haskell Either 和 Validation Applicative

Question

我有一个问题来自“Haskell 从第一原则编程”一书的第 17 章“应用程序”的“Either and Validation Applicative”部分。

我做了以下代码：

data Validation err a =
  Failure err
  | Success a
  deriving (Eq, Show)
data Errors =
  DividedByZero
  | Whosebug
  | MooglesChewedWires
  deriving (Eq, Show)
instance Functor (Validation e) where
  fmap _ (Failure x) = Failure x
  fmap f (Success y) = Success (f y)
instance Monoid e =>
  Applicative (Validation e) where
    pure = Success
    Failure e1 <*> Failure e2
      = Failure (e1 <> e2)
    Failure e <*> _ = Failure e
    _ <*> Failure e = Failure e
    Success f <*> Success r = Success (f r)
success :: Validation [Errors] Int
success = Success (+1)
  <*> Success (1::Int)
fail0 :: Validation [Errors] Int
fail0 = Success (+1)
  <*> Failure [Whosebug::Errors]
-- this doesn't work:
fail1a :: Validation [Errors] Int
fail1a = Failure [Whosebug::Errors]
  <*> Success (1)
-- this works:
fail1b :: Validation [Errors] b
fail1b = Failure [Whosebug::Errors]
  <*> Success (1::Int)
fail2 :: Validation [Errors] Int
fail2 = Failure [MooglesChewedWires]
  <*> Failure [Whosebug::Errors]
fail3 :: Validation [Errors] Int
fail3 = (Failure [Whosebug::Errors]
  <*> Success (+1)) <*> (Failure [MooglesChewedWires]
  <*> Failure [Whosebug::Errors])
fail4 :: Validation [Errors] Int
fail4 = fail1b <*> fail2

fail4 = fail1b <*> fail2 有效，但如果我将其更改为：

fail4 = fail1a <*> fail2

抛出错误：

Couldn't match type ‘Int’ with ‘Int -> Int’
  Expected type: Validation [Errors] (Int -> Int)
    Actual type: Validation [Errors] Int
• In the first argument of ‘(<*>)’, namely ‘fail1a’
  In the expression: fail1a <*> fail2

为什么会这样？ fail1a 与 fail1b 相比的唯一区别是在其类型签名中包含类型 Int 而不是 b ..

Answer 1

发生这种情况是因为 <*> 的类型为 Applicative f => f (a -> b) -> f a -> f b。

让我们看看fail4的定义：

fail4 :: Validation [Errors] Int
fail4 = fail1b <*> fail2

我们可以推断出 fail1b 和 fail2 的预期类型：

fail4 :: Validation [Errors] Int
fail4 =       fail1b          <*>          fail2
              +----+                       +---+
                 v                           v
expected:   f (a -> b)                      f a       (Applicative f)
                 v                           v
real:   Validation [Errors] b      Validation [Errors] Int
                 v
   Validation [Errors] (Int -> c)
                 v
  Validation [Errors] (Int -> Int)

因此，在这种情况下，键入 fail1b 的 Validation [Errors] b 变为 Validation [Errors] (Int -> Int)。

但是，如果将 fail1b 替换为 fail1a，则无法完成：

fail4 :: Validation [Errors] Int
fail4 =       fail1a          <*>          fail2
              +----+                       +---+
                 v                           v
expected:   f (a -> b)                      f a       (Applicative f)
              (error)                        v
real: Validation [Errors] Int      Validation [Errors] Int

将运算符 <*> 替换为 *>:

即可解决

fail4 :: Validation [Errors] Int
fail4 = fail1b *> fail2 -- or fail1a *> fail2

haskell Either 和 Validation Applicative

haskell Either and Validation Applicative

haskell

applicative