Type Constructor – Haskell

In Haskell, a type constructor is a function that takes one or more types as arguments and produces a new type. Type constructors are similar to data constructors, but while data constructors create values, type constructors create types. They’re particularly useful for defining parametric types, which are types that take type parameters (such as lists, Maybe, and Either).

Examples of Type Constructors

1. List ([])

• The list type constructor [] takes a single type argument and produces a type.
• For example, [] Int produces the type [Int], which represents a list of integers.
• Here, [] is the type constructor, and Int is the type argument.

2. Maybe

• The Maybe type constructor also takes one type as an argument and produces a type that represents a value that can either hold Just a (a value of type a) or Nothing.
• For example, Maybe Int represents a type that could be either Just 5 or Nothing.

3. Custom Type Constructor

You can create custom type constructors when defining your own data types. For instance:

data Box a = Box a

In this example:

• Box is a type constructor that takes a type a as an argument, creating a new type Box a.
• Box Int would represent a box containing an integer, and Box String would represent a box containing a string.

Type Constructor vs. Data Constructor

• Type Constructor: Defines a type, often taking other types as arguments (e.g., Maybe, [], Either).
• Data Constructor: Defines a way to create values of that type (e.g., Just, Nothing for Maybe, or Left, Right for Either).

Type constructors allow Haskell to define generic, reusable data structures that can work with any type, making them a fundamental part of Haskell’s type system.