  In \cite{BH20} an elegant choice-free construction of a canonical extension
of a boolean algebra $B$ was given as the boolean algebra of regular open
subsets of the Alexandroff topology on the poset of proper filters of $B$. We
make this construction point-free by replacing the Alexandroff space of proper
filters of $B$ with the free frame $\mathcal{L}$ generated by the bounded
meet-semilattice of all filters of $B$ (ordered by reverse inclusion) and prove
that the booleanization of $\mathcal{L}$ is a canonical extension of $B$. Our
main result generalizes this approach to the category
$\boldsymbol{\mathit{ba}\ell}$ of bounded archimedean $\ell$-algebras, thus
yielding a point-free construction of canonical extensions in
$\boldsymbol{\mathit{ba}\ell}$. We conclude by showing that the algebra of
normal functions on the Alexandroff space of proper archimedean $\ell$-ideals
of $A$ is a canonical extension of $A\in\boldsymbol{\mathit{ba}\ell}$, thus
providing a generalization of the result of \cite{BH20} to
$\boldsymbol{\mathit{ba}\ell}$.
