Hi Brent, I already solved it myself. I wanted to find an systematic way to produce composition operators which composes functions with different arity together. I stated it a bit vague. For example <*||> is (c -> d) -> (a -> b -> c) -> a -> b -> d I can add this types with the composition operator to create a new operator which combines functions with different arity. In this case a function with arity 1 with a function with arity 4: <*||>.<*||> = <*||||> But I couldn't find an systematic way to level the arity of the function on the left side. I wanted to find an operator what did this, like so: <*|> `op` <*|> = <**|> But I found another way already, which can be found in the followup. So I guess this question is closed. But thanks anyway for your response. I really appreciate the way the people on this list react to new haskellers. Your are really helpful, which sometimes on other lists is quitte the oposite. Greets, Edgar