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arXiv · 2512.11762

The Relative Monadic Metalanguage

Jack Liell-Cock·Zev Shirazi·Sam Staton
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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.

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Jack Liell-Cock, Zev Shirazi, Sam Staton. 2025-12-12. The Relative Monadic Metalanguage. https://doi.org/10.1145/3776702

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