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arXiv · 2511.02595

Nominal Algebraic-Coalgebraic Data Types, with Applications to Infinitary Lambda-Calculi

Rémy Cerda
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Abstract

Ten years ago, it was shown that nominal techniques can be used to design coalgebraic data types with variable binding, so that alpha-equivalence classes of infinitary terms are directly endowed with a corecursion principle. We introduce "mixed" binding signatures, as well as the corresponding type of mixed inductive-coinductive terms. We extend the aforementioned work to this setting. In particular, this allows for a nominal description of the sets Lambda_abc of abc-infinitary lambda-terms (for a, b, c in {0,1}) and of capture-avoiding substitution on alpha-equivalence classes of such terms.

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Rémy Cerda. 2025-11-04. Nominal Algebraic-Coalgebraic Data Types, with Applications to Infinitary Lambda-Calculi. https://doi.org/10.4204/eptcs.435.5

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