Optimal Incremental Simple Multi-Pass Attribute Evaluation

Compiler optimizations can be described by tree transformations that replace complicated and non-efficient tree structures by equivalent but simpler and more efficient tree structures. For the specification of such tree transformations the classical attribute grammar framework has to be extended with conditional tree transformation rules, where predicates on attribute values (carrying context information (may enable the application of a transformation (see e.g. [ll]). A tree transformation may invalidate attribute instances, not only in the restructured part of the tree but also elsewhere in the tree. To make the attribution of a derivation tree correct again (which is generally needed in order to be able to test the predicates of subsequent tree transformations), a re-evaluation of the entire tree could be applied. However, a repeated computation of all the attribute instances after each transformation is inefficient and should be avoided (cf. [7,9,10,12]). In this paper an incremental simple multi-pass evaluator is presented, which works optimally in the number of visits to tree nodes and the number of recomputations. By optimal we mean that, whenever possible, subtrees are skipped, and no unnecessary calculations are done. Optimization of the non-incremental simple multi-pass attribute evaluator by skipping subtrees is discussed in IS].