| Copyright | Conor McBride and Ross Paterson 2005 |
|---|---|
| License | BSD-style (see the LICENSE file in the distribution) |
| Maintainer | libraries@haskell.org |
| Stability | stable |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
GHC.Internal.Data.Traversable
Description
Class of data structures that can be traversed from left to right, performing an action on each element. Instances are expected to satisfy the listed laws.
Synopsis
- class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
- sequenceA :: Applicative f => t (f a) -> f (t a)
- mapM :: Monad m => (a -> m b) -> t a -> m (t b)
- sequence :: Monad m => t (m a) -> m (t a)
- for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)
- forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b)
- forAccumM :: (Monad m, Traversable t) => s -> t a -> (s -> a -> m (s, b)) -> m (s, t b)
- mapAccumL :: Traversable t => (s -> a -> (s, b)) -> s -> t a -> (s, t b)
- mapAccumR :: Traversable t => (s -> a -> (s, b)) -> s -> t a -> (s, t b)
- mapAccumM :: (Monad m, Traversable t) => (s -> a -> m (s, b)) -> s -> t a -> m (s, t b)
- fmapDefault :: Traversable t => (a -> b) -> t a -> t b
- foldMapDefault :: (Traversable t, Monoid m) => (a -> m) -> t a -> m
The Traversable class
class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where #
Functors representing data structures that can be transformed to
structures of the same shape by performing an Applicative (or,
therefore, Monad) action on each element from left to right.
A more detailed description of what same shape means, the various methods, how traversals are constructed, and example advanced use-cases can be found in the Overview section of Data.Traversable.
For the class laws see the Laws section of Data.Traversable.
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_.
Examples
Basic usage:
In the first two examples we show each evaluated action mapping to the output structure.
>>>traverse Just [1,2,3,4]Just [1,2,3,4]
>>>traverse id [Right 1, Right 2, Right 3, Right 4]Right [1,2,3,4]
In the next examples, we show that Nothing and Left values short
circuit the created structure.
>>>traverse (const Nothing) [1,2,3,4]Nothing
>>>traverse (\x -> if odd x then Just x else Nothing) [1,2,3,4]Nothing
>>>traverse id [Right 1, Right 2, Right 3, Right 4, Left 0]Left 0
sequenceA :: Applicative f => t (f a) -> f (t a) #
Evaluate each action in the structure from left to right, and
collect the results. For a version that ignores the results
see sequenceA_.
Examples
Basic usage:
For the first two examples we show sequenceA fully evaluating a a structure and collecting the results.
>>>sequenceA [Just 1, Just 2, Just 3]Just [1,2,3]
>>>sequenceA [Right 1, Right 2, Right 3]Right [1,2,3]
The next two example show Nothing and Just will short circuit
the resulting structure if present in the input. For more context,
check the Traversable instances for Either and Maybe.
>>>sequenceA [Just 1, Just 2, Just 3, Nothing]Nothing
>>>sequenceA [Right 1, Right 2, Right 3, Left 4]Left 4
mapM :: Monad m => (a -> m b) -> t a -> m (t b) #
Map each element of a structure to a monadic action, evaluate
these actions from left to right, and collect the results. For
a version that ignores the results see mapM_.
Examples
sequence :: Monad m => t (m a) -> m (t a) #
Evaluate each monadic action in the structure from left to
right, and collect the results. For a version that ignores the
results see sequence_.
Examples
Basic usage:
The first two examples are instances where the input and
and output of sequence are isomorphic.
>>>sequence $ Right [1,2,3,4][Right 1,Right 2,Right 3,Right 4]
>>>sequence $ [Right 1,Right 2,Right 3,Right 4]Right [1,2,3,4]
The following examples demonstrate short circuit behavior
for sequence.
>>>sequence $ Left [1,2,3,4]Left [1,2,3,4]
>>>sequence $ [Left 0, Right 1,Right 2,Right 3,Right 4]Left 0
Instances
Utility functions
for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b) #
forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b) #
forAccumM :: (Monad m, Traversable t) => s -> t a -> (s -> a -> m (s, b)) -> m (s, t b) #
mapAccumL :: Traversable t => (s -> a -> (s, b)) -> s -> t a -> (s, t b) #
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.
Examples
Basic usage:
>>>mapAccumL (\a b -> (a + b, a)) 0 [1..10](55,[0,1,3,6,10,15,21,28,36,45])
>>>mapAccumL (\a b -> (a <> show b, a)) "0" [1..5]("012345",["0","01","012","0123","01234"])
mapAccumR :: Traversable t => (s -> a -> (s, b)) -> s -> t a -> (s, t b) #
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.
Examples
Basic usage:
>>>mapAccumR (\a b -> (a + b, a)) 0 [1..10](55,[54,52,49,45,40,34,27,19,10,0])
>>>mapAccumR (\a b -> (a <> show b, a)) "0" [1..5]("054321",["05432","0543","054","05","0"])
mapAccumM :: (Monad m, Traversable t) => (s -> a -> m (s, b)) -> s -> t a -> m (s, t b) #
The mapAccumM function behaves like a combination of mapM and
mapAccumL that traverses the structure while evaluating the actions
and passing an accumulating parameter from left to right.
It returns a final value of this accumulator together with the new structure.
The accumulator is often used for caching the intermediate results of a computation.
Examples
Basic usage:
>>>let expensiveDouble a = putStrLn ("Doubling " <> show a) >> pure (2 * a)>>>:{mapAccumM (\cache a -> case lookup a cache of Nothing -> expensiveDouble a >>= \double -> pure ((a, double):cache, double) Just double -> pure (cache, double) ) [] [1, 2, 3, 1, 2, 3] :} Doubling 1 Doubling 2 Doubling 3 ([(3,6),(2,4),(1,2)],[2,4,6,2,4,6])
Since: base-4.18.0.0
General definitions for superclass methods
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.)
fmapDefaultf ≡runIdentity.traverse(Identity. f)
foldMapDefault :: (Traversable t, Monoid m) => (a -> m) -> t a -> m #