roc/examples/benchmarks/Deriv.roc
2021-05-28 15:08:46 +02:00

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app "deriv"
packages { base: "platform" }
imports [base.Task]
provides [ main ] to base
# based on: https://github.com/koka-lang/koka/blob/master/test/bench/haskell/deriv.hs
IO a : Task.Task a []
main : IO {}
main =
Task.after Task.getInt \n ->
x : Expr
x = Var "x"
f : Expr
f = pow x x
nest deriv n f # original koka n = 10
|> Task.map (\_ -> {})
Expr : [ Val I64, Var Str, Add Expr Expr, Mul Expr Expr, Pow Expr Expr, Ln Expr ]
divmod : I64, I64 -> Result { div: I64, mod: I64 } [ DivByZero ]*
divmod = \l, r ->
when Pair (l // r) (l % r) is
Pair (Ok div) (Ok mod) -> Ok { div, mod }
_ -> Err DivByZero
pown : I64, I64 -> I64
pown = \a, n ->
when n is
0 -> 1
1 -> a
_ ->
when divmod n 2 is
Ok { div, mod } ->
b = pown a div
b * b * (if mod == 0 then 1 else a)
Err DivByZero -> -1
add : Expr, Expr -> Expr
add = \a,b ->
when Pair a b is
Pair (Val n) (Val m) -> Val (n + m)
Pair (Val 0) f -> f
Pair f (Val 0) -> f
Pair f (Val n) -> add (Val n) f
Pair (Val n) (Add (Val m) f) -> add (Val (n+m)) f
Pair f (Add (Val n) g) -> add (Val n) (add f g)
Pair (Add f g) h -> add f (add g h)
Pair f g -> Add f g
mul : Expr, Expr -> Expr
mul = \a,b ->
when Pair a b is
Pair (Val n) (Val m) -> Val (n*m)
Pair (Val 0) _ -> Val 0
Pair _ (Val 0) -> Val 0
Pair (Val 1) f -> f
Pair f (Val 1) -> f
Pair f (Val n) -> mul (Val n) f
Pair (Val n) (Mul (Val m) f) -> mul (Val (n*m)) f
Pair f (Mul (Val n) g) -> mul (Val n) (mul f g)
Pair (Mul f g) h -> mul f (mul g h)
Pair f g -> Mul f g
pow : Expr, Expr -> Expr
pow = \a,b ->
when Pair a b is
Pair (Val m) (Val n) -> Val (pown m n)
Pair _ (Val 0) -> Val 1
Pair f (Val 1) -> f
Pair (Val 0) _ -> Val 0
Pair f g -> Pow f g
ln : Expr -> Expr
ln = \f ->
when f is
Val 1 -> Val 0
_ -> Ln f
d : Str, Expr -> Expr
d = \x, expr ->
when expr is
(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)))
count : Expr -> I64
count = \expr ->
when expr is
(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
nest : (I64, Expr -> IO Expr), I64, Expr -> IO Expr
nest = \f, n, e -> nestHelp n f n e
nestHelp : I64, (I64, Expr -> IO Expr), I64, Expr -> IO Expr
nestHelp = \s, f, m, x ->
when m is
0 -> Task.succeed x
_ -> f (s - m) x |> Task.after \w -> nestHelp s f (m-1) w
deriv : I64, Expr -> IO Expr
deriv = \i, f ->
fprime = d "x" f
line =
Str.fromInt (i + 1)
|> Str.concat " count: "
|> Str.concat (Str.fromInt (count fprime))
Task.putLine line
|> Task.after \_ -> Task.succeed fprime