How to define function signatures partially in Haskell?

Question

Starting point:

fn :: [a] -> Int
fn = (2 *) . length

Let\'s say we only want to constrain the return value, then we could write:

Answer 1

Sorry for the self-promotion, but exactly this feature is the topic of a recent paper by Ph.D. student Thomas Winant, myself, Frank Piessens and Tom Schrijvers, very recently presented by Thomas at the PADL 2014 symposium. See here for the full paper. It is a feature that is already present in some other languages, but the interaction with features like Haskell GADTs made it interesting enough to work out the details.

Thomas is working on an implementation for GHC. It has further improved since the writing of the paper, but implementing the "wildcard constraint" in GHC is technically a bit harder than we expected. We expect to be able to work further on it and contact the GHC developers to get it adopted, but whether or not this happens may depend on how much people would like to have the feature in Haskell...

Update 14-4-2015: After a lot of work by Thomas and input from SPJ and other GHC people, partial type signatures have been released in GHC 7.10. Thomas Winant wrote an introductory blog post about how you can use them.