Serguey Zefirov wrote:

Is it possible to delete an element from heterogenous list using type families alone?

I can do it using multiparameter type classes: class Del a list result instance Del a (a,list) list instance Del a list list' => Del a (a',list) list' instance Del a () ()

I'm afraid you'll find that class quite difficult to use: lots of type annotations will be required. For example, if we define del :: Del a li lo => a -> li -> lo del = undefined and write test1 = del True ('a',(True,())) the compiler will complain because it doesn't know which instance to choose. BTW, since GHC checks for overlapping lazily, the fact that GHC accepts a set of instance declarations does not tell that the instances `work'. The problems may lurk, becoming apparent when we define values that attempt to use the instances. In order for something like Del to be useful, functional dependencies are needed. It is easy to see that Del uses overlapping instances. That answers the question: since type families do not support overlapping instances, one cannot re-write Del using type families alone. One may ask is it possible to define some sort of type inequality using type families. And the answer is yes, recently discussed at http://www.haskell.org/pipermail/haskell-cafe/2010-July/080473.html