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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]
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Paradigm | Multi-paradigm: term-rewriting, functional, procedural, array |
---|---|
Designed by | Stephen Wolfram |
Developer | Wolfram Research |
First appeared | 1988 |
Stable release | 14.1.0[1]
/ July 31, 2024 |
Typing discipline | Dynamic, strong |
OS | Cross-platform |
License | Proprietary |
Filename extensions | .nb, .m, .wl |
Website | www |
Major implementations | |
Mathematica, Mathics, Expreduce, MockMMA | |
Influenced by | |
Influenced | |
History
editThe 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]
Syntax
editThe Wolfram Language syntax is overall similar to the M-expression of 1960s LISP, with support for infix operators and "function-notation" function calls.
Basics
editThe 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} *)
Syntactic sugar
editThe 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 andInputForm
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] *)
Functional programming
editCurrying is supported.
Pattern matching
editFunctions 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]
Implementations
editThe 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.[26]
Naming
editThe 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
editReferences
edit- ^ "The Story Continues: Announcing Version 14 of Wolfram Language and Mathematica". Stephen Wolfram Writings. 2024-07-31. Retrieved 2024-07-31.
- ^ Wolfram, Stephen. "Tini Veltman (1931–2021): From Assembly Language to a Nobel Prize—Stephen Wolfram Writings". stephenwolfram.comwritings. Retrieved 22 January 2021.
- ^ Maeder, Roman E. (1994). The Mathematica® Programmer. Academic Press, Inc. p. 6. ISBN 978-1-48321-415-3.
- ^ "Wolfram Language Q&A". Wolfram Research. Retrieved 2016-12-05.
- ^ Somers, James. "The Scientific Paper Is Obsolete". The Atlantic. Retrieved 2018-04-10.
- ^ Hickey, Rich. "Clojure Bookshelf". Amazon.com. Archived from the original on 2017-10-03. Retrieved 2020-05-06.
- ^ "Wolfram Open Code, Open Source, Open Data, Open Resources". www.wolfram.com. Retrieved 2023-02-03.
- ^ "Notes for Programming Language Experts about Wolfram Language". Wolfram.com. Retrieved 2015-11-05.
- ^ a b "What Should We Call the Language of Mathematica?—Stephen Wolfram Blog". Blog.stephenwolfram.com. 2013-02-12. Retrieved 2015-11-05.
- ^ "Celebrating Mathematica's First Quarter Century—Wolfram Blog". Blog.wolfram.com. 23 June 2013. Retrieved 2015-11-05.
- ^ Wolfram (1988). Mathematica, a System for Doing Mathematics By Computer.
- ^ Hayes, Brian (1990-01-01). "Thoughts on Mathematica" (PDF). Pixel.
- ^ "Wolfram Language & System Documentation Center". Reference.wolfram.com. Retrieved 2015-11-05.
- ^ "Putting the Wolfram Language (and Mathematica) on Every Raspberry Pi—Wolfram Blog". Blog.wolfram.com. 21 November 2013. Retrieved 2015-11-05.
- ^ Sherr, Ian (2013-11-22). "Premium Mathematica software free on budget Raspberry Pi - CNET". News.cnet.com. Retrieved 2015-11-05.
- ^ Daniel AJ Sokolov (2014-11-22). "Intels Edison: Pentium-System im Format einer SD-Karte | heise online". Heise.de. Retrieved 2015-11-05.
- ^ "The Wolfram Language will soon be integrated into Unity". Gamasutra. 2014-03-10. Retrieved 2015-11-05.
- ^ "Is there a way to use Wolfram Language in Unity3D?". Wolfram. 2017. Archived from the original on 19 July 2017. Retrieved 11 April 2017.
- ^ "FullForm". Wolfram Language Documentation.
- ^ "Welcome to Rubi, the Rule-based Integrator". Rule-based Integration.
- ^ McLoone, J (2 April 2019). "Why Wolfram Tech Isn't Open Source—A Dozen Reasons—Wolfram Blog".
- ^ "codeparser: Parse Wolfram Language source code as abstract syntax trees (ASTs) or concrete syntax trees (CSTs)". GitHub. Wolfram Research, Inc.
- ^ "Open Materials from Wolfram: Open Code, Open Source, Open Data, Open Resources". www.wolfram.com.
- ^ Simon. "Is there an open source implementation of Mathematica-the-language?". Mathematica Stack Exchange.
- ^ Wolfram, Steven (21 May 2019). "Launching Today: Free Wolfram Engine for Developers—Stephen Wolfram Writings".
- ^ "Free Wolfram Engine for Developers". www.wolfram.com. Retrieved 19 January 2021.
- ^ Kastrenakes, Jacob (2013-11-14). "Wolfram announces 'most important' project: a programming language that models the world". The Verge. Retrieved 2023-09-21.
- ^ "Something Very Big Is Coming: Our Most Important Technology Project Yet—Stephen Wolfram Writings". writings.stephenwolfram.com. 2013-11-13. Retrieved 2023-09-21.