Composable, streaming, and efficient left folds.

This library provides strict left folds that stream in constant memory, and you can combine folds using Applicative style to derive new folds. Derived folds still traverse the container just once and are often as efficient as hand-written folds.

foldl

Use this foldl library when you want to compute multiple folds over a collection in one pass over the data without space leaks.

For example, suppose that you want to simultaneously compute the sum of the list and the length of the list. Many Haskell beginners might write something like this:

sumAndLength :: Num a => [a] -> (a, Int)
sumAndLength xs = (sum xs, length xs)

However, this solution will leak space because it goes over the list in two passes. If you demand the result of sum the Haskell runtime will materialize the entire list. However, the runtime cannot garbage collect the list because the list is still required for the call to length.

Usually people work around this by hand-writing a strict left fold that looks something like this:

{-# LANGUAGE BangPatterns #-}

import Data.List (foldl')

sumAndLength :: Num a => [a] -> (a, Int)
sumAndLength xs = foldl' step (0, 0) xs
  where
    step (x, y) n = (x + n, y + 1)

That now goes over the list in one pass, but will still leak space because the tuple is not strict in both fields! You have to define a strict Pair type to fix this:

{-# LANGUAGE BangPatterns #-}

import Data.List (foldl')

data Pair a b = Pair !a !b

sumAndLength :: Num a => [a] -> (a, Int)
sumAndLength xs = done (foldl' step (Pair 0 0) xs)
  where
    step (Pair x y) n = Pair (x + n) (y + 1)

    done (Pair x y) = (x, y)

However, this is not satisfactory because you have to reimplement the guts of every fold that you care about and also define a custom strict data type for your fold. Hand-writing the step function, accumulator, and strict data type for every fold that you want to use gets tedious fast. For example, implementing something like reservoir sampling over and over is very error prone.

What if you just stored the step function and accumulator for each individual fold and let some high-level library do the combining for you? That's exactly what this library does! Using this library you can instead write:

import qualified Control.Foldl as Fold

sumAndLength :: Num a => [a] -> (a, Int)
sumAndLength xs = Fold.fold ((,) <$> Fold.sum <*> Fold.length) xs

-- or, more concisely:
sumAndLength = Fold.fold ((,) <$> Fold.sum <*> Fold.length)

To see how this works, the Fold.sum value is just a datatype storing the step function and the starting state (and a final extraction function):

sum :: Num a => Fold a a
sum = Fold (+) 0 id

Same thing for the Fold.length value:

length :: Fold a Int
length = Fold (\n _ -> n + 1) 0 id

... and the Applicative operators combine them into a new datatype storing the composite step function and starting state:

(,) <$> Fold.sum <*> Fold.length = Fold step (Pair 0 0) done
  where
    step (Pair x y) n = Pair (x + n) (y + 1)

    done (Pair x y) = (x, y)

... and then fold just transforms that to a strict left fold:

fold (Fold step begin done) = done (foldl' step begin)

Since we preserve the step function and accumulator, we can use the Fold type to fold things other than pure collections. For example, we can fold a Producer from pipes using the same Fold:

Fold.purely Pipes.Prelude.fold ((,) <$> sum <*> length)
    :: (Monad m, Num a) => Producer a m () -> m (a, Int)

To learn more about this library, read the documentation in the main Control.Foldl module.

Quick start

Install the stack tool and then run:

$ stack setup
$ stack ghci foldl
Prelude> import qualified Control.Foldl as Fold
Prelude Fold> Fold.fold ((,) <$> Fold.sum <*> Fold.length) [1..1000000]
(500000500000,1000000)

How to contribute

Contribute a pull request if you have a Fold that you believe other people would find useful.

Development Status

The foldl library is pretty stable at this point. I don't expect there to be breaking changes to the API from this point forward unless people discover new bugs.

License (BSD 3-clause)

Copyright (c) 2016 Gabriella Gonzalez All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

• Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

• Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

• Neither the name of Gabriella Gonzalez nor the names of other contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.