Safe Haskell	Safe
Language	Haskell2010

Traversable

Contents

Traversable
Traversable1
Bitraversable
Bitraversable1
Default implementations

Synopsis

class (Functor t, Foldable t) => Traversable (t :: * -> *) where
for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)
mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c)
traverseBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> t a -> f (t b)
sequenceBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> t (f a) -> f (t a)
class (Foldable1 t, Traversable t) => Traversable1 (t :: * -> *) where
class (Bifunctor t, Bifoldable t) => Bitraversable (t :: * -> * -> *) where
bisequence :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b)
bifor :: (Bitraversable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f (t c d)
bimapAccumL :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e)
bimapAccumR :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e)
class (Bifoldable1 t, Bitraversable t) => Bitraversable1 (t :: * -> * -> *) where
fmapDefault :: Traversable t => (a -> b) -> t a -> t b
foldMapDefault :: (Traversable t, Monoid m) => (a -> m) -> t a -> m
bimapDefault :: Bitraversable t => (a -> b) -> (c -> d) -> t a c -> t b d
bifoldMapDefault :: (Bitraversable t, Monoid m) => (a -> m) -> (b -> m) -> t a b -> m
bifoldMap1Default :: (Bitraversable1 t, Semigroup m) => (a -> m) -> (b -> m) -> t a b -> m

Traversable

class (Functor t, Foldable t) => Traversable (t :: * -> *) where #

Functors representing data structures that can be traversed from left to right.

A definition of traverse must satisfy the following laws:

naturality: t . traverse f = traverse (t . f) for every applicative transformation t
identity: traverse Identity = Identity
composition: traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f

A definition of sequenceA must satisfy the following laws:

naturality: t . sequenceA = sequenceA . fmap t for every applicative transformation t
identity: sequenceA . fmap Identity = Identity
composition: sequenceA . fmap Compose = Compose . fmap sequenceA . sequenceA

where an applicative transformation is a function

t :: (Applicative f, Applicative g) => f a -> g a

preserving the Applicative operations, i.e.

```
t (pure x) = pure x
```
```
t (x <*> y) = t x <*> t y
```

and the identity functor Identity and composition of functors Compose are defined as

  newtype Identity a = Identity a

  instance Functor Identity where
    fmap f (Identity x) = Identity (f x)

  instance Applicative Identity where
    pure x = Identity x
    Identity f <*> Identity x = Identity (f x)

  newtype Compose f g a = Compose (f (g a))

  instance (Functor f, Functor g) => Functor (Compose f g) where
    fmap f (Compose x) = Compose (fmap (fmap f) x)

  instance (Applicative f, Applicative g) => Applicative (Compose f g) where
    pure x = Compose (pure (pure x))
    Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)

(The naturality law is implied by parametricity.)

Instances are similar to Functor, e.g. given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Traversable Tree where
   traverse f Empty = pure Empty
   traverse f (Leaf x) = Leaf <$> f x
   traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r

This is suitable even for abstract types, as the laws for <*> imply a form of associativity.

The superclass instances should satisfy the following:

In the Functor instance, fmap should be equivalent to traversal with the identity applicative functor (fmapDefault).
In the Foldable instance, foldMap should be equivalent to traversal with a constant applicative functor (foldMapDefault).

Minimal complete definition

traverse | sequenceA

Methods

traverse :: Applicative f => (a -> f b) -> t a -> f (t b) #

Map each element of a structure to an action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see traverse_.

sequenceA :: Applicative f => t (f a) -> f (t a) #

Evaluate each action in the structure from left to right, and and collect the results. For a version that ignores the results see sequenceA_.

Instances

Traversable []	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> [a] -> f [b] # sequenceA :: Applicative f => [f a] -> f [a] # mapM :: Monad m => (a -> m b) -> [a] -> m [b] # sequence :: Monad m => [m a] -> m [a] #
Traversable Maybe	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) # sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) # mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) # sequence :: Monad m => Maybe (m a) -> m (Maybe a) #
Traversable Par1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Par1 a -> f (Par1 b) # sequenceA :: Applicative f => Par1 (f a) -> f (Par1 a) # mapM :: Monad m => (a -> m b) -> Par1 a -> m (Par1 b) # sequence :: Monad m => Par1 (m a) -> m (Par1 a) #
Traversable IResult
Instance details Defined in Data.Aeson.Types.Internal Methods traverse :: Applicative f => (a -> f b) -> IResult a -> f (IResult b) # sequenceA :: Applicative f => IResult (f a) -> f (IResult a) # mapM :: Monad m => (a -> m b) -> IResult a -> m (IResult b) # sequence :: Monad m => IResult (m a) -> m (IResult a) #
Traversable Result
Instance details Defined in Data.Aeson.Types.Internal Methods traverse :: Applicative f => (a -> f b) -> Result a -> f (Result b) # sequenceA :: Applicative f => Result (f a) -> f (Result a) # mapM :: Monad m => (a -> m b) -> Result a -> m (Result b) # sequence :: Monad m => Result (m a) -> m (Result a) #
Traversable Approximate
Instance details Defined in Data.Approximate.Type Methods traverse :: Applicative f => (a -> f b) -> Approximate a -> f (Approximate b) # sequenceA :: Applicative f => Approximate (f a) -> f (Approximate a) # mapM :: Monad m => (a -> m b) -> Approximate a -> m (Approximate b) # sequence :: Monad m => Approximate (m a) -> m (Approximate a) #
Traversable Complex
Instance details Defined in Data.Complex Methods traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) # sequenceA :: Applicative f => Complex (f a) -> f (Complex a) # mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) # sequence :: Monad m => Complex (m a) -> m (Complex a) #
Traversable Min	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) # sequenceA :: Applicative f => Min (f a) -> f (Min a) # mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) # sequence :: Monad m => Min (m a) -> m (Min a) #
Traversable Max	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) # sequenceA :: Applicative f => Max (f a) -> f (Max a) # mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) # sequence :: Monad m => Max (m a) -> m (Max a) #
Traversable First	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Option	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a -> f b) -> Option a -> f (Option b) # sequenceA :: Applicative f => Option (f a) -> f (Option a) # mapM :: Monad m => (a -> m b) -> Option a -> m (Option b) # sequence :: Monad m => Option (m a) -> m (Option a) #
Traversable ZipList	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b) # sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a) # mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b) # sequence :: Monad m => ZipList (m a) -> m (ZipList a) #
Traversable Identity
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) # sequenceA :: Applicative f => Identity (f a) -> f (Identity a) # mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) # sequence :: Monad m => Identity (m a) -> m (Identity a) #
Traversable First	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) # sequenceA :: Applicative f => First (f a) -> f (First a) # mapM :: Monad m => (a -> m b) -> First a -> m (First b) # sequence :: Monad m => First (m a) -> m (First a) #
Traversable Last	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) # sequenceA :: Applicative f => Last (f a) -> f (Last a) # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) # sequence :: Monad m => Last (m a) -> m (Last a) #
Traversable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) # sequence :: Monad m => Dual (m a) -> m (Dual a) #
Traversable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) # sequence :: Monad m => Sum (m a) -> m (Sum a) #
Traversable Product	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) # sequenceA :: Applicative f => Product (f a) -> f (Product a) # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) # sequence :: Monad m => Product (m a) -> m (Product a) #
Traversable NonEmpty	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) # sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) # mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) # sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) #
Traversable IntMap
Instance details Defined in Data.IntMap.Internal Methods traverse :: Applicative f => (a -> f b) -> IntMap a -> f (IntMap b) # sequenceA :: Applicative f => IntMap (f a) -> f (IntMap a) # mapM :: Monad m => (a -> m b) -> IntMap a -> m (IntMap b) # sequence :: Monad m => IntMap (m a) -> m (IntMap a) #
Traversable SCC	Since: containers-0.5.9
Instance details Defined in Data.Graph Methods traverse :: Applicative f => (a -> f b) -> SCC a -> f (SCC b) # sequenceA :: Applicative f => SCC (f a) -> f (SCC a) # mapM :: Monad m => (a -> m b) -> SCC a -> m (SCC b) # sequence :: Monad m => SCC (m a) -> m (SCC a) #
Traversable Tree
Instance details Defined in Data.Tree Methods traverse :: Applicative f => (a -> f b) -> Tree a -> f (Tree b) # sequenceA :: Applicative f => Tree (f a) -> f (Tree a) # mapM :: Monad m => (a -> m b) -> Tree a -> m (Tree b) # sequence :: Monad m => Tree (m a) -> m (Tree a) #
Traversable Seq
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Seq a -> f (Seq b) # sequenceA :: Applicative f => Seq (f a) -> f (Seq a) # mapM :: Monad m => (a -> m b) -> Seq a -> m (Seq b) # sequence :: Monad m => Seq (m a) -> m (Seq a) #
Traversable FingerTree
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> FingerTree a -> f (FingerTree b) # sequenceA :: Applicative f => FingerTree (f a) -> f (FingerTree a) # mapM :: Monad m => (a -> m b) -> FingerTree a -> m (FingerTree b) # sequence :: Monad m => FingerTree (m a) -> m (FingerTree a) #
Traversable Digit
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Digit a -> f (Digit b) # sequenceA :: Applicative f => Digit (f a) -> f (Digit a) # mapM :: Monad m => (a -> m b) -> Digit a -> m (Digit b) # sequence :: Monad m => Digit (m a) -> m (Digit a) #
Traversable Node
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Node a -> f (Node b) # sequenceA :: Applicative f => Node (f a) -> f (Node a) # mapM :: Monad m => (a -> m b) -> Node a -> m (Node b) # sequence :: Monad m => Node (m a) -> m (Node a) #
Traversable Elem
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> Elem a -> f (Elem b) # sequenceA :: Applicative f => Elem (f a) -> f (Elem a) # mapM :: Monad m => (a -> m b) -> Elem a -> m (Elem b) # sequence :: Monad m => Elem (m a) -> m (Elem a) #
Traversable ViewL
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewL a -> f (ViewL b) # sequenceA :: Applicative f => ViewL (f a) -> f (ViewL a) # mapM :: Monad m => (a -> m b) -> ViewL a -> m (ViewL b) # sequence :: Monad m => ViewL (m a) -> m (ViewL a) #
Traversable ViewR
Instance details Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> ViewR a -> f (ViewR b) # sequenceA :: Applicative f => ViewR (f a) -> f (ViewR a) # mapM :: Monad m => (a -> m b) -> ViewR a -> m (ViewR b) # sequence :: Monad m => ViewR (m a) -> m (ViewR a) #
Traversable ModuleName
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> ModuleName a -> f (ModuleName b) # sequenceA :: Applicative f => ModuleName (f a) -> f (ModuleName a) # mapM :: Monad m => (a -> m b) -> ModuleName a -> m (ModuleName b) # sequence :: Monad m => ModuleName (m a) -> m (ModuleName a) #
Traversable SpecialCon
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> SpecialCon a -> f (SpecialCon b) # sequenceA :: Applicative f => SpecialCon (f a) -> f (SpecialCon a) # mapM :: Monad m => (a -> m b) -> SpecialCon a -> m (SpecialCon b) # sequence :: Monad m => SpecialCon (m a) -> m (SpecialCon a) #
Traversable QName
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> QName a -> f (QName b) # sequenceA :: Applicative f => QName (f a) -> f (QName a) # mapM :: Monad m => (a -> m b) -> QName a -> m (QName b) # sequence :: Monad m => QName (m a) -> m (QName a) #
Traversable Name
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Name a -> f (Name b) # sequenceA :: Applicative f => Name (f a) -> f (Name a) # mapM :: Monad m => (a -> m b) -> Name a -> m (Name b) # sequence :: Monad m => Name (m a) -> m (Name a) #
Traversable IPName
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> IPName a -> f (IPName b) # sequenceA :: Applicative f => IPName (f a) -> f (IPName a) # mapM :: Monad m => (a -> m b) -> IPName a -> m (IPName b) # sequence :: Monad m => IPName (m a) -> m (IPName a) #
Traversable QOp
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> QOp a -> f (QOp b) # sequenceA :: Applicative f => QOp (f a) -> f (QOp a) # mapM :: Monad m => (a -> m b) -> QOp a -> m (QOp b) # sequence :: Monad m => QOp (m a) -> m (QOp a) #
Traversable Op
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Op a -> f (Op b) # sequenceA :: Applicative f => Op (f a) -> f (Op a) # mapM :: Monad m => (a -> m b) -> Op a -> m (Op b) # sequence :: Monad m => Op (m a) -> m (Op a) #
Traversable CName
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> CName a -> f (CName b) # sequenceA :: Applicative f => CName (f a) -> f (CName a) # mapM :: Monad m => (a -> m b) -> CName a -> m (CName b) # sequence :: Monad m => CName (m a) -> m (CName a) #
Traversable Module
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Module a -> f (Module b) # sequenceA :: Applicative f => Module (f a) -> f (Module a) # mapM :: Monad m => (a -> m b) -> Module a -> m (Module b) # sequence :: Monad m => Module (m a) -> m (Module a) #
Traversable ModuleHead
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> ModuleHead a -> f (ModuleHead b) # sequenceA :: Applicative f => ModuleHead (f a) -> f (ModuleHead a) # mapM :: Monad m => (a -> m b) -> ModuleHead a -> m (ModuleHead b) # sequence :: Monad m => ModuleHead (m a) -> m (ModuleHead a) #
Traversable ExportSpecList
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> ExportSpecList a -> f (ExportSpecList b) # sequenceA :: Applicative f => ExportSpecList (f a) -> f (ExportSpecList a) # mapM :: Monad m => (a -> m b) -> ExportSpecList a -> m (ExportSpecList b) # sequence :: Monad m => ExportSpecList (m a) -> m (ExportSpecList a) #
Traversable ExportSpec
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> ExportSpec a -> f (ExportSpec b) # sequenceA :: Applicative f => ExportSpec (f a) -> f (ExportSpec a) # mapM :: Monad m => (a -> m b) -> ExportSpec a -> m (ExportSpec b) # sequence :: Monad m => ExportSpec (m a) -> m (ExportSpec a) #
Traversable EWildcard
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> EWildcard a -> f (EWildcard b) # sequenceA :: Applicative f => EWildcard (f a) -> f (EWildcard a) # mapM :: Monad m => (a -> m b) -> EWildcard a -> m (EWildcard b) # sequence :: Monad m => EWildcard (m a) -> m (EWildcard a) #
Traversable Namespace
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Namespace a -> f (Namespace b) # sequenceA :: Applicative f => Namespace (f a) -> f (Namespace a) # mapM :: Monad m => (a -> m b) -> Namespace a -> m (Namespace b) # sequence :: Monad m => Namespace (m a) -> m (Namespace a) #
Traversable ImportDecl
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> ImportDecl a -> f (ImportDecl b) # sequenceA :: Applicative f => ImportDecl (f a) -> f (ImportDecl a) # mapM :: Monad m => (a -> m b) -> ImportDecl a -> m (ImportDecl b) # sequence :: Monad m => ImportDecl (m a) -> m (ImportDecl a) #
Traversable ImportSpecList
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> ImportSpecList a -> f (ImportSpecList b) # sequenceA :: Applicative f => ImportSpecList (f a) -> f (ImportSpecList a) # mapM :: Monad m => (a -> m b) -> ImportSpecList a -> m (ImportSpecList b) # sequence :: Monad m => ImportSpecList (m a) -> m (ImportSpecList a) #
Traversable ImportSpec
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> ImportSpec a -> f (ImportSpec b) # sequenceA :: Applicative f => ImportSpec (f a) -> f (ImportSpec a) # mapM :: Monad m => (a -> m b) -> ImportSpec a -> m (ImportSpec b) # sequence :: Monad m => ImportSpec (m a) -> m (ImportSpec a) #
Traversable Assoc
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Assoc a -> f (Assoc b) # sequenceA :: Applicative f => Assoc (f a) -> f (Assoc a) # mapM :: Monad m => (a -> m b) -> Assoc a -> m (Assoc b) # sequence :: Monad m => Assoc (m a) -> m (Assoc a) #
Traversable Decl
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Decl a -> f (Decl b) # sequenceA :: Applicative f => Decl (f a) -> f (Decl a) # mapM :: Monad m => (a -> m b) -> Decl a -> m (Decl b) # sequence :: Monad m => Decl (m a) -> m (Decl a) #
Traversable PatternSynDirection
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> PatternSynDirection a -> f (PatternSynDirection b) # sequenceA :: Applicative f => PatternSynDirection (f a) -> f (PatternSynDirection a) # mapM :: Monad m => (a -> m b) -> PatternSynDirection a -> m (PatternSynDirection b) # sequence :: Monad m => PatternSynDirection (m a) -> m (PatternSynDirection a) #
Traversable TypeEqn
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> TypeEqn a -> f (TypeEqn b) # sequenceA :: Applicative f => TypeEqn (f a) -> f (TypeEqn a) # mapM :: Monad m => (a -> m b) -> TypeEqn a -> m (TypeEqn b) # sequence :: Monad m => TypeEqn (m a) -> m (TypeEqn a) #
Traversable Annotation
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Annotation a -> f (Annotation b) # sequenceA :: Applicative f => Annotation (f a) -> f (Annotation a) # mapM :: Monad m => (a -> m b) -> Annotation a -> m (Annotation b) # sequence :: Monad m => Annotation (m a) -> m (Annotation a) #
Traversable BooleanFormula
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> BooleanFormula a -> f (BooleanFormula b) # sequenceA :: Applicative f => BooleanFormula (f a) -> f (BooleanFormula a) # mapM :: Monad m => (a -> m b) -> BooleanFormula a -> m (BooleanFormula b) # sequence :: Monad m => BooleanFormula (m a) -> m (BooleanFormula a) #
Traversable Role
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Role a -> f (Role b) # sequenceA :: Applicative f => Role (f a) -> f (Role a) # mapM :: Monad m => (a -> m b) -> Role a -> m (Role b) # sequence :: Monad m => Role (m a) -> m (Role a) #
Traversable DataOrNew
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> DataOrNew a -> f (DataOrNew b) # sequenceA :: Applicative f => DataOrNew (f a) -> f (DataOrNew a) # mapM :: Monad m => (a -> m b) -> DataOrNew a -> m (DataOrNew b) # sequence :: Monad m => DataOrNew (m a) -> m (DataOrNew a) #
Traversable InjectivityInfo
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> InjectivityInfo a -> f (InjectivityInfo b) # sequenceA :: Applicative f => InjectivityInfo (f a) -> f (InjectivityInfo a) # mapM :: Monad m => (a -> m b) -> InjectivityInfo a -> m (InjectivityInfo b) # sequence :: Monad m => InjectivityInfo (m a) -> m (InjectivityInfo a) #
Traversable ResultSig
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> ResultSig a -> f (ResultSig b) # sequenceA :: Applicative f => ResultSig (f a) -> f (ResultSig a) # mapM :: Monad m => (a -> m b) -> ResultSig a -> m (ResultSig b) # sequence :: Monad m => ResultSig (m a) -> m (ResultSig a) #
Traversable DeclHead
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> DeclHead a -> f (DeclHead b) # sequenceA :: Applicative f => DeclHead (f a) -> f (DeclHead a) # mapM :: Monad m => (a -> m b) -> DeclHead a -> m (DeclHead b) # sequence :: Monad m => DeclHead (m a) -> m (DeclHead a) #
Traversable InstRule
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> InstRule a -> f (InstRule b) # sequenceA :: Applicative f => InstRule (f a) -> f (InstRule a) # mapM :: Monad m => (a -> m b) -> InstRule a -> m (InstRule b) # sequence :: Monad m => InstRule (m a) -> m (InstRule a) #
Traversable InstHead
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> InstHead a -> f (InstHead b) # sequenceA :: Applicative f => InstHead (f a) -> f (InstHead a) # mapM :: Monad m => (a -> m b) -> InstHead a -> m (InstHead b) # sequence :: Monad m => InstHead (m a) -> m (InstHead a) #
Traversable Deriving
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Deriving a -> f (Deriving b) # sequenceA :: Applicative f => Deriving (f a) -> f (Deriving a) # mapM :: Monad m => (a -> m b) -> Deriving a -> m (Deriving b) # sequence :: Monad m => Deriving (m a) -> m (Deriving a) #
Traversable DerivStrategy
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> DerivStrategy a -> f (DerivStrategy b) # sequenceA :: Applicative f => DerivStrategy (f a) -> f (DerivStrategy a) # mapM :: Monad m => (a -> m b) -> DerivStrategy a -> m (DerivStrategy b) # sequence :: Monad m => DerivStrategy (m a) -> m (DerivStrategy a) #
Traversable Binds
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Binds a -> f (Binds b) # sequenceA :: Applicative f => Binds (f a) -> f (Binds a) # mapM :: Monad m => (a -> m b) -> Binds a -> m (Binds b) # sequence :: Monad m => Binds (m a) -> m (Binds a) #
Traversable IPBind
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> IPBind a -> f (IPBind b) # sequenceA :: Applicative f => IPBind (f a) -> f (IPBind a) # mapM :: Monad m => (a -> m b) -> IPBind a -> m (IPBind b) # sequence :: Monad m => IPBind (m a) -> m (IPBind a) #
Traversable Match
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Match a -> f (Match b) # sequenceA :: Applicative f => Match (f a) -> f (Match a) # mapM :: Monad m => (a -> m b) -> Match a -> m (Match b) # sequence :: Monad m => Match (m a) -> m (Match a) #
Traversable QualConDecl
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> QualConDecl a -> f (QualConDecl b) # sequenceA :: Applicative f => QualConDecl (f a) -> f (QualConDecl a) # mapM :: Monad m => (a -> m b) -> QualConDecl a -> m (QualConDecl b) # sequence :: Monad m => QualConDecl (m a) -> m (QualConDecl a) #
Traversable ConDecl
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> ConDecl a -> f (ConDecl b) # sequenceA :: Applicative f => ConDecl (f a) -> f (ConDecl a) # mapM :: Monad m => (a -> m b) -> ConDecl a -> m (ConDecl b) # sequence :: Monad m => ConDecl (m a) -> m (ConDecl a) #
Traversable FieldDecl
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> FieldDecl a -> f (FieldDecl b) # sequenceA :: Applicative f => FieldDecl (f a) -> f (FieldDecl a) # mapM :: Monad m => (a -> m b) -> FieldDecl a -> m (FieldDecl b) # sequence :: Monad m => FieldDecl (m a) -> m (FieldDecl a) #
Traversable GadtDecl
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> GadtDecl a -> f (GadtDecl b) # sequenceA :: Applicative f => GadtDecl (f a) -> f (GadtDecl a) # mapM :: Monad m => (a -> m b) -> GadtDecl a -> m (GadtDecl b) # sequence :: Monad m => GadtDecl (m a) -> m (GadtDecl a) #
Traversable ClassDecl
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> ClassDecl a -> f (ClassDecl b) # sequenceA :: Applicative f => ClassDecl (f a) -> f (ClassDecl a) # mapM :: Monad m => (a -> m b) -> ClassDecl a -> m (ClassDecl b) # sequence :: Monad m => ClassDecl (m a) -> m (ClassDecl a) #
Traversable InstDecl
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> InstDecl a -> f (InstDecl b) # sequenceA :: Applicative f => InstDecl (f a) -> f (InstDecl a) # mapM :: Monad m => (a -> m b) -> InstDecl a -> m (InstDecl b) # sequence :: Monad m => InstDecl (m a) -> m (InstDecl a) #
Traversable BangType
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> BangType a -> f (BangType b) # sequenceA :: Applicative f => BangType (f a) -> f (BangType a) # mapM :: Monad m => (a -> m b) -> BangType a -> m (BangType b) # sequence :: Monad m => BangType (m a) -> m (BangType a) #
Traversable Unpackedness
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Unpackedness a -> f (Unpackedness b) # sequenceA :: Applicative f => Unpackedness (f a) -> f (Unpackedness a) # mapM :: Monad m => (a -> m b) -> Unpackedness a -> m (Unpackedness b) # sequence :: Monad m => Unpackedness (m a) -> m (Unpackedness a) #
Traversable Rhs
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Rhs a -> f (Rhs b) # sequenceA :: Applicative f => Rhs (f a) -> f (Rhs a) # mapM :: Monad m => (a -> m b) -> Rhs a -> m (Rhs b) # sequence :: Monad m => Rhs (m a) -> m (Rhs a) #
Traversable GuardedRhs
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> GuardedRhs a -> f (GuardedRhs b) # sequenceA :: Applicative f => GuardedRhs (f a) -> f (GuardedRhs a) # mapM :: Monad m => (a -> m b) -> GuardedRhs a -> m (GuardedRhs b) # sequence :: Monad m => GuardedRhs (m a) -> m (GuardedRhs a) #
Traversable Type
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Type a -> f (Type b) # sequenceA :: Applicative f => Type (f a) -> f (Type a) # mapM :: Monad m => (a -> m b) -> Type a -> m (Type b) # sequence :: Monad m => Type (m a) -> m (Type a) #
Traversable MaybePromotedName
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> MaybePromotedName a -> f (MaybePromotedName b) # sequenceA :: Applicative f => MaybePromotedName (f a) -> f (MaybePromotedName a) # mapM :: Monad m => (a -> m b) -> MaybePromotedName a -> m (MaybePromotedName b) # sequence :: Monad m => MaybePromotedName (m a) -> m (MaybePromotedName a) #
Traversable Promoted
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Promoted a -> f (Promoted b) # sequenceA :: Applicative f => Promoted (f a) -> f (Promoted a) # mapM :: Monad m => (a -> m b) -> Promoted a -> m (Promoted b) # sequence :: Monad m => Promoted (m a) -> m (Promoted a) #
Traversable TyVarBind
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> TyVarBind a -> f (TyVarBind b) # sequenceA :: Applicative f => TyVarBind (f a) -> f (TyVarBind a) # mapM :: Monad m => (a -> m b) -> TyVarBind a -> m (TyVarBind b) # sequence :: Monad m => TyVarBind (m a) -> m (TyVarBind a) #
Traversable Kind
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Kind a -> f (Kind b) # sequenceA :: Applicative f => Kind (f a) -> f (Kind a) # mapM :: Monad m => (a -> m b) -> Kind a -> m (Kind b) # sequence :: Monad m => Kind (m a) -> m (Kind a) #
Traversable FunDep
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> FunDep a -> f (FunDep b) # sequenceA :: Applicative f => FunDep (f a) -> f (FunDep a) # mapM :: Monad m => (a -> m b) -> FunDep a -> m (FunDep b) # sequence :: Monad m => FunDep (m a) -> m (FunDep a) #
Traversable Context
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Context a -> f (Context b) # sequenceA :: Applicative f => Context (f a) -> f (Context a) # mapM :: Monad m => (a -> m b) -> Context a -> m (Context b) # sequence :: Monad m => Context (m a) -> m (Context a) #
Traversable Asst
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Asst a -> f (Asst b) # sequenceA :: Applicative f => Asst (f a) -> f (Asst a) # mapM :: Monad m => (a -> m b) -> Asst a -> m (Asst b) # sequence :: Monad m => Asst (m a) -> m (Asst a) #
Traversable Literal
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Literal a -> f (Literal b) # sequenceA :: Applicative f => Literal (f a) -> f (Literal a) # mapM :: Monad m => (a -> m b) -> Literal a -> m (Literal b) # sequence :: Monad m => Literal (m a) -> m (Literal a) #
Traversable Sign
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Sign a -> f (Sign b) # sequenceA :: Applicative f => Sign (f a) -> f (Sign a) # mapM :: Monad m => (a -> m b) -> Sign a -> m (Sign b) # sequence :: Monad m => Sign (m a) -> m (Sign a) #
Traversable Exp
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Exp a -> f (Exp b) # sequenceA :: Applicative f => Exp (f a) -> f (Exp a) # mapM :: Monad m => (a -> m b) -> Exp a -> m (Exp b) # sequence :: Monad m => Exp (m a) -> m (Exp a) #
Traversable XName
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> XName a -> f (XName b) # sequenceA :: Applicative f => XName (f a) -> f (XName a) # mapM :: Monad m => (a -> m b) -> XName a -> m (XName b) # sequence :: Monad m => XName (m a) -> m (XName a) #
Traversable XAttr
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> XAttr a -> f (XAttr b) # sequenceA :: Applicative f => XAttr (f a) -> f (XAttr a) # mapM :: Monad m => (a -> m b) -> XAttr a -> m (XAttr b) # sequence :: Monad m => XAttr (m a) -> m (XAttr a) #
Traversable Bracket
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Bracket a -> f (Bracket b) # sequenceA :: Applicative f => Bracket (f a) -> f (Bracket a) # mapM :: Monad m => (a -> m b) -> Bracket a -> m (Bracket b) # sequence :: Monad m => Bracket (m a) -> m (Bracket a) #
Traversable Splice
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Splice a -> f (Splice b) # sequenceA :: Applicative f => Splice (f a) -> f (Splice a) # mapM :: Monad m => (a -> m b) -> Splice a -> m (Splice b) # sequence :: Monad m => Splice (m a) -> m (Splice a) #
Traversable Safety
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Safety a -> f (Safety b) # sequenceA :: Applicative f => Safety (f a) -> f (Safety a) # mapM :: Monad m => (a -> m b) -> Safety a -> m (Safety b) # sequence :: Monad m => Safety (m a) -> m (Safety a) #
Traversable CallConv
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> CallConv a -> f (CallConv b) # sequenceA :: Applicative f => CallConv (f a) -> f (CallConv a) # mapM :: Monad m => (a -> m b) -> CallConv a -> m (CallConv b) # sequence :: Monad m => CallConv (m a) -> m (CallConv a) #
Traversable ModulePragma
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> ModulePragma a -> f (ModulePragma b) # sequenceA :: Applicative f => ModulePragma (f a) -> f (ModulePragma a) # mapM :: Monad m => (a -> m b) -> ModulePragma a -> m (ModulePragma b) # sequence :: Monad m => ModulePragma (m a) -> m (ModulePragma a) #
Traversable Overlap
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Overlap a -> f (Overlap b) # sequenceA :: Applicative f => Overlap (f a) -> f (Overlap a) # mapM :: Monad m => (a -> m b) -> Overlap a -> m (Overlap b) # sequence :: Monad m => Overlap (m a) -> m (Overlap a) #
Traversable Activation
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Activation a -> f (Activation b) # sequenceA :: Applicative f => Activation (f a) -> f (Activation a) # mapM :: Monad m => (a -> m b) -> Activation a -> m (Activation b) # sequence :: Monad m => Activation (m a) -> m (Activation a) #
Traversable Rule
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Rule a -> f (Rule b) # sequenceA :: Applicative f => Rule (f a) -> f (Rule a) # mapM :: Monad m => (a -> m b) -> Rule a -> m (Rule b) # sequence :: Monad m => Rule (m a) -> m (Rule a) #
Traversable RuleVar
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> RuleVar a -> f (RuleVar b) # sequenceA :: Applicative f => RuleVar (f a) -> f (RuleVar a) # mapM :: Monad m => (a -> m b) -> RuleVar a -> m (RuleVar b) # sequence :: Monad m => RuleVar (m a) -> m (RuleVar a) #
Traversable WarningText
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> WarningText a -> f (WarningText b) # sequenceA :: Applicative f => WarningText (f a) -> f (WarningText a) # mapM :: Monad m => (a -> m b) -> WarningText a -> m (WarningText b) # sequence :: Monad m => WarningText (m a) -> m (WarningText a) #
Traversable Pat
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Pat a -> f (Pat b) # sequenceA :: Applicative f => Pat (f a) -> f (Pat a) # mapM :: Monad m => (a -> m b) -> Pat a -> m (Pat b) # sequence :: Monad m => Pat (m a) -> m (Pat a) #
Traversable PXAttr
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> PXAttr a -> f (PXAttr b) # sequenceA :: Applicative f => PXAttr (f a) -> f (PXAttr a) # mapM :: Monad m => (a -> m b) -> PXAttr a -> m (PXAttr b) # sequence :: Monad m => PXAttr (m a) -> m (PXAttr a) #
Traversable RPatOp
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> RPatOp a -> f (RPatOp b) # sequenceA :: Applicative f => RPatOp (f a) -> f (RPatOp a) # mapM :: Monad m => (a -> m b) -> RPatOp a -> m (RPatOp b) # sequence :: Monad m => RPatOp (m a) -> m (RPatOp a) #
Traversable RPat
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> RPat a -> f (RPat b) # sequenceA :: Applicative f => RPat (f a) -> f (RPat a) # mapM :: Monad m => (a -> m b) -> RPat a -> m (RPat b) # sequence :: Monad m => RPat (m a) -> m (RPat a) #
Traversable PatField
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> PatField a -> f (PatField b) # sequenceA :: Applicative f => PatField (f a) -> f (PatField a) # mapM :: Monad m => (a -> m b) -> PatField a -> m (PatField b) # sequence :: Monad m => PatField (m a) -> m (PatField a) #
Traversable Stmt
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Stmt a -> f (Stmt b) # sequenceA :: Applicative f => Stmt (f a) -> f (Stmt a) # mapM :: Monad m => (a -> m b) -> Stmt a -> m (Stmt b) # sequence :: Monad m => Stmt (m a) -> m (Stmt a) #
Traversable QualStmt
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> QualStmt a -> f (QualStmt b) # sequenceA :: Applicative f => QualStmt (f a) -> f (QualStmt a) # mapM :: Monad m => (a -> m b) -> QualStmt a -> m (QualStmt b) # sequence :: Monad m => QualStmt (m a) -> m (QualStmt a) #
Traversable FieldUpdate
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> FieldUpdate a -> f (FieldUpdate b) # sequenceA :: Applicative f => FieldUpdate (f a) -> f (FieldUpdate a) # mapM :: Monad m => (a -> m b) -> FieldUpdate a -> m (FieldUpdate b) # sequence :: Monad m => FieldUpdate (m a) -> m (FieldUpdate a) #
Traversable Alt
Instance details Defined in Language.Haskell.Exts.Syntax Methods traverse :: Applicative f => (a -> f b) -> Alt a -> f (Alt b) # sequenceA :: Applicative f => Alt (f a) -> f (Alt a) # mapM :: Monad m => (a -> m b) -> Alt a -> m (Alt b) # sequence :: Monad m => Alt (m a) -> m (Alt a) #
Traversable Vector
Instance details Defined in Data.Vector Methods traverse :: Applicative f => (a -> f b) -> Vector a -> f (Vector b) # sequenceA :: Applicative f => Vector (f a) -> f (Vector a) # mapM :: Monad m => (a -> m b) -> Vector a -> m (Vector b) # sequence :: Monad m => Vector (m a) -> m (Vector a) #
Traversable Log
Instance details Defined in Numeric.Log Methods traverse :: Applicative f => (a -> f b) -> Log a -> f (Log b) # sequenceA :: Applicative f => Log (f a) -> f (Log a) # mapM :: Monad m => (a -> m b) -> Log a -> m (Log b) # sequence :: Monad m => Log (m a) -> m (Log a) #
Traversable SimpleDocStream	Transform a document based on its annotations, possibly leveraging `Applicative` effects.
Instance details Defined in Data.Text.Prettyprint.Doc.Internal Methods traverse :: Applicative f => (a -> f b) -> SimpleDocStream a -> f (SimpleDocStream b) # sequenceA :: Applicative f => SimpleDocStream (f a) -> f (SimpleDocStream a) # mapM :: Monad m => (a -> m b) -> SimpleDocStream a -> m (SimpleDocStream b) # sequence :: Monad m => SimpleDocStream (m a) -> m (SimpleDocStream a) #
Traversable SmallArray
Instance details Defined in Data.Primitive.SmallArray Methods traverse :: Applicative f => (a -> f b) -> SmallArray a -> f (SmallArray b) # sequenceA :: Applicative f => SmallArray (f a) -> f (SmallArray a) # mapM :: Monad m => (a -> m b) -> SmallArray a -> m (SmallArray b) # sequence :: Monad m => SmallArray (m a) -> m (SmallArray a) #
Traversable Array
Instance details Defined in Data.Primitive.Array Methods traverse :: Applicative f => (a -> f b) -> Array a -> f (Array b) # sequenceA :: Applicative f => Array (f a) -> f (Array a) # mapM :: Monad m => (a -> m b) -> Array a -> m (Array b) # sequence :: Monad m => Array (m a) -> m (Array a) #
Traversable Bound
Instance details Defined in Data.Semilattice.Bound Methods traverse :: Applicative f => (a -> f b) -> Bound a -> f (Bound b) # sequenceA :: Applicative f => Bound (f a) -> f (Bound a) # mapM :: Monad m => (a -> m b) -> Bound a -> m (Bound b) # sequence :: Monad m => Bound (m a) -> m (Bound a) #
Traversable Order
Instance details Defined in Data.Semilattice.Order Methods traverse :: Applicative f => (a -> f b) -> Order a -> f (Order b) # sequenceA :: Applicative f => Order (f a) -> f (Order a) # mapM :: Monad m => (a -> m b) -> Order a -> m (Order b) # sequence :: Monad m => Order (m a) -> m (Order a) #
Traversable Meeting
Instance details Defined in Data.Semilattice.Meet Methods traverse :: Applicative f => (a -> f b) -> Meeting a -> f (Meeting b) # sequenceA :: Applicative f => Meeting (f a) -> f (Meeting a) # mapM :: Monad m => (a -> m b) -> Meeting a -> m (Meeting b) # sequence :: Monad m => Meeting (m a) -> m (Meeting a) #
Traversable GreaterThan
Instance details Defined in Data.Semilattice.Meet Methods traverse :: Applicative f => (a -> f b) -> GreaterThan a -> f (GreaterThan b) # sequenceA :: Applicative f => GreaterThan (f a) -> f (GreaterThan a) # mapM :: Monad m => (a -> m b) -> GreaterThan a -> m (GreaterThan b) # sequence :: Monad m => GreaterThan (m a) -> m (GreaterThan a) #
Traversable Joining
Instance details Defined in Data.Semilattice.Join Methods traverse :: Applicative f => (a -> f b) -> Joining a -> f (Joining b) # sequenceA :: Applicative f => Joining (f a) -> f (Joining a) # mapM :: Monad m => (a -> m b) -> Joining a -> m (Joining b) # sequence :: Monad m => Joining (m a) -> m (Joining a) #
Traversable LessThan
Instance details Defined in Data.Semilattice.Join Methods traverse :: Applicative f => (a -> f b) -> LessThan a -> f (LessThan b) # sequenceA :: Applicative f => LessThan (f a) -> f (LessThan a) # mapM :: Monad m => (a -> m b) -> LessThan a -> m (LessThan b) # sequence :: Monad m => LessThan (m a) -> m (LessThan a) #
Traversable P
Instance details Defined in Data.HashMap.Strict.InsOrd Methods traverse :: Applicative f => (a -> f b) -> P a -> f (P b) # sequenceA :: Applicative f => P (f a) -> f (P a) # mapM :: Monad m => (a -> m b) -> P a -> m (P b) # sequence :: Monad m => P (m a) -> m (P a) #
Traversable (Either a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) # sequence :: Monad m => Either a (m a0) -> m (Either a a0) #
Traversable (V1 :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b) # sequenceA :: Applicative f => V1 (f a) -> f (V1 a) # mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b) # sequence :: Monad m => V1 (m a) -> m (V1 a) #
Traversable (U1 :: * -> *)	Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> U1 a -> f (U1 b) # sequenceA :: Applicative f => U1 (f a) -> f (U1 a) # mapM :: Monad m => (a -> m b) -> U1 a -> m (U1 b) # sequence :: Monad m => U1 (m a) -> m (U1 a) #
Traversable ((,) a)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> (a, a0) -> f (a, b) # sequenceA :: Applicative f => (a, f a0) -> f (a, a0) # mapM :: Monad m => (a0 -> m b) -> (a, a0) -> m (a, b) # sequence :: Monad m => (a, m a0) -> m (a, a0) #
Traversable (HashMap k)
Instance details Defined in Data.HashMap.Base Methods traverse :: Applicative f => (a -> f b) -> HashMap k a -> f (HashMap k b) # sequenceA :: Applicative f => HashMap k (f a) -> f (HashMap k a) # mapM :: Monad m => (a -> m b) -> HashMap k a -> m (HashMap k b) # sequence :: Monad m => HashMap k (m a) -> m (HashMap k a) #
Traversable (Map k)
Instance details Defined in Data.Map.Internal Methods traverse :: Applicative f => (a -> f b) -> Map k a -> f (Map k b) # sequenceA :: Applicative f => Map k (f a) -> f (Map k a) # mapM :: Monad m => (a -> m b) -> Map k a -> m (Map k b) # sequence :: Monad m => Map k (m a) -> m (Map k a) #
Ix i => Traversable (Array i)	Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b) # sequenceA :: Applicative f => Array i (f a) -> f (Array i a) # mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b) # sequence :: Monad m => Array i (m a) -> m (Array i a) #
Traversable (Arg a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods traverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) # sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) # mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) # sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) #
Traversable (Proxy :: * -> *)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b) # sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a) # mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b) # sequence :: Monad m => Proxy (m a) -> m (Proxy a) #
Traversable f => Traversable (MaybeT f)
Instance details Defined in Control.Monad.Trans.Maybe Methods traverse :: Applicative f0 => (a -> f0 b) -> MaybeT f a -> f0 (MaybeT f b) # sequenceA :: Applicative f0 => MaybeT f (f0 a) -> f0 (MaybeT f a) # mapM :: Monad m => (a -> m b) -> MaybeT f a -> m (MaybeT f b) # sequence :: Monad m => MaybeT f (m a) -> m (MaybeT f a) #
Traversable f => Traversable (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods traverse :: Applicative f0 => (a -> f0 b) -> Cofree f a -> f0 (Cofree f b) # sequenceA :: Applicative f0 => Cofree f (f0 a) -> f0 (Cofree f a) # mapM :: Monad m => (a -> m b) -> Cofree f a -> m (Cofree f b) # sequence :: Monad m => Cofree f (m a) -> m (Cofree f a) #
Traversable f => Traversable (Free f)
Instance details Defined in Control.Monad.Free Methods traverse :: Applicative f0 => (a -> f0 b) -> Free f a -> f0 (Free f b) # sequenceA :: Applicative f0 => Free f (f0 a) -> f0 (Free f a) # mapM :: Monad m => (a -> m b) -> Free f a -> m (Free f b) # sequence :: Monad m => Free f (m a) -> m (Free f a) #
Traversable (Entry p)
Instance details Defined in Data.Heap Methods traverse :: Applicative f => (a -> f b) -> Entry p a -> f (Entry p b) # sequenceA :: Applicative f => Entry p (f a) -> f (Entry p a) # mapM :: Monad m => (a -> m b) -> Entry p a -> m (Entry p b) # sequence :: Monad m => Entry p (m a) -> m (Entry p a) #
Traversable (InsOrdHashMap k)
Instance details Defined in Data.HashMap.Strict.InsOrd Methods traverse :: Applicative f => (a -> f b) -> InsOrdHashMap k a -> f (InsOrdHashMap k b) # sequenceA :: Applicative f => InsOrdHashMap k (f a) -> f (InsOrdHashMap k a) # mapM :: Monad m => (a -> m b) -> InsOrdHashMap k a -> m (InsOrdHashMap k b) # sequence :: Monad m => InsOrdHashMap k (m a) -> m (InsOrdHashMap k a) #
Traversable f => Traversable (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods traverse :: Applicative f0 => (a -> f0 b) -> Yoneda f a -> f0 (Yoneda f b) # sequenceA :: Applicative f0 => Yoneda f (f0 a) -> f0 (Yoneda f a) # mapM :: Monad m => (a -> m b) -> Yoneda f a -> m (Yoneda f b) # sequence :: Monad m => Yoneda f (m a) -> m (Yoneda f a) #
(Monad m, Traversable m) => Traversable (ListT m)
Instance details Defined in List.Transformer Methods traverse :: Applicative f => (a -> f b) -> ListT m a -> f (ListT m b) # sequenceA :: Applicative f => ListT m (f a) -> f (ListT m a) # mapM :: Monad m0 => (a -> m0 b) -> ListT m a -> m0 (ListT m b) # sequence :: Monad m0 => ListT m (m0 a) -> m0 (ListT m a) #
(Monad m, Traversable m) => Traversable (Step m)
Instance details Defined in List.Transformer Methods traverse :: Applicative f => (a -> f b) -> Step m a -> f (Step m b) # sequenceA :: Applicative f => Step m (f a) -> f (Step m a) # mapM :: Monad m0 => (a -> m0 b) -> Step m a -> m0 (Step m b) # sequence :: Monad m0 => Step m (m0 a) -> m0 (Step m a) #
Traversable (LogicT Identity)
Instance details Defined in Control.Monad.Logic Methods traverse :: Applicative f => (a -> f b) -> LogicT Identity a -> f (LogicT Identity b) # sequenceA :: Applicative f => LogicT Identity (f a) -> f (LogicT Identity a) # mapM :: Monad m => (a -> m b) -> LogicT Identity a -> m (LogicT Identity b) # sequence :: Monad m => LogicT Identity (m a) -> m (LogicT Identity a) #
Traversable (IntPSQ p)
Instance details Defined in Data.IntPSQ.Internal Methods traverse :: Applicative f => (a -> f b) -> IntPSQ p a -> f (IntPSQ p b) # sequenceA :: Applicative f => IntPSQ p (f a) -> f (IntPSQ p a) # mapM :: Monad m => (a -> m b) -> IntPSQ p a -> m (IntPSQ p b) # sequence :: Monad m => IntPSQ p (m a) -> m (IntPSQ p a) #
Traversable f => Traversable (Rec1 f)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) # sequenceA :: Applicative f0 => Rec1 f (f0 a) -> f0 (Rec1 f a) # mapM :: Monad m => (a -> m b) -> Rec1 f a -> m (Rec1 f b) # sequence :: Monad m => Rec1 f (m a) -> m (Rec1 f a) #
Traversable (URec Char :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Char a -> f (URec Char b) # sequenceA :: Applicative f => URec Char (f a) -> f (URec Char a) # mapM :: Monad m => (a -> m b) -> URec Char a -> m (URec Char b) # sequence :: Monad m => URec Char (m a) -> m (URec Char a) #
Traversable (URec Double :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) # sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) # mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) # sequence :: Monad m => URec Double (m a) -> m (URec Double a) #
Traversable (URec Float :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) # sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) # mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) # sequence :: Monad m => URec Float (m a) -> m (URec Float a) #
Traversable (URec Int :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) # sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) # mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) # sequence :: Monad m => URec Int (m a) -> m (URec Int a) #
Traversable (URec Word :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Word a -> f (URec Word b) # sequenceA :: Applicative f => URec Word (f a) -> f (URec Word a) # mapM :: Monad m => (a -> m b) -> URec Word a -> m (URec Word b) # sequence :: Monad m => URec Word (m a) -> m (URec Word a) #
Traversable (URec (Ptr ()) :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec (Ptr ()) a -> f (URec (Ptr ()) b) # sequenceA :: Applicative f => URec (Ptr ()) (f a) -> f (URec (Ptr ()) a) # mapM :: Monad m => (a -> m b) -> URec (Ptr ()) a -> m (URec (Ptr ()) b) # sequence :: Monad m => URec (Ptr ()) (m a) -> m (URec (Ptr ()) a) #
Traversable (Const m :: * -> *)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) # sequenceA :: Applicative f => Const m (f a) -> f (Const m a) # mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) # sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) #
Bitraversable p => Traversable (Join p)
Instance details Defined in Data.Bifunctor.Join Methods traverse :: Applicative f => (a -> f b) -> Join p a -> f (Join p b) # sequenceA :: Applicative f => Join p (f a) -> f (Join p a) # mapM :: Monad m => (a -> m b) -> Join p a -> m (Join p b) # sequence :: Monad m => Join p (m a) -> m (Join p a) #
Bitraversable p => Traversable (Fix p)
Instance details Defined in Data.Bifunctor.Fix Methods traverse :: Applicative f => (a -> f b) -> Fix p a -> f (Fix p b) # sequenceA :: Applicative f => Fix p (f a) -> f (Fix p a) # mapM :: Monad m => (a -> m b) -> Fix p a -> m (Fix p b) # sequence :: Monad m => Fix p (m a) -> m (Fix p a) #
Traversable f => Traversable (IdentityT f)
Instance details Defined in Control.Monad.Trans.Identity Methods traverse :: Applicative f0 => (a -> f0 b) -> IdentityT f a -> f0 (IdentityT f b) # sequenceA :: Applicative f0 => IdentityT f (f0 a) -> f0 (IdentityT f a) # mapM :: Monad m => (a -> m b) -> IdentityT f a -> m (IdentityT f b) # sequence :: Monad m => IdentityT f (m a) -> m (IdentityT f a) #
Traversable f => Traversable (ExceptT e f)
Instance details Defined in Control.Monad.Trans.Except Methods traverse :: Applicative f0 => (a -> f0 b) -> ExceptT e f a -> f0 (ExceptT e f b) # sequenceA :: Applicative f0 => ExceptT e f (f0 a) -> f0 (ExceptT e f a) # mapM :: Monad m => (a -> m b) -> ExceptT e f a -> m (ExceptT e f b) # sequence :: Monad m => ExceptT e f (m a) -> m (ExceptT e f a) #
Traversable f => Traversable (FreeF f a)
Instance details Defined in Control.Monad.Trans.Free Methods traverse :: Applicative f0 => (a0 -> f0 b) -> FreeF f a a0 -> f0 (FreeF f a b) # sequenceA :: Applicative f0 => FreeF f a (f0 a0) -> f0 (FreeF f a a0) # mapM :: Monad m => (a0 -> m b) -> FreeF f a a0 -> m (FreeF f a b) # sequence :: Monad m => FreeF f a (m a0) -> m (FreeF f a a0) #
(Monad m, Traversable m, Traversable f) => Traversable (FreeT f m)
Instance details Defined in Control.Monad.Trans.Free Methods traverse :: Applicative f0 => (a -> f0 b) -> FreeT f m a -> f0 (FreeT f m b) # sequenceA :: Applicative f0 => FreeT f m (f0 a) -> f0 (FreeT f m a) # mapM :: Monad m0 => (a -> m0 b) -> FreeT f m a -> m0 (FreeT f m b) # sequence :: Monad m0 => FreeT f m (m0 a) -> m0 (FreeT f m a) #
Traversable f => Traversable (CofreeF f a)
Instance details Defined in Control.Comonad.Trans.Cofree Methods traverse :: Applicative f0 => (a0 -> f0 b) -> CofreeF f a a0 -> f0 (CofreeF f a b) # sequenceA :: Applicative f0 => CofreeF f a (f0 a0) -> f0 (CofreeF f a a0) # mapM :: Monad m => (a0 -> m b) -> CofreeF f a a0 -> m (CofreeF f a b) # sequence :: Monad m => CofreeF f a (m a0) -> m (CofreeF f a a0) #
(Traversable f, Traversable w) => Traversable (CofreeT f w)
Instance details Defined in Control.Comonad.Trans.Cofree Methods traverse :: Applicative f0 => (a -> f0 b) -> CofreeT f w a -> f0 (CofreeT f w b) # sequenceA :: Applicative f0 => CofreeT f w (f0 a) -> f0 (CofreeT f w a) # mapM :: Monad m => (a -> m b) -> CofreeT f w a -> m (CofreeT f w b) # sequence :: Monad m => CofreeT f w (m a) -> m (CofreeT f w a) #
Traversable f => Traversable (ErrorT e f)
Instance details Defined in Control.Monad.Trans.Error Methods traverse :: Applicative f0 => (a -> f0 b) -> ErrorT e f a -> f0 (ErrorT e f b) # sequenceA :: Applicative f0 => ErrorT e f (f0 a) -> f0 (ErrorT e f a) # mapM :: Monad m => (a -> m b) -> ErrorT e f a -> m (ErrorT e f b) # sequence :: Monad m => ErrorT e f (m a) -> m (ErrorT e f a) #
Traversable f => Traversable (Backwards f)	Derived instance.
Instance details Defined in Control.Applicative.Backwards Methods traverse :: Applicative f0 => (a -> f0 b) -> Backwards f a -> f0 (Backwards f b) # sequenceA :: Applicative f0 => Backwards f (f0 a) -> f0 (Backwards f a) # mapM :: Monad m => (a -> m b) -> Backwards f a -> m (Backwards f b) # sequence :: Monad m => Backwards f (m a) -> m (Backwards f a) #
Traversable (Forget r a)
Instance details Defined in Data.Profunctor.Types Methods traverse :: Applicative f => (a0 -> f b) -> Forget r a a0 -> f (Forget r a b) # sequenceA :: Applicative f => Forget r a (f a0) -> f (Forget r a a0) # mapM :: Monad m => (a0 -> m b) -> Forget r a a0 -> m (Forget r a b) # sequence :: Monad m => Forget r a (m a0) -> m (Forget r a a0) #
Traversable (Bucket k p)
Instance details Defined in Data.HashPSQ.Internal Methods traverse :: Applicative f => (a -> f b) -> Bucket k p a -> f (Bucket k p b) # sequenceA :: Applicative f => Bucket k p (f a) -> f (Bucket k p a) # mapM :: Monad m => (a -> m b) -> Bucket k p a -> m (Bucket k p b) # sequence :: Monad m => Bucket k p (m a) -> m (Bucket k p a) #
Traversable (LTree k p)
Instance details Defined in Data.OrdPSQ.Internal Methods traverse :: Applicative f => (a -> f b) -> LTree k p a -> f (LTree k p b) # sequenceA :: Applicative f => LTree k p (f a) -> f (LTree k p a) # mapM :: Monad m => (a -> m b) -> LTree k p a -> m (LTree k p b) # sequence :: Monad m => LTree k p (m a) -> m (LTree k p a) #
Traversable (Elem k p)
Instance details Defined in Data.OrdPSQ.Internal Methods traverse :: Applicative f => (a -> f b) -> Elem k p a -> f (Elem k p b) # sequenceA :: Applicative f => Elem k p (f a) -> f (Elem k p a) # mapM :: Monad m => (a -> m b) -> Elem k p a -> m (Elem k p b) # sequence :: Monad m => Elem k p (m a) -> m (Elem k p a) #
Traversable (HashPSQ k p)
Instance details Defined in Data.HashPSQ.Internal Methods traverse :: Applicative f => (a -> f b) -> HashPSQ k p a -> f (HashPSQ k p b) # sequenceA :: Applicative f => HashPSQ k p (f a) -> f (HashPSQ k p a) # mapM :: Monad m => (a -> m b) -> HashPSQ k p a -> m (HashPSQ k p b) # sequence :: Monad m => HashPSQ k p (m a) -> m (HashPSQ k p a) #
Traversable (OrdPSQ k p)
Instance details Defined in Data.OrdPSQ.Internal Methods traverse :: Applicative f => (a -> f b) -> OrdPSQ k p a -> f (OrdPSQ k p b) # sequenceA :: Applicative f => OrdPSQ k p (f a) -> f (OrdPSQ k p a) # mapM :: Monad m => (a -> m b) -> OrdPSQ k p a -> m (OrdPSQ k p b) # sequence :: Monad m => OrdPSQ k p (m a) -> m (OrdPSQ k p a) #
Traversable (Tagged s)
Instance details Defined in Data.Tagged Methods traverse :: Applicative f => (a -> f b) -> Tagged s a -> f (Tagged s b) # sequenceA :: Applicative f => Tagged s (f a) -> f (Tagged s a) # mapM :: Monad m => (a -> m b) -> Tagged s a -> m (Tagged s b) # sequence :: Monad m => Tagged s (m a) -> m (Tagged s a) #
Traversable (K1 i c :: * -> *)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> K1 i c a -> f (K1 i c b) # sequenceA :: Applicative f => K1 i c (f a) -> f (K1 i c a) # mapM :: Monad m => (a -> m b) -> K1 i c a -> m (K1 i c b) # sequence :: Monad m => K1 i c (m a) -> m (K1 i c a) #
(Traversable f, Traversable g) => Traversable (f :+: g)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) #
(Traversable f, Traversable g) => Traversable (f :*: g)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequenceA :: Applicative f0 => (f :: g) (f0 a) -> f0 ((f :: g) a) # mapM :: Monad m => (a -> m b) -> (f :: g) a -> m ((f :: g) b) # sequence :: Monad m => (f :: g) (m a) -> m ((f :: g) a) #
(Traversable f, Traversable g) => Traversable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) # sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 (Product f g a) # mapM :: Monad m => (a -> m b) -> Product f g a -> m (Product f g b) # sequence :: Monad m => Product f g (m a) -> m (Product f g a) #
(Traversable f, Traversable g) => Traversable (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods traverse :: Applicative f0 => (a -> f0 b) -> Sum f g a -> f0 (Sum f g b) # sequenceA :: Applicative f0 => Sum f g (f0 a) -> f0 (Sum f g a) # mapM :: Monad m => (a -> m b) -> Sum f g a -> m (Sum f g b) # sequence :: Monad m => Sum f g (m a) -> m (Sum f g a) #
Traversable (Magma i t b)
Instance details Defined in Control.Lens.Internal.Magma Methods traverse :: Applicative f => (a -> f b0) -> Magma i t b a -> f (Magma i t b b0) # sequenceA :: Applicative f => Magma i t b (f a) -> f (Magma i t b a) # mapM :: Monad m => (a -> m b0) -> Magma i t b a -> m (Magma i t b b0) # sequence :: Monad m => Magma i t b (m a) -> m (Magma i t b a) #
Traversable f => Traversable (M1 i c f)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) # sequenceA :: Applicative f0 => M1 i c f (f0 a) -> f0 (M1 i c f a) # mapM :: Monad m => (a -> m b) -> M1 i c f a -> m (M1 i c f b) # sequence :: Monad m => M1 i c f (m a) -> m (M1 i c f a) #
(Traversable f, Traversable g) => Traversable (f :.: g)
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) #
(Traversable f, Traversable g) => Traversable (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods traverse :: Applicative f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) # sequenceA :: Applicative f0 => Compose f g (f0 a) -> f0 (Compose f g a) # mapM :: Monad m => (a -> m b) -> Compose f g a -> m (Compose f g b) # sequence :: Monad m => Compose f g (m a) -> m (Compose f g a) #
Bitraversable p => Traversable (WrappedBifunctor p a)
Instance details Defined in Data.Bifunctor.Wrapped Methods traverse :: Applicative f => (a0 -> f b) -> WrappedBifunctor p a a0 -> f (WrappedBifunctor p a b) # sequenceA :: Applicative f => WrappedBifunctor p a (f a0) -> f (WrappedBifunctor p a a0) # mapM :: Monad m => (a0 -> m b) -> WrappedBifunctor p a a0 -> m (WrappedBifunctor p a b) # sequence :: Monad m => WrappedBifunctor p a (m a0) -> m (WrappedBifunctor p a a0) #
Traversable g => Traversable (Joker g a)
Instance details Defined in Data.Bifunctor.Joker Methods traverse :: Applicative f => (a0 -> f b) -> Joker g a a0 -> f (Joker g a b) # sequenceA :: Applicative f => Joker g a (f a0) -> f (Joker g a a0) # mapM :: Monad m => (a0 -> m b) -> Joker g a a0 -> m (Joker g a b) # sequence :: Monad m => Joker g a (m a0) -> m (Joker g a a0) #
Bitraversable p => Traversable (Flip p a)
Instance details Defined in Data.Bifunctor.Flip Methods traverse :: Applicative f => (a0 -> f b) -> Flip p a a0 -> f (Flip p a b) # sequenceA :: Applicative f => Flip p a (f a0) -> f (Flip p a a0) # mapM :: Monad m => (a0 -> m b) -> Flip p a a0 -> m (Flip p a b) # sequence :: Monad m => Flip p a (m a0) -> m (Flip p a a0) #
Traversable (Clown f a :: * -> *)
Instance details Defined in Data.Bifunctor.Clown Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Clown f a a0 -> f0 (Clown f a b) # sequenceA :: Applicative f0 => Clown f a (f0 a0) -> f0 (Clown f a a0) # mapM :: Monad m => (a0 -> m b) -> Clown f a a0 -> m (Clown f a b) # sequence :: Monad m => Clown f a (m a0) -> m (Clown f a a0) #
(Traversable f, Bitraversable p) => Traversable (Tannen f p a)
Instance details Defined in Data.Bifunctor.Tannen Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Tannen f p a a0 -> f0 (Tannen f p a b) # sequenceA :: Applicative f0 => Tannen f p a (f0 a0) -> f0 (Tannen f p a a0) # mapM :: Monad m => (a0 -> m b) -> Tannen f p a a0 -> m (Tannen f p a b) # sequence :: Monad m => Tannen f p a (m a0) -> m (Tannen f p a a0) #
(Bitraversable p, Traversable g) => Traversable (Biff p f g a)
Instance details Defined in Data.Bifunctor.Biff Methods traverse :: Applicative f0 => (a0 -> f0 b) -> Biff p f g a a0 -> f0 (Biff p f g a b) # sequenceA :: Applicative f0 => Biff p f g a (f0 a0) -> f0 (Biff p f g a a0) # mapM :: Monad m => (a0 -> m b) -> Biff p f g a a0 -> m (Biff p f g a b) # sequence :: Monad m => Biff p f g a (m a0) -> m (Biff p f g a a0) #

for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b) #

for is traverse with its arguments flipped. For a version that ignores the results see for_.

mapAccumL :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c) #

The mapAccumL function behaves like a combination of fmap and foldl; it applies a function to each element of a structure, passing an accumulating parameter from left to right, and returning a final value of this accumulator together with the new structure.

mapAccumR :: Traversable t => (a -> b -> (a, c)) -> a -> t b -> (a, t c) #

The mapAccumR function behaves like a combination of fmap and foldr; it applies a function to each element of a structure, passing an accumulating parameter from right to left, and returning a final value of this accumulator together with the new structure.

traverseBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (a -> f b) -> t a -> f (t b) #

Traverse a container using its Traversable instance using explicitly provided Applicative operations. This is like traverse where the Applicative instance can be manually specified.

sequenceBy :: Traversable t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> t (f a) -> f (t a) #

Sequence a container using its Traversable instance using explicitly provided Applicative operations. This is like sequence where the Applicative instance can be manually specified.

Traversable1

class (Foldable1 t, Traversable t) => Traversable1 (t :: * -> *) where #

Minimal complete definition

traverse1 | sequence1

Methods

traverse1 :: Apply f => (a -> f b) -> t a -> f (t b) #

sequence1 :: Apply f => t (f b) -> f (t b) #

Instances

Traversable1 Par1
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Par1 a -> f (Par1 b) # sequence1 :: Apply f => Par1 (f b) -> f (Par1 b) #
Traversable1 Complex
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Complex a -> f (Complex b) # sequence1 :: Apply f => Complex (f b) -> f (Complex b) #
Traversable1 Min
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Min a -> f (Min b) # sequence1 :: Apply f => Min (f b) -> f (Min b) #
Traversable1 Max
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Max a -> f (Max b) # sequence1 :: Apply f => Max (f b) -> f (Max b) #
Traversable1 First
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> First a -> f (First b) # sequence1 :: Apply f => First (f b) -> f (First b) #
Traversable1 Last
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Last a -> f (Last b) # sequence1 :: Apply f => Last (f b) -> f (Last b) #
Traversable1 Identity
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Identity a -> f (Identity b) # sequence1 :: Apply f => Identity (f b) -> f (Identity b) #
Traversable1 Dual
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Dual a -> f (Dual b) # sequence1 :: Apply f => Dual (f b) -> f (Dual b) #
Traversable1 Sum
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Sum a -> f (Sum b) # sequence1 :: Apply f => Sum (f b) -> f (Sum b) #
Traversable1 Product
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Product a -> f (Product b) # sequence1 :: Apply f => Product (f b) -> f (Product b) #
Traversable1 NonEmpty
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) # sequence1 :: Apply f => NonEmpty (f b) -> f (NonEmpty b) #
Traversable1 Tree
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Tree a -> f (Tree b) # sequence1 :: Apply f => Tree (f b) -> f (Tree b) #
Traversable1 Log
Instance details Defined in Numeric.Log Methods traverse1 :: Apply f => (a -> f b) -> Log a -> f (Log b) # sequence1 :: Apply f => Log (f b) -> f (Log b) #
Traversable1 (V1 :: * -> *)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> V1 a -> f (V1 b) # sequence1 :: Apply f => V1 (f b) -> f (V1 b) #
Traversable1 ((,) a)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a0 -> f b) -> (a, a0) -> f (a, b) # sequence1 :: Apply f => (a, f b) -> f (a, b) #
Traversable1 f => Traversable1 (Cofree f)
Instance details Defined in Control.Comonad.Cofree Methods traverse1 :: Apply f0 => (a -> f0 b) -> Cofree f a -> f0 (Cofree f b) # sequence1 :: Apply f0 => Cofree f (f0 b) -> f0 (Cofree f b) #
Traversable1 f => Traversable1 (Free f)
Instance details Defined in Control.Monad.Free Methods traverse1 :: Apply f0 => (a -> f0 b) -> Free f a -> f0 (Free f b) # sequence1 :: Apply f0 => Free f (f0 b) -> f0 (Free f b) #
Traversable1 f => Traversable1 (Yoneda f)
Instance details Defined in Data.Functor.Yoneda Methods traverse1 :: Apply f0 => (a -> f0 b) -> Yoneda f a -> f0 (Yoneda f b) # sequence1 :: Apply f0 => Yoneda f (f0 b) -> f0 (Yoneda f b) #
Traversable1 f => Traversable1 (Lift f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Lift f a -> f0 (Lift f b) # sequence1 :: Apply f0 => Lift f (f0 b) -> f0 (Lift f b) #
Traversable1 f => Traversable1 (Rec1 f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) # sequence1 :: Apply f0 => Rec1 f (f0 b) -> f0 (Rec1 f b) #
Traversable1 f => Traversable1 (Alt f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) # sequence1 :: Apply f0 => Alt f (f0 b) -> f0 (Alt f b) #
Bitraversable1 p => Traversable1 (Join p)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a -> f b) -> Join p a -> f (Join p b) # sequence1 :: Apply f => Join p (f b) -> f (Join p b) #
Traversable1 f => Traversable1 (IdentityT f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> IdentityT f a -> f0 (IdentityT f b) # sequence1 :: Apply f0 => IdentityT f (f0 b) -> f0 (IdentityT f b) #
Traversable1 f => Traversable1 (Backwards f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Backwards f a -> f0 (Backwards f b) # sequence1 :: Apply f0 => Backwards f (f0 b) -> f0 (Backwards f b) #
Traversable1 (Tagged a)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a0 -> f b) -> Tagged a a0 -> f (Tagged a b) # sequence1 :: Apply f => Tagged a (f b) -> f (Tagged a b) #
Traversable1 f => Traversable1 (Reverse f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Reverse f a -> f0 (Reverse f b) # sequence1 :: Apply f0 => Reverse f (f0 b) -> f0 (Reverse f b) #
(Traversable1 f, Traversable1 g) => Traversable1 (f :+: g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) # sequence1 :: Apply f0 => (f :+: g) (f0 b) -> f0 ((f :+: g) b) #
(Traversable1 f, Traversable1 g) => Traversable1 (f :*: g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> (f :: g) a -> f0 ((f :: g) b) # sequence1 :: Apply f0 => (f :: g) (f0 b) -> f0 ((f :: g) b) #
(Traversable1 f, Traversable1 g) => Traversable1 (Product f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) # sequence1 :: Apply f0 => Product f g (f0 b) -> f0 (Product f g b) #
(Traversable1 f, Traversable1 g) => Traversable1 (Sum f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Sum f g a -> f0 (Sum f g b) # sequence1 :: Apply f0 => Sum f g (f0 b) -> f0 (Sum f g b) #
Traversable1 f => Traversable1 (M1 i c f)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) # sequence1 :: Apply f0 => M1 i c f (f0 b) -> f0 (M1 i c f b) #
(Traversable1 f, Traversable1 g) => Traversable1 (f :.: g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) # sequence1 :: Apply f0 => (f :.: g) (f0 b) -> f0 ((f :.: g) b) #
(Traversable1 f, Traversable1 g) => Traversable1 (Compose f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) # sequence1 :: Apply f0 => Compose f g (f0 b) -> f0 (Compose f g b) #
Traversable1 g => Traversable1 (Joker g a)
Instance details Defined in Data.Semigroup.Traversable.Class Methods traverse1 :: Apply f => (a0 -> f b) -> Joker g a a0 -> f (Joker g a b) # sequence1 :: Apply f => Joker g a (f b) -> f (Joker g a b) #

Bitraversable

class (Bifunctor t, Bifoldable t) => Bitraversable (t :: * -> * -> *) where #

Bitraversable identifies bifunctorial data structures whose elements can be traversed in order, performing Applicative or Monad actions at each element, and collecting a result structure with the same shape.

As opposed to Traversable data structures, which have one variety of element on which an action can be performed, Bitraversable data structures have two such varieties of elements.

A definition of bitraverse must satisfy the following laws:

naturality: bitraverse (t . f) (t . g) ≡ t . bitraverse f g for every applicative transformation t
identity: bitraverse Identity Identity ≡ Identity
composition: Compose . fmap (bitraverse g1 g2) . bitraverse f1 f2 ≡ traverse (Compose . fmap g1 . f1) (Compose . fmap g2 . f2)

where an applicative transformation is a function

t :: (Applicative f, Applicative g) => f a -> g a

preserving the Applicative operations:

t (pure x) = pure x
t (f <*> x) = t f <*> t x

and the identity functor Identity and composition functors Compose are defined as

newtype Identity a = Identity { runIdentity :: a }

instance Functor Identity where
  fmap f (Identity x) = Identity (f x)

instance Applicative Identity where
  pure = Identity
  Identity f <*> Identity x = Identity (f x)

newtype Compose f g a = Compose (f (g a))

instance (Functor f, Functor g) => Functor (Compose f g) where
  fmap f (Compose x) = Compose (fmap (fmap f) x)

instance (Applicative f, Applicative g) => Applicative (Compose f g) where
  pure = Compose . pure . pure
  Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)

Some simple examples are Either and '(,)':

instance Bitraversable Either where
  bitraverse f _ (Left x) = Left <$> f x
  bitraverse _ g (Right y) = Right <$> g y

instance Bitraversable (,) where
  bitraverse f g (x, y) = (,) <$> f x <*> g y

Bitraversable relates to its superclasses in the following ways:

bimap f g ≡ runIdentity . bitraverse (Identity . f) (Identity . g)
bifoldMap f g = getConst . bitraverse (Const . f) (Const . g)

These are available as bimapDefault and bifoldMapDefault respectively.

Since: base-4.10.0.0

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> t a b -> f (t c d) #

Evaluates the relevant functions at each element in the structure, running the action, and builds a new structure with the same shape, using the results produced from sequencing the actions.

bitraverse f g ≡ bisequenceA . bimap f g

For a version that ignores the results, see bitraverse_.

Since: base-4.10.0.0

Instances

Bitraversable Either	Since: base-4.10.0.0
Instance details Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Either a b -> f (Either c d) #
Bitraversable (,)	Since: base-4.10.0.0
Instance details Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (a, b) -> f (c, d) #
Bitraversable Arg	Since: base-4.10.0.0
Instance details Defined in Data.Semigroup Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) #
Bitraversable ((,,) x)	Since: base-4.10.0.0
Instance details Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, a, b) -> f (x, c, d) #
Bitraversable (Const :: * -> * -> *)	Since: base-4.10.0.0
Instance details Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const a b -> f (Const c d) #
Traversable f => Bitraversable (FreeF f)
Instance details Defined in Control.Monad.Trans.Free Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> FreeF f a b -> f0 (FreeF f c d) #
Traversable f => Bitraversable (CofreeF f)
Instance details Defined in Control.Comonad.Trans.Cofree Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> CofreeF f a b -> f0 (CofreeF f c d) #
Bitraversable (Tagged :: * -> * -> *)
Instance details Defined in Data.Tagged Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Tagged a b -> f (Tagged c d) #
Bitraversable (K1 i :: * -> * -> *)	Since: base-4.10.0.0
Instance details Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> K1 i a b -> f (K1 i c d) #
Bitraversable ((,,,) x y)	Since: base-4.10.0.0
Instance details Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, y, a, b) -> f (x, y, c, d) #
Bitraversable ((,,,,) x y z)	Since: base-4.10.0.0
Instance details Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, y, z, a, b) -> f (x, y, z, c, d) #
Bitraversable p => Bitraversable (WrappedBifunctor p)
Instance details Defined in Data.Bifunctor.Wrapped Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> WrappedBifunctor p a b -> f (WrappedBifunctor p c d) #
Traversable g => Bitraversable (Joker g :: * -> * -> *)
Instance details Defined in Data.Bifunctor.Joker Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Joker g a b -> f (Joker g c d) #
Bitraversable p => Bitraversable (Flip p)
Instance details Defined in Data.Bifunctor.Flip Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Flip p a b -> f (Flip p c d) #
Traversable f => Bitraversable (Clown f :: * -> * -> *)
Instance details Defined in Data.Bifunctor.Clown Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> Clown f a b -> f0 (Clown f c d) #
Bitraversable ((,,,,,) x y z w)	Since: base-4.10.0.0
Instance details Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, y, z, w, a, b) -> f (x, y, z, w, c, d) #
(Bitraversable p, Bitraversable q) => Bitraversable (Sum p q)
Instance details Defined in Data.Bifunctor.Sum Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Sum p q a b -> f (Sum p q c d) #
(Bitraversable f, Bitraversable g) => Bitraversable (Product f g)
Instance details Defined in Data.Bifunctor.Product Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> Product f g a b -> f0 (Product f g c d) #
Bitraversable ((,,,,,,) x y z w v)	Since: base-4.10.0.0
Instance details Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> (x, y, z, w, v, a, b) -> f (x, y, z, w, v, c, d) #
(Traversable f, Bitraversable p) => Bitraversable (Tannen f p)
Instance details Defined in Data.Bifunctor.Tannen Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> Tannen f p a b -> f0 (Tannen f p c d) #
(Bitraversable p, Traversable f, Traversable g) => Bitraversable (Biff p f g)
Instance details Defined in Data.Bifunctor.Biff Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> Biff p f g a b -> f0 (Biff p f g c d) #

bisequence :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b) #

Sequences all the actions in a structure, building a new structure with the same shape using the results of the actions. For a version that ignores the results, see bisequence_.

bisequence ≡ bitraverse id id

Since: base-4.10.0.0

bifor :: (Bitraversable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f (t c d) #

bifor is bitraverse with the structure as the first argument. For a version that ignores the results, see bifor_.

Since: base-4.10.0.0

bimapAccumL :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e) #

The bimapAccumL function behaves like a combination of bimap and bifoldl; it traverses a structure from left to right, threading a state of type a and using the given actions to compute new elements for the structure.

Since: base-4.10.0.0

bimapAccumR :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e) #

The bimapAccumR function behaves like a combination of bimap and bifoldl; it traverses a structure from right to left, threading a state of type a and using the given actions to compute new elements for the structure.

Since: base-4.10.0.0

Bitraversable1

class (Bifoldable1 t, Bitraversable t) => Bitraversable1 (t :: * -> * -> *) where #

Minimal complete definition

bitraverse1 | bisequence1

Methods

bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> t a c -> f (t b d) #

bisequence1 :: Apply f => t (f a) (f b) -> f (t a b) #

Instances

Bitraversable1 Either
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Either a c -> f (Either b d) # bisequence1 :: Apply f => Either (f a) (f b) -> f (Either a b) #
Bitraversable1 (,)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> (a, c) -> f (b, d) # bisequence1 :: Apply f => (f a, f b) -> f (a, b) #
Bitraversable1 Arg
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Arg a c -> f (Arg b d) # bisequence1 :: Apply f => Arg (f a) (f b) -> f (Arg a b) #
Bitraversable1 ((,,) x)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> (x, a, c) -> f (x, b, d) # bisequence1 :: Apply f => (x, f a, f b) -> f (x, a, b) #
Bitraversable1 (Const :: * -> * -> *)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Const a c -> f (Const b d) # bisequence1 :: Apply f => Const (f a) (f b) -> f (Const a b) #
Bitraversable1 (Tagged :: * -> * -> *)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Tagged a c -> f (Tagged b d) # bisequence1 :: Apply f => Tagged (f a) (f b) -> f (Tagged a b) #
Bitraversable1 ((,,,) x y)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> (x, y, a, c) -> f (x, y, b, d) # bisequence1 :: Apply f => (x, y, f a, f b) -> f (x, y, a, b) #
Bitraversable1 ((,,,,) x y z)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> (x, y, z, a, c) -> f (x, y, z, b, d) # bisequence1 :: Apply f => (x, y, z, f a, f b) -> f (x, y, z, a, b) #
Bitraversable1 p => Bitraversable1 (WrappedBifunctor p)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> WrappedBifunctor p a c -> f (WrappedBifunctor p b d) # bisequence1 :: Apply f => WrappedBifunctor p (f a) (f b) -> f (WrappedBifunctor p a b) #
Traversable1 g => Bitraversable1 (Joker g :: * -> * -> *)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Joker g a c -> f (Joker g b d) # bisequence1 :: Apply f => Joker g (f a) (f b) -> f (Joker g a b) #
Bitraversable1 p => Bitraversable1 (Flip p)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f => (a -> f b) -> (c -> f d) -> Flip p a c -> f (Flip p b d) # bisequence1 :: Apply f => Flip p (f a) (f b) -> f (Flip p a b) #
Traversable1 f => Bitraversable1 (Clown f :: * -> * -> *)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f0 => (a -> f0 b) -> (c -> f0 d) -> Clown f a c -> f0 (Clown f b d) # bisequence1 :: Apply f0 => Clown f (f0 a) (f0 b) -> f0 (Clown f a b) #
(Bitraversable1 f, Bitraversable1 g) => Bitraversable1 (Product f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f0 => (a -> f0 b) -> (c -> f0 d) -> Product f g a c -> f0 (Product f g b d) # bisequence1 :: Apply f0 => Product f g (f0 a) (f0 b) -> f0 (Product f g a b) #
(Traversable1 f, Bitraversable1 p) => Bitraversable1 (Tannen f p)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f0 => (a -> f0 b) -> (c -> f0 d) -> Tannen f p a c -> f0 (Tannen f p b d) # bisequence1 :: Apply f0 => Tannen f p (f0 a) (f0 b) -> f0 (Tannen f p a b) #
(Bitraversable1 p, Traversable1 f, Traversable1 g) => Bitraversable1 (Biff p f g)
Instance details Defined in Data.Semigroup.Traversable.Class Methods bitraverse1 :: Apply f0 => (a -> f0 b) -> (c -> f0 d) -> Biff p f g a c -> f0 (Biff p f g b d) # bisequence1 :: Apply f0 => Biff p f g (f0 a) (f0 b) -> f0 (Biff p f g a b) #

Default implementations

fmapDefault :: Traversable t => (a -> b) -> t a -> t b #

This function may be used as a value for fmap in a Functor instance, provided that traverse is defined. (Using fmapDefault with a Traversable instance defined only by sequenceA will result in infinite recursion.)

fmapDefault f ≡ runIdentity . traverse (Identity . f)

foldMapDefault :: (Traversable t, Monoid m) => (a -> m) -> t a -> m #

This function may be used as a value for foldMap in a Foldable instance.

foldMapDefault f ≡ getConst . traverse (Const . f)

bimapDefault :: Bitraversable t => (a -> b) -> (c -> d) -> t a c -> t b d #

A default definition of bimap in terms of the Bitraversable operations.

bimapDefault f g ≡
     runIdentity . bitraverse (Identity . f) (Identity . g)

Since: base-4.10.0.0

bifoldMapDefault :: (Bitraversable t, Monoid m) => (a -> m) -> (b -> m) -> t a b -> m #

A default definition of bifoldMap in terms of the Bitraversable operations.

bifoldMapDefault f g ≡
    getConst . bitraverse (Const . f) (Const . g)

Since: base-4.10.0.0

bifoldMap1Default :: (Bitraversable1 t, Semigroup m) => (a -> m) -> (b -> m) -> t a b -> m #