  We study the properties of the constructible universe, L, over intuitionistic
theories. We give an extended set of fundamental operations which is sufficient
to generate the universe over Intuitionistic Kripke-Platek set theory without
Infinity. Following this, we investigate when L can fail to be an inner model
in the traditional sense. Namely, we show that over Constructive
Zermelo-Fraenkel (even with the Power Set axiom) one cannot prove that the
Axiom of Exponentiation holds in L.
