Program.fs

type ListOf<'T> = | Cons of head:'T * ListOf<'T> | Empty

let x =  Empty // An empty list 
let y =  Cons(1, Empty) // Single item in list
let z =  Cons(1, Cons(2, Empty)) // Two item in list

printfn "x=%O" x
printfn "y=%O" y
printfn "z=%O" z

let nil() = Empty
let createTwoItemList a b = Cons(a, Cons(b, Empty))

let a = createTwoItemList 1 2
printfn "a=%O" a

let isNil<'T>(list: ListOf<'T>): bool= 
  match list with
  | Empty -> true
  | _ -> false

let head<'T>(list: ListOf<'T>): Option<'T> = 
  match list with
  | Cons( head:'T , _) -> Some(head)
  | _ -> None

let tail<'T>(list: ListOf<'T>): ListOf<'T> = 
  match list with
  | Cons( head:'T , tail) -> tail
  | Empty -> Empty

let sum(list: ListOf<int>): int = 
  let rec sumList(list: ListOf<int>, total: int): int = 
    match head(list) with
    | Some(x) -> sumList(tail(list), total + x)
    | None -> total

  sumList(list, 0)

let rec fold<'L, 'A>(list: ListOf<'L>)(acc: 'A)(folder: ('A*'L)->'A ): 'A =
  match head(list) with
  | Some(x) -> fold(tail(list))(folder(acc , x))(folder)
  | None -> acc


printfn "isNil for empty list is %O" (isNil(x))
printfn "isNil for non empty list is %O" (isNil(y))

printfn "head for a list with stuff in %O" (head(y))

printfn "tail for a list with stuff in %O" (tail(z))
printfn "tail for a list which is empty %O" (tail(x))

printfn "Sum a list = %O" (sum(z))

printfn "Fold  a list = %O" (fold(z)(0)(fun (a,b) -> a + b))

printfn "Fold  a list into a string = %O" (fold(z)("")(fun (a,b) -> sprintf "%s%d" a  b))