Editing Attribute grammar (section)

==Synthesized attributes==
A synthesized attribute is computed from the values of attributes of the children. Since the values of the children must be computed first, this is an example of bottom-up propagation.{{Sfn|Knuth|1968|p=130}} To formally define a synthesized attribute, let <math>G= \langle V_n,V_t,P,S \rangle</math> be a formal grammar, where

* <math>V_n</math> is the set of non terminal symbols
* <math>V_t</math> is the set of terminal symbols
* <math>P</math> is the set of [[Formal grammar#The syntax of grammars|productions]]
* <math>S</math> is the distinguished, or start, symbol

Then, given a string of nonterminal symbols <math>A</math> and an attribute name <math>a</math>, <math>A.a</math> is a synthesized attribute if all three of these conditions are met:

* <math>A \rightarrow \alpha \in P</math> (i.e. <math>A \rightarrow \alpha</math> is one of the rules in the grammar)
*<math>\alpha = \alpha_1 \ldots \alpha_n, \forall i, 1 \leq i \leq n: \alpha_i \in (V_n \cup V_t)</math> (i.e. every symbol in the body of the rule is either nonterminal or terminal)
*<math>A.a = f(\alpha_{j_1}.a_1, \ldots ,\alpha_{j_m}.a_m)</math>, where <math>\{\alpha_{j_1}, \ldots ,\alpha_{j_m}\} \subseteq \{\alpha_1, \ldots ,\alpha_n\}</math> (i.e. the value of the attribute is a function <math>f</math> applied to some values from the symbols in the body of the rule)