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

Article
02/04/2013

Applies a function to each element of the collection, threading an accumulator argument through the computation. If the input function is f and the elements are i0...iN then computes f (... (f s i0)...) iN.

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

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

// Signature:
Array.fold : ('State -> 'T -> 'State) -> 'State -> 'T [] -> 'State

// Usage:
Array.fold folder state array

Parameters

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

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

The initial state.
array
Type: 'T []

The input array.

Return Value

The final state.

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 code illustrates the use of Array.fold.

let sumArray array = Array.fold (fun acc elem -> acc + elem) 0 array
printfn "Sum of the elements of array %A is %d." [ 1 .. 3 ] (sumArray [| 1 .. 3 |])

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

// The following example computes the standard deviation of a array.
// 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 stdDevArray array =
    let avg = averageArray array
    sqrt (Array.fold (fun acc elem -> acc + (float elem - avg) ** 2.0 ) 0.0 array / float array.Length)

let testArray arrayTest =
    printfn "Array %A average: %f stddev: %f" arrayTest (averageArray arrayTest) (stdDevArray arrayTest)

testArray [|1; 1; 1|]
testArray [|1; 2; 1|]
testArray [|1; 2; 3|]

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

Output

Sum of the elements of array [1; 2; 3] is 6.
Array [|1; 1; 1|] average: 1.000000 stddev: 0.000000
Array [|1; 2; 1|] average: 1.333333 stddev: 0.471405
Array [|1; 2; 3|] average: 2.000000 stddev: 0.816497
0.0
1.0
2.5
5.1

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