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A quantitative model for simply typed λ-calculus

Published online by Cambridge University Press:  29 November 2021

Martin Hofmann  and
Jérémy Ledent Open the ORCID record for Jérémy Ledent [Opens in a new window]
Martin Hofmann
Affiliation:
Institut für Informatik, Ludwig-Maximilians-Universität München, Germany
Jérémy Ledent*
Affiliation:
Mathematically Structured Programming Group, University of Strathclyde, Glasgow, Scotland
*
*Corresponding author. Email: jeremy.ledent@strath.ac.uk
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Abstract

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We use a simplified version of the framework of resource monoids, introduced by Dal Lago and Hofmann, to interpret simply typed λ-calculus with constants zero and successor. We then use this model to prove a simple quantitative result about bounding the size of the normal form of λ-terms. While the bound itself is already known, this is to our knowledge the first semantic proof of this fact. Our use of resource monoids differs from the other instances found in the literature, in that it measures the size of λ-terms rather than time complexity.

Keywords

Resource monoidlength spacesquantitative semanticslambda-calculus
Type
Special Issue: In Homage to Martin Hofmann
Information
Mathematical Structures in Computer Science , Volume 32 , Special Issue 6: In Homage to Martin Hofmann , June 2022 , pp. 777 - 793
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial licence (http://creativecommons.org/licenses/by/4.0/), which permits non-commercial re-use, distribution, and reproduction in anymedium, provided the original article is properly cited. The written permission of Cambridge University Press must be obtained prior to any commercial use.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

†

Martin Hofmann died on January 23, 2018. This work was carried out in 2016, while the second author was doing a Masters internship supervised by Martin at the Ludwig Maximilian University of Munich. While he could not take part in writing this article, Martin is undoubtedly an author of the work presented here.

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