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## 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

xstarting from positiony

substr(x,y,z)substring of

xstarting from positionyand having lengthz

time2str(t,f)converting calendar time to character string(4)

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

HierarchyEvaluation of numeric operations

1st-7th

Concatenation (

&)8th

Conditional evaluation (

if…then…else)9th

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

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