Abstract Development of formal proofs of correctness of programs can increase actual and
perceived reliability and facilitate better understanding of program specifications and their …

We formalize the soundness theorem for differential dynamic logic, a logic for verifying
hybrid systems. To increase confidence in the formalization, we present two versions: one in …

We present a dependent type theory organized around a Cartesian notion of cubes (with
faces, degeneracies, and diagonals), supporting both fibrant and non-fibrant types. The …

Mechanical reasoning is a key area of research that lies at the crossroads of mathematical
logic and artificial intelligence. The main aim to develop mechanical reasoning systems …

We present a mechanised semantics for higher-order logic (HOL), and a proof of soundness
for the inference system, including the rules for making definitions, implemented by the …

We present the design, implementation, and foundation of a verifier for higher-order
functional programs with generics and recursive data types. Our system supports proving …

This paper presents a fully verified interactive theorem prover for higher-order logic, more
specifically: a fully verified clone of HOL Light. Our verification proof of this new system …

Intermediate verification languages like Why3 and Boogie have made it much easier to build
program verifiers, transforming the process into a logic compilation problem rather than a …

Correct and Complete Type Checking and Certified Erasure for Coq, in Coq Page 1 HAL Id:
hal-04077552 https://inria.hal.science/hal-04077552 Preprint submitted on 21 Apr 2023 HAL is …

Dependent type theories are a family of logical systems that serve as expressive functional
programming languages and as the basis of many proof assistants. In the past decade, type …