{-# LANGUAGE GADTs #-}
{-# LANGUAGE InstanceSigs #-}

class Prefix p where
    unitNum :: f p -> Double
    name :: f p -> String


data Kilo
instance Prefix Kilo where
    unitNum _ = 10^3
    name _ = "Kilo"

data Hekto
instance Prefix Hekto where
    unitNum _ = 10^2
    name _ = "Hekto"


data Meters prefix where
    Meters :: Prefix p => Double -> Meters p



--Unødvendig abstraktsjon, men orker ikke fjerne
mapMeters :: Prefix p => (Double -> Double) -> Meters p -> Meters p
mapMeters f (Meters m1) = Meters $ f m1

lift2Meters :: Prefix p => (Double -> Double -> Double) -> Meters p -> Meters p -> Meters p
lift2Meters f (Meters m1) (Meters m2) = Meters $ f m1 m2

instance Prefix p => Num (Meters p) where
    (+) = lift2Meters (+)
    (*) = error "WRONG *"
    (-) = lift2Meters (-)
    abs = mapMeters abs
    fromInteger = Meters . fromInteger
    signum = mapMeters signum

instance Prefix p => Show (Meters p) where
    show m = show (getMeters m) ++ " : m (" ++ name m ++ ")"


getMeters :: Meters p -> Double
getMeters (Meters m) = m





convMeters :: (Prefix p1,Prefix p2) => Meters p1 -> Meters p2 -> Meters p1
convMeters m1 m2 = Meters $ (getMeters m2 * unitNum m2) / unitNum m1

class Unit u where
    (!+) :: (Prefix p1,Prefix p2) => u p1 -> u p2 -> u p1



--Altfor tom
instance Unit Meters where
    (!+) :: (Prefix p1,Prefix p2) => Meters p1 -> Meters p2 -> Meters p1
    m1 !+ m2 = Meters $ getMeters m1 + m3
        where
            Meters m3 = convMeters m1 m2


--Tester

hek5 :: Meters Hekto
hek5 = Meters 5

hek10 :: Meters Hekto
hek10 = Meters 10

kilo5 :: Meters Kilo
kilo5 = Meters 5

--Pga Num-typeclass kan man lage Meters-tall direkte
hek5' :: Meters Hekto
hek5' = 5




main :: IO ()
main = do
    print $ hek5 !+ hek10
    print $ hek10 !+ kilo5
    print kilo5
    print $ convMeters hek10 kilo5

    print $ hek5 + 10 -- 10 blir her 10 hekto automatisk

    --print $ hek5 + kilo5
    --Går ikke pga kan ikke legge sammen hekto og kilo på vanlig ikke-konverterende måte