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Three Syntactic Theories for Combinatory Graph Reduction

  • Olivier Danvy
  • Ian Zerny
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6564)

Abstract

We present a purely syntactic theory of graph reduction for the canonical combinators S, K, and I, where graph vertices are represented with evaluation contexts and let expressions. We express this syntactic theory as a reduction semantics. We then factor out the introduction of let expressions to denote as many graph vertices as possible upfront instead of on demand, resulting in a second syntactic theory, this one of term graphs in the sense of Barendregt et al. We then interpret let expressions as operations over a global store (thus shifting, in Strachey’s words, from denotable entities to storable entities), resulting in a third syntactic theory, which we express as a reduction semantics. This store-based reduction semantics corresponds to a store-based abstract machine whose architecture coincides with that of Turner’s original reduction machine. The three syntactic theories presented here therefore properly account for combinatory graph reduction As We Know It.

Keywords

Functional Programming Abstract Machine Reduction Sequence Graph Reduction Syntactic Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Olivier Danvy
    • 1
  • Ian Zerny
    • 1
  1. 1.Department of Computer ScienceAarhus UniversityAarhus NDenmark

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