How can I use and call Haskell functions with higher-order type signatures from C# (DLLImport), like...
double :: (Int -> Int) -> Int -> Int -- higher o
Did you tried exporting the functions via the FFI? This allows you to create a more C-ish interface to the functions. I doubt that it is possible to call Haskell functions directly from C#. See the doc for more information. (Link above).
After doing some tests, I think that generally, it is not possible to export high order functions and functions with type-parameters via the FFI.[Citation needed]