Data types basics

[Hal Daume III]

Hi again,

On Wed, 5 Nov 2003, Patty Fong wrote:

> Hi to anyone reading this. i'm still strugling a bit with data type
> declarations.
> 
> The was i understand it is that if i delcare a new data type:
> 
> data myType = myType a | b | c

This isn't entirely correct.  The names of types have to begin with 
capital letters, as do constructors (more later).  So you would need this 
to be:

data MyType = MyType A | B | C

where A is an existing type.

This type now has three constructors:

  MyType :: A -> MyType
  B :: MyType
  C :: MyType

It's perhaps a bit easier to understand when the names are different.

When we say:

data Foo = Bar Int | Baz String

this means that a "Foo" is of one of two forms (the "|" can be read as 
disjunction).  A value of type Foo is either of the form "Bar x" for some 
x which is an Int or "Baz y" for some y which is a String.

"Bar" and "Baz" are called "constructors" because they take arguments and 
"construct" a Foo.  So, in this case,

  Bar :: Int -> Foo
  Baz :: String -> Foo

are the two constructors.

Of course, you have have any number of constructors and each can have any 
number of arguments.

data Foo = Bar | Baz Int | Bazaa String Bool

Now there are three constructors:

  Bar :: Foo
  Baz :: Int -> Foo
  Bazaa :: String -> Bool -> Foo

they can be recursive:

data Foo = Bar | Baz Int Foo

  Bar :: Foo
  Baz :: Int -> Foo -> Foo

and can have "type variables", for instance:

data Foo a = Bar | Baz a

here, something of type "Foo a" is either of the form Bar or of the form 
Baz x for some x which is of type a.  This has constructors:

  Bar :: Foo a
  Baz :: a -> Foo a

I hope this sheds some light on the issue...


-- 
 Hal Daume III                                   | hdaume at isi.edu
 "Arrest this man, he talks in maths."           | www.isi.edu/~hdaume