# What Is Inductive Data Type?

//

Heather Bennett

An inductive data type is a concept in computer programming that allows us to define a new type of data by specifying its constructors and their arguments. It is a way to create complex data structures by combining simpler ones. In this article, we will explore the concept of inductive data types and understand how they are used in programming.

## What Are Constructors?

In the context of inductive data types, constructors are functions or procedures that create instances of the new type. They take one or more arguments and return an instance of the type being defined. Constructors allow us to build values of the new type by combining values from other types.

## Defining Inductive Data Types

To define an inductive data type, we use a combination of constructors and pattern matching. Pattern matching is a way to deconstruct values of the new type based on their constructors.

Let’s take a look at an example to understand this better:

```type List = Nil | Cons(a, List)
```

In this example, we define a new type called “List” which can hold elements of any other type “a”. The constructors for this new type are “Nil” and “Cons”.

• Nil: Represents an empty list.
• Cons: Represents a non-empty list and takes two arguments – an element of type “a” and another list of elements of type “a”.

We can now use these constructors to create instances of the List type:

```List myList = Cons(1, Cons(2, Cons(3, Nil)))
```

The above code snippet creates a list of integers with three elements – 1, 2, and 3.

## Pattern Matching

Pattern matching allows us to deconstruct values of the new type based on their constructors. It is a powerful tool for manipulating and working with complex data structures.

In our List example, we can use pattern matching to perform operations on the list. Here’s an example:

```fun sum(list: List): int {
match list {
case Nil => 0
case Cons(x, xs) => x + sum(xs)
}
}
```

The above code snippet defines a function called “sum” that calculates the sum of all elements in a list of integers. The pattern matching allows us to handle both the case of an empty list (Nil) and a non-empty list (Cons).

## Conclusion

Inductive data types are a powerful concept in computer programming that allow us to define new types by specifying their constructors. Constructors and pattern matching enable us to create and manipulate complex data structures in a structured and organized manner.

By understanding inductive data types, you can enhance your programming skills and build more efficient and elegant solutions.