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Modular languages support generative type abstraction, ensuring that an abstract type is distinct from its representation, except inside the implementation where the two are synonymous. We show that this well-established feature is in tension with the non-parametric features of newer type systems, such as indexed type families and GADTs. In this paper we solve the problem by using kinds to distinguish between parametric and non-parametric contexts. The result is directly applicable to Haskell, which is rapidly developing support for type-level computation, but the same issues should arise whenever generativity and non-parametric features are combined.
Weirich, Stephanie; Vytiniotis, Dimitrios; Peyton Jones, Simon; and Zdancewic, Stephan A., "Generative Type Abstraction and Type-level Computation" (2011). Departmental Papers (CIS). Paper 573.
Date Posted: 18 July 2012