Verified proof checking for higher-order logic
Licentiate thesis, 2020

This thesis is about verified computer-aided checking of mathematical proofs. We build on tools for proof-producing program synthesis, and verified compilation, and a verified theorem proving kernel. Using these tools, we have produced a mechanized proof checker for higher-order logic that is verified to only accept valid proofs. To the best of our knowledge, this is the only proof checker for HOL that has been verified to this degree of rigor.

Mathematical proofs exist to provide a high degree of confidence in the truth of statements. The level of confidence we place in a proof depends on its correctness. This correctness is usually established through proof checking, performed either by human or machine. One benefit of using a machine for this task is that the correctness of the machine itself can be proven.

The main contribution of this work is a verified mechanized proof checker for theorems in higher-order logic (HOL). The checker is implemented as functions in the logic of the HOL4 theorem prover, and it comes with a soundness result, which states that it will only accept proofs of true theorems of HOL. Using a technique for proof-producing code generation (which is extended as part of this thesis), we synthesize a CakeML program that is compiled using the CakeML compiler. The CakeML compiler is verified to preserve program semantics. As a consequence, we are able to obtain a soundness result about the machine code which implements the proof checker.

Opponent: Dr. Joe Leslie-Hurd, Intel Corporation, Portland, Oregon, USA

Author

Oskar Abrahamsson

Chalmers, Computer Science and Engineering (Chalmers), Formal methods

A verified proof checker for higher-order logic

Journal of Logical and Algebraic Methods in Programming,; Vol. 112(2020)

Journal article

Proof-Producing Synthesis of CakeML from Monadic HOL Functions

Journal of Automated Reasoning,; Vol. In Press(2020)

Journal article

Pålitlig mjukvara via programmering och kompilering i logik

Swedish Foundation for Strategic Research (SSF), 2017-01-01 -- 2021-12-31.

Subject Categories

Computer Science

Publisher

Chalmers University of Technology

Online

Opponent: Dr. Joe Leslie-Hurd, Intel Corporation, Portland, Oregon, USA

More information

Latest update

8/26/2020