What Is Data Structure in Lisp?


Angela Bailey

In Lisp, a data structure is a way of organizing and storing data in memory. It provides a way to represent and manipulate complex data in a structured manner. Lisp offers several built-in data structures that can be used to solve various computational problems.


The most fundamental data structure in Lisp is the list. A list is an ordered collection of elements enclosed in parentheses.

Each element in the list can be of any type, including other lists. Lists are flexible and can be used to represent various data structures such as arrays, stacks, queues, trees, and more.

To define a list in Lisp, you simply enclose the elements within parentheses:

(setq my-list '(1 2 3 4))

This creates a list named my-list containing the elements 1, 2, 3, and 4.

List Operations

Lisp provides numerous operations for manipulating lists. Some common operations include:

  • car: Returns the first element of a list.
  • cdr: Returns all but the first element of a list.
  • cons: Constructs a new list by adding an element to the front of an existing list.
  • append: Concatenates multiple lists together into a single list.
  • length: Returns the number of elements in a list.
  • nth: Returns the nth element from a list.

You can use these operations to perform various operations on lists, such as accessing specific elements, adding or removing elements, and combining multiple lists.


In addition to lists, Lisp also provides support for arrays. Unlike lists, arrays have a fixed size and can only contain elements of the same type. Arrays are useful when you need constant-time access to elements based on their index.

To define an array in Lisp, you can use the make-array function:

(setq my-array (make-array '(3 3) :initial-contents '((1 2 3) (4 5 6) (7 8 9))))

This creates a 3×3 array named my-array with the specified initial contents.

Array Operations

Lisp provides various operations for working with arrays. Some common operations include:

  • aref: Retrieves the element at a specific index in an array.
  • aset: Sets the value of an element at a specific index in an array.
  • array-dimensions: Returns the dimensions of an array.
  • array-total-size: Returns the total number of elements in an array.

You can use these operations to access and modify elements in an array, retrieve information about its dimensions, and perform other array-related tasks.


Lisp also supports the creation and manipulation of trees. A tree is a hierarchical data structure composed of nodes, where each node can have zero or more child nodes. Trees are commonly used to represent hierarchical relationships between entities.

Lisp does not provide built-in tree data structures, but you can easily create trees using lists or custom data structures. Each node in the tree can be represented by a list, with the first element being the value of the node and the rest of the elements representing its children.

Here’s an example of a simple tree represented as a list:

(setq my-tree '(1 (2 (3) (4)) (5 (6))))

This creates a tree with root value 1 and two child nodes, each with their respective sub-trees.

Tree Traversal

To traverse a tree in Lisp, you can use recursive functions. Common tree traversal algorithms include:

  • pre-order: Visit the current node before its children.
  • in-order: Visit the current node between its left and right children.
  • post-order: Visit the current node after its children.

You can implement these algorithms using recursive functions that recursively traverse the left and right sub-trees, performing operations at each node visited.

In conclusion, Lisp provides powerful built-in data structures such as lists, arrays, and trees that allow you to represent complex data and solve various computational problems. By understanding these data structures and their associated operations, you can effectively manipulate and process data in Lisp programs.

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