Cons

Template:Short description Template:About Template:More citations needed Template:Lowercase title In computer programming, Template:Lisp2 (Template:IPAc-en or Template:IPAc-en) is a fundamental function in most dialects of the Lisp programming language. Template:Lisp2 constructs memory objects which hold two values or pointers to two values. These objects are referred to as (cons) cells, conses, non-atomic s-expressions ("NATSes"), or (cons) pairs. In Lisp jargon, the expression "to cons x onto y" means to construct a new object with (cons x y). The resulting pair has a left half, referred to as the Template:Lisp2 (the first element, or contents of the address part of register), and a right half, referred to as the Template:Lisp2 (the second element, or contents of the decrement part of register).

It is loosely related to the object-oriented notion of a constructor, which creates a new object given arguments, and more closely related to the constructor function of an algebraic data type system.

The word "cons" and expressions like "to cons onto" are also part of a more general functional programming jargon. Sometimes operators that have a similar purpose, especially in the context of list processing, are pronounced "cons". (A good example is the :: operator in ML, Scala, F#, Lean, Coq, and Elm or the : operator in Haskell, which adds an element to the beginning of a list.)

UseEdit

Although cons cells can be used to hold ordered pairs of data, they are more commonly used to construct more complex compound data structures, notably lists and binary trees.

Ordered pairsEdit

For example, the Lisp expression Template:Lisp2 constructs a cell holding 1 in its left half (the so-called Template:Lisp2 field) and 2 in its right half (the Template:Lisp2 field). In Lisp notation, the value Template:Lisp2 looks like:

(1 . 2)

Note the dot between 1 and 2; this indicates that the S-expression is a "dotted pair" (a so-called "cons pair"), rather than a "list."

ListsEdit

File:Cons-cells.svg

Cons cell diagram for the list (42 69 613), written with cons: <syntaxhighlight lang="lisp">(cons 42 (cons 69 (cons 613 nil)))</syntaxhighlight> and written with list: <syntaxhighlight lang="lisp">(list 42 69 613)</syntaxhighlight>

In Lisp, lists are implemented on top of cons pairs. More specifically, any list structure in Lisp is either:

An empty list Template:Lisp2, which is a special object usually called Template:Lisp2.
A cons cell whose Template:Lisp2 is the first element of the list and whose Template:Lisp2 is a list containing the rest of the elements.

This forms the basis of a simple, singly linked list structure whose contents can be manipulated with Template:Lisp2, Template:Lisp2, and Template:Lisp2. Note that Template:Lisp2 is the only list that is not also a cons pair. As an example, consider a list whose elements are 1, 2, and 3. Such a list can be created in three steps:

Cons 3 onto Template:Lisp2, the empty list
Cons 2 onto the result
Cons 1 onto the result

which is equivalent to the single expression:

<syntaxhighlight lang="lisp">(cons 1 (cons 2 (cons 3 nil)))</syntaxhighlight>

or its shorthand:

<syntaxhighlight lang="lisp">(list 1 2 3)</syntaxhighlight>

The resulting value is the list:

(1 . (2 . (3 . nil)))

i.e.

 *--*--*--nil
 |  |  |
 1  2  3

which is generally abbreviated as:

(1 2 3)

Thus, Template:Lisp2 can be used to add one element to the front of an existing linked list. For example, if x is the list we defined above, then Template:Lisp2 will produce the list:

(5 1 2 3)

Another useful list procedure is append, which concatenates two existing lists (i.e. combines two lists into a single list).

TreesEdit

Binary trees that only store data in their leaves are also easily constructed with Template:Lisp2. For example, the code:

<syntaxhighlight lang="lisp">(cons (cons 1 2) (cons 3 4))</syntaxhighlight>

results in the tree:

((1 . 2) . (3 . 4))

i.e.

   *
  / \
 *   *
/ \ / \
1 2 3 4

Technically, the list (1 2 3) in the previous example is also a binary tree, one which happens to be particularly unbalanced. To see this, simply rearrange the diagram:

 *--*--*--nil
 |  |  |
 1  2  3

to the following equivalent:

   *
  / \
 1   *
    / \
   2   *
      / \
     3  nil

Use in conversationEdit

Cons can refer to the general process of memory allocation, as opposed to using destructive operations of the kind that would be used in an imperative programming language.Template:Citation needed For example:

I sped up the code a bit by putting in side effects instead of having it cons ridiculously.

Functional implementationEdit

Since Lisp has first-class functions, all data structures, including cons cells, can be implemented using functions. For example, in Scheme: <syntaxhighlight lang="scheme"> (define (cons x y)

 (lambda (m) (m x y)))

(define (car z)

 (z (lambda (p q) p)))

(define (cdr z)

 (z (lambda (p q) q)))

</syntaxhighlight> This technique is known as Church encoding. It re-implements the cons, car, and cdr operations, using a function as the "cons cell". Church encoding is a usual way of defining data structures in pure lambda calculus, an abstract, theoretical model of computation that is closely related to Scheme.

This implementation, while academically interesting, is impractical because it renders cons cells indistinguishable from any other Scheme procedure, as well as introduces unnecessary computational inefficiencies.

However, the same kind of encoding can be used for more complex algebraic data types with variants, where it may even turn out to be more efficient than other kinds of encoding.<ref>{{#invoke:citation/CS1|citation |CitationClass=web }}</ref> This encoding also has the advantage of being implementable in a statically typed language that doesn't have variants, such as Java, using interfaces instead of lambdas.

ReferencesEdit

External linksEdit

SDRAW, Common Lisp code for drawing draws cons cell structures. From David S. Touretzky.

Template:Data types