Type.Family.Monoid

Type-level Monoid, defined as an open type family.

Documentation

type family Mempty :: k

Instances

type Mempty [k]

type Mempty [k] = Ø k

type Mempty (Maybe a)

type Mempty (Maybe a) = Nothing a

type Mempty (Either a b)

type Mempty (Either a b) = Left a b (Mempty a)

type Mempty (a, b)

type Mempty (a, b) = (#) a b (Mempty a) (Mempty b)

type Mempty (k, k1, k2)

type Mempty (k, k1, k2) = (,,) k k1 k2 (Mempty k) (Mempty k1) (Mempty k2)

type family (a :: k) <> (b :: k) :: k

Instances

type (<>) [k] a b

type (<>) [k] a b = (++) k a b

type (<>) (Maybe k) a b

type (<>) (Maybe k) a b = (<|>) k a b

type (<>) (Either m k) a b

type (<>) (Either m k) a b = (<|>) m k a b

type (<>) (a, b) ((#) a b r a1) ((#) a b s b1)

type (<>) (a, b) ((#) a b r a1) ((#) a b s b1) = (#) a b ((<>) a r s) ((<>) b a1 b1)

type (<>) (k, k1, k2) ((,,) k k1 k2 a b c) ((,,) k k1 k2 d e f)

type (<>) (k, k1, k2) ((,,) k k1 k2 a b c) ((,,) k k1 k2 d e f) = (,,) k k1 k2 ((<>) k a d) ((<>) k1 b e) ((<>) k2 c f)