-- | A type to represent (flat) subdivisions of a part.
module Music.Parts.Division (
        Division,
        division,
        getDivision,
        divisions,
        showDivision,
        showDivisionR,
  ) where

import           Control.Applicative
import           Control.Lens            (toListOf)
import           Data.Default
import           Data.Functor.Adjunction (unzipR)
import           Data.Semigroup
import           Data.Semigroup.Option.Instances
import           Data.Traversable                (traverse)
import           Data.Typeable
import           Text.Numeral.Roman              (toRoman)



{-
    For each part we want to know:
        - Classification:
            - Type: (i.e. woodwind)
            - Family: (i.e. saxophone)
            - Range: (i.e. tenor)
        - Range (i.e. [c_:e'])
        - Transposition:
            sounding = written .+^ transp
        - Suggested clefs
-}

-- |
-- A division represents a subset of a finite group of performers.
--
-- For example a group may be divided into three equal divisions,
-- designated @(0, 3)@, @(1, 3)@ and @(2, 3)@ respectively.
--
newtype Division = Division { getDivision :: (Int, Int) }
    deriving (Eq, Ord)

instance Show Division where
  show (Division (n,m)) = "division " ++ show n ++ show m

instance Default Division where
    def = Division (0,1)

-- | Show division in roman numerals.
showDivisionR :: Division -> String
showDivisionR = toRoman . succ . fst . getDivision

-- | Show division in ordinary numerals.
showDivision :: Division -> String
showDivision  = show . succ . fst . getDivision

-- | Create a division out of a ratio. Dual of getDivision.
division :: Int -> Int -> Division
division n m
  | n < 0 || m <= 0  = error "Invalid division"
  | n <  m           = Division (n, m)
  | otherwise        = error "Invalid division"

-- | Get all possible divisions for a given divisor in ascending order.
divisions :: Int -> [Division]
divisions n = [Division (x,n) | x <- [0..n-1]]