Generalising Tree Traversals to DAGs: Exploiting Sharing without the Pain

Patrick Bahr, Emil Axelsson

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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.
TitelProceedings of the 2015 Workshop on Partial Evaluation and Program Manipulation
Antal sider12
UdgivelsesstedNew York, NY, USA
ForlagAssociation for Computing Machinery
Publikationsdato1 jan. 2015
ISBN (Trykt)978-1-4503-3297-2
StatusUdgivet - 1 jan. 2015


  • attribute grammar, tree automata, graph automata, sharing, rewriting, EDSLs, graph traversals


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