阅读器变形金刚

Question

newtype ReaderT r m a :: * -> (* -> *) -> * -> *

我不明白如何理解上述表达式，尤其是* -> (* -> *) -> * -> *

Answer 1

It should actually be

ReaderT :: * -> (* -> *) -> * -> *

Loosely speaking, the type above is a the type of a function which takes an argument of type * , another of type * -> * , another of type * , and produces a result of type * . The type * is the "type of all types". Eg Int :: * , Char :: * , etc.

To avoid confusion, * is not really called "a type" but "a kind", to reflect that it works at an higher level. For instance, 'a' has type Char , and Char has kind * .

Finally, the kind * -> * is the kind of unary type constructors, such as Maybe , [] , IO , (,) Char , Either Bool , etc. All of these take a type argument and return a type. The kind * -> * is also the kind of any functor, applicative, or monad.

So, if we have type r , a type constructor m (typically, a monad), and a type a , we have:

r :: *
m :: (* -> *)
a :: *
ReaderT :: * -> (* -> *) -> * -> *
ReaderT r :: (* -> *) -> * -> *
ReaderT r m :: * -> *
ReaderT r m a :: *

Hence, when all three arguments are passed, the result ReaderT rma is a type.