Fcf.Class.Monoid

Semigroups and monoids.

Pure type families

Nicer to use when applied explicitly.

type family (x :: a) <> (y :: a) :: a

Type-level semigroup composition (<>).

Instances

type LT <> (_b :: Ordering)

Defined in Fcf.Class.Monoid

type LT <> (_b :: Ordering) = LT

type EQ <> (b :: Ordering)

Defined in Fcf.Class.Monoid

type EQ <> (b :: Ordering) = b

type GT <> (_b :: Ordering)

Defined in Fcf.Class.Monoid

type GT <> (_b :: Ordering) = GT

type (a :: Ordering) <> EQ

Defined in Fcf.Class.Monoid

type (a :: Ordering) <> EQ = a

type (x :: Symbol) <> (y :: Symbol)

With base >= 4.10.0.0.

Defined in Fcf.Class.Monoid

type (x :: Symbol) <> (y :: Symbol) = AppendSymbol x y

type (_a :: ()) <> (_b :: ())

Defined in Fcf.Class.Monoid

type (_a :: ()) <> (_b :: ()) = ()

type (All a :: All) <> (All b :: All)

Defined in Fcf.Class.Monoid

type (All a :: All) <> (All b :: All) = All (a && b)

type (Any a :: Any) <> (Any b :: Any)

Defined in Fcf.Class.Monoid

type (Any a :: Any) <> (Any b :: Any) = Any (a || b)

type (a2 :: Maybe a1) <> (Nothing :: Maybe a1)

Defined in Fcf.Class.Monoid

type (a2 :: Maybe a1) <> (Nothing :: Maybe a1) = a2

type ([] :: [k]) <> (ys :: [k])

Defined in Fcf.Class.Monoid

type ([] :: [k]) <> (ys :: [k]) = ys

type (Nothing :: Maybe a) <> (b :: Maybe a)

Defined in Fcf.Class.Monoid

type (Nothing :: Maybe a) <> (b :: Maybe a) = b

type (Just a2 :: Maybe a1) <> (Just b :: Maybe a1)

Defined in Fcf.Class.Monoid

type (Just a2 :: Maybe a1) <> (Just b :: Maybe a1) = Just (a2 <> b)

type (Endo f :: Endo a) <> (Endo g :: Endo a)

Defined in Fcf.Class.Monoid.Types

type (Endo f :: Endo a) <> (Endo g :: Endo a) = Endo (f <=< g)

type (x ': xs :: [a]) <> (ys :: [a])

Defined in Fcf.Class.Monoid

type (x ': xs :: [a]) <> (ys :: [a]) = x ': (xs <> ys)

type ((,) a1 a2 :: (k2, k1)) <> ((,) b1 b2 :: (k2, k1))

Defined in Fcf.Class.Monoid

type ((,) a1 a2 :: (k2, k1)) <> ((,) b1 b2 :: (k2, k1)) = (,) (a1 <> b1) (a2 <> b2)

type ((,,) a1 a2 a3 :: (k2, k1, k3)) <> ((,,) b1 b2 b3 :: (k2, k1, k3))

Defined in Fcf.Class.Monoid

type ((,,) a1 a2 a3 :: (k2, k1, k3)) <> ((,,) b1 b2 b3 :: (k2, k1, k3)) = (,,) (a1 <> b1) (a2 <> b2) (a3 <> b3)

type family MEmpty :: a

Type-level monoid identity mempty.

Examples

>>> :kind! 'LT <> MEmpty
'LT <> MEmpty :: Ordering
= 'LT

>>> :kind! MEmpty <> '( 'EQ, '[1, 2])
MEmpty <> '( 'EQ, '[1, 2]) :: (Ordering, [Nat])
= '( 'EQ, '[1, 2])

>>> :kind! '( 'GT, 'Just '()) <> MEmpty
'( 'GT, 'Just '()) <> MEmpty :: (Ordering, Maybe ())
= '( 'GT, 'Just '())

Instances

type MEmpty

Defined in Fcf.Class.Monoid

type MEmpty = EQ

type MEmpty

Defined in Fcf.Class.Monoid

type MEmpty = ""

type MEmpty

Defined in Fcf.Class.Monoid

type MEmpty = ()

type MEmpty

Defined in Fcf.Class.Monoid

type MEmpty = All True

type MEmpty

Defined in Fcf.Class.Monoid

type MEmpty = Any False

type MEmpty

Defined in Fcf.Class.Monoid

type MEmpty = ([] :: [k])

type MEmpty

Defined in Fcf.Class.Monoid

type MEmpty = (Nothing :: Maybe a)

type MEmpty

Defined in Fcf.Class.Monoid.Types

type MEmpty = Endo (Pure :: a -> a -> Type)

type MEmpty

Defined in Fcf.Class.Monoid

type MEmpty = (,) (MEmpty :: k1) (MEmpty :: k2)

type MEmpty

Defined in Fcf.Class.Monoid

type MEmpty = (,,) (MEmpty :: k1) (MEmpty :: k2) (MEmpty :: k3)

First-class families

Can be composed and passed to higher-order functions.

data (.<>) :: a -> a -> Exp a

Type-level semigroup composition (<>).

This is the fcf-encoding of (<>). To define a new semigroup, add type instances to (<>).

Instances

type Eval (x .<> y :: a -> Type)

Defined in Fcf.Class.Monoid

type Eval (x .<> y :: a -> Type) = x <> y

data MEmpty_ :: Exp a

Type-level monoid identity mempty.

This is the fcf-encoding of MEmpty.

Instances

type Eval (MEmpty_ :: a -> Type)

Defined in Fcf.Class.Monoid

type Eval (MEmpty_ :: a -> Type) = (MEmpty :: a)