Do we Need Dependent Types?

Inspired by [1], we describe a technique for defining, within theHindley-Milner type system, some functions which seem to require alanguage with dependent types. We illustrate this by giving a generaldefinition of zipWith for which the Haskell library provides a familyof functions, each member of the family having a different type andarity. Our technique consists in introducing ad hoc codings for naturalnumbers which resemble numerals in lambda-calculus