← 研踪 PaperTrailarXiv:2607.11329 · v2
Fuss-free cumulative universes: theory and practice
首次提交 2026-07-13 17:48
版本更新 2026-11-07 00:27
雷达观测 2026-11-09 13:22
摘要
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. We study the fuss-free formulation by means 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.
作者备注：Extended version of a paper to appear in POPL 2027
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v2 · 2026-11-07 00:27 · 最新观测版本
Fuss-free cumulative universes: theory and practice
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. We study the fuss-free formulation by means 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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