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π-RED*—A graph reducer for a full-fledged γ-calculus

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Abstract

This paper describes an applicative order graph reducer which under interactive control performs high-level program transformations that are governed by the reduction semantics of a full-fledged untyped γ-calculus. To do so with competitive speed, high-level functional programs are by a pre-processor reversibly converted into graph representations of γ-terms. Its subterms are closed by the abstraction of relatively free variables only to the extent absolutely necessary to avoid the complexity of full β-reductions at run-time. Processing these γ-terms is based on high-level interpretation which exploits the simplicity and efficiency of naive graph pointer substitutions when reducing function calls. Partially or completely reduced graphs are by a post-processor re-converted into high-level programs. Full β-reductions are only employed by the pre- and post-processor to maintain correct binding levels when abstracting free variables from γ-terms and when undoing these abstractions or reducing partial applications left over as closures, respectively.

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Author notes

  1. C. Schmittgen

    Present address: Computer Systems Lab. Sony Europe, Cologne, Germany

Authors and Affiliations

  1. Department of Computer Science, University of Kiel, 2300, Kiel 1, Germany

    C. Schmittgen, H. Blödorn & W. Kluge

Authors
  1. C. Schmittgen
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  2. H. Blödorn
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  3. W. Kluge
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Schmittgen, C., Blödorn, H. & Kluge, W. π-RED*—A graph reducer for a full-fledged γ-calculus. New Gener Comput 10, 173–195 (1992). https://doi.org/10.1007/BF03037478

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  • DOI: https://doi.org/10.1007/BF03037478

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