Foundational Extensible Corecursion

This paper presents a formalized framework for defining corecursive functions safely in a total setting, based on corecursion up-to and relational parametricity. The end product is a general corecursor that allows corecursive (and even recursive) calls under well-behaved operations, including constructors. Corecursive functions that are well behaved can be registered as such, thereby increasing the corecursor's expressiveness. The metatheory is formalized in the Isabelle proof assistant and forms the core of a prototype tool. The corecursor is derived from first principles, without requiring new axioms or extensions of the logic

An open extensible tool environment for Event-B

Abstract. We consider modelling indispensable for the development of complex systems. Modelling must be carried out in a formal notation to reason and make meaningful conjectures about a model. But formal modelling of complex systems is a difficult task. Even when theorem provers improve further and get more powerful, modelling will remain difficult. The reason for this that modelling is an exploratory activity that requires ingenuity in order to arrive at a meaningful model. We are aware that automated theorem provers can discharge most of the onerous trivial proof obligations that appear when modelling systems. In this article we present a modelling tool that seamlessly integrates modelling and proving similar to what is offered today in modern integrated development environments for programming. The tool is extensible and configurable so that it can be adapted more easily to different application domains and development methods.

Rodin: an open toolset for modelling and reasoning in Event-B

Event-B is a formal method for system-level modelling and analysis. Key features of Event-B are the use of set theory as a modelling notation, the use of refinement to represent systems at different abstraction levels and the use of mathematical proof to verify consistency between refinement levels. In this article we present the Rodin modelling tool that seamlessly integrates modelling and proving. We outline how the Event-B language was designed to facilitate proof and how the tool has been designed to support changes to models while minimising the impact of changes on existing proofs. We outline the important features of the prover architecture and explain how well-definedness is treated. The tool is extensible and configurable so that it can be adapted more easily to different application domains and development methods