Related papers: A formalization of Borel determinacy in Lean
Schmidt's game, and other similar intersection games have played an important role in recent years in applications to number theory, dynamics, and Diophantine approximation theory. These games are real games, that is, games in which the…
Distribution theory is a cornerstone of the theory of partial differential equations. We report on the progress of formalizing the theory of tempered distributions in the interactive proof assistant Lean, which is the first formalization in…
We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate…
Classical probability theory is formulated using sets. In this paper, we extend classical probability theory with propositional computability logic. Unlike other formalisms, computability logic is built on the notion of events/games, which…
Solving a problem of Diestel and Pott, we construct a large class of infinite matroids. These can be used to provide counterexamples against the natural extension of the Well-quasi-ordering-Conjecture to infinite matroids and to show that…
We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of…
This work is intended for researchers in the field of side-channel attacks, countermeasure analysis, and probing security. It reports on a formalization of simulatability in terms of categorical properties, which we think will provide a…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that typically arise from applying decision rules…
Logic programming with fixed-point definitions is a useful extension of traditional logic programming. Fixed-point definitions can capture simple model checking problems and closed-world assumptions. Its operational semantics is typically…
The physics community relies on index notation to effectively manipulate types of tensors. This paper introduces the first formally verified implementation of index notation in the interactive theorem prover Lean 4. By integrating index…
We prove that in a locally finite dimensional Lie algebra L, any maximal, locally solvable subalgebra (Borel subalgebra) is the stabilizer of a maximal, generalized flag in an integrable, faithful module over L.
We report on a formalization of the change of variables formula in integrals, in the mathlib library for Lean. Our version of this theorem is extremely general, and builds on developments in linear algebra, analysis, measure theory and…
Canonical is a solver for type inhabitation in dependent type theory, that is, the problem of producing a term of a given type. We present a Lean tactic which invokes Canonical to generate proof terms and synthesize programs. The tactic…
We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We…
Hedonic games provide a natural model of coalition formation among self-interested agents. The associated problem of finding stable outcomes in such games has been extensively studied. In this paper, we identify simple conditions on…
We show that the higher-order matching problem is decidable using a game-theoretic argument.
To obtain the highest confidence on the correction of numerical simulation programs implementing the finite element method, one has to formalize the mathematical notions and results that allow to establish the soundness of the method. The…
Seymour's decomposition theorem is a hallmark result in matroid theory presenting a structural characterization of the class of regular matroids. Formalization of matroid theory faces many challenges, most importantly that only a limited…
We discuss partial specifications in first-order logic FO and also in a Turing-complete extension of FO. We compare the compositional and game-theoretic approaches to the systems.
We present a formalization of convex polyhedra in the proof assistant Coq. The cornerstone of our work is a complete implementation of the simplex method, together with the proof of its correctness and termination. This allows us to define…