Abstract
We present a mechanised semantics and soundness proof for the HOL Light kernel including its definitional principles, extending Harrison’s verification of the kernel without definitions. Soundness of the logic extends to soundness of a theorem prover, because we also show that a synthesised implementation of the kernel in CakeML refines the inference system. Our semantics is the first for Wiedijk’s stateless HOL; our implementation, however, is stateful: we give semantics to the stateful inference system by translation to the stateless. We improve on Harrison’s approach by making our model of HOL parametric on the universe of sets. Finally, we prove soundness for an improved principle of constant specification, in the hope of encouraging its adoption. This paper represents the logical kernel aspect of our work on verified HOL implementations; the production of a verified machine-code implementation of the whole system with the kernel as a module will appear separately.
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Kumar, R., Arthan, R., Myreen, M.O., Owens, S. (2014). HOL with Definitions: Semantics, Soundness, and a Verified Implementation. In: Klein, G., Gamboa, R. (eds) Interactive Theorem Proving. ITP 2014. Lecture Notes in Computer Science, vol 8558. Springer, Cham. https://doi.org/10.1007/978-3-319-08970-6_20
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DOI: https://doi.org/10.1007/978-3-319-08970-6_20
Publisher Name: Springer, Cham
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