module Foldsum;

data Nat = Zero | S(Nat);

// Returns a function!
def B foldrFun<A,B>(f,z)(A xs) =
    case xs {
    Nil => z;
    Cons(x,xsP) => f(x, foldrFun(xsP));
};

def Nat plus(Nat x, Nat y) =
    case x {
    Zero => y;
    S(xP) => S(plus(xP, y));
};

// Already defined
// let rec map f xs =
//   match xs with
//   | Nil -> Nil
//   | Cons(x,xsP) -> Cons(f x, map f xsP)
// ;;

def B comp<A,B>(f, g)(A z) = f (g( z));

def A id<A>(A x) = x;

// Error: No higher order constructs possible in abs :-/
def Nat foldsum(List<Nat> l) = (foldrFun(comp, id)(map(plus, l)))(Zero);


{

}