用泛型键入代数数据类型

Question

data List t = E | C t (List t)
  deriving Show

lst1 :: List Int
lst1 = C 2 E

Why is t typed to 2 in case ? As the first guard defines "t = E" is this reason (List t) is allowed, so "C t (List t)" can also be read "C t E" ?

data NonEmptyList a = NEL a [a]
lst2 :: NonEmptyList = 2

Why can't 2 be typed to a as t is typed to 2 in above case ?

Answer 1

In the first type:

data List t = E | C t (List t)

t is a type parameter , it must be provided as an existing type. E is not a type, it is a data constructor , or value constructor . C is also a data constructor. They have the types:

E :: List t
C :: t -> List t -> List t

You could construct values like

> E :: List Int  -- Equivalent to []
E
> C 1 E :: List Int  -- Equivalent to [1]
C 1 E
> C 1 (C 2 E) :: List Int  -- Equivalent to [1, 2]
C 1 (C 2 E)

And so on. You can treat E as the empty list [] and C as the list constructor : , so C 1 (C 2 (C 3 E)) is equivalent to 1 : 2 : 3 : [] which is the same as [1, 2, 3] .

In the second type:

data NonEmptyList a = NEL a [a]

You have the data constructor

NEL :: a -> [a] -> NonEmptyList a

You can construct values like

> NEL 1 [] :: NonEmptyList Int  -- Equivalent to [1]
NEL 1 []
> NEL 1 [2] :: NonEmptyList Int  -- Equivalent to [1, 2]

And so on. This type forces you to always have at least one value, so it can't be non-empty.

When you write lst2 :: NonEmptyList = 2 , this is a syntax error, and it's hard to guess what you meant, but the equivalent NonEmptyList Int to the lst1 :: List Int would be written as NEL 2 [] :: NonEmptyList Int .