Closed Type Families with Overlapping Equations

Richard A. Eisenberg, Bryn Mawr College
Dimitrios Vytiniotis, Microsoft Research, Cambridge
Simon Peyton Jones, Microsoft Research, Cambridge
Stephanie Weirich, University of Pennsylvania


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.