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APL Programming Language Family
APL (named after the book ''A Programming Language'') is a programming language developed in the 1960s by Kenneth E. Iverson. Its central datatype is the Array data type#Multi-dimensional arrays, multidimensional array. It uses a large range of APL syntax and symbols, special graphic symbols to represent most functions and operators, leading to very concise code. It has been an important influence on the development of concept modeling, spreadsheets, functional programming, and computer math packages. It has also inspired several other programming languages. History Mathematical notation A mathematical notation for manipulating arrays was developed by Kenneth E. Iverson, starting in 1957 at Harvard University. In 1960, he began work for IBM where he developed this notation with Adin Falkoff and published it in his book ''A Programming Language'' in 1962. The preface states its premise: This notation was used inside IBM for short research reports on computer systems, such as ...
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Array Programming
In computer science, array programming refers to solutions that allow the application of operations to an entire set of values at once. Such solutions are commonly used in computational science, scientific and engineering settings. Modern programming languages that support array programming (also known as vector (data structure), vector or multidimensional analysis, multidimensional languages) have been engineered specifically to generalize operations on scalar (computing), scalars to apply transparently to vector (geometric), vectors, matrix (mathematics), matrices, and higher-dimensional arrays. These include APL (programming language), APL, J (programming language), J, Fortran, MATLAB, Analytica (software), Analytica, GNU Octave, Octave, R (programming language), R, Cilk Plus, Julia (programming language), Julia, Perl Data Language, Perl Data Language (PDL), Raku (programming language). In these languages, an operation that operates on entire arrays can be called a ''vectorized' ...
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MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ...
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Functional Programming
In computer science, functional programming is a programming paradigm where programs are constructed by Function application, applying and Function composition (computer science), composing Function (computer science), functions. It is a declarative programming paradigm in which function definitions are Tree (data structure), trees of Expression (computer science), expressions that map Value (computer science), values to other values, rather than a sequence of Imperative programming, imperative Statement (computer science), statements which update the State (computer science), running state of the program. In functional programming, functions are treated as first-class citizens, meaning that they can be bound to names (including local Identifier (computer languages), identifiers), passed as Parameter (computer programming), arguments, and Return value, returned from other functions, just as any other data type can. This allows programs to be written in a Declarative programming, d ...
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Spreadsheet
A spreadsheet is a computer application for computation, organization, analysis and storage of data in tabular form. Spreadsheets were developed as computerized analogs of paper accounting worksheets. The program operates on data entered in cells of a table. Each cell may contain either numeric or text data, or the results of formulas that automatically calculate and display a value based on the contents of other cells. The term ''spreadsheet'' may also refer to one such electronic document. Spreadsheet users can adjust any stored value and observe the effects on calculated values. This makes the spreadsheet useful for "what-if" analysis since many cases can be rapidly investigated without manual recalculation. Modern spreadsheet software can have multiple interacting sheets and can display data either as text and numerals or in graphical form. Besides performing basic arithmetic and mathematical functions, modern spreadsheets provide built-in functions for common financial ...
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APL Syntax And Symbols
The programming language APL is distinctive in being ''symbolic'' rather than ''lexical'': its primitives are denoted by ''symbols'', not words. These symbols were originally devised as a mathematical notation to describe algorithms. APL programmers often assign informal names when discussing functions and operators (for example, "product" for ×/) but the core functions and operators provided by the language are denoted by non-textual symbols. Monadic and dyadic functions Most symbols denote ''functions'' or ''operators''. A ''monadic'' function takes as its argument the result of evaluating everything to its right. (Moderated in the usual way by parentheses.) A ''dyadic'' function has another argument, the first item of data on its left. Many symbols denote both monadic and dyadic functions, interpreted according to use. For example, ⌊3.2 gives 3, the largest integer not above the argument, and 3⌊2 gives 2, the lower of the two arguments. Functions and operators APL uses ...
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Array Data Type
In computer science, array is a data type that represents a collection of ''elements'' ( values or variables), each selected by one or more indices (identifying keys) that can be computed at run time during program execution. Such a collection is usually called an array variable or array value.Robert W. Sebesta (2001) ''Concepts of Programming Languages''. Addison-Wesley. 4th edition (1998), 5th edition (2001), By analogy with the mathematical concepts vector and matrix, array types with one and two indices are often called vector type and matrix type, respectively. More generally, a multidimensional array type can be called a tensor type, by analogy with the mathematical concept, tensor. Language support for array types may include certain built-in array data types, some syntactic constructions (''array type constructors'') that the programmer may use to define such types and declare array variables, and special notation for indexing array elements. For example, in the P ...
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Programming Language
A programming language is a system of notation for writing computer programs. Programming languages are described in terms of their Syntax (programming languages), syntax (form) and semantics (computer science), semantics (meaning), usually defined by a formal language. Languages usually provide features such as a type system, Variable (computer science), variables, and mechanisms for Exception handling (programming), error handling. An Programming language implementation, implementation of a programming language is required in order to Execution (computing), execute programs, namely an Interpreter (computing), interpreter or a compiler. An interpreter directly executes the source code, while a compiler produces an executable program. Computer architecture has strongly influenced the design of programming languages, with the most common type (imperative languages—which implement operations in a specified order) developed to perform well on the popular von Neumann architecture. ...
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Wolfram Language
The Wolfram Language ( ) is a proprietary, very high-level multi-paradigm programming language developed by Wolfram Research. It emphasizes symbolic computation, functional programming, and rule-based programming and can employ arbitrary structures and data. It is the programming language of the mathematical symbolic computation program Mathematica. History The Wolfram Language was part of the initial version of Mathematica in 1988. 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. Wolfram also added features for more complex tasks, such as 3D modeling. 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 ...
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Speakeasy (computational Environment)
Speakeasy was a numerical computing interactive environment also featuring an interpreted programming language. It was initially developed for internal use at the Physics Division of Argonne National Laboratory by the theoretical physicist Stanley Cohen. He eventually founded Speakeasy Computing Corporation to make the program available commercially. Speakeasy is a very long-lasting numerical package. In fact, the original version of the environment was built around a core dynamic data repository called "Named storage" developed in the early 1960s, while the most recent version has been released in 2006. Speakeasy was aimed to make the computational work of the physicists at the Argonne National Laboratory easier. History ''Speakeasy'' was initially conceived to work on mainframes (the only kind of computers at that time), and was subsequently ported to new platforms ( minicomputers, personal computers) as they became available. The porting of the same code on different pl ...
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Snap! (programming Language)
Snap''!'' (formerly Build Your Own Blocks) is a free block-based List of educational programming languages, educational graphical programming language and online community. Snap allows students to explore, create, and remix interactive animations, games, stories, and more, while learning about mathematical and computational ideas. While inspired by Scratch (programming language), Scratch, Snap''!'' has many advanced features. The Snap''!'' editor, and programs created in it, are web applications that run in the browser (like Scratch (programming language), Scratch) without requiring Installation (computer programs), installation. It is built on top of ''Morphic.js'', a Morphic (software), Morphic GUI, written by Jens Mönig as 'middle layer' between Snap! itself and 'bare' JavaScript. User interface In Snap''!'', the screen is organized in three resizable columns containing five regions: the block group selector (top of left column), the blocks palette (left column), the main ar ...
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S (programming Language)
S is a statistical programming language developed primarily by John Chambers (statistician), John Chambers and (in earlier versions) Rick Becker, Trevor Hastie, William S. Cleveland, William Cleveland and Allan Wilks of Bell Labs, Bell Laboratories. The aim of the language, as expressed by John Chambers, is "to turn ideas into software, quickly and faithfully". It was formerly widely used by academic researchers., but has now been superseded by the partially backwards compatible R (programming language), R language, a part of the GNU free software project. S-PLUS was a widely used commercial implementation of S that was formerly sold by TIBCO Software. History "Old S" S is one of several statistical computing languages that were designed at Bell Laboratories, and first took form between 1975–1976. Up to that time, much of the statistical computing was done by directly calling Fortran subroutines; however, S was designed to offer an alternate and more interactive approach, moti ...
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Q (programming Language From Kx Systems)
Q is a programming language for array processing, developed by Arthur Whitney. It is proprietary software, commercialized by Kx Systems. Q serves as the query language for kdb+, a disk based and in-memory, column-based database. Kdb+ is based on the language k, a terse variant of the language APL. Q is a thin wrapper around k, providing a more readable, English-like interface. One of the use cases is financial time series analysis, as one could do inexact time matches. An example is to match the a bid and the ask before that. Both timestamps slightly differ and are matched anyway. Overview The fundamental building blocks of q are ''atoms'', ''lists'', and ''functions''. Atoms are scalars and include the data types numeric, character, date, and time. Lists are ordered collections of atoms (or other lists) upon which the higher level data structures ''dictionaries A dictionary is a listing of lexemes from the lexicon of one or more specific languages, often a ...
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