A short example:

    data T = Tag1 Type1 Type2 

           | Tag2 Type3

    -- A type T can contain elements of two different types, which can be differentiated in a program by their 'Tag'

    -- 'Tag1 Type1 Type2' is a product type, just like a cartesian product of sets. It has elements

    -- of the form (Type1, Type2) but written as 'Tag1 Type1 Type2' for programming convenience.

    -- Tag2 Type3 is just Type3, with additional syntax to differentiate it from Type3.

    -- The pipe '|' creates a sum type, just like the union of sets.

    -- Overall, you have a type which has elements of the form (Type1, Type2) or Type3. Written differently so that

    -- they can be distinguished from (Type1, Type2) and Type3 elements.

    -- (x :: Type1, y :: Type2) is not equal to 'Tag1 x y'.

    -- The first has the type (Type1, Type2) and the second has the type T.

    -- Thus, Tag1 takes a Type1 and a Type2 and converts them to a T.

    -- Tag1 :: Type1 -> Type2 -> T

    -- A data constructor, constructs element of type T using elements of type Type1 and Type2

Read the two pages below, to get more intuition. Will be more helpful if you come from C and know about unions in that language.

https://en.wikipedia.org/wiki/Algebraic_data_type

https://en.wikipedia.org/wiki/Tagged_union

Hope this helps.

On 16 June 2015 at 14:25, Ovidiu Deac <ovidiudeac@gmail.com> wrote:

I want to add a little more thing that makes me understand this easier:

    data Bool = True | False

You can think if True not as a value but as a function from unit to Bool

That being said in Bob's example:

    data PersonOrPlace = Person String | Place String

...Person is a function from the type String to the type PersonOrPlace

As a conclusion: Haskell is, as they say, "a strong & static typed purely functional language", everything is either a type or a function. If it's not a type then it must be a function. You can say that even 0 is a function from unit to Int so it works quite nice.

On Tue, Jun 16, 2015 at 10:42 AM, Bob Ippolito <bob@redivi.com> wrote:

T is the type. A and B are the only constructors for values of that type. A and B are not terms in the type language. T is not a term in the value language.

It's simpler to consider a type without any fields in the constructor:

data Bool = True | False

True and False are values, Bool is the type. You can't use Bool as a constructor, and you can't use True or False as a type.

When you add fields it can get a bit more confusing, because the fields of a constructor are types, so it looks like "ValueConstructor1 FieldType1 FieldType2 | ValueConstructor2 FieldType3"

data PersonOrPlace = Person String | Place String

To make it more clear, here the types are annotated with <AngleBrackets> and the constructors annotated with [SquareBrackets]:

data <PersonOrPlace> = [Person] <String> | [Place] <String>

On Tue, Jun 16, 2015 at 8:52 AM, Matt Williams <matt.williams45.mw@gmail.com> wrote:

Dear All,

I am sure this is a common mistake, and I am happy to be pointed elsewhere for reading.

I have spent the last couple of days on the Haskell irc channel, which was very helpful.

However, one of the points of discussion left me confused.

When we have a type, T, with constructors A and B

(e.g. data T = A x y z | B x y)

How do I understand the relationship between A, B and T? I had thought I could use the sub-class relationship, but that doesn't seem to be true.

Any other pointers very welcome.

Matt

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Regards

Sumit Sahrawat