List.fold<'T,'State> Function (F#)

Article
02/04/2013

Applies a function f to each element of the collection, threading an accumulator argument through the computation. The fold function takes the second argument, and applies the function f to it and the first element of the list. Then, it feeds this result into the function f along with the second element, and so on. It returns the final result. If the input function is f and the elements are i0...iN, then this function computes f (... (f s i0) i1 ...) iN.

Namespace/Module Path: Microsoft.FSharp.Collections.List

Assembly: FSharp.Core (in FSharp.Core.dll)

// Signature:
List.fold : ('State -> 'T -> 'State) -> 'State -> 'T list -> 'State

// Usage:
List.fold folder state list

Parameters

folder
Type: 'State -> 'T -> 'State

The function to update the state given the input elements.
state
Type: 'State

The initial state.
list
Type: 'T list

The input list.

Return Value

The final state value.

Remarks

This function is named Fold in compiled assemblies. If you are accessing the function from a language other than F#, or through reflection, use this name.

Example

The following example demonstrates the use of List.fold

let data = [("Cats",4);
            ("Dogs",5);
            ("Mice",3);
            ("Elephants",2)]
let count = List.fold (fun acc (nm,x) -> acc+x) 0 data
printfn "Total number of animals: %d" count

Total number of animals: 14

The following code example illustrates additional uses of List.fold. Note that library functions exist that already encapsulate the functionality implemented below. For example, List.sum is available to add up all the elements of a list.

let sumList list = List.fold (fun acc elem -> acc + elem) 0 list
printfn "Sum of the elements of list %A is %d." [ 1 .. 3 ] (sumList [ 1 .. 3 ])

// The following example computes the average of a list.
let averageList list = (List.fold (fun acc elem -> acc + float elem) 0.0 list / float list.Length)

// The following example computes the standard deviation of a list.
// The standard deviation is computed by taking the square root of the
// sum of the variances, which are the differences between each value
// and the average.
let stdDevList list =
    let avg = averageList list
    sqrt (List.fold (fun acc elem -> acc + (float elem - avg) ** 2.0 ) 0.0 list / float list.Length)

let testList listTest =
    printfn "List %A average: %f stddev: %f" listTest (averageList listTest) (stdDevList listTest)

testList [1; 1; 1]
testList [1; 2; 1]
testList [1; 2; 3]

// List.fold is the same as to List.iter when the accumulator is not used.
let printList list = List.fold (fun acc elem -> printfn "%A" elem) () list
printList [0.0; 1.0; 2.5; 5.1 ]

// The following example uses List.fold to reverse a list.
// The accumulator starts out as the empty list, and the function uses the cons operator
// to add each successive element to the head of the accumulator list, resulting in a
// reversed form of the list.
let reverseList list = List.fold (fun acc elem -> elem::acc) [] list
printfn "%A" (reverseList [1 .. 10])

Output

Sum of the elements of list [1; 2; 3] is 6.
List [1; 1; 1] average: 1.000000 stddev: 0.000000
List [1; 2; 1] average: 1.333333 stddev: 0.471405
List [1; 2; 3] average: 2.000000 stddev: 0.816497
0.0
1.0
2.5
5.1
[10; 9; 8; 7; 6; 5; 4; 3; 2; 1]

Platforms

Windows 7, Windows Vista SP2, Windows XP SP3, Windows XP x64 SP2, Windows Server 2008 R2, Windows Server 2008 SP2, Windows Server 2003 SP2

Version Information

F# Runtime

Supported in: 2.0, 4.0

Silverlight

Supported in: 3

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