Wolfram Language
The Wolfram Language (/ˈwʊlfrəm/ WUUL-frəm) is a proprietary,[7] 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] HistoryThe 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] SyntaxThe Wolfram Language syntax is overall similar to the M-expression of 1960s LISP, with support for infix operators and "function-notation" function calls. BasicsThe 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 sugarThe language may deviate from the M-expression paradigm when an alternative, more human-friendly way of showing an expression is available:
A FullForm[1+2]
(* = Plus[1, 2] *)
Functional programmingCurrying is supported. Pattern matchingFunctions in the Wolfram Language are effectively a case of simple patterns for replacement: F[x_] := x ^ 0
The 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 A ReplaceRepeated { 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]
ImplementationsThe 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] NamingThe 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 alsoReferences
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