Hello! It has occurred to me a year ago that the type-changing gMap is easily possible in SYB. The recent discussion has prompted me to implement that solution. I have committed a patch to http://darcs.haskell.org/generics/comparison/SYB1_2/GMap.lhs with the implementation. I hope this is OK: the previous version of that file was a stub saying that gMap is not supported. The function gMap has the expected type gmap :: (Data a, Data b, Data x, Data y) => (a -> b) -> x -> y There are no unsafe operations used; there is not a single occurrence of insafePerformIO and the ilk. Incidentally, Data.Generics could, in principle at least, be implemented using a safe cast. Of course gmap is not a total operation: one can't really expect (gmap id True) to produce a character. It seems that gunfold is not total anyway. Regarding the instance of Data for functions: SmashA does define (co-variant) traversal `under lambda'. For example, we can (gmap fromEnum) on a function and convert (Bool->Bool) to (Bool->Int). Please see testt3 in http://darcs.haskell.org/generics/comparison/SmashA/Syb4A.hs I do not claim to have any use for that transformation, but it was easy to implement... I will be out of town for two weeks and so unlikely to participate in further discussions until I come back. Cheers, Oleg