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arXiv · 2510.12304

Substitution Without Copy and Paste

Thorsten Altenkirch·Nathaniel Burke·Philip Wadler
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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.

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Thorsten Altenkirch, Nathaniel Burke, Philip Wadler. 2025-10-14. Substitution Without Copy and Paste. https://doi.org/10.4204/eptcs.431.5

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