Names for free: polymorphic views of names and binders

We propose a novel technique to represent names and binders in Haskell. The dynamic (run-time) representation is based on de Bruijn indices, but it features an interface to write and manipulate variables conviently, using Haskell-level lambdas and variables. The key idea is to use rich types: a subterm with an additional free variable is viewed either as forallν.ν → Term(ɑ + ν) or ϶ν.ν x Term(ν.ν) depending on whether it is constructed or analysed. We demonstrate on a number of examples how this approach permits to express term construction and manipulation in a natural way, while retaining the good properties of representations based on de Bruijn indices.