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.
Keywords
Cite
@article{arxiv.2512.11762,
title = {The Relative Monadic Metalanguage},
author = {Jack Liell-Cock and Zev Shirazi and Sam Staton},
journal= {arXiv preprint arXiv:2512.11762},
year = {2025}
}
Comments
41 pages. Published in Proceedings of the ACM on Programming Languages (POPL 2026)