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Documents authored by Møgelberg, Rasmus Ejlers

Document
DOI: 10.4230/LIPIcs.LICS.2026.4
A Convenient Fibration for Dependently-Typed Probability Theory

Authors: Danel Ahman, Ohad Kammar, and Rasmus Ejlers Møgelberg

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)

Abstract
We describe semantic structures relevant for interpreting dependent types for statistical and probabilistic modelling. Our development extends the theory of quasi-Borel spaces (qbses) of Staton et. al, which support simply-typed, higher-order probability theory with continuous distributions. It is well-known that qbses can interpret a dependent-type theory supporting dependent function-spaces through the codomain fibration. We define an equivalent split fibration based on the family fibration, which we call quasi-Borel families (qbfs), characterise its structure, equip it with fibred monads of measures and probability, and use them to develop dependently-typed probability theory. We characterise the structure of the qbf fibration that is relevant for dependently-typed probability theory in elementary form. Our characterisations include: context extension, dependent pairs, dependent functions, extensional identity types, fibred products and coproducts, subspaces, a universe of propositions, and straightforward internalisation and externalisation principles for discrete spaces. We use these concepts to define fibred distribution and probability monads, the semantic structure needed to interpret probability distributions under a dependent context. We show that this structure satisfies a fibred version of Kock’s synthetic measure theory. We also use these concepts to develop a qbs counterpart to Kolmogorov’s conditional expectation. Our main result is a version of the conditional expectation that, under standard regularity assumptions, is measurable in both the random variables we are conditioning, and the observation map we are conditioning by.
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Danel Ahman, Ohad Kammar, and Rasmus Ejlers Møgelberg. A Convenient Fibration for Dependently-Typed Probability Theory. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 4:1-4:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ahman_et_al:LIPIcs.LICS.2026.4,
  author =	{Ahman, Danel and Kammar, Ohad and M{\o}gelberg, Rasmus Ejlers},
  title =	{{A Convenient Fibration for Dependently-Typed Probability Theory}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{4:1--4:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.4},
  URN =		{urn:nbn:de:0030-drops-267915},
  doi =		{10.4230/LIPIcs.LICS.2026.4},
  annote =	{Keywords: probability theory, quasi-Borel space, Grothendieck fibration, fibred monad, conditional expectation, measure theory, random variables, dependent types, quasitopos, probabilistic programming, denotational semantics, synthetic measure theory}
}
Document
DOI: 10.4230/LIPIcs.LICS.2026.6
Induction and Recursion Principles in a Higher-Order Quantitative Logic for Probability

Authors: Giorgio Bacci and Rasmus Ejlers Møgelberg

Published in: LIPIcs, Volume 380, 41st Annual Symposium on Logic in Computer Science (LICS 2026)

Abstract
Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and processes. We construct an affine calculus for 1-bounded complete metric spaces and the monad for probability measures equipped with the Kantorovich distance. The calculus includes a form of guarded recursion interpreted via Banach’s fixed point theorem, useful, e.g., for recursive programming with processes. We then define an affine higher-order quantitative logic for reasoning about terms of our calculus. The logic includes novel principles for guarded recursion, and induction over probability measures and natural numbers. We illustrate the expressivity of the logic by a sequence of case studies: Proving upper limits on bisimilarity distances of Markov processes, showing convergence of a temporal learning algorithm and of a random walk using a coupling argument.
Cite as

Giorgio Bacci and Rasmus Ejlers Møgelberg. Induction and Recursion Principles in a Higher-Order Quantitative Logic for Probability. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 6:1-6:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bacci_et_al:LIPIcs.LICS.2026.6,
  author =	{Bacci, Giorgio and M{\o}gelberg, Rasmus Ejlers},
  title =	{{Induction and Recursion Principles in a Higher-Order Quantitative Logic for Probability}},
  booktitle =	{41st Annual Symposium on Logic in Computer Science (LICS 2026)},
  pages =	{6:1--6:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-434-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{380},
  editor =	{Faggian, Claudia and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.LICS.2026.6},
  URN =		{urn:nbn:de:0030-drops-267935},
  doi =		{10.4230/LIPIcs.LICS.2026.6},
  annote =	{Keywords: Quantitative Logic, Probabilistic Processes, Affine Logic, Guarded Recursion, Metric Spaces}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.TYPES.2024
LIPIcs, Volume 336, TYPES 2024, Complete Volume

Authors: Rasmus Ejlers Møgelberg and Benno van den Berg

Published in: LIPIcs, Volume 336, 30th International Conference on Types for Proofs and Programs (TYPES 2024)

Abstract
LIPIcs, Volume 336, TYPES 2024, Complete Volume
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30th International Conference on Types for Proofs and Programs (TYPES 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 336, pp. 1-190, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Proceedings{mogelberg_et_al:LIPIcs.TYPES.2024,
  title =	{{LIPIcs, Volume 336, TYPES 2024, Complete Volume}},
  booktitle =	{30th International Conference on Types for Proofs and Programs (TYPES 2024)},
  pages =	{1--190},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-376-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{336},
  editor =	{M{\o}gelberg, Rasmus Ejlers and van den Berg, Benno},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2024},
  URN =		{urn:nbn:de:0030-drops-237954},
  doi =		{10.4230/LIPIcs.TYPES.2024},
  annote =	{Keywords: LIPIcs, Volume 336, TYPES 2024, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.TYPES.2024.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Rasmus Ejlers Møgelberg and Benno van den Berg

Published in: LIPIcs, Volume 336, 30th International Conference on Types for Proofs and Programs (TYPES 2024)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

30th International Conference on Types for Proofs and Programs (TYPES 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 336, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mogelberg_et_al:LIPIcs.TYPES.2024.0,
  author =	{M{\o}gelberg, Rasmus Ejlers and van den Berg, Benno},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{30th International Conference on Types for Proofs and Programs (TYPES 2024)},
  pages =	{0:i--0:xii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-376-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{336},
  editor =	{M{\o}gelberg, Rasmus Ejlers and van den Berg, Benno},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TYPES.2024.0},
  URN =		{urn:nbn:de:0030-drops-237837},
  doi =		{10.4230/LIPIcs.TYPES.2024.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.CSL.2024.39
What Monads Can and Cannot Do with a Bit of Extra Time

Authors: Rasmus Ejlers Møgelberg and Maaike Annebet Zwart

Published in: LIPIcs, Volume 288, 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

Abstract
The delay monad provides a way to introduce general recursion in type theory. To write programs that use a wide range of computational effects directly in type theory, we need to combine the delay monad with the monads of these effects. Here we present a first systematic study of such combinations. We study both the coinductive delay monad and its guarded recursive cousin, giving concrete examples of combining these with well-known computational effects. We also provide general theorems stating which algebraic effects distribute over the delay monad, and which do not. Lastly, we salvage some of the impossible cases by considering distributive laws up to weak bisimilarity.
Cite as

Rasmus Ejlers Møgelberg and Maaike Annebet Zwart. What Monads Can and Cannot Do with a Bit of Extra Time. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 39:1-39:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mgelberg_et_al:LIPIcs.CSL.2024.39,
  author =	{M{\o}gelberg, Rasmus Ejlers and Zwart, Maaike Annebet},
  title =	{{What Monads Can and Cannot Do with a Bit of Extra Time}},
  booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
  pages =	{39:1--39:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-310-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{288},
  editor =	{Murano, Aniello and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2024.39},
  URN =		{urn:nbn:de:0030-drops-196823},
  doi =		{10.4230/LIPIcs.CSL.2024.39},
  annote =	{Keywords: Delay Monad, Monad Compositions, Distributive Laws, Guarded Recursion, Type Theory}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2018.23
The Clocks They Are Adjunctions Denotational Semantics for Clocked Type Theory

Authors: Bassel Mannaa and Rasmus Ejlers Møgelberg

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)

Abstract
Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract form of step-indexing. CloTT has previously been shown to enjoy a number of syntactic properties including strong normalisation, canonicity and decidability of type checking. In this paper we present a denotational semantics for CloTT useful, e.g., for studying future extensions of CloTT with constructions such as path types. The main challenge for constructing this model is to model the notion of ticks used in CloTT for coinductive reasoning about coinductive types. We build on a category previously used to model guarded recursion, but in this category there is no object of ticks, so tick-assumptions in a context can not be modelled using standard tools. Instead we show how ticks can be modelled using adjoint functors, and how to model the tick constant using a semantic substitution.
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Bassel Mannaa and Rasmus Ejlers Møgelberg. The Clocks They Are Adjunctions Denotational Semantics for Clocked Type Theory. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 23:1-23:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{mannaa_et_al:LIPIcs.FSCD.2018.23,
  author =	{Mannaa, Bassel and M{\o}gelberg, Rasmus Ejlers},
  title =	{{The Clocks They Are Adjunctions Denotational Semantics for Clocked Type Theory}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{23:1--23:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.23},
  URN =		{urn:nbn:de:0030-drops-91938},
  doi =		{10.4230/LIPIcs.FSCD.2018.23},
  annote =	{Keywords: Guarded type theory, Coinduction, Presheaf model, Clocked type theory, Dependent adjunction}
}
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