Journal of Automated Reasoning

, Volume 56, Issue 3, pp 221–259

Self-Formalisation of Higher-Order Logic

Semantics, Soundness, and a Verified Implementation
  • Ramana Kumar
  • Rob Arthan
  • Magnus O. Myreen
  • Scott Owens
Open Access

DOI: 10.1007/s10817-015-9357-x

Cite this article as:
Kumar, R., Arthan, R., Myreen, M.O. et al. J Autom Reasoning (2016) 56: 221. doi:10.1007/s10817-015-9357-x


We present a mechanised semantics for higher-order logic (HOL), and a proof of soundness for the inference system, including the rules for making definitions, implemented by the kernel of the HOL Light theorem prover. Our work extends Harrison’s verification of the inference system 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. Apart from adding support for definitions and synthesising an implementation, we improve on Harrison’s work by making our model of HOL parametric on the universe of sets, and we prove soundness for an improved principle of constant specification in the hope of encouraging its adoption. Our semantics supports defined constants directly via a context, and we find this approach cleaner than our previous work formalising Wiedijk’s Stateless HOL.


HOL Higher-order logic Verification Interactive theorem proving Theorem proving Consistency Semantics Self-formalisation Self-verification 
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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Ramana Kumar
    • 1
  • Rob Arthan
    • 2
  • Magnus O. Myreen
    • 3
  • Scott Owens
    • 4
  1. 1.Computer LaboratoryUniversity of CambridgeCambridgeUK
  2. 2.Department of Computer ScienceUniversity of OxfordOxfordUK
  3. 3.CSE DepartmentChalmers University of TechnologyGöteborgSweden
  4. 4.School of ComputingUniversity of KentKentUK

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