prime.hs

-- 型クラスの練習

import Data.Set

-- aをNumに制限Numのインスタンスにしばる
mySum :: Num a => [a] -> a
mySum list = list !! 0

data Point = Pt Int Int deriving Show


instance Eq Point where
  (Pt x y) == (Pt x' y') = x==x' && y==y'


-- Containerはcmap関数を持つとする
class Container c where
  cmap :: (a -> b) -> c a -> c b

-- MaybeはContainerクラスのインスタンスである
-- cmap :: (a->b) -> Maybe a -> Maybe b
instance Container Maybe where
  cmap f Nothing = Nothing
  cmap f (Just x) = Just (f x)

-- http://d.hatena.ne.jp/kazu-yamamoto/20091116/1258357568
data Modulo = Mod Integer Integer deriving (Eq, Show, Ord)

instance Num Modulo where
  (Mod n1 m1) * (Mod n2 m2)
    | m1 == m2 = Mod (n1 * n2 `mod` m1) m1
    | otherwise = error "module mismatch"

myIdeal x m = fromList [Mod x m * Mod n m | n <-[0..(m-1)]]
myIdeals m = fromList [myIdeal x m| x <- [0..m]]

-- つまり Z/6Z
-- {0},{0,2,4},{0,3},{0,1,2,3,4,5}

-- 局所化
data Fraction = Frac Modulo Modulo deriving (Eq, Show)

instance Num Fraction where
  (Frac n1 s1) * (Frac n2 s2)
    | s1 != 0 && s2 != 0 = Frac (n1*s2 + n2*s1) (s1*s2)
    | otherwise = error "mismatch"