:: (a -> b) -> [a] -> b package:base

Map each element of the structure into a monoid, and combine the results with (<>). This fold is right-associative and lazy in the accumulator. For strict left-associative folds consider foldMap' instead.

Examples

Basic usage:

>>> foldMap Sum [1, 3, 5]
Sum {getSum = 9}

>>> foldMap Product [1, 3, 5]
Product {getProduct = 15}

>>> foldMap (replicate 3) [1, 2, 3]
[1,1,1,2,2,2,3,3,3]

When a Monoid's (<>) is lazy in its second argument, foldMap can return a result even from an unbounded structure. For example, lazy accumulation enables Data.ByteString.Builder to efficiently serialise large data structures and produce the output incrementally:

>>> import qualified Data.ByteString.Lazy as L

>>> import qualified Data.ByteString.Builder as B

>>> let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20

>>> let lbs = B.toLazyByteString $ foldMap bld [0..]

>>> L.take 64 lbs
"0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"

A left-associative variant of foldMap that is strict in the accumulator. Use this method for strict reduction when partial results are merged via (<>).

Examples

Define a Monoid over finite bit strings under xor. Use it to strictly compute the xor of a list of Int values.

>>> :set -XGeneralizedNewtypeDeriving

>>> import Data.Bits (Bits, FiniteBits, xor, zeroBits)

>>> import Data.Foldable (foldMap')

>>> import Numeric (showHex)

>>> 

>>> newtype X a = X a deriving (Eq, Bounded, Enum, Bits, FiniteBits)

>>> instance Bits a => Semigroup (X a) where X a <> X b = X (a `xor` b)

>>> instance Bits a => Monoid    (X a) where mempty     = X zeroBits

>>> 

>>> let bits :: [Int]; bits = [0xcafe, 0xfeed, 0xdeaf, 0xbeef, 0x5411]

>>> (\ (X a) -> showString "0x" . showHex a $ "") $ foldMap' X bits
"0x42"

This function may be used as a value for foldMap in a Foldable instance.

foldMapDefault f ≡ getConst . traverse (Const . f)