Simple multi-visit attribute grammars

An attribute grammar is simple multi-visit if each attribute of a nonterminal has a fixed visit-number associated with it such that, during attribute evaluation, the attributes of a node which have visit-number j are computed at the jth visit to the node. An attribute grammar is l-ordered if for each nonterminal a linear order of its attributes exists such that the attributes of a node can always be evaluated in that order (cf. the work of Kastens).An attribute grammar is simple multi-visit if and only if it is l-ordered. Every noncircular attribute grammar can be transformed into an equivalent simple multi-visit attribute grammar which uses the same semantic operations.For a given distribution of visit-numbers over the attributes, it can be decided in polynomial time whether the attributes can be evaluated according to these visit-numbers. The problem whether an attribute grammar is simple multi-visit is NP-complete.