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On graph rewriting, reduction, and evaluation in the presence of cycles

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Higher-Order and Symbolic Computation

Abstract

We inter-derive two prototypical styles of graph reduction: reduction machines à la Turner and graph rewriting systems à la Barendregt et al. To this end, we adapt Danvy et al.’s mechanical program derivations from the world of terms to the world of cyclic graphs. We also outline how to inter-derive a third style of graph reduction: a graph evaluator.

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Notes

  1. Terms are directed acyclic graphs where a node can have at most one parent.

  2. Graphs are directed cyclic graphs where a node can have more than one parent.

  3. Compared to the previous machine, this placement of rewire can result in an additional but harmless assignment that replaces the contents of a cell by itself, e.g., in the case of .

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Acknowledgments

Thanks are due to the anonymous HOSC reviewers and to Dennis Decker Jensen and the anonymous TFP’09 reviewers for their comments on earlier versions of this article. I am also grateful to Olivier Danvy for his supervision and for his course on functional programming at Aarhus University, where this work originates.

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  1. Department of Computer Science, Aarhus University, Aabogade 34, 8200 , Aarhus, Denmark

    Ian Zerny

  2. Google Aarhus, Aabogade 15, 8200, Aarhus, Denmark

    Ian Zerny

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Correspondence to Ian Zerny.

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Ian Zerny is a recipient of the Google Europe Fellowship in Programming Technology, and this research is supported in part by this Google Fellowship.

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Zerny, I. On graph rewriting, reduction, and evaluation in the presence of cycles. Higher-Order Symb Comput 26, 63–84 (2013). https://doi.org/10.1007/s10990-014-9103-9

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