  We construct ample groupoids from certain categories of paths, and prove that
their $C^*$-algebras coincide with the continued fraction AF algebras of Effros
and Shen. The proof relies on recent classification results for simple nuclear
$C^*$-algebras. The groupoids are not principal. This provides examples of
Cartan subalgebras in the continued fraction AF algebras that are isomorphic,
but not conjugate, to the standard diagonal subalgebras.
