Self-Formalisation of Higher-Order Logic Semantics, Soundness, and a Verified Implementation
Artikel i vetenskaplig tidskrift, 2016

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

Verification

Theorem proving

Higher-order logic

Interactive theorem proving

Consistency

Författare

R. Kumar

University of Cambridge

R. Arthan

University of Oxford

Magnus Myreen

Chalmers, Data- och informationsteknik, Programvaruteknik

S. Owens

University Of Kent

Journal of Automated Reasoning

0168-7433 (ISSN) 1573-0670 (eISSN)

Vol. 56 3 221-259

Styrkeområden

Informations- och kommunikationsteknik

Ämneskategorier

Data- och informationsvetenskap

DOI

10.1007/s10817-015-9357-x