haskell - 什么是 "coverage condition"？

Question

The source for the State transformer in mtl状态:

-- ---------------------------------------------------------------------------
-- Instances for other mtl transformers
--
-- All of these instances need UndecidableInstances,
-- because they do not satisfy the coverage condition.

什么是“覆盖条件”？我只能说它与 MTPC 和基金组织有关。

Answer 1

the GHC manual 的第 7.6.3.2 节告诉我们覆盖条件是什么:

The Coverage Condition. For each functional dependency, tvsleft -> tvsright, of the class, every type variable in S(tvsright) must appear in S(tvsleft), where S is the substitution mapping each type variable in the class declaration to the corresponding type in the instance declaration.

用简单的英语来说，这意味着如果你有一个带有fundeps的类型类，例如:

class Convert a b | a -> b where
  convert :: a -> b

您可以定义以下实例:

instance Convert String String   -- no type variables
instance Convert [a]    [a]      -- type var a present on both sides
instance Convert (a,b)  a        -- a on the right => a on the left

但不包括以下情况:

instance Convert String a        -- a only present on the right
instance Convert a      (a,b)    -- b only present on the right