Wolfram Language

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.

(* 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 *)

Sin[Pi]
(* = 0 *)

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

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

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

F[x_] := x ^ 0

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]] *)

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

(* 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 C++ parser of the language under the open source MIT License.[22] 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 a 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]

• Notebook interface

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