单例的单例(模拟哈斯克尔中的复杂 pi 类型)

Question

我在Idris中有一个简单的概念证明，它使用依赖类型来强制执行一些不太复杂的业务逻辑。为了保护不那么无辜的人，已经更改了一些名称，但这个想法是我们想按顺序收集"行"。每行都与一个特定的部分有关，但只有一行(EconProduction(有我们关心的内容。通常，行具有特定于部分的关键字和表达式，其形式/类型可能取决于所使用的关键字。

对于这个特定的部分，每行要么描述"相"(Prod(的一些数字，要么继续最后一个命名的"相"(Continue(。

在伊德里斯中，我们可以这样做：

data EconSection
= EconGeneral
| EconProduction
data EconPhase
= Oil
| Water
| NumPhase Nat
data ContState
= ContNone
| ContProd EconPhase
data Keyword : EconSection -> ContState -> ContState -> Type where
Prod : (p : EconPhase) -> Keyword EconProduction c (ContProd p)
Continue : Keyword s c c
data Expression : (s : EconSection) ->
(d : ContState) ->
Keyword s c d ->
Type where
ExProc : Double -> Double -> Expression EconProduction (ContProd p) k
data Line : EconSection -> ContState -> ContState -> Type where
L : (k : Keyword s c d) -> Expression s d k -> Line s c d
data Lines : EconSection -> ContState -> Type where
First : Line s ContNone d -> Lines s d
Then : Lines s c -> Line s c d -> Lines s d
infixl 0 `Then`
good : Lines EconProduction (ContProd (NumPhase 1))
good = First (L (Prod Oil) (ExProc 23.2 70.1))
`Then` (L (Continue) (ExProc 27.9 1.2))
`Then` (L (Prod (NumPhase 1)) (ExProc 91.2 7014.1))
`Then` (L (Continue) (ExProc 91.2 7014.1))

目前为止，一切都好！通常的依赖类型状态业务。出于非常实际的商业原因，我们希望在GHC Haskell中实际实现此逻辑。我已经用单例构建了它(根据需要推出我自己的，而不是使用singletons包，只是为了一个简短的概念证明(：

{-# LANGUAGE GADTs, KindSignatures, DataKinds #-}
{-# LANGUAGE RankNTypes, TypeInType, TypeOperators #-}
{-# LANGUAGE TypeFamilies, TypeFamilyDependencies, MultiParamTypeClasses #-}
import Data.Kind (Type)
data Nat
= Z
| S Nat
data SNat :: Nat -> Type where
SZ :: SNat 'Z
SS :: SNat n -> SNat ('S n)
data SSNat :: forall (n :: Nat) . SNat n -> Type where
SSZ :: SSNat 'SZ
SSS :: SSNat n -> SSNat ('SS n)
type family SingNat (n :: Nat) :: SNat n where
SingNat 'Z = 'SZ
SingNat ('S n) = 'SS (SingNat n)
data EconSection
= EconGeneral
| EconProduction
data SEconSection :: EconSection -> Type where
SEconGeneral :: SEconSection 'EconGeneral
SEconProduction :: SEconSection 'EconProduction
type family SingSection (s :: EconSection) :: SEconSection s where
SingSection 'EconGeneral = 'SEconGeneral
SingSection 'EconProduction = 'SEconProduction 
data EconPhase
= Oil
| Water
| NumPhase Nat
data SEconPhase :: EconPhase -> Type where
SOil :: SEconPhase 'Oil
SWater :: SEconPhase 'Water
SNumPhase :: SNat n -> SEconPhase ('NumPhase n)
data SSEconPhase :: forall (p :: EconPhase) . SEconPhase p -> Type where
SSOil :: SSEconPhase 'SOil
SSWater :: SSEconPhase 'SWater
SSNumPhase :: SSNat n -> SSEconPhase ('SNumPhase n)
type family SingEconPhase (p :: EconPhase) :: SEconPhase p where
SingEconPhase 'Oil = 'SOil
SingEconPhase 'Water = 'SWater
SingEconPhase ('NumPhase n) = 'SNumPhase (SingNat n)
data ContState
= ContNone
| ContProd EconPhase
data SContState :: ContState -> Type where
SContNone :: SContState 'ContNone
SContProd :: SEconPhase p -> SContState ('ContProd p)
type family SingContState (c :: ContState) :: SContState c where
SingContState 'ContNone = 'SContNone
SingContState (ContProd p) = 'SContProd (SingEconPhase p)
data Keyword :: EconSection -> ContState -> ContState -> Type where
Prod :: SEconPhase p -> Keyword 'EconProduction c ('ContProd p)
Continue :: Keyword s c c
data SKeyword :: forall (s :: EconSection) (c :: ContState) (d :: ContState) .
Keyword s c d -> Type where
SProd :: SSEconPhase p -> SKeyword ('Prod p)
SContinue :: SKeyword 'Continue
data Expression :: forall (s :: EconSection) (c :: ContState) (d :: ContState) .
SEconSection s -> SContState d -> Keyword s c d -> Type where
ExProc :: Double -> Double -> Expression SEconProduction (SContProd p) k
type family KWSection k where
KWSection (Keyword s _ _) = s
type family KWFrom k where
KWFrom (Keyword _ c _) = c
type family KWTo k where
KWTo (Keyword _ _ d) = d
data Line :: EconSection -> ContState -> ContState -> Type where
L :: SKeyword (k :: Keyword s c d)
-> Expression (SingSection s) (SingContState d) k
-> Line s c d
data Lines :: EconSection -> ContState -> Type where
First :: Line s 'ContNone d -> Lines s d
Then :: Lines s c -> Line s c d -> Lines s d
infixl 0 `Then`
good :: Lines 'EconProduction ('ContProd ('NumPhase ('S 'Z)))
good = First (L (SProd SSOil) (ExProc 23.2 70.1))
`Then` (L (SContinue) (ExProc 27.9 1.2))
`Then` (L (SProd (SSNumPhase (SSS SSZ))) (ExProc 91.2 7014.1))
`Then` (L (SContinue) (ExProc 91.2 7014.1))

这是我的问题。有没有办法避免"单例的单例"？我根本不喜欢像SSNat之类的东西的外观，但这就是我通过将每个 pi 类型转换为额外的单例层来获得的地方。我无法使任何更简单的方法起作用，而且我在singletons包中也没有看到任何聪明的想法来简化此操作，尽管我可能很容易错过所有模板 Haskell 下的某些内容。

Answer 1

是的。

请考虑，根据单一实例类型的定义，您在单一实例中拥有的类型信息与该单一实例的单一实例一样多，因为它们都具有唯一的实例。

在您的代码中

考虑到上述情况，我们可以从代码中删除SSNat和SSEconPhase声明。然后，在SProd构造函数中

SProd :: SSEconPhase p - > SKeyword ('Prod p)

我们知道SEconPhase足以决定p，所以我们可以将其重写为

SProd :: SEconPhase p - > SKeyword ('Prod p)

这会产生一种错误 - 我们需要的是像这样的类型转换

SomeType :: (p :: EconPhase) -> SEconPhase p

您已经在代码中将其定义为SingEconPhase.结果是

SProd :: SEconPhase p - > SKeyword ('Prod (SingEconPhase p))

通常

您永远不必编写单例的单例 - 如果您需要将类型参数"提升"为单例类型，那么正确的选择是像您所做的那样编写类型族。