I would like to have a program that can synthesize programs for a given type, composing only functions from a given library. For example, suppose my library has isZero :: Int -> Bool map :: (a -> b) -> [a] -> [b] and :: Bool -> Bool -> Bool fold :: (a -> b -> a) -> a -> [b] -> a True :: Bool (.) :: (b -> c) -> (a -> b) -> a -> c then I want to ask, say, for a program of type [Int] -> Bool and get as answer (fold and True) . (map isZero) I have found two approaches in this direction. The first one is the De-Typechecker http://www.haskell.org/pipermail/haskell/2005-March/015423.html and the other one is Djinn http://permalink.gmane.org/gmane.comp.lang.haskell.general/12747 However, with none of these approaches I managed to do anything with list functions. What else is available (besides Djinn and De-Typechecker)? Are lists a problem? In general, what are the practical and theoretical limits of these program synthesizers? Are there any overview papers for this topic? Regards, Klaus