This section describes libSBML's facilities for working with SBML representations of mathematical expressions.

Basic concepts

LibSBML uses Abstract Syntax Trees (ASTs) to provide a canonical, in-memory representation for all mathematical formulas regardless of their original format (i.e., C-like infix strings or MathML 2.0). In libSBML, an AST is a collection of one or more objects of class ASTNode.

Converting between ASTs and text strings

SBML Levels 2 and 3 represent mathematical expressions using using MathML 2.0 (more specifically, a subset of the content portion of MathML 2.0), but most applications using libSBML do not use MathML directly. Instead, applications generally either interact with mathematics in text-string form, or else they use the API for working with Abstract Syntax Trees (described below). LibSBML provides support for both approaches. The libSBML formula parser has been carefully engineered so that transformations from MathML to infix string notation and back is possible with a minimum of disruption to the structure of the mathematical expression.

The example below shows a simple program that, when run, takes a MathML string compiled into the program, converts it to an AST, converts that to an infix representation of the formula, compares it to the expected form of that formula, and finally translates that formula back to MathML and displays it. The output displayed on the terminal should have the same structure as the MathML it started with. The program is a simple example of using the various MathML and AST reading and writing methods, and shows that libSBML preserves the ordering and structure of the mathematical expressions.

The text-string form of mathematical formulas produced by are in a simple C-inspired infix notation. It is summarized in the next section below. A formula in this text-string form therefore can be handed to a program that understands SBML mathematical expressions, or used as part of a translation system. The libSBML distribution comes with an example program in the "examples" subdirectory called translateMath that implements an interactive command-line demonstration of translating infix formulas into MathML and vice-versa. In summary, the functions available are the following:

The string formula syntax and differences with MathML

The text-string formula syntax is an infix notation essentially derived from the syntax of the C programming language and was originally used in SBML Level 1. The formula strings may contain operators, function calls, symbols, and white space characters. The allowable white space characters are tab and space. The following are illustrative examples of formulas expressed in the syntax:

0.10 * k4^2

(vm * s1)/(km + s1)

The following table shows the precedence rules in this syntax. In the Class column, operand implies the construct is an operand, prefix implies the operation is applied to the following arguments, unary implies there is one argument, and binary implies there are two arguments. The values in the Precedence column show how the order of different types of operation are determined. For example, the expression a * b + c is evaluated as (a * b) + c because the * operator has higher precedence. The Associates column shows how the order of similar precedence operations is determined; for example, a - b + c is evaluated as (a - b) + c because the + and - operators are left-associative. The precedence and associativity rules are taken from the C programming language, except for the symbol ^, which is used in C for a different purpose. (Exponentiation can be invoked using either ^ or the function power.)

A table of the expression operators and their precedence in the text-string format for mathematical expressions used by SBML_parseFormula().
Token	Operation	Class	Precedence	Associates
name	symbol reference	operand	6	n/a
`(`expression`)`	expression grouping	operand	6	n/a
`f(`...`)`	function call	prefix	6	left
`-`	negation	unary	5	right
`^`	power	binary	4	left
`*`	multiplication	binary	3	left
`/`	divison	binary	3	left
`+`	addition	binary	2	left
`-`	subtraction	binary	2	left
`,`	argument delimiter	binary	1	left

A program parsing a formula in an SBML model should assume that names appearing in the formula are the identifiers of Species, Parameter, Compartment, FunctionDefinition, (in Level 2) Reaction, or (in Level 3) SpeciesReference objects defined in a model. When a function call is involved, the syntax consists of a function identifier, followed by optional white space, followed by an opening parenthesis, followed by a sequence of zero or more arguments separated by commas (with each comma optionally preceded and/or followed by zero or more white space characters), followed by a closing parenthesis. There is an almost one-to-one mapping between the list of predefined functions available, and those defined in MathML. All of the MathML functions are recognized; this set is larger than the functions defined in SBML Level 1. In the subset of functions that overlap between MathML and SBML Level 1, there exist a few differences. The following table summarizes the differences between the predefined functions in SBML Level 1 and the MathML equivalents in SBML Levels 2 and 3:

Table comparing the names of certain functions in the SBML text-string formula syntax and MathML. The left column shows the names of functions recognized by SBML_parseFormula(); the right column shows their equivalent function names in MathML 2.0, used in SBML Levels 2 and 3.
Text string formula functions	MathML equivalents in SBML Levels 2 and 3
`acos`	`arccos`
`asin`	`arcsin`
`atan`	`arctan`
`ceil`	`ceiling`
`log`	`ln`
`log10(x)`	`log(10, x)`
`pow(x, y)`	`power(x, y)`
`sqr(x)`	`power(x, 2)`
`sqrt(x)`	`root(2, x)`

Methods for working with libSBML's Abstract Syntax Trees

There are a number of methods for interrogating the type of an ASTNode and for testing whether a node belongs to a general category of constructs. The methods on ASTNode for this purpose are the following:

Programs manipulating AST node structures should check the type of a given node before calling methods that return a value from the node. The following are the ASTNode object methods available for returning values from nodes:

Of course, all of this would be of little use if libSBML didn't also provide methods for setting the values of AST node objects! And it does. The methods are the following:

Finally, ASTNode also defines some miscellaneous methods for manipulating ASTs:

Reading and Writing Mathematical Expressions into ASTs

As mentioned above, applications often can avoid working with raw MathML by using either libSBML's text-string interface or the AST API. However, when needed, reading MathML content directly and creating ASTs is easily done in libSBML using a method designed for this purpose:

Similarly, writing out Abstract Syntax Tree structures is easily done using the following method:

The example program given above demonstrate the use of these methods.