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KeYmaera X: An Axiomatic Tactical Theorem Prover for Hybrid Systems

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journal contribution
posted on 01.01.2004, 00:00 by Nathan Fulton, Stefan Mitsch, Jan-David Quesel, Marcus Volp, Andre Platzer

KeYmaera X is a theorem prover for differential dynamic logic

), 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 tactics, execute these tactics in parallel, and interface with partial proofs via an extensible user interface.

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 small trusted kernel. The prover kernel contains a list of sound

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.