fib.ts

type Tuple<V, N extends number, T extends V[] = []> =
    N extends T['length'] ? T : Tuple<V, N, [...T, V]>;

type Nat = Nat[]
type ToNumber<N extends Nat> = N['length']
type FromNumber<N extends number> = Tuple<Nat, N>

type Zero = []
type One = [Nat]
type N2 = Add<One, One>
type N4 = Add<N2, N2>
type N8 = Add<N4, N4>
type N16 = Add<N8, N8>
type N32 = Add<N16, N16>
type N64 = Add<N32, N32>
type N128 = Add<N64, N64>

type Add<A extends Nat, B extends Nat> = [...A, ...B]
type LessThan<A extends Nat, B extends Nat> = B[A['length']] extends undefined ? false : true

type Fib<
    N extends Nat,
    I extends Nat = Zero,
    Prev extends Tuple<Nat, 2> = [Zero, One],
    PrevSum extends Nat = Add<Prev[0], Prev[1]>,
> =
    LessThan<I, N> extends true
    ? Fib<N, Add<I, One>, [Prev[1], PrevSum]>
    : PrevSum


type Result = ToNumber<Fib<N16>>
// the first three numbers are precalculated, so this is actually the number for the 19th place.