Technical Reports (CIS)

Document Type

Technical Report

Date of this Version



University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-13-10.


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.


Type families, Type-level computation, Haskell, System FC



Date Posted: 23 June 2014