Of course the data type is not exact, but is this how (more or less) the Monoid Bool
is implemented?
import Data.Monoid
data Bool' = T | F deriving (Show)
instance Monoid (Bool') where
mempty = T
mappend T _ = T
mappend _ T = T
mappend _ _ = F
If so/not, what is the reasoning for making Bool
's mappend
an OR
versus AND
?
There are two possible Monoid
instances for Bool
, so Data.Monoid
has newtypes to distinguish which one we intend:
-- | Boolean monoid under conjunction.
newtype All = All { getAll :: Bool }
deriving (Eq, Ord, Read, Show, Bounded, Generic)
instance Monoid All where
mempty = All True
All x `mappend` All y = All (x && y)
-- | Boolean monoid under disjunction.
newtype Any = Any { getAny :: Bool }
deriving (Eq, Ord, Read, Show, Bounded, Generic)
instance Monoid Any where
mempty = Any False
Any x `mappend` Any y = Any (x || y)
Edit: There are actually four valid instances as Ørjan notes