KeYmaera X: An Axiomatic Tactical Theorem Prover for Hybrid Systems

<p>KeYmaera X is a theorem prover for <em>differential dynamic logic</em></p> ), a logic for specifying and verifying properties of hybrid systems. Reasoning about complicated hybrid systems models 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 <em>tactics</em>, execute these tactics in parallel, and interface with partial proofs via an extensible user interface. <p>Advanced proof search features—and user-defined tactics in particular—are difficult to check for soundness. To admit extension and experimentation in proof search without reducing trust in the prover, KeYmaera X is built up from a <em>small trusted kernel</em>. The prover kernel contains a list of sound</p> <p>axioms that are instantiated using a uniform substitution proof rule. Isolating all soundness-critical reasoning to this prover kernel obviates the intractable task of ensuring that each new proof search algorithm is implemented correctly. Preliminary experiments suggest that a single layer of tactics on top of the prover kernel provides a rich language for implementing novel and sophisticated proof search techniques.</p>