Combining Two Forms of Type Refinements

Type refinements allow invariants about algebraic datatypes to be expressed through the type system. We present a small functional language and type system that elegantly combines datasort refinements (commonly called refinement types) and dependent index refinements, so that one can specify invariants using whatever refinement is most suitable. Our type system has intersections (novel in the presence of index refinements) and restricted dependent products; we believe ML-style references and polymorphism could be added easily. As an example, we show how the type system cleanly captures several representation invariants of red-black trees. The author is supported in part by the National Science Foundation, under a Graduate Research Fellowship and by grant ITR/SY+SI 0121633: “Language Technology for Trustless Software Dissemination.” Any opinions, findings, conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the National Science Foundation.