Yannick Forster

Programming Systems

Yannick Forster

About me I am now a permanent researcher in the Cambium team at Inria Paris, you can find my current website here. The page below will not be updated, I however continue to be interested in all of the topics. If you want to write a Bachelor's or Master's thesis at the Programming Systems Lab on any of these topics, please get in touch, I'd be excited to do a (remote) joint supervision with any member of the group. From 2016 to 2021 I was a PhD student at the Saarbrücken Graduate School of Computer Science and the Programming Systems Lab under supervision of Gert Smolka. My research centers around analysing, formalising, and mechanising different aspects of computation in constructive type theory, and especially in the proof assistant Coq. One line of work is synthetic computability theory, where the fact that all definable functions in constructive type theory are computable is made explicit via axioms (LFCS '22, PhD thesis). A second line is formed by mechanising equivalence proofs between different models of computation. As part of this work we have proved that the weak call-by-value λ-calculus is reasonable for both time and space (POPL '20) and provided a machine-checked version of the result for time (ITP '21). The third line is formed by synthetic undecidability proofs. Since all functions definable in Coq's type theory are by definition computable, undecidability of a problem can be proved by a reduction from Turing machine halting to the problem in question. A prime result is our synthetic undecidability proof of Hilbert's tenth problem (FSCD '19). I co-maintain the Coq Library of Undecidability Proofs, a collaborative project containing machine-checked undecidability proofs. Lastly, I am interested in using Coq as a system to obtain verified executable programs: I am involved in the MetaCoq project, a mechanisation and implementation of Coq in Coq, where I verified type and proof erasure (POPL '20), and in CertiCoq, a verified compiler for Coq. I obtained my Bachelor's degree at Saarland University and my Master's degree at the University of Cambridge.

CV Google Scholar ORCID dblp GitHub

Publications

Full papers

Parametric Church's Thesis: Synthetic Computability Without Choice (doi) (cite)
Yannick Forster
LFCS 2022.

A Mechanised Proof of the Time Invariance Thesis for the Weak Call-by-value λ-Calculus (first draft) (doi) (cite)
Yannick Forster, Fabian Kunze, Gert Smolka, Maximilan Wuttke
ITP 2021.

Church’s thesis and related axioms in Coq’s type theory (pdf) (talk recording) (doi) (cite)
Yannick Forster
CSL 2021, Ljubljana, Slovenia, 2021.

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

Hilbert's Tenth Problem in Coq (extended version) (pdf)
Dominique Larchey-Wendling and Yannick Forster
Submitted for review.

Coq Coq Correct! - Verification of Type Checking and Erasure for Coq, in Coq (pdf) (doi) (cite)
Matthieu Sozeau, Simon Boulier, Yannick Forster, Nicolas Tabareau and Théo Winterhalter
POPL 2020, New Orleans, USA, 2020.

The Weak Call-By-Value λ-Calculus is Reasonable for Both Time and Space (pdf) (slides) (doi) (cite)
Yannick Forster, Fabian Kunze, Marc Roth
POPL 2020, New Orleans, USA, 2020.

Coq à la Carte - A Practical Approach to Modular Syntax with Binders (pdf) (doi) (cite)
Yannick Forster and Kathrin Stark
CPP 2020, New Orleans, USA, 2020.

Verified Programming of Turing Machines in Coq (pdf) (doi) (cite)
Yannick Forster, Fabian Kunze, Maximilian Wuttke
CPP 2020, New Orleans, USA, 2020.

Undecidability of Higher-Order Unification Formalised in Coq (pdf) (slides) (doi) (cite)
Simon Spies and Yannick Forster
CPP 2020, New Orleans, USA, 2020.

Completeness Theorems for First-Order Logic Analysed in Constructive Type Theory (pdf) (doi) (cite)
Yannick Forster, Dominik Kirst, Dominik Wehr
Symposium on Logical Foundations Of Computer Science (LFCS 2020), January 4-7, 2020, Deerfield Beach, Florida, U.S.A.

On the expressive power of user-defined effects: effect handlers, monadic reflection, delimited control (updated version) (pdf) (doi) (cite)
Yannick Forster, Ohad Kammar, Sam Lindley, Matija Pretnar
Journal of Functional Programming Special Issue: Post-Proceedings of ICFP 2017, 2019.

A certifying extraction with time bounds from Coq to call-by-value λ-calculus (pdf) (slides) (doi) (cite)
Yannick Forster and Fabian Kunze
ITP 2019, Portland, USA, 2019. Pre-print on arxiv.

Hilbert's Tenth Problem in Coq (pdf) (slides) (doi) (cite)
Dominique Larchey-Wendling and Yannick Forster
FSCD 2019, Dortmund, Germany, 2019.

Call-By-Push-Value in Coq: Operational, Equational and Denotational Theory (pdf) (slides) (doi) (cite)
Yannick Forster, Steven Schäfer, Simon Spies, Kathrin Stark
CPP 2019, Cascais, Portugal, 2019.

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

Certified Undecidability of Intuitionistic Linear Logic via Binary Stack Machines and Minsky Machines (pdf) (slides) (doi) (cite)
Yannick Forster and Dominique Larchey-Wendling
CPP 2019, Cascais, Portugal, 2019.

Formal Small-step Verification of a Call-by-value Lambda Calculus Machine (doi) (cite)
Fabian Kunze, Gert Smolka, Yannick Forster
APLAS 2018, Wellington, New Zealand, 2018

Call-by-Value Lambda Calculus as a Model of Computation in Coq (pdf) (doi) (cite)
Yannick Forster and Gert Smolka
Journal of Automated Reasoning, 2018.

Verification of PCP-Related Computational Reductions in Coq (slides) (doi) (cite)
Yannick Forster, Edith Heiter, Gert Smolka
ITP 2018, Oxford, UK, 2018. Pre-print on arxiv.

Weak Call-by-Value Lambda Calculus as a Model of Computation in Coq (pdf) (slides) (doi) (cite)
Yannick Forster and Gert Smolka
ITP 2017, Brasilia, Brazil, 2017.

On the Expressive Power of User-Defined Effects: Effect Handlers,
Monadic Reflection, Delimited Control (doi) (cite)
Yannick Forster, Ohad Kammar, Sam Lindley, Matija Pretnar
ICFP 2017, Oxford, UK, 2017.

Extended abstracts and talks

Generating induction principles and subterm relations for inductive types using MetaCoq (pdf) (slides)
Bohdan Liesnikov, Marcel Ullrich, Yannick Forster
Coq Workshop 2020, online, 2020.

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) (slides) (talk recording)
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.

Coq Coq Codet! - Towards a Verified Toolchain for Coq in MetaCoq (pdf) (slides)
Matthieu Sozeau, Yannick Forster, Simon Boulier, Nicolas Tabareau and Théo Winterhalter
Coq Workshop 2019, Portland, USA, 2019.

Mechanically verified type and proof erasure for Coq
Yannick Forster and Matthieu Sozeau
Facets of Realizability 2019, Paris, France, 2019.

A constructive Coq library for the mechanization of undecidability (pdf) (slides)
Yannick Forster and Dominique Larchey-Wendling
MLA 2019, Nancy, France, 2019.

Towards a library of formalised undecidable problems in Coq: The undecidability of intuitionistic linear logic (slides)
Yannick Forster and Dominique Larchey-Wendling
LOLA 2018, Oxford, UK, 2018.

The strong invariance thesis for a lambda-calculus (slides)
Yannick Forster, Fabian Kunze, Marc Roth
LOLA 2017, Reykjavik, Iceland, 2017.

Verified Extraction from Coq to a Lambda-Calculus (pdf) (slides)
Yannick Forster and Fabian Kunze
Coq Workshop 2016, ITP 2016, Nancy, France, 2016.

Theses

Computability in Constructive Type Theory
Yannick Forster
PhD thesis, Saarland University, 2021.

On the expressive power of effect handlers and monadic reflection (pdf)
Yannick Forster
Master's Thesis, Robinson College, University of Cambridge, 2016.

A Formal and Constructive Theory of Computation (pdf)
Yannick Forster
Bachelor's Thesis, Programming Systems Lab, Saarland University, 2014.

Supervised Students

Felix Jahn, 2020, Bachelor's thesis
Synthetic One-One, Many-One, and Truth-Table Reducibility in Coq

Marcel Ullrich, 2020, Bachelor's thesis
Generating induction principles for nested inductive types in MetaCoq

Dominik Wehr, 2019, Bachelor's thesis, co-advised with Dominik Kirst
A Constructive Analysis of First-Order Completeness Theorems in Coq

Simon Spies, 2019, Bachelor's thesis
Formalising the Undecidability of Higher-Order Unification

Maximilian Wuttke, 2017, Bachelor's thesis
Verified Programming Of Turing Machines In Coq

Edith Heiter, 2017, Bachelor's thesis, co-advised with Gert Smolka
Undecidability of the Post Correspondence Problem in Coq

Teaching

Contact