Pattern match on a data family in Haskell

Question

I have wrapped up whole data family in a single existential:

data Type = Numeric | Boolean 

data family Operator (t :: Type)
data instance Operator 'Numeric = Add | Sub
data instance Operator 'Boolean = And | Or

data AnyOp where
  AnyOp :: Operator t -> AnyOp

Now I would like to do some pattern matching on it

pp :: AnyOp -> String
pp op = case op of
  AnyOp Add -> "+"
  AnyOp Sub -> "-"
  AnyOp And -> "&"
  AnyOp Or  -> "|"

But the typechecker yells at me because

      ‘t’ is a rigid type variable bound by
        a pattern with constructor:
          AnyOp :: forall (t :: TType). Operator t -> AnyOp,
        in a case alternative
        at somesource/somefile/someposition
      Expected type: Operator t
        Actual type: Operator 'Boolean ```

Why? What is the proper way of doing this?

Answer 1

从远处看，数据族看起来有点像 GADT，因为数据族的两个构造函数可以产生不同类型的结果。但数据族与 GADT 不同！他们真的更像是典型的家庭。在您知道自己有一个 之前，您实际上无法匹配Add或。为什么是这样？你可以从操作上来思考。每个构造函数都必须有一个“标签”，以便表达式可以区分它们。如果两个 Data 实例定义在不同的模块中，那么它们很可能最终会为不同的构造函数使用相同的标签！此外，newtype 实例甚至没有标签，因此根本无法区分它们！正如 chi 所示，您可以通过在存在性中包装一个单例来跟踪您拥有的数据实例来解决此问题。SubOperator 'Numericcase

我的理解是，数据系列并不能真正提供太多（如果有的话）没有它们就无法获得的功能。让我们看看如何使用新类型、类型族和模式同义词来非常笨拙地表达比您的数据族稍微复杂的数据族。

import Data.Kind (Type)

data Typ = Numeric Bool | Boolean

newtype Operator t = Operator (OperatorF t)

type family OperatorF (t :: Typ) :: Type

type instance OperatorF ('Numeric b) = OpNum b
type instance OperatorF 'Boolean = OpBool

-- This makes no sense; it's just for demonstration
-- purposes.
data OpNum b where
  Add' :: OpNum 'True
  Sub' :: OpNum 'False

data OpBool = And' | Or'

pattern Add :: () => (b ~ 'True) => Operator ('Numeric b)
pattern Add = Operator Add'

pattern Sub :: () => (b ~ 'False) => Operator ('Numeric b)
pattern Sub = Operator Sub'

pattern And :: Operator 'Boolean
pattern And = Operator And'

pattern Or :: Operator 'Boolean
pattern Or = Operator Or'