Substitution Without Copy and Paste

Defining substitution for a language with binders like the simply typed -calculus requires repetition, defining substitution and renaming separately.To verify the categorical properties of this calculus, we must repeat the same argument many times.We present a lightweight method that avoids repetition and that gives rise to a simply typed category with families (CwF) isomorphic to the initial simply typed CwF.Our paper is a literate Agda script.

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Publication Details

Journal
Electronic Proceedings in Theoretical Computer Science
Published
2025-10-13
DOI
https://doi.org/10.4204/eptcs.431.5
Primary Topic
Logic, programming, and type systems
Type
article
Field-Weighted Citation Impact
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article

Substitution Without Copy and Paste

Philip Wadler, Thorsten Altenkirch, Nancy A. Burke
Electronic Proceedings in Theoretical Computer Science
Logic, programming, and type systems
article

Substitution Without Copy and Paste

Philip Wadler, Thorsten Altenkirch, Nancy A. Burke
article en

Abstract

Defining substitution for a language with binders like the simply typed -calculus requires repetition, defining substitution and renaming separately.To verify the categorical properties of this calculus, we must repeat the same argument many times.We present a lightweight method that avoids repetition and that gives rise to a simply typed category with families (CwF) isomorphic to the initial simply typed CwF.Our paper is a literate Agda script.

Electronic Proceedings in Theoretical Computer ScienceVol. 431
University of Nottingham (GB), Imperial College London (GB), University of Edinburgh (GB)
Openalex Percentile: Top 85%
Logic, programming, and type systems
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Substitution Without Copy and Paste — Philip Wadler, Thorsten Altenkirch, et al. · Electronic Proceedings in Theoretical Computer Science (2025) | TGRS Research Map | TGRS