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arXiv · 2607.11329

Fuss-free cumulative universes: theory and practice

Raphaël Sterbac·Jonathan Sterling
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Abstract

Universes are central to dependent type theory, and they are notoriously difficult to handle in a way that is both correct and usable. We propose a new "fuss-free" generalised algebraic presentation for polymorphic cumulative universes that dispenses with the intricate theory of coherent universe coercions in favour of a simpler formulation, which we prove equivalent by means of a normalisation theorem for the former. Evidence for the utility of the fuss-free formulation is provided in the form of (1) an abstract specification of its bidirectional elaboration algorithm, and (2) a concrete implementation in Haskell. We also describe and implement an extension of the fuss-free universe hierarchy with a judgemental notion of datatype description from which prior notions of cumulative inductive type may be derived.

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Raphaël Sterbac, Jonathan Sterling. 2026-07-13. Fuss-free cumulative universes: theory and practice. https://arxiv.org/abs/2607.11329

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