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Conference Papers Year : 2023

A positive perspective on term representation: Extended paper

Abstract

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.
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Dates and versions

hal-03843587 , version 1 (08-11-2022)
hal-03843587 , version 2 (10-11-2022)

Identifiers

  • HAL Id : hal-03843587 , version 2

Cite

Dale Miller, Jui-Hsuan Wu. A positive perspective on term representation: Extended paper. CSL 2023 - Computer Science Logic, Feb 2023, Warsaw, Poland. ⟨hal-03843587v2⟩
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