4 research outputs found
Interaction Tree Specifications: A Framework for Specifying Recursive, Effectful Computations That Supports Auto-Active Verification (Artifact)
This paper presents a specification framework for monadic, recursive, interactive programs that supports auto-active verification, an approach that combines user-provided guidance with automatic verification techniques. This verification tool is designed to have the flexibility of a manual approach to verification along with the usability benefits of automatic approaches. We accomplish this by augmenting Interaction Trees, a Coq datastructure for representing effectful computations, with logical quantifier events. We show that this yields a language of specifications that are easy to understand, automatable, and are powerful enough to handle properties that involve non-termination. Our framework is implemented as a library in Coq. We demonstrate the effectiveness of this framework by verifying real, low-level code
Interaction Tree Specifications: A Framework for Specifying Recursive, Effectful Computations That Supports Auto-Active Verification
This paper presents a specification framework for monadic, recursive, interactive programs that supports auto-active verification, an approach that combines user-provided guidance with automatic verification techniques. This verification tool is designed to have the flexibility of a manual approach to verification along with the usability benefits of automatic approaches. We accomplish this by augmenting Interaction Trees, a Coq datastructure for representing effectful computations, with logical quantifier events. We show that this yields a language of specifications that are easy to understand, automatable, and are powerful enough to handle properties that involve non-termination. Our framework is implemented as a library in Coq. We demonstrate the effectiveness of this framework by verifying real, low-level code
Legendrian satellites and decomposable cobordisms
We investigate the interactions between the Legendrian satellite construction
and the existence of exact, orientable Lagrangian cobordisms between Legendrian
knots. Given Lagrangian cobordisms between two Legendrian knots and between two
Legendrian tangles, we construct a Lagrangian cobordism between Legendrian
satellites of the knots by the closures of the tangles, with extra twists on
both the top and the bottom satellite to compensate for the genus of the
cobordism. If the original cobordisms were decomposable, then a decomposable
cobordism between satellites exists as well, again with extra twists.Comment: 31 pages, 15 figures. Section 4 generalizes the main results in
arXiv:1710.00943, which will remain unpublishe