{-# LANGUAGE RankNTypes #-}

data RegionFold a =
   RegionFold { uc :: a ,            -- unit circle
                sc :: (Float,a) -> a,  -- scale
                un :: (a,a) -> a     -- union
              }


type Region = forall a. RegionFold a -> a

unitcircle :: Region
unitcircle = uc

scale :: Float -> Region -> Region
scale f r fld = (sc fld) (f,r fld)

union :: Region -> Region -> Region
union r1 r2 fld = un fld $ (r1 fld, r2 fld)

example :: Region
example = union (scale 2.0 unitcircle) unitcircle

eval :: Region -> ((Float,Float) -> Bool)
eval r = r (RegionFold (\(x,y) -> x*x+y*y <= 1)
                       (\(f,r) (x,y) -> r (f*x,f*y))
                       (\(r1,r2) p -> r1 p || r2 p))