haskell - 在 Haskell 中推导是如何工作的？

Question

Haskell 中的代数数据类型(ADT) 可以通过派生某些类型类（如Show,自动成为它们的实例。Eq

data  Maybe a  =  Nothing | Just a
  deriving (Eq, Ord)

我的问题是，这是如何deriving工作的，即 Haskell 如何知道如何为派生 ADT 实现派生类型类的功能？

另外，为什么deriving仅限于某些类型类？为什么我不能编写自己的可以派生的类型类？

Answer 1

简短的回答是，魔术:-)。这就是说自动派生被纳入 Haskell 规范，每个编译器都可以选择以自己的方式实现它。然而，关于如何使其可扩展，还有很多工作要做。

Derive是 Haskell 的一个工具，可以让你编写自己的派生机制。

GHC 曾经提供一个可派生的类型类扩展，称为Generic Classes，但它很少使用，因为它有些弱。现在已将其删除，并且正在进行整合本文所述的新通用派生机制的工作：http ://www.dreixel.net/research/pdf/gdmh.pdf

有关这方面的更多信息，请参阅：

• GHC 维基：http ://hackage.haskell.org/trac/ghc/wiki/Commentary/Compiler/GenericDeriving
• Haskell 维基：http ://www.haskell.org/haskellwiki/Generics
• 黑客攻击： http ://hackage.haskell.org/package/generic-deriving

Answer 2

来自 Haskell 98 报告：

Prelude 中唯一允许派生实例的类是 Eq、Ord、Enum、Bounded、Show 和 Read...

以下是如何派生这些类型类的描述：http ://www.haskell.org/onlinereport/derived.html#derived-appendix

Answer 3

可以使用Template Haskell以类似于派生子句的方式生成实例声明。

以下示例是从Haskell Wiki中无耻地窃取的：

在此示例中，我们使用以下 Haskell 代码

$(gen_render ''Body)

产生以下实例：

instance TH_Render Body where
  render (NormalB exp) = build 'normalB exp
  render (GuardedB guards) = build 'guardedB  guards

上面的函数gen_render定义如下。（请注意，此代码必须位于与上述用法不同的模块中）。

-- Generate an intance of the class TH_Render for the type typName
gen_render :: Name -> Q [Dec]
gen_render typName =
  do (TyConI d) <- reify typName -- Get all the information on the type
     (type_name,_,_,constructors) <- typeInfo (return d) -- extract name and constructors                  
     i_dec <- gen_instance (mkName "TH_Render") (conT type_name) constructors
                      -- generation function for method "render"
                      [(mkName "render", gen_render)]
     return [i_dec]  -- return the instance declaration
             -- function to generation the function body for a particular function
             -- and constructor
       where gen_render (conName, components) vars 
                 -- function name is based on constructor name  
               = let funcName = makeName $ unCapalize $ nameBase conName 
                 -- choose the correct builder function
                     headFunc = case vars of
                                     [] -> "func_out"
                                     otherwise -> "build" 
                      -- build 'funcName parm1 parm2 parm3 ...
                   in appsE $ (varE $ mkName headFunc):funcName:vars -- put it all together
             -- equivalent to 'funcStr where funcStr CONTAINS the name to be returned
             makeName funcStr = (appE (varE (mkName "mkName")) (litE $ StringL funcStr))

其中使用以下功能和类型。

首先一些类型同义词使代码更具可读性。

type Constructor = (Name, [(Maybe Name, Type)]) -- the list of constructors
type Cons_vars = [ExpQ] -- A list of variables that bind in the constructor
type Function_body = ExpQ 
type Gen_func = Constructor -> Cons_vars -> Function_body
type Func_name = Name   -- The name of the instance function we will be creating
-- For each function in the instance we provide a generator function
-- to generate the function body (the body is generated for each constructor)
type Funcs = [(Func_name, Gen_func)]

主要的可重用功能。我们将函数列表传递给它以生成实例的函数。

-- construct an instance of class class_name for type for_type
-- funcs is a list of instance method names with a corresponding
-- function to build the method body
gen_instance :: Name -> TypeQ -> [Constructor] -> Funcs -> DecQ
gen_instance class_name for_type constructors funcs = 
  instanceD (cxt [])
    (appT (conT class_name) for_type)
    (map func_def funcs) 
      where func_def (func_name, gen_func) 
                = funD func_name -- method name
                  -- generate function body for each constructor
                  (map (gen_clause gen_func) constructors)

上面的一个辅助函数。

-- Generate the pattern match and function body for a given method and
-- a given constructor. func_body is a function that generations the
-- function body
gen_clause :: (Constructor -> [ExpQ] -> ExpQ) -> Constructor -> ClauseQ
gen_clause func_body data_con@(con_name, components) = 
      -- create a parameter for each component of the constructor
   do vars <- mapM var components
      -- function (unnamed) that pattern matches the constructor 
      -- mapping each component to a value.
      (clause [(conP con_name (map varP vars))]
            (normalB (func_body data_con (map varE vars))) [])
       -- create a unique name for each component. 
       where var (_, typ) 
                 = newName 
                   $ case typ of 
                     (ConT name) -> toL $ nameBase name
                     otherwise   -> "parm"
               where toL (x:y) = (toLower x):y

unCapalize :: [Char] -> [Char]
unCapalize (x:y) = (toLower x):y

还有一些从 Syb III / replib 0.2 中借来的帮助代码。

typeInfo :: DecQ -> Q (Name, [Name], [(Name, Int)], [(Name, [(Maybe Name, Type)])])
typeInfo m =
     do d <- m
        case d of
           d@(DataD _ _ _ _ _) ->
            return $ (simpleName $ name d, paramsA d, consA d, termsA d)
           d@(NewtypeD _ _ _ _ _) ->
            return $ (simpleName $ name d, paramsA d, consA d, termsA d)
           _ -> error ("derive: not a data type declaration: " ++ show d)

     where
        consA (DataD _ _ _ cs _)    = map conA cs
        consA (NewtypeD _ _ _ c _)  = [ conA c ]

        {- This part no longer works on 7.6.3
        paramsA (DataD _ _ ps _ _) = ps
        paramsA (NewtypeD _ _ ps _ _) = ps
        -}

        -- Use this on more recent GHC rather than the above
        paramsA (DataD _ _ ps _ _) = map nameFromTyVar ps
        paramsA (NewtypeD _ _ ps _ _) = map nameFromTyVar ps

        nameFromTyVar (PlainTV a) = a
        nameFromTyVar (KindedTV a _) = a


        termsA (DataD _ _ _ cs _) = map termA cs
        termsA (NewtypeD _ _ _ c _) = [ termA c ]

        termA (NormalC c xs)        = (c, map (\x -> (Nothing, snd x)) xs)
        termA (RecC c xs)           = (c, map (\(n, _, t) -> (Just $ simpleName n, t)) xs)
        termA (InfixC t1 c t2)      = (c, [(Nothing, snd t1), (Nothing, snd t2)])

        conA (NormalC c xs)         = (simpleName c, length xs)
        conA (RecC c xs)            = (simpleName c, length xs)
        conA (InfixC _ c _)         = (simpleName c, 2)

        name (DataD _ n _ _ _)      = n
        name (NewtypeD _ n _ _ _)   = n
        name d                      = error $ show d

simpleName :: Name -> Name
simpleName nm =
   let s = nameBase nm
   in case dropWhile (/=':') s of
        []          -> mkName s
        _:[]        -> mkName s
        _:t         -> mkName t