Agda 级别错误信息的含义： ... : .Agda.Primitive.Level

Question

我正在尝试破译有关级别的错误消息。在 Haskell 中，我可以用简单的方式编写以下流函数 twist：

data Stream a = a :> Stream a
twist :: (a -> (b , (Either a c))) -> (c -> (b , (Either a c))) -> (Either a c) -> Stream b
twist lt rt (Left a) = b :> twist lt rt ac
   where
     (b , ac) = lt a
twist lt rt (Right c) = b :> twist lt rt ac
   where
     (b , ac) = rt c

到目前为止，一切都很好。现在，当我尝试在 Agda 中定义类似函数时，我收到一条关于我不理解的级别的错误消息。具体来说，我收到以下错误消息：

_a_41 : .Agda.Primitive.Level  [ at ...snip.../MinimalStream.agda:20,34-35 ]
_b_42 : .Agda.Primitive.Level  [ at ...snip.../MinimalStream.agda:20,34-35 ]

好像是在吐槽twist的类型声明中的类型变量a和b的级别，但我不确定我是否理解问题所在。任何人都可以提供的任何指示或解释将不胜感激！

谢谢， 比尔

---

这是生成完整的薄的 Agda 代码：

module MinimalStream where

open import Data.Product using (_×_; _,_; proj₁)
open import Data.Sum -- using (_⊎_)

case_of_ : ∀ {a b} {A : Set a} {B : Set b} → A → (A → B) → B
case x of f = f x

record Stream A : Set where
  coinductive
  field headStr : A
        tailStr : Stream A
open Stream; S = Stream

-- standard kinds of stream functions work as expected.
unzip₁ : ∀ {a b : Set} → Stream (a × b) → Stream a
headStr (unzip₁ sab) = proj₁ (headStr sab)
tailStr (unzip₁ sab) = unzip₁ (tailStr sab)

twist : ∀ {a b c} → (a → (b × (a ⊎ c))) → (c → (b × (a ⊎ c))) → (a ⊎ c) → Stream b
headStr (twist lt rt (inj₁ a)) = case lt a of
                                    λ { (b , (inj₁ _)) → b ;
                                        (b , (inj₂ _)) → b }
headStr (twist lt rt (inj₂ c)) = case rt c of
                                    λ { (b , (inj₁ _)) → b ;
                                        (b , (inj₂ _)) → b }
tailStr (twist lt rt (inj₁ a)) = case lt a of
                                    λ { (_ , (inj₁ a')) → twist lt rt (inj₁ a') ;
                                        (_ , (inj₂ c))  → twist lt rt (inj₂ c)  }
tailStr (twist lt rt (inj₂ c)) = case rt c of
                                    λ { (_ , (inj₁ a))  → twist lt rt (inj₁ a) ;
                                        (_ , (inj₂ c')) → twist lt rt (inj₂ c')  }

Answer 1

欢迎来到堆栈溢出！这种错误表示未解决的元变量，这意味着 Agda 无法推断出隐式参数。错误消息指示元变量的（自动生成的）名称及其类型。在这种情况下，问题可能出在twist 中的{a, b, c} 类型上：尚不清楚它们应该处于哪个级别。要解决此问题，请指定级别：{a b c : Set}。