Type checking of partial programs

Is anybody interested in working on this? This is a project I've been interested in for some time, but recognize I probably need some guidance before I go off and start hacking on it. As dcoutts pointed out on #haskell-soc, this may be of particular interest to people working on yi and HaRe. Other interesting and related projects include parsing partial programs to insert "placeholders" in appropriate places. An example of a partial program could be: foo :: [Foo] -> foo xs = map xs What are the possible type signatures for placeholder 1 and the possible expressions for placeholder 2? I would like to stir up a discussion about this, and eventually write some useful code. -Abram