{"ID":2829940,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.11762","arxiv_id":"2512.11762","title":"The Relative Monadic Metalanguage","abstract":"Relative monads provide a controlled view of computation. We generalise the monadic metalanguage to a relative setting and give a complete semantics with strong relative monads. Adopting this perspective, we generalise two existing program calculi from the literature. We provide a linear-non-linear language for graded monads, LNL-RMM, along with a semantic proof that it is a conservative extension of the graded monadic metalanguage. Additionally, we provide a complete semantics for the arrow calculus, showing it is a restricted relative monadic metalanguage. This motivates the introduction of ARMM, a computational lambda calculus-style language for arrows that conservatively extends the arrow calculus.","short_abstract":"Relative monads provide a controlled view of computation. We generalise the monadic metalanguage to a relative setting and give a complete semantics with strong relative monads. Adopting this perspective, we generalise two existing program calculi from the literature. We provide a linear-non-linear language for graded...","url_abs":"https://arxiv.org/abs/2512.11762","url_pdf":"https://arxiv.org/pdf/2512.11762v1","authors":"[\"Jack Liell-Cock\",\"Zev Shirazi\",\"Sam Staton\"]","published":"2025-12-12T18:17:25Z","proceeding":"cs.PL","tasks":"[\"cs.PL\",\"math.CT\"]","methods":"[]","has_code":false}