#include "share/atspre_define.hats"
#include "share/atspre_staload.hats"
// is_fib(i, n): n is the i-th fibonacci number
dataprop is_fib(int, int) =
| F0(0, 0) | F1(1, 1)
| {i, m, n : nat} Fplus(i + 2, m + n) of (is_fib(i, m), is_fib(i + 1, n))
typedef fib(i : int) = [n : nat] (is_fib(i, n) | int(n))
fun fib {t : nat} .<>. (t : int(t)) :<> fib(t) =
let
// m, n : accs
// i : index of m
// t : target index
fun go {m, n, i, t : nat | i <= t} .<t - i>.
(M : is_fib(i, m), N : is_fib(i + 1, n) |
m : int(m), n : int(n), i : int(i), t : int(t)) :<>
fib(t) =
if i = t then
(M | m)
else
go(N, Fplus(M, N) | n, m + n, i + 1, t)
in
go(F0, F1 | 0, 1, 0, t)
end
fun fib_(i : Nat) : Nat = let val (_ | res) = fib(i) in res end
implement main0() = println!("fib(15) = ", fib_(15))