foldl
Composable, streaming, and efficient left folds
Version on this page:  1.2.5 
LTS Haskell 12.1:  1.4.2 
Stackage Nightly 20180716:  1.4.2 
Latest on Hackage:  1.4.2 
Module documentation for 1.2.5
foldl
v1.4.2
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 handwriting 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. Handwriting 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 highlevel 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:
(,) <$> Fold.sum <*> Fold.length = Fold step (Pair 0 0) done
where
step (Pair x y) = Pair (x + n) (y + 1)
done (Pair x y) = (x, y)
… and then fold
just transforms that to a strict left fold:
fold (Fold step begin done) = done (foldl' step begin)
Since we preserve the step function and accumulator, we can use the Fold
type to
fold things other than pure collections. For example, we can fold a Producer
from pipes
using the same Fold
:
Fold.purely Pipes.Prelude.fold ((,) <$> 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 3clause)
Copyright (c) 2016 Gabriel 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 Gabriel 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.
Changes
1.4.2
 Add
Semigroupoid
instance forFold
 Increase upper bound on
contravariant
andprofunctors
1.4.1
 Add
Control.Scanl
 Drop support for GHC 7.8 and older
1.4.0
 BREAKING CHANGE: Change type of
premapM
to accept a monadic function
1.3.7
 Add
groupBy
1.3.6
 Documentation improvements
1.3.5
 Add
Choice
instance forFold
1.3.4
 Add
prefilter
andprefilterM
1.3.3
 Add back the old
vector
asvectorM
1.3.2
 Compatibility with
Semigroup
becoming a superclass ofMonoid
 Fix
asin
forFold
1.3.1
 Fix
asin
forFoldM
1.3.0
 BREAKING CHANGE: Change
vector
to be a pureFold
(which is faster, too!)
1.2.5
 Add support for folding new containers:
hashSet
,map
, andhashMap
 Add
prescan
/postscan
which generalizescan
toTraversable
types
1.2.4
 Add
lazy
folds forText
andByteString
 Documentation fixes and improvements
1.2.3
 Add
lookup
1.2.2
 Add numerically stable
mean
,variance
, andstd
folds  Add
Control.Foldl.{Text,ByteString}.foldM
 Add
foldOver
/foldOverM
1.2.1
 Performance improvements
 Reexport
filtered
1.2.0
 Breaking change: Fix
handles
to fold things in the correct order (was previously folding things backwards and also leaking space as a result). No change to behavior ofhandlesM
, which was folding things in the right order  Breaking change: Change the
Monoid
used byHandler
/HandlerM
 Add
folded
1.1.6
 Add
maximumBy
andminimumBy
1.1.5
 Increase lower bound on
base
from< 4
to< 4.5
1.1.4
 Increase upper bound on
comonad
from< 5
to< 6
1.1.3
 Increase upper bound on
profunctors
from< 5.2
to< 5.3
 Add
mapM_
,hoists
,purely
, andimpurely
1.1.2
 Add
lastN
,randomN
,sink
, andduplicateM
 Add
Comonad
instance forFold
 Add
Profunctor
instance forFoldM
1.1.1
 Increase upper bound on
vector
from< 0.11
to< 0.12
1.1.0
 Breaking change: Rename
pretraverse
/pretraverseM
tohandles
/handlesM
 Add
Handler
 Export
EndoM
1.0.11
 Add
Profunctor
instance forFold
1.0.10
 Add
random
and_Fold1
1.0.9
 Increase upper bound on
primitive
from< 0.6
to< 0.7
1.0.8
 Add
revList
1.0.7
 Add
Num
andFractional
instances forFold
/FoldM
 Add
count
fold forText
andByteString
1.0.6
 Add
pretraverse
andpretraverseM
1.0.5
 Add
lastDef
1.0.4
 Increase upper bounds on
transformers
from< 0.4
to< 0.6
 Add
nub
,eqNub
, andset
1.0.3
 Add
scan
,generalize
,simplify
, andpremapM
1.0.2
 Add
list
andvector
folds  Add
fold
function forText
andByteString
1.0.1
 Add support for
ByteString
andText
folds  Add
Monoid
instance forFold
/FoldM
1.0.0
 Initial release