  Canonical formulas are a powerful tool for studying intuitionistic and modal
logics. Actually, they provide a uniform and semantic way to axiomatise all
extensions of intuitionistic logic and all modal logics above K4. Although the
method originally hinged on the relational semantics of those logics, recently
it has been completely recast in algebraic terms. In this new perspective
canonical formulas are built from a finite subdirectly irreducible algebra by
describing completely the behaviour of some operations and only partially the
behaviour of some others. In this paper we export the machinery of canonical
formulas to substructural logics by introducing canonical formulas for
$k$-potent, commutative, integral, residuated lattices ($k$-$\mathsf{CIRL}$).
We show that any subvariety of $k$-$\mathsf{CIRL}$ is axiomatised by canonical
formulas. The paper ends with some applications and examples.
