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