data Region a = UnitCircle | Scale Float Region | Union Region Region

interp :: Region -> ((Float,Float) -> Bool)
interp UnitCircle (x,y) = x*x+y*y <= 1
interp (Scale s r) (x,y) = interp r (x*s,y*s)
interp (Union r1 r2) p = interp r1 p || interp r2 p

example = Union (Scale 2.0 UnitCircle) UnitCircle

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type Region' a =
                 a ->                  -- unit circle
                 (Float -> a -> a) ->  -- scale
                 (a -> a -> a) ->      -- union
                 a


unitcircle :: Region' a
unitcircle uc sc un = uc

scale :: Float -> Region' a -> Region' a
scale s r uc sc un = sc s (r uc sc un)

union :: Region' a -> Region' a -> Region' a
union r1 r2 uc sc un = un (r1 uc sc un) (r2 uc sc un)

place :: a -> Region' a
place x uc sc un = x

example' = union (scale 2.0 unitcircle) unitcircle

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

tostring :: Region' String -> String
tostring r = r (  "unioncircle" )
               (\s r -> "scale("++(show s) ++ "," ++ r ++ ")")
               (\r1 r2 -> "union ("++ r1 ++"," ++ r2++")")

type Picture = (Float,Float) -> Int
somepic (x,y) = 42

test1 :: Region' ((Float,Float) -> Bool)
test1 = union example' (place ( \q -> (somepic q) /= 0))

test2 :: Region' String
test2 = union example' (place "hello world")