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Closed Type Families With Overlapping Equations (Extended Version), Richard A. Eisenberg, Dimitrios Vytiniotis, Simon Peyton Jones, Stephanie Weirich
Closed Type Families With Overlapping Equations (Extended Version), Richard A. Eisenberg, Dimitrios Vytiniotis, Simon Peyton Jones, Stephanie Weirich
Stephanie Weirich
Open, type-level functions are a recent innovation in Haskell that move Haskell towards the expressiveness of dependent types, while retaining the look and feel of a practical programming language. This paper shows how to increase expressiveness still further, by adding closed type functions whose equations may overlap, and may have non-linear patterns over an open type universe. Although practically useful and simple to implement, these features go beyond conventional dependent type theory in some respects, and have a subtle metatheory.