haskell - 为什么在Num中没有定义(/)时编译 "1/2"？

Question

对不起，一个新手问题，但我真的不明白重载的值:

GHCi, version 7.8.3: http://www.haskell.org/ghc/  :? for help
Prelude> let x = 1
Prelude> let y = 2

两者 x和 y有型 Num a => a .但是没有 (/)定义于 Num !那么为什么表达式 x / y类型检查？

Prelude> x / y
0.5

(/)在类 Fractional 中定义.是否有来自 Num 的隐式转换至 Fractional ?

UPD :

所以，正如预期的那样，我得到了人们在 x / y 中声称的答案。 a专于 Fractional a => a .

我创建了自己的数字层次结构:

data MyInt = MyInt Integer deriving Show
data MyDouble = MyDouble Double deriving Show

class MyNum a where
    (+#) :: a -> a -> a -- + renamed to +# to avoid collision with standard +
    myFromInteger :: MyNum a => Integer -> a

class MyNum a => MyFractional a where
    (/#) :: a -> a -> a

instance MyNum MyInt where
    (MyInt a) +# (MyInt b) = MyInt (a + b)
    myFromInteger i = MyInt i

instance MyNum MyDouble where
    (MyDouble a) +# (MyDouble b) = MyDouble (a + b)
    myFromInteger i = MyDouble (fromInteger i)

instance MyFractional MyDouble where
    (MyDouble a) /# (MyDouble b) = MyDouble (a / b)

如果asnwers中的所有内容都是真的，类似的代码 Num替换为 MyNum也应该工作。但是ghci报错:

Prelude> :load myint.hs
*Main> let x = myFromInteger 1
*Main> let y = myFromInteger 2
*Main> x /# y

<interactive>:14:1:
    No instance for (MyFractional a0) arising from a use of `it'
    The type variable `a0' is ambiguous
    Note: there is a potential instance available:
      instance MyFractional MyDouble -- Defined at myint.hs:19:10
    In the first argument of `print', namely `it'
    In a stmt of an interactive GHCi command: print it

Answer 1

看来您使用的是较新版本的 ghci，默认情况下，该版本具有 NoMonomorphismRestriction启用。在这种情况下 x和 y确实有类型Num a => a :

Prelude> :set -XNoMonomorphismRestriction
Prelude> let x = 1
Prelude> let y = 2
Prelude> :t x
x :: Num a => a

而这种类型，由于它是多态的，专门用于 Fractional a => a当您评估时 x/y :

Prelude> :t x/y
x/y :: Fractional a => a

自 Num是 Fractional 的父类(super class)任何 Fractional类型也是 Num类型，因此专门针对 x 的类型和 y至 Fractional a => a是可能的。这与做类似的事情没有什么不同:

($) = id :: (a -> b) -> (a -> b)

函数 $只是 id :: c -> c 的专长哪里 c = a -> b .在您的情况下，您正在专门化受约束的类型，并且可以专门用子类替换父类(即更通用的更具体的约束)，所以 Fractional a => a是 Num a => a的专业.

当 ghci 必须输出结果时，它必须选择 / 的实现。运算符才能计算结果，因此它必须将类型实例化为具体类型。这是由 defaulting 完成的，因此执行的操作是 Double 的操作实例，但可以使用 default 更改它们宣言。

请注意，默认值仅适用于内置类。引用上面的链接:

Ambiguities in the class Num are most common, so Haskell provides another way to resolve them---with a default declaration:

default (t1 , ... , tn)

where n>=0, and each ti must be a type for which Num ti holds. In situations where an ambiguous type is discovered, an ambiguous type variable, v, is defaultable if:

• v appears only in constraints of the form C v, where C is a class, and at least one of these classes is a numeric class, (that is, Num or a subclass of Num), and
• all of these classes are defined in the Prelude or a standard library (Figures 6.2--6.3, pages -- show the numeric classes, and Figure 6.1, page , shows the classes defined in the Prelude.)