Why are types declared in value constructors not types in Haskell?

Question

Suppose I have the following value constructor:

data Shape = Circle Float Float Float | Rectangle Float Float Float Float

Now I can run:

ghci> :t Circle
Circle :: Float -> Float -> Float -> Shape

Now I can write a type declaration

surface :: Shape -> Float

But I can't type a type declaration

surface :: Circle -> Float

This is because " Circle is not a type, Shape is"

My question is: Why are types declared in value constructors not types in Haskell?

Answer 1

data Shape = Circle Float Float Float | Rectangle Float Float Float Float

Shape is a type (and a type constructor). Float is another type.

Circle and Rectangle are the value constructors for type Shape .

I guess that your confusion comes from OOP subtyping -- note that Haskell has no analogous to that. The above does not declare two types Circle and Rectangle to be subtypes of Shape .

Using some advanced extensions like GADTs you can actually write something like foo :: Circle -> Float meaning that the argument is a Shape value which has been constructed as a Circle . This requires some type-level techniques.

Alternatively, a plain Haskell approach could be

data Circle = Circle Float Float Float
data Rectangle = Rectangle Float Float Float Float
data Shape = Scircle Circle | Srectangle Rectangle