APL (for A Programming Language) is an array programming language based on a notation invented in 1957 by Kenneth E. Iverson while at Harvard University. It originated in an attempt to provide consistent notation for the teaching and analysis of topics related to the application of computers. The notation was later used to describe the IBM System/360 machine architecture, a description much more concise and exact than the existing documentation and revealing several previously unnoticed problems. Then, a Selectric typeball was made to write a linear representation of this notation. In 1964, a subset of the notation was implemented as a programming language. Array programming languages (also known as vector or multidimensional languages) generalize operations on scalars to apply transparently to vectors, matrices, and higher dimensional arrays. ... 1957 (MCMLVII) was a common year starting on Tuesday of the Gregorian calendar. ... Kenneth Eugene Iverson (17 December 1920, Camrose, Alberta/Canada –October 19, 2004,Toronto, Ontario/Canada) was a computer scientist most notable for developing the APL programming language. ... Harvard University campus (old map) Harvard University (incorporated as The President and Fellows of Harvard College) is a private university in Cambridge, Massachusetts. ... Big Blue redirects here. ... System/360 Model 65 operators console, with register value lamps and toggle switches (middle of picture) and emergency pull switch (upper right). ... The IBM Selectric typewriter (occasionally known as the IBM Golfball typewriter) is the electric typewriter design that brought the typewriter into the electronic age starting in 1961. ... For the Nintendo 64 emulator, see 1964 (Emulator). ...

Iverson published his notation in 1962 in a book titled A Programming Language and APL got its name from the title of this book. Iverson received the Turing Award in 1979 for his work. As with all programming languages that have had several decades of continual use, APL has changed significantly from the notation described by Iverson in his book. One thing that has remained constant is that APL is interpretive and interactive, features much appreciated by its users. Conversely, its initial lack of support for both structured and modular programming has been solved by all the modern APL incarnations. One much criticized aspect of APL is the use of a special character set (see Character set below.) These characters have all been incorporated into Unicode, which is now the base character set of several APL products. Iverson later reworked APL into a language called J which not only greatly increases expressive power but also uses pure ASCII instead of a special character set. 1962 (MCMLXII) was a common year starting on Monday (the link is to a full 1962 calendar). ... The A.M. Turing Award is given annually by the Association for Computing Machinery to a person selected for contributions of a technical nature made to the computing community. ... This page refers to the year 1979. ... In computer programming, an interpreted language is a programming language whose programs may be executed from source form, by an interpreter. ... There are several conceptual views of interactivity, the most general being the contingency view. ... Structured programming can be seen as a subset or subdiscipline of procedural programming, one of the major programming paradigms. ... Modularity is a concept that has applications in the contexts of computer science, particularly programming, as well as cognitive science in investigating the structure of mind. ... APL (for A Programming Language, or sometimes Array Processing Language) is an array programming language based on a notation invented in 1957 by Kenneth E. Iverson while at Harvard University. ... The J programming language, developed in the early 1990s by Ken Iverson and Roger Hui, is a synthesis of APL (also by Iverson) and the FP and FL functional programming languages created by John Backus (of FORTRAN, ALGOL, and BNF fame). ...

Overview

Over a very wide set of problem domains (math, science, engineering, computer design, robotics, data visualization, actuarial science, traditional DP, etc.) APL is an extremely powerful, expressive and concise programming language, typically set in an interactive environment. It was originally created as a way to describe computers, by expressing mathematical notation in a rigorous way that could be interpreted by a computer. It is easy to learn but APL programs can take some time to understand. Unlike traditional structured programming languages, code in APL is typically structured as chains of monadic or dyadic functions and operators acting on arrays. Because APL has so many nonstandard primitives (functions, operators, or features built into the language and indicated by a single symbol or a combination of a few symbols), APL does not have function or operator precedence. The original APL did not have control structures (loops, if-then-else), but the array operations it included could simulate structured programming constructs. For example, the iota function (which yields an array from 1 to N) can simulate for-loop iteration. More recent implementations of APL generally include explicit control structures, so that data structure and control-flow structure can be more clearly separated. Mathematical notation is used in mathematics, and throughout the physical sciences, engineering, and economics. ... The term monadic has multiple uses in mathematics: In category theory, an adjunction is monadic or tripleable if it is equivalent to the adjunction given by the Eilenberg-Moore algebras of its associated monad. ... Dyadic Dyadic tensor Dyadic fraction Dyadic counterpoint, the voice-against-voice conception of polyphony Dyad This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... In computer science, a subroutine (function, procedure, or subprogram) is a sequence of code which performs a specific task, as part of a larger program, and is grouped as one, or more, statement blocks; such code is sometimes collected into software libraries. ... In mathematics, an operator is a function that performs some sort of operation on a number, variable, or function. ... In computer programming, an array, also known as a vector or list (for one-dimensional arrays) or a matrix (for two-dimensional arrays), is one of the simplest data structures. ... This article is about the concept of operator precedence. ... In computer science and in computer programming, statements in pseudocode or in a program are normally obeyed (or executed) one after the other in the order in which they are written (sequential flow of control). ... Structured programming can be seen as a subset or subdiscipline of procedural programming, one of the major programming paradigms. ... Iteration is the repetition of a process, typically within a computer program. ...

The APL environment is called a workspace. In a workspace the user can define programs and data, i.e. the data values exist also outside the programs, and the user can manipulate the data without the necessity to define a program, for example:

Assign the vector values 4 5 6 7 to N. In linear algebra, a coordinate vector is an explicit representation of a vector in an abstract vector space as an ordered list of numbers or, equivalently, as an element of the coordinate space Fn. ...

Add 4 to all values (giving 8 9 10 11) and Print them (absence of the assignment arrow means "show").

Print the sum of N, i.e. 22.

The user can save the workspace with all values, programs and execution status. In any case, the programs are usually not compiled but interpreted. A commercial compiler was brought to market by STSC (now Manugistics). A compiled language is a programming language whose implementations are typically compilers (translators which generate machine code from source code), and not interpreters (step-by-step executors of source code, where no translation takes place). ... In computer programming, an interpreted language is a programming language whose programs may be executed from source form, by an interpreter. ...

APL is well-known for its use of a set of non-ASCII symbols that are an extension of traditional arithmetic and algebraic notation. These cryptic symbols, some have joked, make it possible to construct an entire air traffic control system in two lines of code. Indeed, in some versions of APL, it is theoretically possible to express any computable function in one expression, that is in one line of code. You can use the other line for I/O, or constructing a GUI. Because of its condensed nature and non-standard characters, APL has sometimes been termed a "write-only language", and reading an APL program can at first feel like decoding an alien tongue. Because of the unusual character set, many programmers used special APL keyboards in the production of APL code. Nowadays there are various ways to write APL code using only ASCII characters. Indeed most if not all modern implementations use the standard keyboard, displaying APL symbols by use of a particular font. For other uses, see ASCII (disambiguation). ... Air Traffic Control Towers (ATCTs) at Schiphol Airport Air Traffic Control (ATC) is a service provided by ground-based controllers who direct aircraft on the ground and in the air. ... A write-only language is a programming language with the attribute that programs written in it are more easily scrapped and re-written than modified. ... A character encoding is a code that pairs a set of characters (such as an alphabet or syllabary) with a set of something else, such as numbers or electrical pulses. ... A computer keyboard is a peripheral modeled after the typewriter keyboard. ...

Advocates of APL claim that the examples of "write-only" code are almost invariably examples of poor programming practice or novice mistakes, which can occur in any language.

APL has perhaps had an unusually high percentage of users who are subject-matter experts who know some APL, rather than professional programmers who know something about a subject.

Iverson designed a successor to APL called J which uses ASCII "natively". So far there is only a single source of J implementations: http://www.jsoftware.com/ Other programming languages offer functionality similar to APL. A+ is a programming language with many commands identical to APL, and with an open source implementation. The J programming language, developed in the early 1990s by Ken Iverson and Roger Hui, is a synthesis of APL (also by Iverson) and the FP and FL functional programming languages created by John Backus (of FORTRAN, ALGOL, and BNF fame). ... Computer code (HTML with JavaScript) in a tool that uses syntax highlighting (colors) to help the developer see the purpose of each piece of code. ... Open source refers to projects that are open to the public and which draw on other projects that are freely available to the general public. ...

Examples

Here's how you would write a program that would sort a word list stored in matrix X according to word length: Sorting refers to a process of arranging items in some sequence and/or in different sets, and accordingly, it has two common, yet distinct meanings: ordering: aranging items of the same kind, class, nature, etc. ...

 X[⍋X+.≠' ';] 

Here's a program that finds all prime numbers from 1 to R in time and space both O(R²): In mathematics, a prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. ...

Here's how to read it, from right to left:

1. creates a vector containing integers from 1 to R (if R = 6 at the beginning of the program, is 1 2 3 4 5 6)
2. Drop first element of this vector ( function), i.e. 1. So is 2 3 4 5 6
3. Set R to the vector (, assignment primitive)
4. Generate outer product of R multiplied by R, i.e. a matrix which is the multiplication table of R by R (function)
5. Build a vector the same length as R with 1 in each place where the corresponding number in R is in the outer product matrix (, set inclusion function), i.e. 0 0 1 0 1
6. Logically negate the values in the vector (change zeros to ones and ones to zeros) (, negation function), i.e. 1 1 0 1 0
7. Select the items in R for which the corresponding element is 1 ( function), i.e. 2 3 5

The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. ... In mathematics, a multiplication table is a mathematical table used to define a multiplication operation for an algebraic system. ...

Calculation

APL was unique in the speed with which it could perform complex matrix operations. For example, a very large matrix multiplication would take only a few seconds on a machine which was much less powerful than those today. There were some technical and other economic reasons for this advantage:

• Commercial interpreters delivered highly-tuned linear algebra library routines.
• Very low interpretive overhead was incurred per-array—not per-element.
• APL response time compared favorably to the runtimes of early optimizing compilers.

A widely cited paper "The APL Machine" perpetuated the myth that APL made pervasive use of lazy evaluation where calculations would not actually be performed until the results were needed and then only those calculations strictly required. Although this technique was used by just a few implementations, it embodies the language's best survival mechanism: not specifying the order of scalar operations. Even as eventually standardized by X3J10, APL is so highly data-parallel, it gives language implementers immense freedom to schedule operations as efficiently as possible. As computer innovations such as cache memory, and SIMD execution became commercially available, APL programs ported with little extra effort spent re-optimizing low-level details. In computer programming, lazy evaluation is a technique that attempts to delay computation of expressions until the results of the computation are known to be needed. ... This article is about the computer term. ... -1...

Terminology

APL makes a clear distinction between functions and operators. Functions take values (variables or constants or expressions) as arguments, and return values as results. Operators take functions as arguments, and return related, derived, functions as results. For example the "sum" function is derived by applying the "reduction" operator to the "addition" function. Applying the same reduction operator to the "ceiling" function (which returns the larger of two values) creates a derived "maximum" function, which returns the largest of a group (vector) of values. In the J language, Iverson substituted the terms 'verb' and 'adverb' for 'function' and 'operator'.

APL also identifies those features built into the language, and represented by a symbol, or a fixed combination of symbols, as primitives. Most primitives are either functions or operators. Coding APL is largely a process of writing non-primitive functions and (in some dialects of APL) operators. However a few primitives are considered to be neither functions nor operators, most noticeably assignment.

Character set

APL has always been criticized for its choice of a unique, non-standard character set. The fact that those who learn it usually become ardent adherents shows that there is some weight behind Iverson's idea that the notation used does make a difference. In the beginning, there were few terminal devices which could reproduce the APL character set — the most popular ones employing the IBM Selectric print mechanism along with a custom type element. With the popularization of the Unicode standard, which contains an APL character set, the eternal problem of obtaining the required particular fonts seems poised to go away. Big Blue redirects here. ... The IBM Selectric typewriter (occasionally known as the IBM Golfball typewriter) is the electric typewriter design that brought the typewriter into the electronic age starting in 1961. ... Due to technical limitations, some web browsers may not display some special characters in this article. ...

APL symbols and keyboard layout

APL keyboard with special characters

Note the mnemonics associating an APL character with a letter: question mark on Q, power on P, rho on R, base value on B, eNcode on N, modulus on M and so on. This makes it easier for an English-language speaker to type APL on a non-APL keyboard providing one has visual feedback on one's screen. This work is copyrighted, and used with permission. ...

A more up to date keyboard diagram, applicable for APL2 and other modern implementations, is available: Union layout for windows.

All APL symbols are present in Unicode:
It may be required to significantly reconfigure your browser in order to display Unicode fonts. Due to technical limitations, some web browsers may not display some special characters in this article. ...

See also

• APL function symbols for a list of built-in monadic and dyadic functions and their Unicode representation.
• IBM 3270 Keyboard layout for APL[1]

The following APL operators are given, separated into their monadic and dyadic forms. ... Big Blue redirects here. ... Clemson Universitys Library Catalog The IBM 3270 is a class of terminals made by IBM (known as Display Devices) normally used to communicate with IBM mainframes. ... A computer keyboard is a peripheral modeled after the typewriter keyboard. ...

Usage

APL has long had a small but fervent user base. It has been particularly popular in financial and insurance applications, in simulations, and in some mathematical applications. But APL has been used in a wide variety of contexts and for many and varied purposes.

Standardization

APL has been standardized by the ANSI working group X3J10 and ISO/IEC Joint Technical Committee 1 Subcommittee 22 Working Group 3. The Core APL language is specified in ISO 8485:1989, and the Extended APL language is specified in ISO/IEC 13751:2001. The American National Standards Institute or ANSI (pronounced an-see) is a nonprofit organization that oversees the development of standards for products, services, processes and systems in the United States. ... Wikipedia does not have an article with this exact name. ... The International Organization for Standardization (ISO) is an international standard-setting body composed of representatives from national standards bodies. ... The International Electrotechnical Commission (IEC) is an international standards organization dealing with electrical, electronic and related technologies. ...

Quotes

• "APL, in which you can write a program to simulate shuffling a deck of cards and then dealing them out to several players in four characters, none of which appear on a standard keyboard."
  • David Given
• "APL is a mistake, carried through to perfection. It is the language of the future for the programming techniques of the past: it creates a new generation of coding bums."
  • Edsger Dijkstra, 1968
• "By the time the practical people found out what had happened; APL was so important a part of how IBM ran its business that it could not possibly be uprooted."
  • Micheal S. Montalbano 1982 (see A Personal History of APL)

Portrait of Edsger Dijkstra (courtesy Brian Randell) Prof Dr Edsger Wybe Dijkstra (Rotterdam, May 11, 1930 – Nuenen, August 6, 2002) was a Dutch computer scientist. ... 1968 (MCMLXVIII) was a leap year starting on Monday (the link is to a full 1968 calendar). ... 1982 (MCMLXXXII) was a common year starting on Friday of the Gregorian calendar. ...

Awards

There is an annual award for contributions to APL, the Iverson Award named after the language's creator. The Iverson Award, more formally the Kenneth E. Iverson Award for Outstanding Contribution to APL, is presented by the Special Interest Group on APL (SIGAPL) of the Association for Computing Machinery (ACM). ...

See also

• IBM 1130: APL 1130 was an early implementation (circa 1970) of APL on the IBM 1130
• J: APL's successor, by Kenneth E. Iverson and Roger Hui
• K: an alternative APL successor, by Arthur Whitney
• Nial
• I. P. Sharp Associates

The IBM 1130 Computing System was introduced in 1965. ... The J programming language, developed in the early 1990s by Ken Iverson and Roger Hui, is a synthesis of APL (also by Iverson) and the FP and FL functional programming languages created by John Backus (of FORTRAN, ALGOL, and BNF fame). ... Kenneth Eugene Iverson (17 December 1920, Camrose, Alberta/Canada –October 19, 2004,Toronto, Ontario/Canada) was a computer scientist most notable for developing the APL programming language. ... Roger Hui was co-developer of the J Programming Language. ... K is a high level array programming language developed by Arthur Whitney, a very influential member of the APL community. ... Arthur Whitney is a computer scientist most notable for developing the K programming language. ... Nial (from Nested Interactive Array Language) is a high-level array-based programming language developed from about 1981 by Mike Jenkins of Queens University, Kingston, Ontario, Canada. ... I. P. Sharp Associates, IPSA for short, was a major Canadian computer time sharing, consulting and services firm of the 1970s and 80s. ...

References

• A Programming Language (1962), by Kenneth E. Iverson
• A formal description of SYSTEM/360, IBM Systems Journal 3:3, New York: 1964
• History of Programming Languages, chapter 14

Kenneth Eugene Iverson (17 December 1920, Camrose, Alberta/Canada –October 19, 2004,Toronto, Ontario/Canada) was a computer scientist most notable for developing the APL programming language. ...

External links

• APL2 available from IBM
• APL - A Programming Language
• Rex Swain's APL info
• SIGAPL Home Page
• APL2C Compiler
• Sam Sirlin's APL FAQ (Frequently Asked Questions list)
• Scanned manuals for early APL implementations (APL 360 and APL 1130)
• A Personal History Of APL by Micheal S. Montalbano
• Conway's Game of Life in one line of APL
• J is Iverson's reworking of APL to use the standard ASCII font
• A+ is a programming language with many commands identical to APL and an open source implementation
• Simmunity is a compiled programming language based on APL designed for Internet collaborative applications

FAQ is an abbreviation for Frequently Asked Question(s). The term refers to listed questions and answers, all supposed to be frequently asked in some context, and pertaining to a particular topic. ... Open source refers to projects that are open to the public and which draw on other projects that are freely available to the general public. ...

Articles

• A Formal Description of SYSTEM/360 (1964 article by Adin D. Falkoff, Kenneth E. Iverson, Edward H. Sussenguth)
• An APL Machine (1970 Stanford doctoral dissertation by Philip Abrams)
• The Design of APL (1973 article by Adin D. Falkoff and Kenneth E. Iverson)
• The IBM Family of APL Systems (1991 article by Adin D. Falkoff)
• A Personal view of APL by Kenneth E. Iverson