POPL

Incorrectness Logic (IL) has recently been advanced as a logical under-approximate theory for proving the presence of bugs - dual to Hoare Logic, which is an over-approximate theory for proving the absence of bugs. To facilitate scalable bug detection, ...

FV Time is a small-scale verification project developed in the Coq proof assistant using the Mathematical Components libraries. It is a library for managing conversions between time formats (UTC and timestamps), as well as commonly used functions for ...

The development of sound and efficient tools that automatically perform floating-point round-off error analysis is an active area of research with applications to embedded systems and scientific computing. In this paper we describe VCFloat2, a novel ...

The field of high-assurance cryptography is quickly maturing, yet a unified foundational framework for end-to-end formal verification of efficient cryptographic implementations is still missing. To address this gap, we use the Coq proof assistant to ...

Array-based encodings of tree structures are often preferable to linked or abstract data type-based representations for efficiency reasons. Compared to the more traditional encodings, array-based trees do not immediately offer convenient induction ...

Concurrent search structure templates are a technique for separating the verification of a concurrent data structure into concurrency-control and data-structure components, which can then be modularly combined with no additional proof effort. In this ...

Subformula linking is a technique that allows one to simplify proof goals by identifying subformulas of hypotheses that share atoms with the goal. It has been used by recent prototypes for gesture-based interactive theorem proving, but also for theorem ...

We present PfComp, a verified compiler for stateless firewall policies. The policy is first compiled into an intermediate representation taking the form of a binary decision diagram that is optimised in terms of decision nodes. The decision diagram is ...

Current compilers implement security features and optimizations that require nontrivial semantic reasoning about pointers and memory allocation: the program after the insertion of the security feature, or after applying the optimization, must simulate ...

We present a formalization of a matching algorithm for extended regular expression matching based on locations and symbolic derivatives which supports intersection, complement and lookarounds and whose implementation mirrors an extension of the recent ...

Formalised libraries of combinatorial mathematics have rapidly expanded over the last five years, but few use one of the most important tools: probability. How can often intuitive probabilistic arguments on the existence of combinatorial structures, such ...

Parallel critical pairs (PCPs) have been used to design sufficient criteria for confluence of term rewrite systems. In this work we formalize PCPs and the criteria of Gramlich, Toyama, and Shintani and Hirokawa in the proof assistant Isabelle. In order ...

Differential temporal dynamic logic dTL2 is a logic to specify and verify temporal properties of hybrid systems. It extends differential dynamic logic (dL) with temporal operators that enable reasoning on intermediate states in both discrete and ...

We describe a formalization in Lean 4 of Giles Gardam's disproof of Kaplansky's Unit Conjecture. This makes use of a combination of deductive proving and formally verified computation, using the nature of Lean 4 as a programming language which is also a ...

Local fields, and fields complete with respect to a discrete valuation, are essential objects in commutative algebra, with applications to number theory and algebraic geometry. We formalize in Lean the basic theory of discretely valued fields. In ...

Ordinals can be used to prove the termination of dependently typed programs. Brouwer trees are a particular ordinal notation that make it very easy to assign sizes to higher order data structures. They extend unary natural numbers with a limit ...

Using the Coq proof assistant, we investigate the minimal non-constructive principles needed to show soundness and completeness of propositional bi-intuitionistic logic. Before being revisited and corrected by Goré and Shillito, the completeness of bi-...

We present an extensive mechanization of the metatheory of Martin-Löf Type Theory (MLTT) in the Coq proof assistant. Our development builds on pre-existing work in Agda to show not only the decidability of conversion, but also the decidability of type ...

Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also "morphisms", which ...

We present a formalization of different categorical structures used to interpret linear logic. Our formalization takes place in UniMath, a library of univalent mathematics based on the Coq proof assistant.

All the categorical structures we formalize ...

Formalized 1-category theory forms a core component of various libraries of mathematical proofs. However, more sophisticated results in fields from algebraic topology to theoretical physics, where objects have “higher structure,” rely on infinite-...