# Data.Traversable

- Package
- purescript-foldable-traversable
- Repository
- purescript/purescript-foldable-traversable

### #TraversableSource

`class (Functor t, Foldable t) <= Traversable t where`

`Traversable`

represents data structures which can be *traversed*,
accumulating results and effects in some `Applicative`

functor.

`traverse`

runs an action for every element in a data structure, and accumulates the results.`sequence`

runs the actions*contained*in a data structure, and accumulates the results.

The `traverse`

and `sequence`

functions should be compatible in the
following sense:

`traverse f xs = sequence (f <$> xs)`

`sequence = traverse id`

`Traversable`

instances should also be compatible with the corresponding
`Foldable`

instances, in the following sense:

`foldMap f = runConst <<< traverse (Const <<< f)`

Default implementations are provided by the following functions:

`traverseDefault`

`sequenceDefault`

#### Members

`sequence :: forall a m. Applicative m => t (m a) -> m (t a)`

`traverse :: forall a b m. Applicative m => (a -> m b) -> t a -> m (t b)`

#### Instances

### #traverseDefaultSource

`traverseDefault :: forall t a b m. Traversable t => Applicative m => (a -> m b) -> t a -> m (t b)`

A default implementation of `traverse`

using `sequence`

and `map`

.

### #sequenceDefaultSource

`sequenceDefault :: forall t a m. Traversable t => Applicative m => t (m a) -> m (t a)`

A default implementation of `sequence`

using `traverse`

.

### #forSource

`for :: forall a b m t. Applicative m => Traversable t => t a -> (a -> m b) -> m (t b)`

A version of `traverse`

with its arguments flipped.

This can be useful when running an action written using do notation for every element in a data structure:

For example:

```
for [1, 2, 3] \n -> do
print n
return (n * n)
```

### #scanlSource

`scanl :: forall a b f. Traversable f => (b -> a -> b) -> b -> f a -> f b`

Fold a data structure from the left, keeping all intermediate results
instead of only the final result. Note that the initial value does not
appear in the result (unlike Haskell's `Prelude.scanl`

).

```
scanl (+) 0 [1,2,3] = [1,3,6]
scanl (-) 10 [1,2,3] = [9,7,4]
```

### #mapAccumLSource

`mapAccumL :: forall a b s f. Traversable f => (s -> a -> Accum s b) -> s -> f a -> Accum s (f b)`

Fold a data structure from the left, keeping all intermediate results instead of only the final result.

Unlike `scanl`

, `mapAccumL`

allows the type of accumulator to differ
from the element type of the final data structure.

### #scanrSource

`scanr :: forall a b f. Traversable f => (a -> b -> b) -> b -> f a -> f b`

Fold a data structure from the right, keeping all intermediate results
instead of only the final result. Note that the initial value does not
appear in the result (unlike Haskell's `Prelude.scanr`

).

```
scanr (+) 0 [1,2,3] = [1,3,6]
scanr (flip (-)) 10 [1,2,3] = [4,5,7]
```

### #mapAccumRSource

`mapAccumR :: forall a b s f. Traversable f => (s -> a -> Accum s b) -> s -> f a -> Accum s (f b)`

Fold a data structure from the right, keeping all intermediate results instead of only the final result.

Unlike `scanr`

, `mapAccumR`

allows the type of accumulator to differ
from the element type of the final data structure.

## Re-exports from **Data.**Foldable

### #FoldableSource

`class Foldable f where`

`Foldable`

represents data structures which can be *folded*.

`foldr`

folds a structure from the right`foldl`

folds a structure from the left`foldMap`

folds a structure by accumulating values in a`Monoid`

Default implementations are provided by the following functions:

`foldrDefault`

`foldlDefault`

`foldMapDefaultR`

`foldMapDefaultL`

Note: some combinations of the default implementations are unsafe to use together - causing a non-terminating mutually recursive cycle. These combinations are documented per function.

#### Members

`foldMap :: forall a m. Monoid m => (a -> m) -> f a -> m`

`foldl :: forall a b. (b -> a -> b) -> b -> f a -> b`

`foldr :: forall a b. (a -> b -> b) -> b -> f a -> b`

#### Instances

### #traverse_Source

`traverse_ :: forall a b f m. Applicative m => Foldable f => (a -> m b) -> f a -> m Unit`

Traverse a data structure, performing some effects encoded by an
`Applicative`

functor at each value, ignoring the final result.

For example:

```
traverse_ print [1, 2, 3]
```

### #sequence_Source

`sequence_ :: forall a f m. Applicative m => Foldable f => f (m a) -> m Unit`

Perform all of the effects in some data structure in the order
given by the `Foldable`

instance, ignoring the final result.

For example:

```
sequence_ [ trace "Hello, ", trace " world!" ]
```

### #orSource

`or :: forall a f. Foldable f => HeytingAlgebra a => f a -> a`

The disjunction of all the values in a data structure. When specialized
to `Boolean`

, this function will test whether any of the values in a data
structure is `true`

.

### #intercalateSource

`intercalate :: forall f m. Foldable f => Monoid m => m -> f m -> m`

Fold a data structure, accumulating values in some `Monoid`

,
combining adjacent elements using the specified separator.

### #for_Source

`for_ :: forall a b f m. Applicative m => Foldable f => f a -> (a -> m b) -> m Unit`

A version of `traverse_`

with its arguments flipped.

This can be useful when running an action written using do notation for every element in a data structure:

For example:

```
for_ [1, 2, 3] \n -> do
print n
trace "squared is"
print (n * n)
```

### #foldrDefaultSource

`foldrDefault :: forall f a b. Foldable f => (a -> b -> b) -> b -> f a -> b`

A default implementation of `foldr`

using `foldMap`

.

Note: when defining a `Foldable`

instance, this function is unsafe to use
in combination with `foldMapDefaultR`

.

### #foldlDefaultSource

`foldlDefault :: forall f a b. Foldable f => (b -> a -> b) -> b -> f a -> b`

A default implementation of `foldl`

using `foldMap`

.

Note: when defining a `Foldable`

instance, this function is unsafe to use
in combination with `foldMapDefaultL`

.

### #foldMapDefaultRSource

`foldMapDefaultR :: forall f a m. Foldable f => Monoid m => (a -> m) -> f a -> m`

A default implementation of `foldMap`

using `foldr`

.

Note: when defining a `Foldable`

instance, this function is unsafe to use
in combination with `foldrDefault`

.

### #foldMapDefaultLSource

`foldMapDefaultL :: forall f a m. Foldable f => Monoid m => (a -> m) -> f a -> m`

A default implementation of `foldMap`

using `foldl`

.

Note: when defining a `Foldable`

instance, this function is unsafe to use
in combination with `foldlDefault`

.

### #anySource

`any :: forall a b f. Foldable f => HeytingAlgebra b => (a -> b) -> f a -> b`

`any f`

is the same as `or <<< map f`

; map a function over the structure,
and then get the disjunction of the results.

### #andSource

`and :: forall a f. Foldable f => HeytingAlgebra a => f a -> a`

The conjunction of all the values in a data structure. When specialized
to `Boolean`

, this function will test whether all of the values in a data
structure are `true`

.

### #allSource

`all :: forall a b f. Foldable f => HeytingAlgebra b => (a -> b) -> f a -> b`

`all f`

is the same as `and <<< map f`

; map a function over the structure,
and then get the conjunction of the results.