Hilbert Meets Isabelle: Formalisation of the DPRM Theorem in Isabelle

Title:Hilbert Meets Isabelle: Formalisation of the DPRM Theorem in Isabelle

Authors:Benedikt Stock, Abhik Pal, Maria Antonia Oprea, Yufei Liu, Malte Sophian Hassler, Simon Dubischar, Prabhat Devkota, Yiping Deng, Marco David, Bogdan Ciurezu, Jonas Bayer and Deepak Aryal

Conference:Isabelle 2018

Tags:Diophantine equations, DPRM Theorem, Hilbert's tenth problem, Isabelle and recursively enumerable

Abstract:

Hilbert's tenth problem, posed in 1900 by David Hilbert, asks for a general algorithm to determine the solvability of any given Diophantine equation. In 1970, Yuri Matiyasevich proved the DPRM theorem which implies such an algorithm cannot exist. This paper will outline our attempt to formally state the DPRM theorem and verify Matiyasevich's proof using the proof assistant Isabelle/HOL.