Author

Eric Paul

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Preprint Aug 2026

The Additive Arithmetic of Linear Orders

We present a systematic development of the arithmetic of the class of linear orders under the ordered sum $(LO, +)$ and prove a number of new results. Our approach is based on a Euclidean algorithm for pairs of linear orders that almost additively commute. Among our results: (i.) We generalize and give unified proofs o...

Garrett Ervin, Eric Paul · 0 citations

Proof Repair and (Co)algebra Equivalences

This work gives the first foundational treatment of proof repair, focusing in particular on type-theoretic proof repair in response to changes in datatypes, and formalizes and proves that the core component of this proof repair algorithm—a “configuration”—is exactly an algebra isomorphism.

E. G. Plante, Eric Paul, G. A. Kavvos · 0 citations