Wolfram Language

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Wolfram Language

Paradigm	Multi-paradigm: term-rewriting, functional, procedural, array
Designed by	Stephen Wolfram
Developer	Wolfram Research
First appeared	1988; 36 years ago (1988)
Stable release	14.1.0[1] / July 31, 2024; 3 months ago (2024-07-31)
Typing discipline	Dynamic, strong
OS	Cross-platform
License	Proprietary
Filename extensions	.nb, .m, .wl
Website	www.wolfram.com/language/
Major implementations
Mathematica, Mathics, Expreduce, MockMMA
Influenced by
APL C C++ FORTRAN Lisp Pascal Prolog Schoonschip[2] Simula Smalltalk[3] SMP[4]
Influenced
Jupyter[5] Clojure[6] Julia

The Wolfram Language (/ˈwʊlfrəm/ WUUL-frəm) is a proprietary,^[7] general-purpose, very high-level multi-paradigm programming language^[8] developed by Wolfram Research. It emphasizes symbolic computation, functional programming, and rule-based programming^[9] and can employ arbitrary structures and data.^[9] It is the programming language of the mathematical symbolic computation program Mathematica.^[10]

The Wolfram Language was part of the initial version of Mathematica in 1988.^[11]

Symbolic aspects of the engine make it a computer algebra system. The language can perform integration, differentiation, matrix manipulations, and solve differential equations using a set of rules. Also, the initial version introduced the notebook model and the ability to embed sound and images, according to Theodore Gray's patent.^[12]

Wolfram also added features for more complex tasks, such as 3D modeling.^[13]

A name was finally adopted for the language in 2013, as Wolfram Research decided to make a version of the language engine free for Raspberry Pi users, and they needed to come up with a name for it.^[14] It was included in the recommended software bundle that the Raspberry Pi Foundation provides for beginners, which caused some controversy due to the Wolfram language's proprietary nature.^[15] Plans to port the Wolfram language to the Intel Edison were announced after the board's introduction at CES 2014 but were never released.^[16] In 2019, a link was added to make Wolfram libraries compatible with the Unity game engine, giving game developers access to the language's high-level functions.^[17][18]

The Wolfram Language syntax is overall similar to the M-expression of 1960s LISP, with support for infix operators and "function-notation" function calls.

The Wolfram language writes basic arithmetic expressions using infix operators.

(* This is a comment. *)

4 + 3
(* = 7 *)

1 + 2 * (3 + 4)
(* = 15 *)
(* Note that Multiplication can be omitted: 1 + 2 (3 + 4) *)

(* Divisions return rational numbers: *)
6 / 4
(* = 3/2 *)

Function calls are denoted with square brackets:

Sin[Pi]
(* = 0 *)

(* This is the function to convert rationals to floating point: *)
N[3 / 2]
(* = 1.5 *)

Lists are enclosed in curly brackets:

Oddlist={1,3,5}
(* = {1,3,5} *)

The language may deviate from the M-expression paradigm when an alternative, more human-friendly way of showing an expression is available:

• A number of formatting rules are used in this language, including TeXForm for typeset expressions and InputForm for language input.
• Functions can also be applied using the prefix expression @ and the postfix expression //.
• Derivatives can be denoted with the apostrophe '.
• The infix operators themselves are considered "sugar" for the function notation system.

A FullForm formatter desugars the input:^[19]

FullForm[1+2]
(* = Plus[1, 2] *)

Currying is supported.

Functions in the Wolfram Language are effectively a case of simple patterns for replacement:

F[x_] := x ^ 0

The := is a "SetDelayed operator", so that the x is not immediately looked for. x_ is syntax sugar for Pattern[x, Blank[]], i.e. a "blank" for any value to replace x in the rest of the evaluation.

An iteration of bubble sort is expressed as:

sortRule := {x___,y_,z_,k___} /; y>z -> {x,z,y,k}
(* Rule[Condition[List[PatternSequence[x, BlankNullSequence[]], Pattern[y, Blank[]], Pattern[z, Blank[]], PatternSequence[k, BlankNullSequence[]]], Greater[y, z]], List[x, z, y, k]] *)

The /; operator is "condition", so that the rule only applies when y>z. The three underscores are a syntax for a BlankNullSequence[], for a sequence that can be null.

A ReplaceRepeated //. operator can be used to apply this rule repeatedly, until no more change happens:

{ 9, 5, 3, 1, 2, 4 } //. sortRule
(* = ReplaceRepeated[{ 9, 5, 3, 1, 2, 4 }, sortRule] *)
(* = {1, 2, 3, 4, 5, 9} *)

The pattern matching system also easily gives rise to rule-based integration and derivation. The following are excerpts from the Rubi package of rules:^[20]

(* Reciprocal rule *)
Int[1/x_,x_Symbol] :=
  Log[x];
(* Power rule *)
Int[x_^m_.,x_Symbol] :=
  x^(m+1)/(m+1) /;
FreeQ[m,x] && NeQ[m,-1]

The official and reference implementation of the Wolfram Language lies in Mathematica and associated online services. These are closed source.^[21] Wolfram Research has, however, released a parser of the language under the open source MIT License.^[22] The parser was originally developed in C++ but was rewritten in Rust in 2023. The reference book is open access.^[23]

In the over three-decade-long existence of the Wolfram language, a number of open-source third-party implementations have also been developed. Richard Fateman's MockMMA from 1991 is of historical note, both for being the earliest reimplementation and for having received a cease-and-desist from Wolfram. Modern ones still being maintained as of April 2020^[update] include Symja in Java, expreduce in Golang, and SymPy-based Mathics.^[24] These implementations focus on the core language and the computer algebra system that it implies, not on the online "knowledgebase" features of Wolfram.

In 2019,^[25] Wolfram Research released the freeware Wolfram Engine, to be used as a programming library in non-commercial software. This developer-only engine provides a command-line shell of the Mathematica evaluator (with a limited number of kernels) and requires signup and license activation over the web. The freely available Jupyter Notebook/Lab project provides a protocol (ZMQ) to connect their notebooks to various languages, this is available as an alternative to the text-only CLI interface via the Wolfram Kernel for Jupyter. ^[26]

The language was officially named in June 2013 and has been used as the backend of Mathematica and other Wolfram technologies for over 30 years.^[27][28]

• Notebook interface

• Official website
• Documentation for the Wolfram Language
• An Elementary Introduction to the Wolfram Language