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Hi all,

I am looking at what sort of grammar can be used to represent and edit
the content MathML included inside components and reactions in CellML
models. I propose the following grammar (this is a valid and unambiguous
bison grammar). This has been designed to be intuitive to people who
know MATLAB (or C, or other languages which use a mixture of pre and
in-order operators). It would be nice if there was some consistency
between tools, so I am interested in feedback both from potential users,
and the developers of other tools.

%token IDENTIFIER
%token QUOTED NUMBER
%token PIECEWISE CASE THEN ELSE
%left T_EQEQ T_NOTEQ T_GREATEREQUAL T_LESSEQUAL '<' '>'
%left '!'
%left '+' '-'
%left '*' '/'
%%

textrep: expr '=' attrs expr | textrep '=' attrs expr;
attrs: '{' attrlist '}' | /* empty */;
attrlist: attr attrlist | /* empty */;
attr: IDENTIFIER '=' QUOTED;
arglist: expr ',' arglist | expr;
expr: IDENTIFIER attrs '(' arglist ')' | '(' expr ')' | expr '*' attrs
expr |
expr '+' attrs expr | expr '-' attrs expr | expr T_EQEQ attrs expr |
expr T_NOTEQ attrs expr | expr '<' attrs expr |
expr '>' attrs expr | expr T_GREATEREQUAL attrs expr |
expr T_LESSEQUAL attrs expr | expr '/' attrs expr | IDENTIFIER attrs |
NUMBER attrs | PIECEWISE attrs '(' caselist maybeelse ')' | '!' attrs
expr |
'-' attrs expr;
caselist: casepair caselist | /* empty */;
casepair: CASE expr THEN expr;
maybeelse: ELSE expr | /* empty */;

Examples of valid syntax:
x ={id="myequation"} piecewise(case y==1 then abs(z*y) /
integral(sin(a), a, 0, 10) case y < 1 then pow(y, z) else -(y + z -
3{units="volts"}*c))
y * z = a * b = c / pow(2, remainder(5, 3)) / 7{units="second"}
diff(position, time) = velocity
a =
sin{definitionURL="http://www.weirdmath.org/my-weird-version-of-sine#"}(pi
* x)

There is one minor issue with the identifier syntax, and that is the
possibility that names can conflict, e.g. if we had a variable called
pi. We would have to mangle it (I suggest that the tokeniser would use #
to override symbol names, so, for example #pi maps to <ci>pi</ci>, while
pi maps to <pi/>, but of course, # is not normally required, so x maps
to <ci>x</ci>).

My editing syntax allows the encoding of things which are valid MathML,
but which no tools will be able to be used (e.g a CellML tool would be
able to integrate equations like the last one, as the semantics of sine
have been overriden using definitionURL). The aim is to represent all
valid content MathML, rather than everything that PCEnv or any other
tool supports. This means that going in to edit mode on an equation, not
changing anything, and then returning back is guaranteed not to change
the semantic meaning of the model.

The units attribute will default to dimensionless if not present, but
can be explicitly set on constants.

For the IDENTIFIER attrs '(' arglist ')', all standard MathML operators
(other than those for which an in-order operator is defined) will be
supported as IDENTIFIER, as well as some special values for tagging
certain qualifiers (the integral example above uses lowlimit and
uplimit, which are inferred from their position, but you could
alternatively write something like
integral(sin(a), a, condition(in(a, interval{type="open"}(0, 10))) ).

Opinions?

Best regards
Andrew

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• [cellml-discussion] User input language for MathML in CellML, Andrew Miller, 11/17/2006
  • [cellml-discussion] User input language for MathML in CellML, Andrew Miller, 11/17/2006

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