Type-Theory in Color

Paper in proceeding, 2013

Dependent-type theory is on the verge of becoming the standard way to formalise mathematics at the same time as displace traditional platforms for high-insurance programming. However, current implementations of type theory are still lacking, in the sense that obvious truths are simply impossible to prove, making type-theory awkward to use for many applications, both in formalisation or programming. In particular, notions of erasure are poorly supported. In this paper we propose to conservatively extend type-theory with colored terms, color erasure and color selection. The result is a more powerful type-theory: some definitions and proofs may be omitted as they become trivial; it becomes easier to program with precise types; and some parametricity results can be internalized.