Hilbert's Tenth Problem in Coq

03/10/2020 ∙ by Dominique Larchey-Wendling, et al. ∙ 0

We formalise the undecidability of solvability of Diophantine equations, i.e. polynomial equations over natural numbers, in Coq's constructive type theory. To do so, we give the first full mechanisation of the Davis-Putnam-Robinson-Matiyasevich theorem, stating that every recursively enumerable problem – in our case by a Minsky machine – is Diophantine. We obtain an elegant and comprehensible proof by using a synthetic approach to computability and by introducing Conway's FRACTRAN language as intermediate layer. Additionally, we prove the reverse direction and show that every Diophantine relation is recognisable by μ-recursive functions and give a certified compiler from μ-recursive functions to Minsky machines.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

Code Repositories

Lecturas_GLC

Lecturas del Grupo de Lógica Computacional


view repo
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.