Generalising Tree Traversals to DAGs: Exploiting Sharing without the Pain

Patrick Bahr, Emil Axelsson

Research output: Conference Article in Proceeding or Book/Report chapterBook chapterResearchpeer-review


We present a recursion scheme based on attribute grammars that can be transparently applied to trees and acyclic graphs. Our recursion scheme allows the programmer to implement a tree traversal and then apply it to compact graph representations of trees instead. The resulting graph traversals avoid recomputation of intermediate results for shared nodes -- even if intermediate results are used in different contexts. Consequently, this approach leads to asymptotic speedup proportional to the compression provided by the graph representation. In general, however, this sharing of intermediate results is not sound. Therefore, we complement our implementation of the recursion scheme with a number of correspondence theorems that ensure soundness for various classes of traversals. We illustrate the practical applicability of the implementation as well as the complementing theory with a number of examples.
Original languageEnglish
Title of host publicationProceedings of the 2015 Workshop on Partial Evaluation and Program Manipulation
Number of pages12
Place of PublicationNew York, NY, USA
PublisherAssociation for Computing Machinery
Publication date1 Jan 2015
ISBN (Print)978-1-4503-3297-2
Publication statusPublished - 1 Jan 2015


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