『Haskellの代数的構造入門　半群・モノイド・環とは何か？』

Haskellでマグマ・半群・環を定義していってる記事

code:memo.hs

class Magma a where

(<>) :: = a -> a -> a

-- 普通に定義してしまうと

instance Magma Integer where

(<>) = (+)

instance Magma Bool where

(<>) = (&&)

-- このままだと掛け算が定義できない。

-- Haskellではnewtypeで定義する

-- Sum, Product

newtype Sum a = Sum {

unSum :: a

} deriving (Show, Eq, Enum)

newtype Product a = Product {

unProduct :: a

} deriving (Show, Eq, Enum)

deriving instance Num a => Num (Sum a)

deriving instance Num a => Num (Product a)

instance Num a => Magma (Sum a) where

(<>) = (+)

instance Num a => Magma (Product a) where

(<>) = (*)

-- And, Or

newtype And a = And deriving (Show, Eq)

newtype Or a = OR deriving (Show, Eq)

instance Num a => Magma (And a) where

(<>) = (&&)

instance Num a => Magma (Or a) where

(<>) = (||)