University of Pennsylvania Department of Computer and Information Science Technical Report
Final Published Version
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.
R. A. Eisenberg, D. Vytiniotis, S. Peyton Jones, S. Weirich. Closed Type Families with Overlapping Equations (extended version). University of Pennsylvania Technical Report MS-CIS-13-10, 2013