tests(tests/playground/deriv): deriv in OCaml

tests/playground/deriv.lean

@@ -78,7 +78,7 @@ instance : has_to_string Expr :=
 
 def nest_aux (s : nat) (f : nat → Expr → io Expr) : nat → Expr → io Expr
 | 0       x := pure x
-| m@(n+1) x := (timeit "step: " $ f (s - m) x) >>= nest_aux n
+| m@(n+1) x := f (s - m) x >>= nest_aux n
 
 def nest (f : nat → Expr → io Expr) (n : nat) (e : Expr) : io Expr :=
 nest_aux n f n e
@@ -92,8 +92,5 @@ do
 def main (xs : list string) : io uint32 :=
 do let x := Var "x",
    let f := pow x x,
-   nest deriv 11 f,
+   nest deriv 10 f,
    pure 0
-
--- set_option profiler true
--- #eval main []

tests/playground/deriv.ml

@@ -0,0 +1,85 @@
+type expr =
+| Val of int
+| Var of string
+| Add of expr * expr
+| Mul of expr * expr
+| Pow of expr * expr
+| Ln of expr;;
+
+let rec pown a n =
+if n == 0 then 1
+else if n == 1 then a
+else let b = pown a (n / 2) in
+b * b * (if n mod 2 == 0 then 1 else a);;
+
+let rec add n m =
+match (n, m) with
+| (Val n, Val m) -> Val (n+m)
+| (Val 0, f)     -> f
+| (f, Val 0)     -> f
+| (f, Val n)     -> add (Val n) f
+| (Val n, Add(Val m, f)) -> add (Val (n+m)) f
+| (f, Add(Val n, g))     -> add (Val n) (add f g)
+| (Add(f, g), h)         -> add f (add g h)
+| (f, g)                 -> Add (f, g);;
+
+let rec mul n m =
+match (n, m) with
+| (Val n, Val m) -> Val (n*m)
+| (Val 0, _)     -> Val 0
+| (_, Val 0)     -> Val 0
+| (Val 1, f)     -> f
+| (f, Val 1)     -> f
+| (f, Val n)     -> mul (Val n) f
+| (Val n, Mul (Val m, f)) -> mul (Val (n*m)) f
+| (f, Mul (Val n, g))     -> mul (Val n) (mul f g)
+| (Mul (f, g), h)         -> mul f (mul g h)
+| (f, g)                  -> Mul (f, g);;
+
+let rec pow m n =
+match (m, n) with
+| (Val m, Val n) -> Val (pown m n)
+| (_,  Val 0)    -> Val 1
+| (f, Val 1)     -> f
+| (Val 0, _)     -> Val 0
+| (f, g)         -> Pow (f, g);;
+
+let rec ln n =
+match n with
+| (Val 1) -> Val 0
+| f       -> Ln f;;
+
+let rec d x f =
+match f with
+| Val _      -> Val 0
+| Var y      -> if x = y then Val 1 else Val 0
+| Add (f, g) -> add (d x f) (d x g)
+| Mul (f, g) -> add (mul f (d x g)) (mul g (d x f))
+| Pow (f, g) -> mul (pow f g) (add (mul (mul g (d x f)) (pow f (Val (-1)))) (mul (ln f) (d x g)))
+| Ln f       -> mul (d x f) (pow f (Val (-1)));;
+
+let rec count f =
+match f with
+| Val _ -> 1
+| Var _ -> 1
+| Add (f, g) -> count f + count g
+| Mul (f, g) -> count f + count g
+| Pow (f, g) -> count f + count g
+| Ln f       -> count f;;
+
+let rec nest_aux s f n x =
+if n == 0 then x
+else let x = f (s - n) x in
+     nest_aux s f (n - 1) x;;
+
+let nest f n e =
+nest_aux n f n e;;
+
+let deriv i f =
+  let d = d "x" f in
+  Printf.printf "%8d count: %8d\n" (i+1) (count d);
+  d;;
+
+let x = Var "x" in
+let f = pow x x in
+nest deriv 10 f;;