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Substitution Without Copy and Paste

Published: October 14, 2025 | arXiv ID: 2510.12304v1

By: Thorsten Altenkirch, Nathaniel Burke, Philip Wadler

Potential Business Impact:

Makes computer code easier to write and check.

Business Areas:
Casual Games Gaming

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.

Country of Origin
🇬🇧 United Kingdom

Page Count
17 pages

Category
Computer Science:
Logic in Computer Science