Generalising tree traversals and tree transformations to DAGs: Exploiting sharing without the pain
Journal article, 2017

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 or a tree transformation and then apply it to compact graph representations of trees instead. The resulting graph traversal or graph transformation avoids 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.

Attribute grammars

Graph traversal

Directed acyclic graphs

Graph transformation



Patrick Bahr

IT University of Copenhagen

Emil Axelsson

Software Technology (Chalmers)

Science of Computer Programming

0167-6423 (ISSN)

Vol. 137 63-97

Areas of Advance

Information and Communication Technology

Subject Categories

Software Engineering

Computer Science



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