Is it possible to write type family SameType a b :: Bool which returns True if a and b are the same type, and False otherwise? I encountered this problem when I was practicing promoted lists and tuples in ghc-7.6.1. One of my goal for practice is to write more "modular" version of extensible-dimensional calculations, and to understand whether ghc-7.6.1 is capable of it. http://hackage.haskell.org/packages/archive/dimensional/0.10.2/doc/html/Nume... Some of my attempts: https://github.com/nushio3/dimensional-tf/blob/master/attic/list-02.hs This fails because :==: is not an equality test between a and b, but is a equality test within a (promoted) kind. https://github.com/nushio3/dimensional-tf/blob/master/attic/list-03.hs This fails because type instance declarations are not read from top to bottom. (not like function declarations.) https://github.com/nushio3/dimensional-tf/blob/master/attic/map-03.hs I could define a lookup using class constraints, but when I use it, results in overlapping instances. So, will somebody teach me which of the following is correct? * We can write a type family SameType a b :: Bool * We cannot do that because of theoretical reason (that leads to non-termination etc.) * We cannot write SameType, but there are ways to write functions like 'filter' and 'merge' , over type-level lists, without using SameType. Always grateful to your help, -- Takayuki MURANUSHI The Hakubi Center for Advanced Research, Kyoto University http://www.hakubi.kyoto-u.ac.jp/02_mem/h22/muranushi.html