--
-- Type class for traversing AI game trees
-- auxiliary definitions for labeling with static valuations 
-- 
module AI.Gametree where

-- | a type class for gametrees 
-- parametrized by node type
class Gametree p where
  children :: p -> [p]   -- list of move, position
  is_terminal :: p -> Bool
  is_terminal = null . children  -- default definition

-- | type for valuation functions 
type Valuation a = a -> Int


-- | a pair of something with a strict integer valuation
-- supporting equality, ordering and limited arithmetic on valuation
data Valued a = Valued { value :: !Int, unvalued :: a } deriving Show

instance Functor Valued where
  fmap f (Valued v x) = Valued v (f x)

-- | apply a valuation 
valued :: Valuation a -> a -> Valued a
valued f x = Valued (f x) x

-- | modify the valuation
revalue :: (Int -> Int) -> Valued a -> Valued a
revalue f (Valued v x) = Valued (f v) x

instance Eq (Valued a) where
  x == y = value x==value y
  
instance Ord (Valued a) where
  compare x y = compare (value x) (value y)
  

-- some instances of numeric type class (only negate and fromInteger)
instance Num (Valued a) where
  (+) = undefined
  (-) = undefined
  (*) = undefined
  negate = revalue negate
  fromInteger n = valued (const (fromIntegral n)) undefined
  abs = undefined
  signum = undefined


-- | add a constant to a value
infix 6 $+
($+) :: Int -> Valued a -> Valued a
k $+ x = revalue (+k) x