A Positive Perspective on Term Representation (Invited Talk)

Authors Dale Miller , Jui-Hsuan Wu

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Dale Miller
  • Inria Saclay, Palaiseau, France
  • LIX, Institut Polytechnique de Paris, France
Jui-Hsuan Wu
  • LIX, Institut Polytechnique de Paris, France


We thank Beniamino Accattoli and Kaustuv Chaudhuri for their valuable discussions and suggestions. We also thank anonymous reviewers for their comments on an earlier draft of this paper.

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Dale Miller and Jui-Hsuan Wu. A Positive Perspective on Term Representation (Invited Talk). In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 3:1-3:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


We use the focused proof system LJF as a framework for describing term structures and substitution. Since the proof theory of LJF does not pick a canonical polarization for primitive types, two different approaches to term representation arise. When primitive types are given the negative polarity, LJF proofs encode terms as tree-like structures in a familiar fashion. In this situation, cut elimination also yields the familiar notion of substitution. On the other hand, when primitive types are given the positive polarity, LJF proofs yield a structure in which explicit sharing of term structures is possible. Such a representation of terms provides an explicit method for sharing term structures. In this setting, cut elimination yields a different notion of substitution. We illustrate these two approaches to term representation by applying them to the encoding of untyped λ-terms. We also exploit concurrency theory techniques - namely traces and simulation - to compare untyped λ-terms using such different structuring disciplines.

Subject Classification

ACM Subject Classification
  • Theory of computation → Proof theory
  • term representation
  • sharing
  • focused proof systems


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