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IMELL Cut Elimination with Linear Overhead

Authors Beniamino Accattoli , Claudio Sacerdoti Coen

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LIPIcs.FSCD.2024.24.pdf
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Author Details

Beniamino Accattoli
  • Inria & LIX, École Poytechnique, UMR 7161, Palaiseau, France
Claudio Sacerdoti Coen
  • Alma Mater Studiorum - Università di Bologna, Italy

Funding

  • Sacerdoti Coen, Claudio: Supported by the INdAM-GNCS project "Modelli Composizionali per l'Analisi di Sistemi Reversibili Distribuiti" and by the Cost Action CA2011 EuroProofNet.

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Beniamino Accattoli and Claudio Sacerdoti Coen. IMELL Cut Elimination with Linear Overhead. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 24:1-24:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.FSCD.2024.24

Abstract

Recently, Accattoli introduced the Exponential Substitution Calculus (ESC) given by untyped proof terms for Intuitionistic Multiplicative Exponential Linear Logic (IMELL), endowed with rewriting rules at-a-distance for cut elimination. He also introduced a new cut elimination strategy, dubbed the good strategy, and showed that its number of steps is a time cost model with polynomial overhead for ESC/IMELL, and the first such one.
Here, we refine Accattoli’s result by introducing an abstract machine for ESC and proving that it implements the good strategy and computes cut-free terms/proofs within a linear overhead.

Subject Classification

ACM Subject Classification
  • Theory of computation → Operational semantics
Keywords
  • Lambda calculus
  • linear logic
  • abstract machines

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