Type-Level Computation Using Narrowing in Omega

Haven't seen this paper by Tim Sheard mentioned on Ltu before. As in previous papers Sheard tries to put Howard Curry to work in terms that are understandable for those that don't have a Phd in type theory.

Omega is an experimental system that combines features of both a programming language and a logical reasoning system. Omega is a language with an infinite hierarchy of computational levels. Terms at one level are classified (or typed) by terms at the next higher level. In this paper we report on using two different computational mechanisms. At the value level, computation is performed by reduction, and is largely unconstrained. At all higher levels, computation is performed by narrowing.