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Wolfram Language

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Wolfram Language
ParadigmMulti-paradigm: term-rewriting, functional, procedural, array
Designed byStephen Wolfram
DeveloperWolfram Research
First appeared1988; 36 years ago (1988)
Stable release
14.0.0[1] / January 9, 2024; 5 months ago (2024-01-09)
Typing disciplineDynamic, strong
Filename extensions.nb, .m, .wl
Websitewww.wolfram.com/language/ Edit this at Wikidata
Major implementations
Mathematica, Mathics, Expreduce, MockMMA
Influenced by

The Wolfram Language (/ˈwʊlfrəm/ WUUL-frəm) is a proprietary,[7] general 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 a 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 was 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:

(* = 0 *)

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

Lists are enclosed in curly brackets:

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

Syntactic sugar[edit]

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 an apostrophe '.
  • The infix operators themselves are considered "sugar" for the function notation system.

A FullForm formatter desugars the input:[19]

(* = Plus[1, 2] *)

Functional programming[edit]

Currying is supported.

Pattern matching[edit]

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] :=
(* 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 include Symja in Java, expreduce in Golang, and the 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.[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]

See also[edit]


  1. ^ "The Story Continues: Announcing Version 14 of Wolfram Language and Mathematica". Stephen Wolfram Writings. 2024-01-09. Retrieved 2024-01-10.
  2. ^ Wolfram, Stephen. "Tini Veltman (1931–2021): From Assembly Language to a Nobel Prize—Stephen Wolfram Writings". stephenwolfram.comwritings. Retrieved 22 January 2021.
  3. ^ Maeder, Roman E. (1994). The Mathematica® Programmer. Academic Press, Inc. p. 6. ISBN 978-1-48321-415-3.
  4. ^ "Wolfram Language Q&A". Wolfram Research. Retrieved 2016-12-05.
  5. ^ Somers, James. "The Scientific Paper Is Obsolete". The Atlantic. Retrieved 2018-04-10.
  6. ^ Hickey, Rich. "Clojure Bookshelf". Amazon.com. Archived from the original on 2017-10-03. Retrieved 2020-05-06.
  7. ^ "Wolfram Open Code, Open Source, Open Data, Open Resources". www.wolfram.com. Retrieved 2023-02-03.
  8. ^ "Notes for Programming Language Experts about Wolfram Language". Wolfram.com. Retrieved 2015-11-05.
  9. ^ a b "What Should We Call the Language of Mathematica?—Stephen Wolfram Blog". Blog.stephenwolfram.com. 2013-02-12. Retrieved 2015-11-05.
  10. ^ "Celebrating Mathematica's First Quarter Century—Wolfram Blog". Blog.wolfram.com. 23 June 2013. Retrieved 2015-11-05.
  11. ^ Wolfram (1988). Mathematica, a System for Doing Mathematics By Computer.
  12. ^ Hayes, Brian (1990-01-01). "Thoughts on Mathematica" (PDF). Pixel.
  13. ^ "Wolfram Language & System Documentation Center". Reference.wolfram.com. Retrieved 2015-11-05.
  14. ^ "Putting the Wolfram Language (and Mathematica) on Every Raspberry Pi—Wolfram Blog". Blog.wolfram.com. 21 November 2013. Retrieved 2015-11-05.
  15. ^ Sherr, Ian (2013-11-22). "Premium Mathematica software free on budget Raspberry Pi - CNET". News.cnet.com. Retrieved 2015-11-05.
  16. ^ Daniel AJ Sokolov (2014-11-22). "Intels Edison: Pentium-System im Format einer SD-Karte | heise online". Heise.de. Retrieved 2015-11-05.
  17. ^ "The Wolfram Language will soon be integrated into Unity". Gamasutra. 2014-03-10. Retrieved 2015-11-05.
  18. ^ "Is there a way to use Wolfram Language in Unity3D?". Wolfram. 2017. Archived from the original on 19 July 2017. Retrieved 11 April 2017.
  19. ^ "FullForm". Wolfram Language Documentation.
  20. ^ "Welcome to Rubi, the Rule-based Integrator". Rule-based Integration.
  21. ^ McLoone, J (2 April 2019). "Why Wolfram Tech Isn't Open Source—A Dozen Reasons—Wolfram Blog".
  22. ^ "codeparser: Parse Wolfram Language source code as abstract syntax trees (ASTs) or concrete syntax trees (CSTs)". GitHub. Wolfram Research, Inc.
  23. ^ "Open Materials from Wolfram: Open Code, Open Source, Open Data, Open Resources". www.wolfram.com.
  24. ^ Simon. "Is there an open source implementation of Mathematica-the-language?". Mathematica Stack Exchange.
  25. ^ Wolfram, Steven (21 May 2019). "Launching Today: Free Wolfram Engine for Developers—Stephen Wolfram Writings".
  26. ^ "Free Wolfram Engine for Developers". www.wolfram.com. Retrieved 19 January 2021.
  27. ^ Kastrenakes, Jacob (2013-11-14). "Wolfram announces 'most important' project: a programming language that models the world". The Verge. Retrieved 2023-09-21.
  28. ^ "Something Very Big Is Coming: Our Most Important Technology Project Yet—Stephen Wolfram Writings". writings.stephenwolfram.com. 2013-11-13. Retrieved 2023-09-21.

External links[edit]