Related papers: Formalizing Monoidal Categories and Actions for Sy…
Context-free language theory is a subject of high importance in computer language processing technology as well as in formal language theory. This paper presents a formalization, using the Coq proof assistant, of fundamental results related…
Text editors represent one of the fundamental tools that writers use - software developers, book authors, mathematicians. A text editor must work as intended in that it should allow the users to do their job. We start by introducing a small…
Every database system contains a query optimizer that performs query rewrites. Unfortunately, developing query optimizers remains a highly challenging task. Part of the challenges comes from the intricacies and rich features of query…
Theorem provers are important tools for people working in formal verification. There are a myriad of interactive systems available today, with varying features and approaches motivating their development. These design choices impact their…
Practical checkers based on refinement types use the combination of implicit semantic sub-typing and parametric polymorphism to simplify the specification and automate the verification of sophisticated properties of programs. However, a…
Common Knowledge Logic is meant to describe situations of the real world where a group of agents is involved. These agents share knowledge and make strong statements on the knowledge of the other agents (the so called \emph{common…
This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through *-autonomous monoidal categories and related structures.
Development of Interactive Theorem Provers has led to the creation of big libraries and varied infrastructures for formal proofs. However, despite (or perhaps due to) their sophistication, the re-use of libraries by non-experts or across…
Sized types are a modular and theoretically well-understood tool for checking termination of recursive and productivity of corecursive definitions. The essential idea is to track structural descent and guardedness in the type system to make…
Randomly masking and predicting word tokens has been a successful approach in pre-training language models for a variety of downstream tasks. In this work, we observe that the same idea also applies naturally to sequential decision-making,…
Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and…
We define the affinization of an arbitrary monoidal category $\mathcal{C}$, corresponding to the category of $\mathcal{C}$-diagrams on the cylinder. We also give an alternative characterization in terms of adjoining dot generators to…
We develop synthetic notions of oracle computability and Turing reducibility in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. As usual in synthetic approaches, we employ a…
We develop the formal theory of monads, as established by Street, in univalent foundations. This allows us to formally reason about various kinds of monads on the right level of abstraction. In particular, we define the bicategory of monads…
We present the Sequent Calculus Trainer, a tool that supports students in learning how to correctly construct proofs in the sequent calculus for first-order logic with equality. It is a proof assistant fostering the understanding of all the…
We obtain the specialization of monomial symmetric functions on the alphabet (a-b)/(1-q). This gives a remarkable algebraic identity, and four new developments for the Macdonald polynomial associated with a row. The proofs are given in the…
We present the proof assistant homotopy.io for working with finitely-presented semistrict higher categories. The tool runs in the browser with a point-and-click interface, allowing direct manipulation of proof objects via a graphical…
In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the…
Semantic typing has become a powerful tool for program verification, applying the technique of logical relations as not only a proof method, but also a device for prescribing program behavior. In recent work, Yao et al. scaled semantic…
In this paper, we present a formalization of Kozen's propositional modal $\mu$-calculus, in the Calculus of Inductive Constructions. We address several problematic issues, such as the use of higher-order abstract syntax in inductive sets in…