  We consider constrained Horn clause solving from the more general point of
view of solving formula equations. Constrained Horn clauses correspond to the
subclass of Horn formula equations. We state and prove a fixed-point theorem
for Horn formula equations which is based on expressing the fixed-point
computation of a minimal model of a set of Horn clauses on the object level as
a formula in first-order logic with a least fixed point operator. We describe
several corollaries of this fixed-point theorem, in particular concerning the
logical foundations of program verification, and sketch how to generalise it to
incorporate abstract interpretations.
