* returns a valid end tag for the element \%x */ [7] _empty(\%x) ::= "<\%x" (Char - '>')* "/>" /* returns a valid empty tag for the element \%x */ [8] _sg(\%x) ::= S _start(\%x) /* start tag preceded by optional whitespace */ [9] _eg(\%x) ::= _end(\%x) S /* end tag followed by optional whitespace */ [10] _ey(\%x) ::= S _empty(\%x) S /* empty tag preceded and followed by optional whitespace */ semantics, annotation, etc. [11] semantics ::= _sg(semantics) _mmlarg _annot* _eg(semantics) [12] annotation ::= _sg(annotation) #PCDATA _eg(annotation) [13] annotation-xml ::= _sg(annotation-xml) _ANY _eg(annotation-xml) [14] _ANY ::= "AnyXML" /* placeholder for wellformed XML Fragment (not Mixed Content) */ [15] _annot ::= annotation | annotation-xml mathml content constructs [16] _mmlarg ::= _container | _token | _operator | _relation [17] _container ::= _special | _constructor [18] _token ::= ci | cn | csymbol | _constantsym [19] _special ::= apply | lambda | reln | fn | semantics [20] _constructor ::= interval | list | matrix | matrixrow | set | vector | piecewise | piece | otherwise [21] _qualifier ::= lowlimit | uplimit | degree | logbase | domainofapplication | momentabout | condition /* interval is both a qualifier and a constructor */ [22] _constantsym ::= integers | rationals | reals | naturalnumbers | complexes | primes | exponentiale | imaginaryi | notanumber | true | false | pi | eulergamma | infinity relations operators functional operators [32] _funcop ::= _funcop1ary | _funcopnary [33] _funcop1ary ::= inverse | ident | domain | codomain | image [34] _funcopnary ::= fn| compose /* general user-defined function is n-ary */
(note minus is both 1ary and 2ary)
_arithop ::= _arithop1ary | _arithop2ary | _arithopnary | root [36] _arithop1ary ::= abs | conjugate | factorial | minus | arg | real | imaginary | floor | ceiling [37] _arithop2ary ::= quotient | divide | minus | power | rem [38] _arithopnary ::= plus | times | max | min | gcd | lcm calculus and vector calculus [39] _calcop ::= int | diff | partialdiff [40] _vcalcop ::= divergence | grad | curl | laplacian sequences and series [41] _seqop ::= sum | product | limit elementary classical functions and trigonometry [42] _classop ::= exp | ln | log [43] _trigop ::= sin | cos | tan | sec | csc | cot | sinh | cosh | tanh | sech | csch | coth | arcsin | arccos | arctan statistics operators [44] _statop ::= _statopnary | moment [45] _statopnary ::= mean | sdev | variance | median | mode linear algebra operators [46] _lalgop ::= _lalgop1ary |_lalgop2ary | _lalgopnary [47] _lalgop1ary ::= determinant | transpose [48] _lalgop2ary ::= vectorproduct | scalarproduct | outerproduct [49] _lalgopnary ::= selector logical operators set theoretic operators [55] _setop ::= _setop1ary |_setop2ary | _setopnary [56] _setop1ary ::= card [57] _setop2ary ::= setdiff [58] _setopnary ::= union | intersect | cartesianproduct operator groups separator leaf tokens and data content of leaf elements
condition - constraints. constraints contains either a single reln (relation), or an apply holding a logical combination of relations, or a set (over which the operator should be applied).
condition ::= _sg(condition) reln | apply | set _eg(condition) domains for integral, sum , product, and specials [74] _domainofapp ::= domainofapplication | _domainabbrev [75] _domainabbrev ::= (lowlimit uplimit?) | uplimit | interval | condition
Note that apply is used in place of the deprecated reln in MathML2.0 for relational operators as well as arithmetic, algebraic etc.
Equations and relations - reln uses lisp-like syntax (like apply) the bvar and condition elements are used to construct a "such that" or "where" constraint on the relation. Note that reln is deprecated but still valid in MathML2.0.
lambda construct declare construct [84] declare ::= _sg(declare) _declarebody _eg(declare) [85] _declarebody ::= ci (fn | constructor)? constructors bound variables other qualifiers - note the contained _mmlarg could be a reln
The top level math element. Allow declare only at the head of a math element.
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