Description:
<jats:p>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 $\mu$-recursive functions and give a
certified compiler from $\mu$-recursive functions to Minsky machines.</jats:p>