Substitution without copy and paste

Defining substitution for a language with binders like the simply typed $\lambda$-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.

Publication Details

Journal
Repository@Nottingham (University of Nottingham)
Published
2025-07-19
Primary Topic
Logic, programming, and type systems
Type
article
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article

Substitution without copy and paste

Repository@Nottingham (University of Nottingham)
Logic, programming, and type systems
article

Substitution without copy and paste

article en

Abstract

Defining substitution for a language with binders like the simply typed $\lambda$-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.

Repository@Nottingham (University of Nottingham)
Quality Education
Openalex Percentile: Top 72%
Logic, programming, and type systems
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Substitution without copy and paste · Repository@Nottingham (University of Nottingham) (2025) | TGRS Research Map | TGRS