3.2 Symbolic expressions

Symbolic expression is a rule for computing a single symbolic value represented in the form of character string.

The primary symbolic expression may be a string literal, dummy index, unsubscripted parameter, subscripted parameter, built-in function reference, conditional symbolic expression, or another symbolic expression enclosed in parentheses.

It is also allowed to use a numeric expression as the primary symbolic expression, in which case the resultant value of the numeric expression is automatically converted to the symbolic type.

Examples

'May 2003'	(string literal)
j	(dummy index)
p	(unsubscripted parameter)
s['abc',j+1]	(subscripted parameter)
substr(name[i],k+1,3)	(function reference)
if i in I then s[i,j] else t[i+1]	(conditional expression)
((10 * b[i,j]) & '.bis')	(parenthesized expression)

More general symbolic expressions containing two or more primary symbolic expressions may be constructed by using the concatenation operator.

Examples

'abc[' & i & ',' & j & ']'
"from " & city[i] & " to " & city[j]

The principles of evaluation of symbolic expressions are completely analogous to that ones given for numeric expressions (see above).

Function references

In MathProg there are the following built-in functions which may be used in symbolic expressions:

substr(x, y)	substring of x starting from position y
substr(x, y, z)	substring of x starting from position y and having length z
time2str(t, f)	converting calendar time to character string4

The first argument of substr must be a symbolic expression while its second and optional third arguments must be numeric expressions.

The first argument of time2str must be a numeric expression, and its second argument must be a symbolic expression.

The resultant value of the symbolic expression, which is a function reference, is the result of applying the function to its arguments.

Symbolic operators

Currently in MathProg there is the only symbolic operator:

x & y

where x and y are symbolic expressions. This operator means concatenation of its two symbolic operands, which are character strings.

Hierarchy of operations

The following list shows the hierarchy of operations in symbolic expressions:

Operation	Hierarchy
Evaluation of numeric operations	1st-7th
Concatenation (&)	8th
Conditional evaluation (if $\dots$ then $\dots$ else)	9th

This hierarchy has the same meaning as explained in Section “Numeric expressions”.