How to Believe a Machine-Checked Proof

How to Believe a Machine-Checked Proof

How to Believe a Machine-Checked Proof1

How to Believe a Twelf Proof

Logical systems are represented in LF by giving a full and faithful (adequate) embedding of the deductive apparatus of the logic as canonical forms of certain types and kinds in LF in specified contexts. The collection of contexts over which the representation is adequate is called a world, because it provides generators for the canonical forms in question. Transferring adequacy from one world ...

A Machine-Checked Proof of A State-Space Construction Algorithm

This paper presents the correctness proof of Saturation, an algorithm for generating state spaces of concurrent systems, implemented in the SMART tool. Unlike the Breadth First Search exploration algorithm, which is easy to understand and formalise, Saturation is a complex algorithm, employing a mutually-recursive pair of procedures that compute a series of non-trivial, nested local fixed point...

A Machine-Checked Proof of the Odd Order Theorem

This paper reports on a six-year collaborative effort that culminated in a complete formalization of a proof of the Feit-Thompson Odd Order Theorem in the Coq proof assistant. The formalized proof is constructive, and relies on nothing but the axioms and rules of the foundational framework implemented by Coq. To support the formalization, we developed a comprehensive set of reusable libraries o...