Do we Need Dependent Types?

Abstract

Inspired by [1], we describe a technique for defining, within the
Hindley-Milner type system, some functions which seem to require a
language with dependent types. We illustrate this by giving a general
definition of zipWith for which the Haskell library provides a family
of functions, each member of the family having a different type and
arity. Our technique consists in introducing ad hoc codings for natural
numbers which resemble numerals in lambda-calculus.