Wolfram Language: Difference between revisions

The Wolfram Language is a general

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 there in 1988 was the notebook model and the ability to embed sound and images, according to Theodore Gray's patent.^[12]

An online frontend for the language, WolframAlpha, was released in 2009. Wolfram implemented this website by translating natural language statements into Wolfram-language queries that link to its database. This frontend greatly enlarged the audience of the language, and the work leading to Wolfram Alpha also means that Wolfram's implementation of the language now has built-in access to a knowledge-base as well as natural language processing functions. 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

(* 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: *)
3 / 2
(* = 3/2 *)

Sin[Pi]
(* = 0 *)

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

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

A FullForm formatter desugars the input:[19]

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

Functional programming

Currying is supported.

Pattern matching

Functions in the Wolfram Language are basically 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

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] A number of libraries and functions written in this language are open source, and the reference book itself is open access.^[23]

In the three-decade-long existence of the Wolfram language, a number of

In 2019,[25] Wolfram Research released a freeware Wolfram Engine, to be used as a programming library in non-commercial software.^[26]

Naming

The language was officially named in June 2013 although, as the backend of the computing system

• Stephen Wolfram
• Wolfram Mathematica
• Notebook interface
• Wolfram Research
• Wolfram Alpha
• Wolfram Demonstrations Project

References