Data.Foldable

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

• foldr :: forall a b. (a -> b -> b) -> b -> f a -> b
• foldl :: forall a b. (b -> a -> b) -> b -> f a -> b
• foldMap :: forall a m. Monoid m => (a -> m) -> f a -> m

Instances

• Foldable Array
• Foldable Maybe
• Foldable First
• Foldable Last
• Foldable Additive
• Foldable Dual
• Foldable Disj
• Foldable Conj
• Foldable Multiplicative

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.

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.

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.

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.

fold :: forall f m. Foldable f => Monoid m => f m -> m

Fold a data structure, accumulating values in some Monoid.

foldM :: forall f m a b. Foldable f => Monad m => (a -> b -> m a) -> a -> f b -> m a

Similar to 'foldl', but the result is encapsulated in a monad.

Note: this function is not generally stack-safe, e.g., for monads which build up thunks a la Eff.

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]

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)

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!" ]

oneOf :: forall f g a. Foldable f => Plus g => f (g a) -> g a

Combines a collection of elements using the Alt operation.

oneOfMap :: forall f g a b. Foldable f => Plus g => (a -> g b) -> f a -> g b

Folds a structure into some Plus.

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 example:

> intercalate ", " ["Lorem", "ipsum", "dolor"]
= "Lorem, ipsum, dolor"

> intercalate "*" ["a", "b", "c"]
= "a*b*c"

> intercalate [1] [[2, 3], [4, 5], [6, 7]]
= [2, 3, 1, 4, 5, 1, 6, 7]

surroundMap :: forall f a m. Foldable f => Semigroup m => m -> (a -> m) -> f a -> m

foldMap but with each element surrounded by some fixed value.

For example:

> surroundMap "*" show []
= "*"

> surroundMap "*" show [1]
= "*1*"

> surroundMap "*" show [1, 2]
= "*1*2*"

> surroundMap "*" show [1, 2, 3]
= "*1*2*3*"

surround :: forall f m. Foldable f => Semigroup m => m -> f m -> m

fold but with each element surrounded by some fixed value.

For example:

> surround "*" []
= "*"

> surround "*" ["1"]
= "*1*"

> surround "*" ["1", "2"]
= "*1*2*"

> surround "*" ["1", "2", "3"]
= "*1*2*3*"

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.

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.

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.

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.

sum :: forall a f. Foldable f => Semiring a => f a -> a

Find the sum of the numeric values in a data structure.

product :: forall a f. Foldable f => Semiring a => f a -> a

Find the product of the numeric values in a data structure.

elem :: forall a f. Foldable f => Eq a => a -> f a -> Boolean

Test whether a value is an element of a data structure.

notElem :: forall a f. Foldable f => Eq a => a -> f a -> Boolean

Test whether a value is not an element of a data structure.

indexl :: forall a f. Foldable f => Int -> f a -> Maybe a

Try to get nth element from the left in a data structure

indexr :: forall a f. Foldable f => Int -> f a -> Maybe a

Try to get nth element from the right in a data structure

find :: forall a f. Foldable f => (a -> Boolean) -> f a -> Maybe a

Try to find an element in a data structure which satisfies a predicate.

findMap :: forall a b f. Foldable f => (a -> Maybe b) -> f a -> Maybe b

Try to find an element in a data structure which satisfies a predicate mapping.

maximum :: forall a f. Ord a => Foldable f => f a -> Maybe a

Find the largest element of a structure, according to its Ord instance.

maximumBy :: forall a f. Foldable f => (a -> a -> Ordering) -> f a -> Maybe a

Find the largest element of a structure, according to a given comparison function. The comparison function should represent a total ordering (see the Ord type class laws); if it does not, the behaviour is undefined.

minimum :: forall a f. Ord a => Foldable f => f a -> Maybe a

Find the smallest element of a structure, according to its Ord instance.

minimumBy :: forall a f. Foldable f => (a -> a -> Ordering) -> f a -> Maybe a

Find the smallest element of a structure, according to a given comparison function. The comparison function should represent a total ordering (see the Ord type class laws); if it does not, the behaviour is undefined.

null :: forall a f. Foldable f => f a -> Boolean

Test whether the structure is empty. Optimized for structures that are similar to cons-lists, because there is no general way to do better.

length :: forall a b f. Foldable f => Semiring b => f a -> b

Returns the size/length of a finite structure. Optimized for structures that are similar to cons-lists, because there is no general way to do better.