GADTs和Functor类的问题

Question

那么，我已经定义了我自己的数据类型，它代表了Haskell中的一变量多项式。

data Polinomio a where 
    Pol :: (Num a) => a -> Integer -> Polinomio a -> Polinomio a 
    Cons :: (Num a) => a -> Polinomio a 

我在这里使用GADT来约束一个变量属于Num类。 现在我想定义自己的实例为仿函数类

instance Functor Polinomio where 
    fmap f (Cons x) = Cons $ f x 
    fmap f (Pol x g p) = Pol (f x) g (fmap f p) 

，它一点儿也不编译给我这样的理由：

Polinomio_GADT.hs:31:23: 
Could not deduce (Num b) arising from a use of `Cons' 
from the context (Num a) 
    bound by a pattern with constructor 
      Cons :: forall a. Num a => a -> Polinomio a, 
      in an equation for `fmap' 
    at Polinomio_GADT.hs:31:13-18 
Possible fix: 
    add (Num b) to the context of 
    the data constructor `Cons' 
    or the type signature for 
     fmap :: (a -> b) -> Polinomio a -> Polinomio b 
In the expression: Cons 
In the expression: Cons $ f x 
In an equation for `fmap': fmap f (Cons x) = Cons $ f x 

Polinomio_GADT.hs:32:26: 
Could not deduce (Num b) arising from a use of `Pol' 
from the context (Num a) 
    bound by a pattern with constructor 
      Pol :: forall a. 
        Num a => 
        a -> Integer -> Polinomio a -> Polinomio a, 
      in an equation for `fmap' 
    at Polinomio_GADT.hs:32:13-21 
Possible fix: 
    add (Num b) to the context of 
    the data constructor `Pol' 
    or the type signature for 
     fmap :: (a -> b) -> Polinomio a -> Polinomio b 
In the expression: Pol (f x) g (fmap f p) 
In an equation for `fmap': 
    fmap f (Pol x g p) = Pol (f x) g (fmap f p) 
In the instance declaration for `Functor Polinomio' 

所以我尝试使用此约束添加到FMAP定义语言扩展InstanceSigs：

instance Functor Polinomio where 
    fmap :: (Num a,Num b) -> (a -> b) -> Polinomio a -> Polinomio b 
    fmap f (Cons x) = Cons $ f x 
    fmap f (Pol x g p) = Pol (f x) g (fmap f p) 

，它不是从作品的编译器得到这样的：

Polinomio_GADT.hs:31:13: 
Predicate `(Num a, Num b)' used as a type 
In the type signature for `fmap': 
    fmap :: (Num a, Num b) -> (a -> b) -> Polinomio a -> Polinomio b 
In the instance declaration for `Functor Polinomio' 

任何想法如何解决这个问题？

Answer 1

你的数据类型是

data Polinomio a where 
    Pol :: (Num a) => a -> Integer -> Polinomio a -> Polinomio a 
    Cons :: (Num a) => a -> Polinomio a 

现在在您的函子

instance Functor Polinomio where 
    fmap f (Cons x) = Cons $ f x 
    fmap f (Pol x g p) = Pol (f x) g (fmap f p) 

的定义看的GHC能够推断x约束Num a由于GADT约束。但是 问题处于无限制函数f中，因为f :: a -> b, x :: Num a => a推断f x的类型为b。所以无法将f x限制为Num b => b，这是Cons所要求的。

正如丹尼尔指出的那样，您不能为您的Functor 类添加约束条件。要么你可以定义你自己的受限制的Functor类，如here或使用从rmonad的RFunctor。