GADT和Functor类的问题

Question

我在Haskell中定义了自己的数据类型来表示单变量多项式。

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

我在这里使用了GADT来约束a变量，使其属于Num Class。现在，我想为Functor类定义我自己的实例

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

它不能编译给我这样的原因：

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'

因此，我尝试使用语言扩展InstanceSigs将此约束添加到fmap定义中：

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)

它不能从编译器中获取以下代码：

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'

你知道怎么解决这个问题吗？

Answer 1

您的数据类型为

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

现在看一下您对Functor的定义

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

由于GADT的约束，ghc能够推断出x的约束Num a。但问题出在不受限制的函数f中，因为f :: a -> b, x :: Num a => a推断f x是b类型。因此它不能将f x限制为Cons所要求的Num b => b。

因此，正如Daniel所指出的，您不能向您的Functor类添加约束。您可以定义自己的受限函数器类，如here，也可以使用rmonad中的RFunctor。