diff --git a/warmup.ml b/warmup.ml
new file mode 100644
index 0000000..c535b1c
--- /dev/null
+++ b/warmup.ml
@@ -0,0 +1,47 @@
+(* requires: y >= 0 *)
+(* requires: d >= 0 *)
+let valid_date (y: int) (m: string) (d: int) = 
+  if y < 0 || d < 0 then false
+  else match m with
+  | "Jan" | "Mar" | "May" | "Jul" | "Aug" | "Oct" | "Dec" -> d < 32
+  | "Feb" -> if (y mod 4 == 0) && (y mod 100 <> 0) then d < 30 else d < 29
+  | "Apr" | "Jun" | "Sep" | "Nov" -> d < 31
+  | _ -> false
+
+(* Test leap day in a non-century leap year. *)
+let () = assert (valid_date 2020 "Feb" 29)
+(* Test invalid day. *)
+let () = assert (not (valid_date 2010 "Jun" 50))
+
+
+(* requires: n > 0 *)
+let syr n =
+  let rec collatz n res =
+    if n == 1 then res
+    else if n mod 2 == 0 then collatz (n/2) (res+1)
+    else collatz ((n*3)+1) (res+1) in collatz n 0
+
+(* Test syr *)
+let () = assert (syr 1 = 0)
+let () = assert (syr 2 = 1)
+let () = assert (syr 10 = 6)
+let () = assert (syr 3 = 7)
+
+
+let rec next_nacci n l sum =
+  if n = 0 then sum
+  else match l with
+       | [] -> next_nacci (n - 1) [] sum
+       | h :: t -> next_nacci (n - 1) t (sum + h)
+
+let nacci n k =
+  let rec tail_nacci n k res =
+    if k = 0 then res
+    else tail_nacci n (k - 1) ((next_nacci n res 0) :: res)
+  in if k = 1 || k = 0 then [1] else List.rev (tail_nacci n (k - 2) [1; 1])
+
+
+let () = assert (nacci 2 6 = [1; 1; 2; 3; 5; 8])
+let () = assert (nacci 4 9 = [1; 1; 2; 4; 8; 15; 29; 56; 108])
+let () = assert (nacci 5 9 = [1; 1; 2; 4; 8; 16; 31; 61; 120])
+let () = assert (nacci 7 9 = [1; 1; 2; 4; 8; 16; 32; 64; 127])