  In this paper we define several notions of term expansion, used to define
terms with less sharing, but with the same computational properties of terms
typable in an intersection type system. Expansion relates terms typed by
associative, commutative and idempotent intersections with terms typed in the
Curry type system and the relevant type system, terms typed by non-idempotent
intersections with terms typed in the affine and linear type systems and terms
typed by non-idempotent and non-commutative intersections with terms typed in
an ordered type system. Finally, we show how idempotent intersection is related
with the contraction rule, commutative intersection with the exchange rule and
associative intersection with the lack of structural rules in a type system.
