Verification of Provers and Solvers

Formally Verified Matching of Regular Expressions

We demonstrate the benefit of computer assisted reasoning by proving correctness of some matching algorithms for regular expressions. We give a brief survey of the VeriFun system used for verification, illustrate the problem, discuss the computation and usage of derivatives, present the machine assisted proofs and repo...

C Software Formal Verification Review, challenges and future directions

Proof Primitives for Equality Saturation-based Automated Provers

This work presents a proof extraction algorithm for versioned e-graphs, an extension of e-graphs that supports branching reasoning contexts and proof by cases and implements it in Vegie, a lightweight automated inductive theorem prover.

Formal Verification of Proofs from Automated Theorem Provers for Higher-Order Logic

The resulting prototype reconstructs about 80% of generated proof steps automatically, making Leo-III the first higher-order automated theorem prover to support independently checkable proof reconstruction and providing a basis for cross-system reuse.

Mechanizing G\"odel's Incompleteness Theorems and Provability Logic

We mechanized proof of G\"odel's first and second incompleteness theorems, Solovay's arithmetical completeness theorem of \mathbf{GL}, and related results in the Lean 4 theorem prover.

Formalizing the Omega Test in Dafny

We present a formalization in Dafny of the Omega Test, an algorithm used to decide the satisfiability of a system of inequalities. The implementation defines executable representations for rational numbers, linear expressions, inequalities, equalities, divisibility constraints, and systems of constraints, together with...