Difference between fold and reduce?

Question

Trying to learn F# but got confused when trying to distinguish between fold and reduce. Fold seems to do the same thing but takes an extra parameter. Is there a legitimate r

Answer 1

fold is a much more valuable function than reduce. You can define many different functions in terms of fold.

reduce is just a subset of fold.

Definition of fold:

let rec fold f v xs =
    match xs with 
    | [] -> v
    | (x::xs) -> f (x) (fold f v xs )

Examples of functions defined in terms of fold:

let sum xs = fold (fun x y -> x + y) 0 xs

let product xs = fold (fun x y -> x * y) 1 xs

let length xs = fold (fun _ y -> 1 + y) 0 xs

let all p xs = fold (fun x y -> (p x) && y) true xs

let reverse xs = fold (fun x y -> y @ [x]) [] xs

let map f xs = fold (fun x y -> f x :: y) [] xs

let append xs ys = fold (fun x y -> x :: y) [] [xs;ys]

let any p xs = fold (fun x y -> (p x) || y) false xs 

let filter p xs = 
    let func x y =
        match (p x) with
        | true -> x::y
        | _ -> y
    fold func [] xs