Safe Haskell | None |
---|---|
Language | Haskell2010 |
- class (Functor t, Foldable t) => Traversable t where
- traverse :: Traversable t => forall f a b. Applicative f => (a -> f b) -> t a -> f (t b)
- traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()
- sequenceA :: Traversable t => forall f a. Applicative f => t (f a) -> f (t a)
- sequence :: (Traversable t, Applicative f) => t (f a) -> f (t a)
- sequence_ :: (Foldable t, Applicative f) => t (f a) -> f ()
- for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)
- for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f ()
- 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)
- zipInto :: (Traversable t, Foldable f) => (a -> Maybe b -> c) -> t a -> f b -> t c
The Traversable
class
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 .
for every applicative transformationtraverse
f =traverse
(t . f)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 .
for every applicative transformationsequenceA
=sequenceA
.fmap
tt
- 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.
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
).
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_
.
traverse :: Traversable t => forall f a b. 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_
.
traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f () #
Map each element of a structure to an action, evaluate these
actions from left to right, and ignore the results. For a version
that doesn't ignore the results see traverse
.
sequenceA :: Traversable t => forall f a. 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_
.
sequence :: (Traversable t, Applicative f) => t (f a) -> f (t a) Source #
Evaluate each action in the structure from left to right, and
and collect the results. For a version that ignores the results
see sequence_
.
sequence_ :: (Foldable t, Applicative f) => t (f a) -> f () Source #
Evaluate each action in the structure from left to right, and
ignore the results. For a version that doesn't ignore the results
see sequence
.
Utility functions
for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b) #
for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f () #
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) #