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| {-# LANGUAGE BlockArguments #-} | |
| {-# LANGUAGE LambdaCase #-} | |
| data Expr | |
| = Lit Integer | |
| | Var | |
| | Add Expr Expr | |
| | Mul Expr Expr | |
| | Pow Expr Expr | |
| | Sin Expr | |
| | Cos Expr | |
| deriving Eq | |
| instance Show Expr where | |
| show = \case | |
| Lit n -> show n | |
| Var -> "x" | |
| Add a b -> show a ++ " + " ++ show b | |
| Mul a b -> show a ++ " * " ++ show b | |
| Pow a b -> show a ++ " ** " ++ show b | |
| Sin a -> "sin " ++ show a | |
| Cos a -> "cos " ++ show a | |
| instance Floating Expr where | |
| sin = Sin | |
| (**) = Pow | |
| instance Fractional Expr | |
| instance Num Expr where | |
| (*) = Mul | |
| (+) = Add | |
| fromInteger = Lit | |
| derive :: (Expr -> Expr) -> Expr | |
| derive f = simplify $ d $ f Var where | |
| d = \case | |
| Var -> 1 | |
| Mul a b -> d a * b + a * d b | |
| Sin a -> Cos a * d a | |
| Pow a (Lit n) -> Lit n * Pow a (Lit $ n - 1) * d a | |
| simplify = \case | |
| Mul a 1 -> simplify a | |
| Mul a b -> Mul (simplify a) (simplify b) | |
| a -> a | |
| source :: (Expr -> Expr) -> String | |
| source f = show $ f Var | |
| eval :: Expr -> Double -> Double | |
| eval f x = | |
| case f of | |
| Lit i -> fromIntegral i | |
| Var -> x | |
| Mul a b -> eval a x * eval b x | |
| Pow a b -> eval a x ** eval b x | |
| Sin a -> sin $ eval a x | |
| Cos a -> cos $ eval a x | |
| _ -> error $ show f | |
| f x = sin x ** 4 | |
| -- $> f (pi / 2) | |
| -- $> source f | |
| -- $> derive f | |
| -- $> let f' = eval (derive f) in f' 1 |
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