KeYmaera X: An aXiomatic Tactical Theorem Prover for Hybrid Systems

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Announcements

• Best Tool Paper Award at FM 2019 was awarded for Pegasus, the continuous invariant generator for KeYmaera X
• FM 2019 Tutorial on KeYmaera X: Modular Formal Verification of Cyber-Physical Systems with KeYmaera X
• New video lectures: Logical Foundations of Cyber-Physical Systems
• New textbook: Logical Foundations of Cyber-Physical Systems, Springer, 2018

Overview

Self-driving cars, autonomous robots, modern airplanes, or robotic surgery: we increasingly entrust our lives to computers and therefore should strive for nothing but the highest safety standards - mathematical correctness proof. Proofs for such cyber-physical systems can be constructed with the KeYmaera X prover. As a hybrid systems and hybrid games theorem prover, KeYmaera X analyzes the control program and the physical behavior of the controlled system together.

KeYmaera X features a minimal core of just 1700 lines of code that isolates all soundness-critical reasoning. Such a small and simple prover core makes it much easier to trust verification results. Pre-defined and custom tactics built on top of the core drive automated proof search. KeYmaera X comes with a web-based front-end that provides a clean interface for both interactive and automated proving, highlighting the most crucial parts of a verification activity.

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Summary

KeYmaera X is a theorem prover for differential dynamic logic (dL), a logic for specifying and verifying properties of hybrid systems with mixed discrete and continuous dynamics. Reasoning about complicated hybrid systems requires support for sophisticated proof techniques, efficient computation, and a user interface that crystallizes salient properties of the system. KeYmaera X allows users to specify custom proof search techniques as tactics, execute tactics in parallel, and interface with partial proofs via an extensible user interface. KeYmaera X also is a verification tool for differential game logic (dGL), a logic for specifying and verifying properties of hybrid games with mixed discrete, continuous and adversarial dynamics.

KeYmaera X is built up from a small trusted core. The core contains a finite list of locally sound dL axioms that are instantiated using a uniform substitution proof rule. Isolating all soundness-critical reasoning in this axiomatic core obviates the otherwise intractable task of ensuring that proof search algorithms are implemented correctly. This enables advanced proof search features---such as aggressive, speculative proof search and user-defined tactics built using a flexible tactic language---without correctness concerns that could undermine the usefulness of automated analysis. KeYmaera X demonstrates that tactics on top of the axiomatic core provide a rich language for implementing novel and highly sophisticated automatic proof procedures.

Case Studies

These are a few of the many other case studies that have been verified in KeYmaera X:

Other case studies are reported in corresponding publications.

Quick Usage

Also get quick usage help any time with the  ?  menu button in KeYmaera X.

Any opinions, findings, and conclusions or recommendations expressed are those of the author(s) and do not necessarily reflect the views of any sponsoring institution.