:: (Foldable t, Monoid a) => t a -> a package:protolude

Given a structure with elements whose type is a Monoid, combine them via the monoid's (<>) operator. This fold is right-associative and lazy in the accumulator. When you need a strict left-associative fold, use foldMap' instead, with id as the map.

Examples

Basic usage:

>>> fold [[1, 2, 3], [4, 5], [6], []]
[1,2,3,4,5,6]

>>> fold $ Node (Leaf (Sum 1)) (Sum 3) (Leaf (Sum 5))
Sum {getSum = 9}

Folds of unbounded structures do not terminate when the monoid's (<>) operator is strict:

>>> fold (repeat Nothing)
* Hangs forever *

Lazy corecursive folds of unbounded structures are fine:

>>> take 12 $ fold $ map (\i -> [i..i+2]) [0..]
[0,1,2,1,2,3,2,3,4,3,4,5]

>>> sum $ take 4000000 $ fold $ map (\i -> [i..i+2]) [0..]
2666668666666

The largest element of a non-empty structure. This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the maximum in faster than linear time.

Examples

Basic usage:

>>> maximum [1..10]
10

>>> maximum []
*** Exception: Prelude.maximum: empty list

>>> maximum Nothing
*** Exception: maximum: empty structure

WARNING: This function is partial for possibly-empty structures like lists.

The least element of a non-empty structure. This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the minimum in faster than linear time.

Examples

Basic usage:

>>> minimum [1..10]
1

>>> minimum []
*** Exception: Prelude.minimum: empty list

>>> minimum Nothing
*** Exception: minimum: empty structure

WARNING: This function is partial for possibly-empty structures like lists.