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arXiv · 2604.26829

Full Definability in a Profunctorial Model

Takeshi Tsukada·Kazuyuki Asada·Kengo Hirata
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Abstract

A semantic model enjoys full definability if every semantic element in the model is a denotation of some proof or program. Full definability indicates that the model captures programs and proofs in a highly detailed manner. This paper studies full definability in a model based on the (bi)category of profunctors on groupoids, which is a proof-relevant variant of the relational model. Despite the fact that a profunctor is far more complicated than a relation, we show that a rather straightforward application of the ideas for the relational model, together with the notion of stability in profunctors, provides a complete characterisation of definable profunctors. More precisely, all logical families of stable and total profunctors are definable by proof-nets of multiplicative linear logic with MIX. As a part of the full definability proof, we show that the stability serves as a correctness criterion, which we think is of independent interest.

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Takeshi Tsukada, Kazuyuki Asada, Kengo Hirata. 2026-04-29. Full Definability in a Profunctorial Model. https://arxiv.org/abs/2604.26829

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