# Constructor

**Constructor** can mean:

- Type constructor
- Data constructor (or value constructor)

A `data`

declaration introduces a *type* constructor and some *data* constructors for this type constructor.

## Contents

## Type constructor

A **type constructor** may have zero or more arguments, if it has zero arguments it is called a *nullary* type constructor (or simply a **type**). An example of a nullary type constructor `Bool`

with two nullary data constructors `True`

and `False`

```
data Bool = True | False
```

*unary*type constructor

```
Tree
```

```
data Tree a = Tip | Node a (Tree a) (Tree a)
```

illustrates how to define a data type with type constructors (and data constructors at the same time). The type constructor is named `Tree`

, but a tree of what? Of any specific type `a`

, be it `Integer`

, `Maybe String`

, or even `Tree b`

, in which case it will be a tree of tree of `b`

. The data type is polymorphic (and `a`

is a type variable that is to be substituted by a specific type). So when used, the values will have types like `Tree Int`

or `Tree (Tree Boolean)`

.

## Data constructor

A **data constructor** (or **value constructor**) can have zero or more arguments where a data constructor taking zero arguments is called a *nullary* data constructor or simply a **constant**. They group values together and tag alternatives in an algebraic data type. E.g., the `Tree a`

type from above

```
data Tree a = Tip | Node a (Tree a) (Tree a)
```

has two data constructors, `Tip`

and `Node`

. Any value that belongs to the type `Tree a`

(again, we leave the type parameter unspecified) will be a constructed by either `Tip`

or `Node`

. `Tip`

is a constructor that groups no value, i.e, it's a nullary constructor. There is only one value, conveniently denoted `Tip`

that has this constructor. So, nullary constructors contain no data apart from their name! For example, the `Bool`

data type is defined as

```
data Bool = True | False
```

and for all practical purposes you can just think of `True`

and `False`

as *constants* belonging to a type. On the other hand, `Node`

contains other data. The types of those data are its parameters. The first one has type `a`

, so it's just a value of the parameter type `a`

. This one is the value the tree node holds in it. The remaining two are the branches. Each of them have type `Tree a`

, naturally.

### Data constructors as first class values

Data constructors are first class values in Haskell and actually have a type. For instance, the type of the `Left`

constructor of the `Either`

data type is:

```
Left :: a -> Either a b
```

As first class values, they may be passed to functions, held in a list, be data elements of other algebraic data types and so forth.

### Data constructors are not types

As discussed above, they denote values. It is illegal to write `Node a (Node a) (Node a)`

there, because the type is `Tree`

, not `Node`

.

## Deconstructing data constructors

All a data constructor does is holding values together. But you want to separate them if you want to use them. This is done via pattern matching,

```
depth Tip = 0
depth (Node _ l r) = 1 + max (depth l) (depth r)
```

So, the depth of a tip is zero. The depth of a node depends on its branches, but not its content. See how the constructor in the left hand side names its parts? we don't need the content so we don't name it (using `_`

). The left branch is named `l`

, the right `r`

, allowing us to use these values in the right hand side.

## Notes and tips

- You can declare a constructor (for both type and data) to be an infix operator, and this can make your code a lot more readable. However, for alphanumeric names, the names of both the type constructor and the data constructor(s) must start with an uppercase letter.
- Tuples are a built in feature of the syntax but are plain old algebraic data types! They have only one constructor though. Having the same name as their types (don't freak out, it's just a matter of convenience, as the type constructors and the data constructors have separate namespaces). So,
`(4, True)`

is really a value of the form`(,) 4 True`

having the type`(,) Int Bool`

, which, too, is written conveniently as`(Int, Bool)`

to make it more readable. Incidentally, the empty tuple type`()`

with its only value`()`

is used throughout, and is called*unit*. - You can, in fact, name the values grouped together, using the record syntax, so that for a person
data Person = Person { name :: String, age :: Int, address :: String }

`p`

, you can say`age p`

to select his/her age, without resorting to pattern matching. - Sometimes you need a little editing or checking when constructing your data. If you do, check smart constructors.
- Sometimes you do not want the user of your library to group arbitrary values together. This is achieved by
*hiding*your constructor (not mentioning it in the export list of the module), creating an abstract data type as a result. Along with smart constructors mentioned above, one can achieve encapsulation. - Type constructors are used to denote the types of functions, e.g.,Data or value constructors are used to pattern match, e.g.,
depth :: Tree a -> Int

depth (Node _ l r) = ...

- If you want to dig deeper into the Haskell type system: a data or value constructor has a
*type*, e.g.,`Node 3 Tip Tip`

has type`Tree Int`

; a*type*of a type constructor itself is called kind.

## References

- Programming in Standard ML: Chapter 10 (Concrete Data Types)