Initial data commit

Task/Fibonacci-sequence/ATS/fibonacci-sequence-3.ats

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+(*
+** This implementation is verified!
+*)
+
+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))
+// end of [FIB] // end of [dataprop]
+
+fun
+fibats{n:nat}
+  (n: int (n))
+: [r:int] (FIB (n, r) | int r) = let
+  fun loop
+    {i:nat | i <= n}{r0,r1:int}
+  (
+    pf0: FIB (i, r0), pf1: FIB (i+1, r1)
+  | ni: int (n-i), r0: int r0, r1: int r1
+  ) : [r:int] (FIB (n, r) | int r) =
+    if (ni > 0)
+      then loop{i+1}(pf1, FIB2 (pf0, pf1) | ni - 1, r1, r0 + r1)
+      else (pf0 | r0)
+    // end of [if]
+  // end of [loop]
+in
+  loop {0} (FIB0 (), FIB1 () | n, 0, 1)
+end // end of [fibats]