Wolfram Language

The Wolfram Language was part of the initial version of Mathematica in 1988.Wolfram (1988). Mathematica, a System for Doing Mathematics By Computer.

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.{{Cite news|url=http://bit-player.org/wp-content/extras/bph-publications/Pixel-1990-01-Hayes-Mathematica.pdf|title=Thoughts on Mathematica|last=Hayes|first=Brian|date=1990-01-01|work=Pixel}}

Wolfram also added features for more complex tasks, such as 3D modeling.{{cite web|url=https://reference.wolfram.com/language/|title=Wolfram Language & System Documentation Center|publisher=Reference.wolfram.com|access-date=2015-11-05}}

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.{{cite web|url=https://blog.wolfram.com/2013/11/21/putting-the-wolfram-language-and-mathematica-on-every-raspberry-pi/|title=Putting the Wolfram Language (and Mathematica) on Every Raspberry Pi—Wolfram Blog|date=21 November 2013 |publisher=Blog.wolfram.com|access-date=2015-11-05}} 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.{{cite web|url=https://www.cnet.com/news/premium-mathematica-software-free-on-budget-raspberry-pi/|title=Premium Mathematica software free on budget Raspberry Pi - CNET|last=Sherr|first=Ian|date=2013-11-22|publisher=News.cnet.com|access-date=2015-11-05}} Plans to port the Wolfram language to the Intel Edison were announced after the board's introduction at CES 2014 but were never released.{{cite web|url=https://www.heise.de/newsticker/meldung/Intels-Edison-Pentium-System-im-Format-einer-SD-Karte-2076917.html|title=Intels Edison: Pentium-System im Format einer SD-Karte | heise online|author=Daniel AJ Sokolov|date=2014-11-22|publisher=Heise.de|access-date=2015-11-05}} 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.{{cite web|url=https://www.gamedeveloper.com/design/the-wolfram-language-will-soon-be-integrated-into-unity|title=The Wolfram Language will soon be integrated into Unity|date=2014-03-10|publisher=Gamasutra|access-date=2015-11-05}}{{cite web|url=https://community.wolfram.com/groups/-/m/t/312155|title=Is there a way to use Wolfram Language in Unity3D?|year=2017|publisher=Wolfram|access-date=11 April 2017|archive-url=https://web.archive.org/web/20170719095116/https://community.wolfram.com/groups/-/m/t/312155|url-status=deviated|archive-date=19 July 2017}}

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 {{code|TeXForm}} for typeset expressions and {{code|InputForm}} for language input.
• Functions can also be applied using the prefix expression {{code|@}} and the postfix expression {{code|//}}.
• Derivatives can be denoted with the apostrophe {{code|'}}.
• The infix operators themselves are considered "sugar" for the function notation system.

A {{code|FullForm}} formatter desugars the input:{{cite web |title=FullForm |url=https://reference.wolfram.com/language/ref/FullForm.html |website=Wolfram Language Documentation}}

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 {{code|1=:=}} is a "SetDelayed operator", so that the x is not immediately looked for. {{code|x_}} is syntax sugar for {{code|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 {{code|/;}} operator is "condition", so that the rule only applies when {{code|y>z}}. The three underscores are a syntax for a {{code|BlankNullSequence[]}}, for a sequence that can be null.

A ReplaceRepeated {{code|//.}} 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:{{cite web |title=Welcome to Rubi, the Rule-based Integrator |url=https://rulebasedintegration.org/ |website=Rule-based Integration}}

(* 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.{{cite web |last1=McLoone |first1=J |title=Why Wolfram Tech Isn't Open Source—A Dozen Reasons—Wolfram Blog |date=2 April 2019 |url=https://blog.wolfram.com/2019/04/02/why-wolfram-tech-isnt-open-source-a-dozen-reasons/ |language=en}} Wolfram Research has, however, released a parser of the language under the open source MIT License.{{cite web |title=codeparser: Parse Wolfram Language source code as abstract syntax trees (ASTs) or concrete syntax trees (CSTs) |url=https://github.com/WolframResearch/codeparser |website=GitHub |publisher=Wolfram Research, Inc.}} The parser was originally developed in C++ but was rewritten in Rust in 2023. The reference book is open access.{{cite web |title=Open Materials from Wolfram: Open Code, Open Source, Open Data, Open Resources |url=https://www.wolfram.com/open-materials/ |website=www.wolfram.com |language=en}}

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|2020|04|lc=yes}} include Symja in Java, expreduce in Golang, and SymPy-based Mathics.{{cite web |author1=Simon |title=Is there an open source implementation of Mathematica-the-language? |url=https://mathematica.stackexchange.com/a/4456 |website=Mathematica Stack Exchange}} 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,{{cite web |last1=Wolfram |first1=Steven |title=Launching Today: Free Wolfram Engine for Developers—Stephen Wolfram Writings |date=21 May 2019 |url=https://writings.stephenwolfram.com/2019/05/launching-today-free-wolfram-engine-for-developers/ |language=en}} 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 [https://github.com/WolframResearch/WolframLanguageForJupyter Wolfram Kernel for Jupyter].{{cite web |title=Free Wolfram Engine for Developers |url=https://www.wolfram.com/engine/ |website=www.wolfram.com |access-date=19 January 2021 |language=en}}

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.{{Cite web |last=Kastrenakes |first=Jacob |date=2013-11-14 |title=Wolfram announces 'most important' project: a programming language that models the world |url=https://www.theverge.com/2013/11/14/5103446/wolfram-language-announced-intelligent-knowledge-based-programming |access-date=2023-09-21 |website=The Verge |language=en-US}}{{Cite web |date=2013-11-13 |title=Something Very Big Is Coming: Our Most Important Technology Project Yet—Stephen Wolfram Writings |url=https://writings.stephenwolfram.com/2013/11/something-very-big-is-coming-our-most-important-technology-project-yet/ |access-date=2023-09-21 |website=writings.stephenwolfram.com |language=en}}

{{Portal|Computer programming|Mathematics}}

• Notebook interface

{{Reflist|30em}}

• {{official website}}
• [https://reference.wolfram.com/language/ Documentation for the Wolfram Language]
• [https://www.wolfram.com/language/elementary-introduction/2nd-ed/ An Elementary Introduction to the Wolfram Language]

{{Wolfram Research}}

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Category:Array programming languages

Category:Notebook interface

Category:Computer algebra systems

Category:Cross-platform software

Category:Dynamically typed programming languages

Category:Finite element software

Category:Functional languages

Category:High-level programming languages

Category:Multi-paradigm programming languages

Category:Programming languages created in 1988

Category:Term-rewriting programming languages

Category:Wolfram Research