foldl-1.0.10: Composable, streaming, and efficient left folds

Safe Haskell Trustworthy Haskell98

Control.Foldl

Description

This module provides efficient and streaming left folds that you can combine using `Applicative` style.

Import this module qualified to avoid clashing with the Prelude:

````>>> ````import qualified Control.Foldl as L
``````

Use `fold` to apply a `Fold` to a list:

````>>> ````L.fold L.sum [1..100]
```5050
```

`Fold`s are `Applicative`s, so you can combine them using `Applicative` combinators:

````>>> ````import Control.Applicative
````>>> ````let average = (/) <\$> L.sum <*> L.genericLength
``````

These combined folds will still traverse the list only once, streaming efficiently over the list in constant space without space leaks:

````>>> ````L.fold average [1..10000000]
```5000000.5
`>>> ````L.fold ((,) <\$> L.minimum <*> L.maximum) [1..10000000]
```(Just 1,Just 10000000)
```

Synopsis

# Fold Types

data Fold a b Source

Efficient representation of a left fold that preserves the fold's step function, initial accumulator, and extraction function

This allows the `Applicative` instance to assemble derived folds that traverse the container only once

A '`Fold` a b' processes elements of type a and results in a value of type b.

Constructors

 forall x . Fold (x -> a -> x) x (x -> b) `Fold ` ` step ` ` initial ` ` extract`

Instances

 Functor (Fold a) Applicative (Fold a) Floating b => Floating (Fold a b) Fractional b => Fractional (Fold a b) Num b => Num (Fold a b) Monoid b => Monoid (Fold a b)

data FoldM m a b Source

Like `Fold`, but monadic.

A '`FoldM` m a b' processes elements of type a and results in a monadic value of type m b.

Constructors

 forall x . FoldM (x -> a -> m x) (m x) (x -> m b) `FoldM ` ` step ` ` initial ` ` extract`

Instances

 Monad m => Functor (FoldM m a) Monad m => Applicative (FoldM m a) (Monad m, Floating b) => Floating (FoldM m a b) (Monad m, Fractional b) => Fractional (FoldM m a b) (Monad m, Num b) => Num (FoldM m a b) (Monoid b, Monad m) => Monoid (FoldM m a b)

# Folding

fold :: Foldable f => Fold a b -> f a -> b Source

Apply a strict left `Fold` to a `Foldable` container

foldM :: (Foldable f, Monad m) => FoldM m a b -> f a -> m b Source

Like `fold`, but monadic

scan :: Fold a b -> [a] -> [b] Source

Convert a strict left `Fold` into a scan

# Folds

mconcat :: Monoid a => Fold a a Source

Fold all values within a container using `mappend` and `mempty`

foldMap :: Monoid w => (a -> w) -> (w -> b) -> Fold a b Source

Convert a "`foldMap`" to a `Fold`

head :: Fold a (Maybe a) Source

Get the first element of a container or return `Nothing` if the container is empty

last :: Fold a (Maybe a) Source

Get the last element of a container or return `Nothing` if the container is empty

lastDef :: a -> Fold a a Source

Get the last element of a container or return a default value if the container is empty

Returns `True` if the container is empty, `False` otherwise

Return the length of the container

Returns `True` if all elements are `True`, `False` otherwise

Returns `True` if any element is `True`, `False` otherwise

all :: (a -> Bool) -> Fold a Bool Source

`(all predicate)` returns `True` if all elements satisfy the predicate, `False` otherwise

any :: (a -> Bool) -> Fold a Bool Source

`(any predicate)` returns `True` if any element satisfies the predicate, `False` otherwise

sum :: Num a => Fold a a Source

Computes the sum of all elements

product :: Num a => Fold a a Source

Computes the product all elements

maximum :: Ord a => Fold a (Maybe a) Source

Computes the maximum element

minimum :: Ord a => Fold a (Maybe a) Source

Computes the minimum element

elem :: Eq a => a -> Fold a Bool Source

`(elem a)` returns `True` if the container has an element equal to `a`, `False` otherwise

notElem :: Eq a => a -> Fold a Bool Source

`(notElem a)` returns `False` if the container has an element equal to `a`, `True` otherwise

find :: (a -> Bool) -> Fold a (Maybe a) Source

`(find predicate)` returns the first element that satisfies the predicate or `Nothing` if no element satisfies the predicate

index :: Int -> Fold a (Maybe a) Source

`(index n)` returns the `n`th element of the container, or `Nothing` if the container has an insufficient number of elements

elemIndex :: Eq a => a -> Fold a (Maybe Int) Source

`(elemIndex a)` returns the index of the first element that equals `a`, or `Nothing` if no element matches

findIndex :: (a -> Bool) -> Fold a (Maybe Int) Source

`(findIndex predicate)` returns the index of the first element that satisfies the predicate, or `Nothing` if no element satisfies the predicate

random :: FoldM IO a (Maybe a) Source

Pick a random element, using reservoir sampling

# Generic Folds

genericLength :: Num b => Fold a b Source

Like `length`, except with a more general `Num` return value

genericIndex :: Integral i => i -> Fold a (Maybe a) Source

Like `index`, except with a more general `Integral` argument

# Container folds

list :: Fold a [a] Source

Fold all values into a list

revList :: Fold a [a] Source

Fold all values into a list, in reverse order

nub :: Ord a => Fold a [a] Source

O(n log n). Fold values into a list with duplicates removed, while preserving their first occurrences

eqNub :: Eq a => Fold a [a] Source

O(n^2). Fold values into a list with duplicates removed, while preserving their first occurrences

set :: Ord a => Fold a (Set a) Source

Fold values into a set

vector :: (PrimMonad m, Vector v a) => FoldM m a (v a) Source

Fold all values into a vector

# Utilities

`purely` and `impurely` allow you to write folds compatible with the `foldl` library without incurring a `foldl` dependency. Write your fold to accept three parameters corresponding to the step function, initial accumulator, and extraction function and then users can upgrade your function to accept a `Fold` or `FoldM` using the `purely` or `impurely` combinators.

For example, the `pipes` library implements a `foldM` function in `Pipes.Prelude` with the following type:

```foldM
:: Monad m
=> (x -> a -> m x) -> m x -> (x -> m b) -> Producer a m () -> m b```

`foldM` is set up so that you can wrap it with `impurely` to accept a `FoldM` instead:

`impurely foldM :: Monad m => FoldM m a b -> Producer a m () -> m b`

purely :: (forall x. (x -> a -> x) -> x -> (x -> b) -> r) -> Fold a b -> r Source

Upgrade a fold to accept the `Fold` type

impurely :: Monad m => (forall x. (x -> a -> m x) -> m x -> (x -> m b) -> r) -> FoldM m a b -> r Source

Upgrade a monadic fold to accept the `FoldM` type

generalize :: Monad m => Fold a b -> FoldM m a b Source

Generalize a `Fold` to a `FoldM`

```generalize (pure r) = pure r

generalize (f <*> x) = generalize f <*> generalize x```

simplify :: FoldM Identity a b -> Fold a b Source

Simplify a pure `FoldM` to a `Fold`

```simplify (pure r) = pure r

simplify (f <*> x) = simplify f <*> simplify x```

_Fold1 :: (a -> a -> a) -> Fold a (Maybe a) Source

`_Fold1 step` returns a new `Fold` using just a step function that has the same type for the accumulator and the element. The result type is the accumulator type wrapped in `Maybe`. The initial accumulator is retrieved from the `Foldable`, the result is `None` for empty containers.

premap :: (a -> b) -> Fold b r -> Fold a r Source

`(premap f folder)` returns a new `Fold` where f is applied at each step

`fold (premap f folder) list = fold folder (map f list)`
````>>> ````fold (premap Sum mconcat) [1..10]
```Sum {getSum = 55}
```
````>>> ````fold mconcat (map Sum [1..10])
```Sum {getSum = 55}
```
```premap id = id

premap (f . g) = premap g . premap f```
```premap k (pure r) = pure r

premap k (f <*> x) = premap k f <*> premap k x```

premapM :: Monad m => (a -> b) -> FoldM m b r -> FoldM m a r Source

`(premapM f folder)` returns a new `FoldM` where f is applied to each input element

`foldM (premapM f folder) list = foldM folder (map f list)`
```premapM id = id

premapM (f . g) = premap g . premap f```
```premapM k (pure r) = pure r

premapM k (f <*> x) = premapM k f <*> premapM k x```

pretraverse :: Traversal' a b -> Fold b r -> Fold a r Source

`(pretraverse t folder)` traverses each incoming element using `Traversal'` `t` and folds every target of the `Traversal'`

````>>> ````fold (pretraverse traverse sum) [[1..5],[6..10]]
```55
```
````>>> ````fold (pretraverse (traverse.traverse) sum) [[Nothing, Just 2, Just 7],[Just 13, Nothing, Just 20]]
```42
```
````>>> ````fold (pretraverse (filtered even) sum) [1,3,5,7,21,21]
```42
```
````>>> ````fold (pretraverse _2 mconcat) [(1,"Hello "),(2,"World"),(3,"!")]
```"Hello World!"
```
```pretraverse id = id

pretraverse (f . g) = pretraverse f . pretraverse g```
```pretraverse t (pure r) = pure r

pretraverse t (f <*> x) = pretraverse t f <*> pretraverse t x```

pretraverseM :: Monad m => Traversal' a b -> FoldM m b r -> FoldM m a r Source

`(pretraverseM t folder)` traverses each incoming element using `Traversal'` `t` and folds every target of the `Traversal'`

```pretraverseM id = id

pretraverseM (f . g) = pretraverseM f . pretraverseM g```
```pretraverseM t (pure r) = pure r

pretraverseM t (f <*> x) = pretraverseM t f <*> pretraverseM t x```

# Re-exports

`Control.Monad.Primitive` re-exports the `PrimMonad` type class

`Data.Foldable` re-exports the `Foldable` type class

`Data.Vector.Generic` re-exports the `Vector` type class