Dominik Kirst

Programming Systems

Dominik Kirst

Bachelor's Thesis

Research Immersion Lab

Master's Thesis

2nd Bachelor's Thesis

PhD Thesis

Hi, I'm Dominik and I'm a MSCA Postdoctoral Fellow hosted by Hugo Herbelin in the Picube Team part of IRIF and Inria Paris. Before that, I was a Minerva Postdoctoral Fellow hosted by Liron Cohen at Ben-Gurion University and a PhD student at the Saarbrücken Graduate School of Computer Science under the supervision of Gert Smolka.

I did my Bachelor's Thesis and a Research Immersion Lab on set theory mechanised in Coq. I obtained my Master's degree from the University of Oxford with a thesis on intersection type systems and nominal automata. I also completed a second Bachelor's degree in cultural studies with a thesis on foundations of mathematics, hosted by the philosophy department. In my PhD thesis I investigated various topics in metamathematics in constructive type theory and Coq.

I'm broadly interested in constructive and computational logic and its connections to the foundations and philosophy of mathematics. My active lines of work are concerned with effectful realisability, synthetic oracle computability, bi-intuitionistic logic, computational incompleteness proofs, and the constructive reverse mathematics of completeness theorems.

Research Papers

From Partial to Monadic: Combinatory Algebra with Effects
Liron Cohen, Ariel Grunfeld, Dominik Kirst, Étienne Miquey
FSCD 2025, Birmingham, UK, 2025.

The Blurred Drinker Paradox: Constructive Reverse Mathematics of the Downward Löwenheim-Skolem Theorem
Dominik Kirst, Haoyi Zeng
LICS 2025, Singapore, 2025.

Syntactic Effectful Realizability in Higher-Order Logic
Liron Cohen, Ariel Grunfeld, Dominik Kirst, Étienne Miquey
LICS 2025, Singapore, 2025.

Completeness of First-Order Bi-intuitionistic Logic (pdf)
Dominik Kirst, Ian Shillito
CSL 2025, Amsterdam, Netherlands, 2025.

Separating Markov's Principles (pdf)
Liron Cohen, Yannick Forster, Dominik Kirst, Bruno Da Rocha Paiva, Vincent Rahli
LICS 2024, Tallinn, Estonia, 2024.

An Analysis of Tennenbaum's Theorem in Constructive Type Theory (Extended Version) (pdf)
Marc Hermes, Dominik Kirst
Logical Methods in Computer Science, 2024.

A Mechanised and Constructive Reverse Analysis of Soundness and Completeness of Bi-Intuitionistic Logic (pdf)
Ian Shillito, Dominik Kirst
CPP 2024, London, UK, 2024.

The Kleene-Post and Post’s Theorem in the Calculus of Inductive Constructions (pdf)(slides)
Yannick Forster, Dominik Kirst, Niklas Mück
CSL 2024, Naples, Italy, 2024.

Oracle Computability and Turing Reducibility in the Calculus of Inductive Constructions (pdf)
Yannick Forster, Dominik Kirst, Niklas Mück
APLAS 2023, Taipei, Taiwan, 2023.

Material Dialogues for First-Order Logic in Constructive Type Theory (Extended Version) (pdf)
Dominik Wehr, Dominik Kirst
Mathematical Structures in Computer Science, 2023.

Synthetic Undecidability and Incompleteness of First-Order Axiom Systems in Coq (Extended Version) (pdf)
Dominik Kirst, Marc Hermes
Journal of Automated Reasoning, 2023.

Gödel's Theorem Without Tears: Essential Incompleteness in Synthetic Computability (pdf)(slides)
Dominik Kirst, Benjamin Peters
CSL 2023, Warsaw, Poland, 2023.

Constructive and Mechanised Meta-Theory of IEL and Similar Modal Logics (pdf)
Christian Hagemeier, Dominik Kirst
Journal of Logic and Computation, 2022

Material Dialogues for First-Order Logic in Constructive Type Theory (pdf)
Dominik Wehr, Dominik Kirst
WoLLIC 2022, Iaşi, Romania, 2022.

An Analysis of Tennenbaum's Theorem in Constructive Type Theory (pdf)
Marc Hermes, Dominik Kirst
Best paper award by junior researchers
FSCD 2022, Haifa, Israel, 2022.

Computational Back-and-Forth Arguments in Constructive Type Theory (pdf)(slides)
Dominik Kirst
ITP 2022, Haifa, Israel, 2022.

Undecidability of Dyadic First-Order Logic in Coq (pdf)
Johannes Hostert, Andrej Dudenhefner, Dominik Kirst
ITP 2022, Haifa, Israel, 2022.

Undecidability, Incompleteness, and Completeness of Second-Order Logic in Coq (pdf)(slides)(video)
Mark Koch, Dominik Kirst
CPP 2022, Philadelphia, Pennsylvania, USA, 2022.

Constructive and Mechanised Meta-Theory of Intuitionistic Epistemic Logic (pdf)(slides)(video)
Christian Hagemeier, Dominik Kirst
LFCS 2022, Deerfield Beach, Florida, USA, 2022.

Trakhtenbrot's Theorem in Coq: Finite Model Theory through the Constructive Lens (pdf)
Dominik Kirst, Dominique Larchey-Wendling
Logical Methods in Computer Science, 2022.

Synthetic Undecidability and Incompleteness of First-Order Axiom Systems in Coq (pdf)(slides)(video)
Dominik Kirst, Marc Hermes
ITP 2021, Rome, Italy, 2021.

The Generalised Continuum Hypothesis Implies the Axiom of Choice in Coq (pdf)(slides)(video)
Dominik Kirst, Felix Rech
CPP 2021, Copenhagen, Denmark, 2021.

Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory (Extended Version) (pdf)
Yannick Forster, Dominik Kirst, Dominik Wehr
Journal of Logic and Computation, 2021

Trakhtenbrot's Theorem in Coq: A Constructive Approach to Finite Model Theory (pdf)(slides)(video)
Dominik Kirst, Dominique Larchey-Wendling
IJCAR 2020, Paris, France, 2020.

Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory (pdf)(slides)
Yannick Forster, Dominik Kirst, Dominik Wehr
LFCS 2020, Deerfield Beach, Florida, USA, 2020.

On Synthetic Undecidability in Coq, with an Application to the Entscheidungsproblem (pdf)(slides)
Yannick Forster, Dominik Kirst, Gert Smolka
CPP 2019, Cascais, Portugal, 2019.

Categoricity Results and Large Model Constructions for Second-Order ZF in Dependent Type Theory (pdf)
Dominik Kirst and Gert Smolka
Journal of Automated Reasoning, 2018.

Large Model Constructions for Second-Order ZF in Dependent Type Theory (pdf)(slides)
Dominik Kirst and Gert Smolka
CPP 2018, Los Angeles, California, USA, 2018.

Categoricity Results for Second-Order ZF in Dependent Type Theory (pdf)(slides)
Dominik Kirst and Gert Smolka
ITP 2017, Brasilia, Brazil, 2017.

Extended Abstracts

Constructive algebraic completeness of first-order bi-intuitionistic logic
Dominik Kirst, Ian Shillito
Types 2025 , Glasgow, Scotland, 2025.

Löb's Theorem and Provability Predicates in Rocq
Janis Bailitis, Dominik Kirst, Yannick Forster
Types 2025 , Glasgow, Scotland, 2025.

A Succinct and Verified Completeness Proof for First-Order Bi-Intuitionistic Logic (pdf)
Dominik Kirst, Ian Shillito
Meeting of the Australasian Association for Logic , Sydney, Australia, 2024.

Post's Problem in Constructive Mathematics (pdf) (slides)
Haoyi Zeng, Yannick Forster, Dominik Kirst, Takako Nemoto
Continuity, Computability, Constructivity Workshop , Nice, France, 2024.

Constructive Reverse Mathematics of the Downwards Löwenheim-Skolem Theorem (pdf) (slides)
Dominik Kirst, Haoyi Zeng
Logic Colloquium 2024 , Gothenburg, Sweden, 2024.

The Blurred Drinker Paradox and Blurred Choice Axioms for the Downward Löwenheim-Skolem Theorem (pdf)
Dominik Kirst, Haoyi Zeng
Types 2024 , Copenhagen, Denmark, 2024.

Limited Principles of Omniscience in Constructive Type Theory (pdf)
Bruno da Rocha Paiva, Liron Cohen, Yannick Forster, Dominik Kirst, Vincent Rahli
Types 2024 , Copenhagen, Denmark, 2024.

Post’s Problem and the Priority Method in CIC (pdf)
Haoyi Zeng, Yannick Forster, Dominik Kirst
Types 2024 , Copenhagen, Denmark, 2024.

Mechanised Constructive Reverse Mathematics:
Soundness and Completeness of Bi-Intuitionistic Logic (pdf) (slides)
Ian Shillito, Dominik Kirst
Australasian Logic Colloquium 2023 , Brisbane, Australia, 2023.

New Observations on the Constructive Content of First-Order Completeness Theorems (pdf) (slides)
Hugo Herbelin, Dominik Kirst
Types 2023 , Valencia, Spain, 2023.

Markov's Principles in Constructive Type Theory (pdf)
Yannick Forster, Dominik Kirst, Bruno da Rocha Paiva, Vincent Rahli
Types 2023 , Valencia, Spain, 2023.

A Coq Library for Mechanised First-Order Logic (pdf) (slides)
Dominik Kirst, Johannes Hostert, Andrej Dudenhefner, Yannick Forster, Marc Hermes, Mark Koch, Dominique Larchey-Wendling, Niklas Mück, Benjamin Peters, Gert Smolka, Dominik Wehr
The Coq Workshop , Haifa, Israel, 2022.

Strong, Synthetic, and Computational Proofs of Gödel's First Incompleteness Theorem (pdf)
Benjamin Peters, Dominik Kirst
Types 2022 , Nantes, France, 2022.

Synthetic Versions of the Kleene-Post and Post's Theorem (pdf) (slides)
Dominik Kirst, Niklas Mück, Yannick Forster
Types 2022 , Nantes, France, 2022.

Synthetic Turing Reducibility in CIC (pdf)
Yannick Forster, Dominik Kirst
Types 2022 , Nantes, France, 2022.

The Generalised Continuum Hypothesis Implies the Axiom of Choice in HoTT (pdf) (slides) (video)
Dominik Kirst, Felix Rech
Workshop on Homotopy Type Theory / Univalent Foundations , Buenos Aires, Argentina, 2021.

A Toolbox for Mechanised First-Order Logic (pdf) (slides) (video)
Johannes Hostert, Mark Koch, Dominik Kirst
The Coq Workshop , Rome, Italy, 2021.

Towards Extraction of Continuity Moduli in Coq (pdf) (slides)
Yannick Forster, Dominik Kirst, Florian Steinberg
Types 2020 , Turin, Italy, 2020.

A Coq Library of Undecidable Problems (pdf)
Yannick Forster, Dominique Larchey-Wendling, Andrej Dudenhefner, Edith Heiter, Dominik Kirst, Fabian Kunze, Gert Smolka, Simon Spies, Dominik Wehr, Maximilian Wuttke
CoqPL 2020 , New Orleans, USA, 2020.

Invited Seminar Talks

(Sober Thoughts on) The Blurred Drinker Paradox (slides)
Dominik Kirst
CIRM Realizability Workshop , Marseille, France, 2025.

Applied Synthetic Computability Theory:
Gödel's Incompleteness Theorem and Post's Problem. (slides)
Dominik Kirst
LIPN Logic and Computation Seminar , Paris-Villetaneuse, France, 2025.

Mechanised Constructive Reverse Mathematics:
Completeness, Löwenheim-Skolem Theorem, Post’s Problem (slides)
Dominik Kirst
LIX Proofs and Algorithms Seminar , Paris-Saclay, France, 2024.

Separating Markov's Principles:
An Introduction to Constructive Reverse Mathematics (slides)
Dominik Kirst
CHoCoLa Meeting , Lyon, France, 2024.

Mechanised Metamathematics: Synthetic Computability and Incompleteness in Coq (slides)
Dominik Kirst, Benjamin Peters
Logic Group Seminar, Gothenburg, Sweden, 2024.

The Blurred Drinker Paradox: Constructive Reverse Mathematics of the Löwenheim-Skolem Theorem (slides)
Dominik Kirst, Haoyi Zeng
ANU Logic Seminar, Canberra, Australia, 2024.

Mechanised Completeness, Undecidability, and Incompleteness in Coq (slides)
Dominik Kirst
VERSE Research Group Seminar, Singapore, 2023.

Constructive and Mechanised Meta-Theory of IEL and Similar Modal Logics (slides)
Christian Hagmeier, Dominik Kirst
CUNY Computational Logic Seminar, New York City/Online, United States 2022.

A Feasible Formalisation of Incompleteness (demo)
Formalize!(?) - 2 , Zurich/Online, 2022.

Formalising Metamathematics in Constructive Type Theory (slides)
Autumn School Proof and Computation , Online, 2021.

Analysing First-Order Logic in Constructive Type Theory (slides)
Dominik Kirst, Dominik Wehr, Yannick Forster
ANU Logic Seminar, Canberra/Online, 2021.

Synthetic Undecidability Proofs in Coq (slides)
Computer Science Theory Seminar , Tallinn, Estonia, 2020.

Theses

Mechanised Metamathematics:
An Investigation of First-Order Logic and Set Theory in Constructive Type Theory   (pdf)
Dominik Kirst
PhD Thesis, Programming Systems Lab, Saarland University, 2022.

Foundations of Mathematics: A Discussion of Sets and Types   (pdf)
Dominik Kirst
Bachelor's Thesis, Department of Philosophy, Saarland University, 2018.

Intersection Type Systems Corresponding to Nominal Automata   (pdf)
Dominik Kirst
Master's Thesis, Lady Margaret Hall, University of Oxford, 2016.

Formalised Set Theory: Well-Orderings and the Axiom of Choice   (pdf)
Dominik Kirst
Bachelor's Thesis, Programming Systems Lab, Saarland University, 2014.

Supervised Students

Timothée Huneau, 2025, Master's thesis, co-advised with Yannick Forster :
The Downward Löwenheim-Skolem theorem, from a constructive type theory point of view

Guilhem Turbiau, 2024, Master's thesis, co-advised with Yannick Forster and Hugo Herbelin :
Le Théorème de Löwenheim-Skolem ascendant en mathématiques constructives à rebours

Janis Bailitis, 2023, Bachelor's thesis, co-advised with Yannick Forster :
Löb's Theorem in Coq

Fabian Brenner, 2023, Bachelor's thesis, co-advised with Yannick Forster :
The undecidability of finitary PCF in Coq

Haoyi Zeng, 2023, Bachelor's thesis, co-advised with Yannick Forster :
Post's Problem and the Priority Method

Yannic Muskalla, 2021, Bachelor's thesis, co-advised with Holger Sturm :
Translating Intuitionistic Modal Logic to Classical Bimodal Logic in Coq

Benjamin Peters , 2021, Bachelor's thesis:
Computational Proofs of Gödel's First Incompleteness Theorem in Coq

Niklas Mück , 2021, Bachelor's thesis, co-advised with Yannick Forster :
The Arithmetical Hierarchy and Post’s Theorem in Coq

Mark Koch , 2021, Bachelor's thesis:
Mechanization of Second-order Logic

Johannes Hostert , 2021, Bachelor's thesis, co-advised with Andrej Dudenhefner :
The Undecidability of First-order Logic over Small Signatures

Christian Hagemeier , 2020, Bachelor's thesis, co-advised with Holger Sturm :
Formalizing Intuitonistic Epistemic Logic in Coq

Marc Hermes , 2020, Master's thesis, co-advised with Moritz Weber :
Formalisation of Peano Arithmetic in Coq

Felix Rech , 2019, Master's thesis:
On the Generalized Continuum Hypothesis in Coq

Dominik Wehr , 2019, Bachelor's thesis, co-advised with Yannick Forster :
Formalising Completeness of First-Order Logic

Leonhard Staut , 2017, Bachelor's thesis:
Nu-Trees in Coq

Teaching

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