haskell sum类型的多个声明错误

Question

data A=A
data B=B
data AB=A|B

Which makes a sum type AB from A and B.

but the last line induces a compile error "multiple declarations of B"

I also tried sth like this:

data A=Int|Bool

It compiles. but why ghc disallows me from making sum types for user-defined types?

Answer 1

You're getting fooled. You think when you write data A=Int|Bool that you are saying that a value of type A can be a value of type Int or a value of type Bool ; but what you are actually saying is that there are two new value-level constructors named Int and Bool , each containing no information at all, of type A . Similarly, you think that data AB=A|B says you can either be of type A or type B , but in fact you are saying you can either have value A or value B .

The key thing to keep in mind is that there are two namespaces, type-level and term-level, and that they are distinct.

Here is a simple example of how to do it right:

data A=A
data B=B
data AB=L A|R B

The last line declares two new term-level constructors, L and R . The L constructor carries a value of type A , while the R constructor carries a value of type B .

You might also like the Either type, defined as follows:

data Either a b = Left a | Right b

You could use this to implement your AB if you wanted:

type AB = Either A B

Similarly, you could use Either Int Bool for your tagged union of Int and Bool .

Answer 2

Because the type of the value created using data constructor A or B will be ambiguous. When I have a = B for instance, what is the type of a ? It is A or AB ?

You should consider using different data constructor as follows:

data A = MkA
data B = MkB
data AB = A A | B B

Answer 3

When you say data AB = A | B data AB = A | B , you are not referring to the types A and B , but rather are defining data constructors A and B . These conflict with the constructors defined on the the previous lines.

If you want to create a type AB that is the sum of A and B , you must provide data constructors that wrap the types A and B , eg:

data AB = ABA A | ABB B

Answer 4

Sum types have to be tagged. a+a has to have two injections from a .

To understand how algebraic data types work, take a simple example:

data X = A | B C

This defines a new type constructor, X , along with data constructors A and B . The B constructor takes/holds an argument of type C.

The primary canonical sum type in Haskell is Either :

data Either a b = Left a | Right b