Grammar: $E \to E + T \mid T$, $\;T \to T * F \mid F$, $\;F \to \text{digit}$

Synthesized attribute: give every non-terminal $E$, $T$, $F$ an attribute val (its numeric value). The terminal digit has the attribute lexval supplied by the lexical analyzer.

Syntax-directed definition

Production	Semantic rule
$E \to E_1 + T$	$E.val = E_1.val + T.val$
$E \to T$	$E.val = T.val$
$T \to T_1 * F$	$T.val = T_1.val \times F.val$
$T \to F$	$T.val = F.val$
$F \to \text{digit}$	$F.val = \text{digit}.lexval$

Every attribute is computed from the attributes of the children, so val is synthesized and the definition is S-attributed (it can be evaluated during bottom-up parsing).

Annotated parse tree for $3 + 5 * 2$

Because of the grammar's structure, * sits lower in the tree than +, so 5 * 2 is evaluated first.

Evaluation (bottom-up, post-order)

Step	Node	Rule used	Value
1	$F$ (digit 3)	$F.val = \text{digit}.lexval$	3
2	$T$ over that $F$	$T.val = F.val$	3
3	$E$ over that $T$	$E.val = T.val$	3
4	$F$ (digit 5)	$F.val = \text{digit}.lexval$	5
5	$T$ over that $F$	$T.val = F.val$	5
6	$F$ (digit 2)	$F.val = \text{digit}.lexval$	2
7	$T \to T * F$	$T.val = 5 \times 2$	10
8	$E \to E + T$	$E.val = 3 + 10$	13