  Intersection types have been originally developed as an extension of simple
types, but they can also be used for refining simple types. In this survey we
concentrate on the latter option; more precisely, on the use of intersection
types for describing quantitative properties of simply typed lambda-terms. We
present two type systems. The first allows to estimate (by appropriately
defined value of a derivation) the number of appearances of a fixed constant
'a' in the beta-normal form of a considered lambda-term. The second type system
is more complicated, and allows to estimate the maximal number of appearances
of the constant 'a' on a single branch.
