An attribute grammar is a formal way to define attributes for the productions of a formal grammar, associating these attributes with values. The evaluation occurs in the nodes of the abstract syntax tree, when the language is processed by some parser or compiler. The attributes are divided into two groups: synthesized attributes and inherited attributes. The synthesized attributes are the result of the attribute evaluation rules, and may also use the values of the inherited attributes. The inherited attributes are passed down from parent nodes. In some approaches, synthesized attributes are used to pass semantic information up the parse tree, while inherited attributes help pass semantic information down and across it. For instance, when constructing a language translation tool, such as a compiler, it may be used to assign semantic values to syntax constructions. Also, it is possible to validate semantic checks associated with a grammar, representing the rules of a language not explicitly imparted by the syntax definition. Attribute grammars can also be used to translate the syntax tree directly into code for some specific machine, or into some intermediate language. One strength of attribute grammars is that they can transport information from anywhere in the abstract syntax tree to anywhere else, in a controlled and formal way.
History
Attribute grammars were invented by Donald Knuth and Peter Wegner. While Donald Knuth is credited for the overall concept, Peter Wegner invented inherited attributes during a conversation with Knuth. Some embryonic ideas trace back to the work of Edgar T. "Ned" Irons, the author of IMP.
Example
The following is a simple context-free grammar which can describe a language made up of multiplication and addition of integers. Expr → Expr + Term Expr → Term Term → Term * Factor Term → Factor Factor → "" Factor → integer The following attribute grammar can be used to calculate the result of an expression written in the grammar. Note that this grammar only uses synthesized values, and is therefore an S-attributed grammar. Expr1 → Expr2 + Term Expr → Term Term1 → Term2 * Factor Term → Factor Factor → "" Factor → integer
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. To formally define a synthesized attribute, let be a formal grammar, where
is the set of non terminal symbols
is the set of terminal symbols
is the set of productions
is the distinguished, or start, symbol
Then, given a string of nonterminal symbols and an attribute name, is a synthesized attribute if all three of these conditions are met:
, where
Inherited attributes
An inherited attribute at a node in parse tree is defined using the attribute values at the parent or siblings. Inherited attributes are convenient for expressing the dependence of a programming language construct on the context in which it appears. For example, we can use an inherited attribute to keep track of whether an identifier appears on the left or the right side of an assignment in order to decide whether the address or the value of the identifier is needed. In contrast to synthesized attributes, inherited attributes can take values from parent and/or siblings. As in the following production, where A can get values from S, B, and C. B can take values from S, A, and C. Likewise, C can take values from S, A, and B.
