Concoqtion: indexed types now!

Almost twenty years after the pioneering efforts of Cardelli, the programming languages community is vigorously pursuing ways to incorporate Fω-style indexed types into programming languages. This paper advocates Concoqtion, a practical approach to adding such highly expressive types to full-fledged programming languages. The approach is applied to MetaOCaml using the Coq proof checker to conservatively extend Hindley-Milner type inference. The implementation of MetaOCaml Concoqtion requires minimal modifications to the syntax, the type checker, and the compiler; and yields a language comparable in notation to the leading proposals. The resulting language provides unlimited expressiveness in the type system while maintaining decidability. Furthermore, programmers can take advantage of a wide range of libraries not only for the programming language but also for the indexed types. Programming in MetaOCaml Concoqtion is illustrated with small examples and a case study implementing a statically-typed domain-specific language.

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