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Example text

In our notation, a regular expression is either a single symbol, or it consists of a sequence (R\... Rn), a grouped set of alternatives (Ri | . . *, or an obligatory repeatable part /? + . We do not use the rather inelegant notation for optional and repetitive parts provided by so-called EXTENDED BNF, despite its familiarity from reference manuals, because we have a better use for the brackets it uses for optional parts [iJ], and its {R} is hardly suggestive of ordered repetition! Moreover, EXTENDED BNF requires R {R} to express that R is an obligatory repeatable part, whereas our R+ avoids writing R twice.

Well-formedness is usually defined as a binary relation between context-dependent information and phrases, and the well-formedness of a compound phrase may depend on the well-formedness of its subphrases with modified context-dependent information. As with attribute grammars, this technique is not applicable when scope rules are dynamic. Here, let us keep abstract syntax context-free, and describe context-sensitive aspects separately. This amounts to treating context-sensitive syntax as a kind of seman- 12 Chapter 1.

For instance, equation (2) above defines the application of the semantic function execute _ to nodes with four branches, where the first branch is the string "if", the second an expression E, the third "then", and the last branch is a statement S, in terms of evaluate E and execute S. 3). Readers familiar with denotational semantics should observe that we do not write [ E J and [ S J on the right of the equation, since E and S by themselves already stand for trees. Nevertheless, we can still regard [ .

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