module CalculatorSimple;

data Nat = Zero | Succ(Nat);

data Expr =
    Nat(Nat)
    | Add(Expr, Expr)
    | Sub(Expr, Expr);

def Nat add(Nat n1, Nat n2) =
    case n1 {
    Zero => n2;
    Succ(n) => Succ(add(n,n2));
};

def Nat sub(Nat n1, Nat n2) =
    case n2 {
    Zero => n1;
    Succ(n2P) => case n1 {
        Zero => Zero;
        Succ(n1P) => sub(n1P, n2P);
    };
};


def Nat mult(Nat n1, Nat n2) =
    case n1 {
    Zero => Zero;
    Succ(n) => add(n,mult(n,n2));
};


def Nat eval_simple(Expr exp) =
    case exp {
    Nat(n) => n;
    Add(e1,e2) => add(eval_simple(e1), eval_simple(e2));
    Sub(e1,e2) => sub(eval_simple(e1), eval_simple(e2));
};

def Int nat_to_int(Nat n) =
    case n {
    Zero => 0;
    Succ(n) => nat_to_int(n)+1;
};

def Nat start(Expr exp) = eval_simple(expr);

{

}