Safe Haskell	None
Language	Haskell2010

Transformation.Rank2

Description

This module provides natural transformations Map, Fold, and Traversal, as well as three rank-2 functions that wrap them in a convenient interface.

Synopsis

(<$>) :: Functor (Map p q) g => (forall a. p a -> q a) -> g p p -> g q q
foldMap :: (Foldable (Fold p m) g, Monoid m) => (forall a. p a -> m) -> g p p -> m
traverse :: Traversable (Traversal p q m) g => (forall a. p a -> m (q a)) -> g p p -> m (g q q)
newtype Map (p :: Type -> Type) (q :: Type -> Type) = Map (forall x. p x -> q x)
newtype Fold (p :: Type -> Type) m = Fold (forall x. p x -> m)
newtype Traversal (p :: Type -> Type) (q :: Type -> Type) (m :: Type -> Type) = Traversal (forall x. p x -> m (q x))

Documentation

(<$>) :: Functor (Map p q) g => (forall a. p a -> q a) -> g p p -> g q q infixl 4 Source #

Transform (naturally) the containing functor of every node in the given tree.

foldMap :: (Foldable (Fold p m) g, Monoid m) => (forall a. p a -> m) -> g p p -> m Source #

Fold the containing functor of every node in the given tree.

traverse :: Traversable (Traversal p q m) g => (forall a. p a -> m (q a)) -> g p p -> m (g q q) Source #

Traverse the containing functors of all nodes in the given tree.

newtype Map (p :: Type -> Type) (q :: Type -> Type) Source #

Constructors

Map (forall x. p x -> q x)

Instances

Instances details

Transformation (Map p q) Source #

Instance details

Defined in Transformation.Rank2

Associated Types

type Domain (Map p q)
Instance details Defined in Transformation.Rank2 type Domain (Map p q) = p
type Codomain (Map p q)
Instance details Defined in Transformation.Rank2 type Codomain (Map p q) = q

At (Map p q) x Source #

Instance details

Defined in Transformation.Rank2

Methods

($) :: Map p q -> Domain (Map p q) x -> Codomain (Map p q) x Source #

type Codomain (Map p q) Source #

Instance details

Defined in Transformation.Rank2

type Codomain (Map p q) = q

type Domain (Map p q) Source #

Instance details

Defined in Transformation.Rank2

type Domain (Map p q) = p

newtype Fold (p :: Type -> Type) m Source #

Constructors

Fold (forall x. p x -> m)

Instances

Instances details

Transformation (Fold p m) Source #

Instance details

Defined in Transformation.Rank2

Associated Types

type Domain (Fold p m)
Instance details Defined in Transformation.Rank2 type Domain (Fold p m) = p
type Codomain (Fold p m)
Instance details Defined in Transformation.Rank2 type Codomain (Fold p m) = Const m :: Type -> Type

At (Fold p m) x Source #

Instance details

Defined in Transformation.Rank2

Methods

($) :: Fold p m -> Domain (Fold p m) x -> Codomain (Fold p m) x Source #

type Codomain (Fold p m) Source #

Instance details

Defined in Transformation.Rank2

type Codomain (Fold p m) = Const m :: Type -> Type

type Domain (Fold p m) Source #

Instance details

Defined in Transformation.Rank2

type Domain (Fold p m) = p

newtype Traversal (p :: Type -> Type) (q :: Type -> Type) (m :: Type -> Type) Source #

Constructors

Traversal (forall x. p x -> m (q x))

Instances

Instances details

Transformation (Traversal p q m) Source #

Instance details

Defined in Transformation.Rank2

Associated Types

type Domain (Traversal p q m)
Instance details Defined in Transformation.Rank2 type Domain (Traversal p q m) = p
type Codomain (Traversal p q m)
Instance details Defined in Transformation.Rank2 type Codomain (Traversal p q m) = Compose m q

At (Traversal p q m) x Source #

Instance details

Defined in Transformation.Rank2

Methods

($) :: Traversal p q m -> Domain (Traversal p q m) x -> Codomain (Traversal p q m) x Source #

type Codomain (Traversal p q m) Source #

Instance details

Defined in Transformation.Rank2

type Codomain (Traversal p q m) = Compose m q

type Domain (Traversal p q m) Source #

Instance details

Defined in Transformation.Rank2

type Domain (Traversal p q m) = p