Fibonacci (proofs + loop)

staload _ = "prelude/DATS/integer.dats"

dataprop FIB (int, int) =

| FIB0 (0, 0) | FIB1 (1, 1)

| {n: nat} {r0, r1: int} FIB2 (n + 2, r0 + r1) of (FIB (n, r0), FIB (n + 1, r1))

fun fibver {n: nat} .<>. (n: int n) : [r: int] (FIB (n, r) | int r) =

let

var r0: int = 0

var r1: int = 1

var i : int = 0

prvar pf0 = FIB0 ()

prvar pf1 = FIB1 ()

val () =

while* {i: nat; r0, r1: int | i <= n} .<n - i>. (pf0: FIB (i, r0), pf1: FIB (i + 1, r1), i: int(i), r0: int r0, r1: int r1) : [r: int] (pf0 : FIB (n, r), r0: int r) => (i < n)

{

val () = i := i + 1

val tmp = r0 + r1

val () = r0 := r1

val () = r1 := tmp

prval pf1_ = pf1

prval pf0_ = pf0

prval pftmp = FIB2 (pf0_, pf1_)

prval () = pf0 := pf1_

prval () = pf1 := pftmp

}

in

(pf0 | r0)

end

implement main0 () = () where

{

val () = println! ((fibver(10)).1)

val () = println! ((fibver(20)).1)

}