  Instantiation overflow is the property of those second order types for which
all instances of full comprehension can be deduced from instances of atomic
comprehension. In other words, a type has instantiation overflow when one can
type, by atomic polymorphism, "expansion terms" which realize instances of the
full extraction rule applied to that type. This property was investigated in
the case of the types arising from the well-known Russell-Prawitz translation
of logical connectives into System F, but is not restricted to such types.
Moreover, it can be related to functorial polymorphism, a well-known categorial
approach to parametricity in System F. In this paper we investigate the
instantiation overflow property by exploiting the representation of derivations
by means of linear logic proof nets. We develop a geometric approach to
instantiation overflow yielding a deeper understanding of the structure of
expansion terms and Russell-Prawitz types. Our main result is a
characterization of the class of types of the form $\forall XA$, where $A$ is a
simple type, which enjoy the instantiation overflow property, by means of a
generalization of Russell-Prawitz types.
