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# Extensions to the Fold function

This snippet is helpfull in the following cases: 1) After a consolidation operation using the fold function we need to know how many elements have been processed. 2) A consolidation operation needs to use the index of each of the elements processed and we don't want to use the mapi function first. 3) A combination of the above. Since the following snippet just adds a wrapper to the existing Fold function we can repeat the approach for arrays and sequences (including the plinq ones)

## Extending the Fold function in terms of itself

 ``` 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: ``` ``````module List = //Executes a fold operation within a list returning a two-dimension tuple with //the first element being the result of the fold and the second being the count of the //processed elements. let public foldc fold first source = source |> List.fold(fun (prev,count) c -> (fold prev c,count + 1)) (first,0) //Executes a fold operation within a list passing as parameter of the folder function //the zero based index of each element. let public foldi fold first source = source |> List.fold(fun (prev,i) c -> (fold i prev c,i + 1)) (first,0) |> fst //Executes a fold operation within a list passing as parameter of the folder function //the zero based index of each element and returning a two-dimension tuple with //the first element being the result of the fold and the second being the count of the //processed elements. let public foldic fold first source = source |> List.fold(fun (prev,i) c -> (fold i prev c, i + 1)) (first,0) ``````

## Examples

 ``` 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: ``` ``````let foldc_result = [1 .. 9] |> List.foldc (+) 0 //(45,9) let foldi_result = [1 .. 9] |> List.foldi (fun i (s1,s2) c -> (s1 + (2.0 ** float c), s2 + (2.0 ** float i))) (0.0,0.0) //(1022.0, 511.0) let foldic_result = [1 .. 9] |> List.foldic (fun i (s1,s2) c -> (s1 + (2.0 ** float c), s2 + (2.0 ** float i))) (0.0,0.0) //(1022.0, 511.0,9) ``````
Multiple items
module List

from Microsoft.FSharp.Collections

--------------------
type List<'T> =
| ( [] )
| ( :: ) of Head: 'T * Tail: 'T list
interface IEnumerable
interface IEnumerable<'T>
member IsEmpty : bool
member Item : index:int -> 'T with get
member Length : int
member Tail : 'T list
static member Cons : head:'T * tail:'T list -> 'T list
static member Empty : 'T list

Full name: Microsoft.FSharp.Collections.List<_>
val foldc : fold:('a -> 'b -> 'a) -> first:'a -> source:'b list -> 'a * int

Full name: Script.List.foldc
val fold : ('a -> 'b -> 'a)
val first : 'a
val source : 'b list
val fold : folder:('State -> 'T -> 'State) -> state:'State -> list:'T list -> 'State

Full name: Microsoft.FSharp.Collections.List.fold
val prev : 'a
val count : int
val c : 'b
val foldi : fold:(int -> 'a -> 'b -> 'a) -> first:'a -> source:'b list -> 'a

Full name: Script.List.foldi
val fold : (int -> 'a -> 'b -> 'a)
val i : int
val fst : tuple:('T1 * 'T2) -> 'T1

Full name: Microsoft.FSharp.Core.Operators.fst
val foldic : fold:(int -> 'a -> 'b -> 'a) -> first:'a -> source:'b list -> 'a * int

Full name: Script.List.foldic
val foldc_result : int * int

Full name: Script.foldc_result
Multiple items
module List

from Script

--------------------
module List

from Microsoft.FSharp.Collections

--------------------
type List<'T> =
| ( [] )
| ( :: ) of Head: 'T * Tail: 'T list
interface IEnumerable
interface IEnumerable<'T>
member IsEmpty : bool
member Item : index:int -> 'T with get
member Length : int
member Tail : 'T list
static member Cons : head:'T * tail:'T list -> 'T list
static member Empty : 'T list

Full name: Microsoft.FSharp.Collections.List<_>
val foldi_result : float * float

Full name: Script.foldi_result
val s1 : float
val s2 : float
val c : int
Multiple items
val float : value:'T -> float (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.float

--------------------
type float = System.Double

Full name: Microsoft.FSharp.Core.float

--------------------
type float<'Measure> = float

Full name: Microsoft.FSharp.Core.float<_>
val foldic_result : (float * float) * int

Full name: Script.foldic_result