lab 07

labs/07/exp.ml

@@ -0,0 +1,28 @@
+type 'a lazystream = Cons of 'a * 'a lazystream Lazy.t
+
+let rec from n = Cons (n, lazy (from (n +. 1.)))
+
+let rec take n (Cons (h, t)) =
+  if n <= 0 then []
+  else h :: take (n - 1) (Lazy.force t)
+
+let rec map f (Cons (h, t)) =
+  Cons (f h, lazy (map f (Lazy.force t)))
+
+let fact n =
+  let rec fact' acc i =
+    if i = 0. then acc
+    else fact' (i *. acc) (i -. 1.)
+  in
+  fact' 1. n;;
+
+let rec fold_left f acc l =
+  match l with
+  | [] -> acc
+  | a :: l' -> fold_left f (f acc a) l';;
+
+let exp_terms x = map (fun n -> (x**n) /. (fact n)) @@ from 0.;;
+
+let exp n x = fold_left (+.) 0. (take n @@ exp_terms x);;
+
+exp 20 1.1;;

labs/07/primes.ml

@@ -0,0 +1,21 @@
+type 'a infstream = Cons of 'a * (unit -> 'a infstream)
+
+let rec take n (Cons (h, t)) =
+  if n <= 0 then []
+  else h :: take (n - 1) (t ())
+
+let rec from n = Cons (n, fun () -> from (n + 1))
+
+let rec filter f (Cons (h, t)) =
+  if f h then Cons (h, fun () -> filter f (t ()))
+  else filter f (t ())
+
+let primes =
+  let rec sieve (Cons (h, t)) =
+    Cons (h, fun () ->
+      sieve (filter (fun x -> x mod h <> 0) (t ()))
+    )
+  in
+  sieve @@ from 2;;
+
+take 100 primes;;