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For example, the following simple\nspecification says that a network's output should be monotonically increasing with respect to\nits third input.\n\n\u003c!-- This must be a direct link, because the same README is used on PyPI --\u003e\n![Example specification](https://github.com/vehicle-lang/vehicle/blob/dev/docs/example-spec.png?raw=true)\n\nThese specifications can then automatically be compiled down to loss functions to be\nused when training your network.\nAfter training, the same specification can be compiled down to low-level neural network verifiers such as Marabou which either prove that the specification holds or produce a counter-example. Such a proof is far better than simply testing, as you can prove that\nthe specification holds for _all_ inputs.\nVerified specifications can also be exported to interactive theorem provers (ITPs)\nsuch as Agda.\nThis in turn allows for the formal verification of larger software systems\nthat use neural networks as subcomponents.\nThe generated ITP code is tightly linked to the actual deployed network, so changes\nto the network will result in errors when checking the larger proof.\n\n## Documentation\n\n- [User manual](https://vehicle-lang.readthedocs.io/en/latest/)\n- [Tutorial](https://vehicle-lang.github.io/tutorial/)\n\n## Examples\n\nEach of the following examples comes with an explanatory README file:\n\n- [ACAS Xu](https://github.com/vehicle-lang/vehicle/blob/dev/examples/acasXu/) - The complete specification of the ACAS Xu collision avoidance system from the [Reluplex paper](https://arxiv.org/abs/1702.01135) in a single file.\n\n- [Car controller](https://github.com/vehicle-lang/vehicle/blob/dev/examples/windController/) - A neural network controller that is formally proven to always keep a simple model of a car on the road in the face of noisy sensor data and an unpredictable cross-wind.\n\n- [MNIST robustness](https://github.com/vehicle-lang/vehicle/blob/dev/examples/mnist-robustness/) - A classifier for the MNIST dataset that is proven to be robust around the images in the dataset.\n\nIn addition to the above, further examples of specifications can be found in the [test suite](https://github.com/vehicle-lang/vehicle/tree/dev/test/specs)\nand the corresponding output of the Vehicle compiler can be found [here](https://github.com/vehicle-lang/vehicle/tree/dev/test/Test/Compile/Golden).\n\n## Support\n\nIf you are interested in adding support for a particular format/verifier/ITP\nthen open an issue on the [Issue Tracker](https://github.com/wenkokke/vehicle/issues)\nto discuss it with us.\n\n#### Neural network formats\n\n- [ONNX](https://onnx.ai/)\n\n#### Dataset formats\n\n- [IDX](http://yann.lecun.com/exdb/mnist/)\n\n#### Verifier backends\n\n- [Marabou](https://github.com/NeuralNetworkVerification/Marabou)\n\n#### Interactive Theorem Prover backends\n\n- [Agda](https://agda.readthedocs.io/)\n- [Rocq](https://rocq-prover.org/)\n- [Isabelle](https://isabelle.in.tum.de/)\n\n## Related papers\n\n- [Vehicle tool paper (in FCSD'25)](https://drops.dagstuhl.de/entities/volume/LIPIcs-volume-337)\n- [Vehicle's type checker (in CPP'23)](https://laiv.uk/wp-content/uploads/2022/12/vehicle.pdf)\n- [Vehicle's compilation to verifier queries](https://arxiv.org/abs/2402.01353)\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fvehicle-lang%2Fvehicle","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fvehicle-lang%2Fvehicle","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fvehicle-lang%2Fvehicle/lists"}