  It is a consequence of existing literature that least and greatest
fixed-points of monotone polynomials on Heyting algebras-that is, the alge-
braic models of the Intuitionistic Propositional Calculus-always exist, even
when these algebras are not complete as lattices. The reason is that these
extremal fixed-points are definable by formulas of the IPC. Consequently, the
$\mu$-calculus based on intuitionistic logic is trivial, every $\mu$-formula
being equiv- alent to a fixed-point free formula. We give in this paper an
axiomatization of least and greatest fixed-points of formulas, and an algorithm
to compute a fixed-point free formula equivalent to a given $\mu$-formula. The
axiomatization of the greatest fixed-point is simple. The axiomatization of the
least fixed- point is more complex, in particular every monotone formula
converges to its least fixed-point by Kleene's iteration in a finite number of
steps, but there is no uniform upper bound on the number of iterations. We
extract, out of the algorithm, upper bounds for such n, depending on the size
of the formula. For some formulas, we show that these upper bounds are
polynomial and optimal.
