Could not match expected type with actual type in Haskell

Question

I've written the following code:

type Mass = Double
type Position = (Double, Double)
type Velocity = (Double, Double)

data Body = Body Mass Position Velocity
data System = System [Body]

renderBody :: Body -> Picture
renderBody (Body mass (x, y) velocity) = object
  where 
    object = translated x y (solidCircle mass)

renderSystem :: System -> Picture
renderSystem (System []) = blank
renderSystem (System (x:xs)) = renderBody(x)<>renderSystem(System(xs))

moveBody :: Double -> Body -> Body
moveBody time (Body mass (x, y) (vx, vy)) = new_body
  where
    new_x = x + vx * time
    new_y = y + vy * time
    new_body = (Body mass (new_x, new_y) (vx, vy))

updateSystem :: Double -> System -> System
updateSystem time (System []) = (System [])
updateSystem time (System(x:xs)) = moveBody time x : updateSystem time System(xs)

I could not understand the following ERROR

What's the problem?

Thanks in advance.

Answer 1

You aren't applying updateSystem time to a value of type System ; you are applying it to the data constructor System and a list of Body values xs . You need to adjust your parentheses to create the necessary value of type System .

updateSystem time (System(x:xs)) = moveBody time x : updateSystem time (System xs)

However, you can simply the definition of updateSystem by using map on the list that System wraps.

updateSystem :: Double -> System -> System
updateSystem time (System xs) = System (map (moveBody time) xs)

Extract the value of type [Body] , map moveBody time over it to get a new list of Body 's, and rewrap the list as a new System value.

Answer 2

You can define custom prepending operator for your type, eg .: to wrap list prepending for System :

type Mass = Double                                                             
type Position = (Double, Double)                                               
type Velocity = (Double, Double)                                               
                                                                               
data Body = Body Mass Position Velocity                                        
data System = System [Body]                                                    
                                                                               
moveBody :: Double -> Body -> Body                                             
moveBody time (Body mass (x, y) (vx, vy)) = new_body                           
  where                                                                        
    new_x = x + vx * time                                                      
    new_y = y + vy * time                                                      
    new_body = (Body mass (new_x, new_y) (vx, vy))                             
                                                                               
(.:) :: Body -> System -> System                                               
(.:) b (System x) = System (b : x)                                             
                                                                               
updateSystem :: Double -> System -> System                                     
updateSystem time (System []) = (System [])                                    
updateSystem time (System(x:xs)) = moveBody time x .: updateSystem time (System xs)

You get an error because System is not a list, so you can not prepend elemens to it just by using : operator.

You also had a bad notation of System(xs) instead of (System xs) , you should to construct System from list at first, and pass it to functions after this.