Support algorithms for incremental attribute evaluation of asynchronous subtree replacements

A solution to the problem of incremental attribute evaluation for multiple asynchronous subtree replacements that is applicable to arbitrary noncircular attribute grammars is discussed. The algorithm supports multiple independent editing cursors. Concurrent evaluation processes proceed independently as long as they cover disjoint regions of the derivation tree. Evaluation processes are merged when they overlap, to prevent unnecessary attribute evaluations. The complexity of these three parts of the algorithm is discussed. The algorithm ensures that when evaluation terminates, the tree is consistently attributed. The results solve two open problems that arose in connection with the original algorithm for asynchronous subtree replacements reported by S.M. Kaplan and G.F. Kaiser (1986)