The Structure of a Type of syntax
Introduction: Inherited attributes are useful when the structure of the parse tree differs from the abstract syntax of the input; attributes can then be used to carry information from one part of the parse tree to another. The next example shows how a mismatch in structure can be due to the design of the language, and not due to constraints imposed by the parsing method.
Example: In C, the type int  can be read as, "array of 2 arrays of 3 integers." The corresponding type expression array (2, array(3, integer)) is represented by the tree in Fig. 5.15. The operator array takes two parameters, a number and a type. If types are represented by trees, then this operator returns a tree node labeled array with two children for a number and a type.
With the SDD in Fig. 5.16, nonterminal T generates either a basic type or an array type. Nonterminal B generates one of the basic types int and float. T generates a basic type when T derives B C and C derives e. Otherwise, C generates array components consisting of a sequence of integers, each integer surrounded by brackets.
The nonterminals B and T have a synthesized attribute t representing a type. The nonterminal C has two attributes: an inherited attribute b and a synthesized attribute t. The inherited b attributes pass a basic type down the tree, and the synthesized t attributes accumulate the result.
An annotated parse tree for the input string int [ 2 ] [ 3 ] is shown in Fig. 5.17. The corresponding type expression in Fig. 5.15 is constructed by passing the type integer from B, down the chain of C's through the inherited attributes b. The array type is synthesized up the chain of C's through the attributes t. In more detail, at the root for T -» B C, nonterminal C inherits the type from B, using the inherited attribute C.b. At the rightmost node for C, the production is C e, so C.t equals C.6. The semantic rules for the production C [ n um ] C\ form C.t by applying the operator array to the operands num.ua/ and C\.t.