ⓘ APL (programming language)

                                     

ⓘ APL (programming language)

APL is a programming language developed in the 1960s by Kenneth E. Iverson. Its central datatype is the multidimensional array. It uses a large range of 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.

                                     

1.1. 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:

Applied mathematics is largely concerned with the design and analysis of explicit procedures for calculating the exact or approximate values of various functions. Such explicit procedures are called algorithms or programs. Because an effective notation for the description of programs exhibits considerable syntactic structure, it is called a programming language.

This notation was used inside IBM for short research reports on computer systems, such as the Burroughs B5000 and its stack mechanism when stack machines versus register machines were being evaluated by IBM for upcoming computers.

Iverson also used his notation in a draft of the chapter A Programming Language, written for a book he was writing with Fred Brooks, Automatic Data Processing, which would be published in 1963.

In 1979, Iverson received the Turing Award for his work on APL.

                                     

1.2. History Development into a computer programming language

As early as 1962, the first attempt to use the notation to describe a complete computer system happened after Falkoff discussed with William C. Carter his work to standardize the instruction set for the machines that later became the IBM System/360 family.

In 1963, Herbert Hellerman, working at the IBM Systems Research Institute, implemented a part of the notation on an IBM 1620 computer, and it was used by students in a special high school course on calculating transcendental functions by series summation. Students tested their code in Hellermans lab. This implementation of a part of the notation was called Personalized Array Translator PAT.

In 1963, Falkoff, Iverson, and Edward H. Sussenguth Jr., all working at IBM, used the notation for a formal description of the IBM System/360 series machine architecture and functionality, which resulted in a paper published in IBM Systems Journal in 1964. After this was published, the team turned their attention to an implementation of the notation on a computer system. One of the motivations for this focus of implementation was the interest of John L. Lawrence who had new duties with Science Research Associates, an educational company bought by IBM in 1964. Lawrence asked Iverson and his group to help use the language as a tool to develop and use computers in education.

After Lawrence M. Breed and Philip S. Abrams of Stanford University joined the team at IBM Research, they continued their prior work on an implementation programmed in FORTRAN IV for a part of the notation which had been done for the IBM 7090 computer running on the IBSYS operating system. This work was finished in late 1965 and later named IVSYS for Iverson system. The basis of this implementation was described in detail by Abrams in a Stanford University Technical Report, "An Interpreter for Iverson Notation" in 1966, the academic aspect of this was formally supervised by Niklaus Wirth. Like Hellermans PAT system earlier, this implementation did not include the APL character set but used special English reserved words for functions and operators. The system was later adapted for a time-sharing system and, by November 1966, it had been reprogrammed for the IBM System/360 Model 50 computer running in a time sharing mode and was used internally at IBM.

                                     

1.3. History Hardware

A key development in the ability to use APL effectively, before the wide use of cathode ray tube CRT terminals, was the development of a special IBM Selectric typewriter interchangeable typing element with all the special APL characters on it. This was used on paper printing terminal workstations using the Selectric typewriter and typing element mechanism, such as the IBM 1050 and IBM 2741 terminal. Keycaps could be placed over the normal keys to show which APL characters would be entered and typed when that key was struck. For the first time, a programmer could type in and see proper APL characters as used in Iversons notation and not be forced to use awkward English keyword representations of them. Falkoff and Iverson had the special APL Selectric typing elements, 987 and 988, designed in late 1964, although no APL computer system was available to use them. Iverson cited Falkoff as the inspiration for the idea of using an IBM Selectric typing element for the APL character set.

Many APL symbols, even with the APL characters on the Selectric typing element, still had to be typed in by over-striking two extant element characters. An example is the grade up character, which had to be made from a delta shift-H and a Sheffer stroke shift-M. This was necessary because the APL character set was much larger than the 88 characters allowed on the typing element, even when letters were restricted to upper-case capitals.



                                     

1.4. History Commercial availability

The first APL interactive login and creation of an APL workspace was in 1966 by Larry Breed using an IBM 1050 terminal at the IBM Mohansic Labs near Thomas J. Watson Research Center, the home of APL, in Yorktown Heights, New York.

IBM was chiefly responsible for introducing APL to the marketplace. APL was first available in 1967 for the IBM 1130 as APL\1130. It would run in as little as 8k 16-bit words of memory, and used a dedicated 1 megabyte hard disk.

APL gained its foothold on mainframe timesharing systems from the late 1960s through the early 1980s, in part because it would support multiple users on lower-specification systems that had no dynamic address translation hardware. Additional improvements in performance for selected IBM System/370 mainframe systems included the APL Assist Microcode in which some support for APL execution was included in the processors firmware, as distinct from being implemented entirely by higher-level software. Somewhat later, as suitably performing hardware was finally growing available in the mid- to late-1980s, many users migrated their applications to the personal computer environment.

Early IBM APL interpreters for IBM 360 and IBM 370 hardware implemented their own multi-user management instead of relying on the host services, thus they were their own timesharing systems. First introduced in 1966, the APL\360 system was a multi-user interpreter. The ability to programmatically communicate with the operating system for information and setting interpreter system variables was done through special privileged "I-beam" functions, using both monadic and dyadic operations.

In 1973, IBM released APL.SV, which was a continuation of the same product, but which offered shared variables as a means to access facilities outside of the APL system, such as operating system files. In the mid-1970s, the IBM mainframe interpreter was even adapted for use on the IBM 5100 desktop computer, which had a small CRT and an APL keyboard, when most other small computers of the time only offered BASIC. In the 1980s, the VSAPL program product enjoyed wide use with Conversational Monitor System CMS, Time Sharing Option TSO, VSPC, MUSIC/SP, and CICS users.

In 1973–1974, Patrick E. Hagerty directed the implementation of the University of Maryland APL interpreter for the 1100 line of the Sperry UNIVAC 1100/2200 series mainframe computers. At the time, Sperry had nothing. In 1974, student Alan Stebbens was assigned the task of implementing an internal function. Xerox APL was available from June 1975 for Xerox 560 and Sigma 6, 7, and 9 mainframes running CP-V and for Honeywell CP-6.

In the 1960s and 1970s, several timesharing firms arose that sold APL services using modified versions of the IBM APL\360 interpreter. In North America, the better-known ones were I. P. Sharp Associates, Scientific Time Sharing Corporation STSC, Time Sharing Resources TSR, and The Computer Company TCC. CompuServe also entered the market in 1978 with an APL Interpreter based on a modified version of Digital Equipment Corp and Carnegie Mellons, which ran on DECs KI and KL 36-bit machines. CompuServes APL was available both to its commercial market and the consumer information service. With the advent first of less expensive mainframes such as the IBM 4300, and later the personal computer, by the mid-1980s, the timesharing industry was all but gone.

Sharp APL was available from I. P. Sharp Associates, first as a timesharing service in the 1960s, and later as a program product starting around 1979. Sharp APL was an advanced APL implementation with many language extensions, such as packages the ability to put one or more objects into a single variable, file system, nested arrays, and shared variables.

APL interpreters were available from other mainframe and mini-computer manufacturers also, notably Burroughs, Control Data Corporation CDC, Data General, Digital Equipment Corporation DEC, Harris, Hewlett-Packard HP, Siemens AG, Xerox, and others.

Garth Foster of Syracuse University sponsored regular meetings of the APL implementers community at Syracuses Minnowbrook Conference Center in Blue Mountain Lake, New York. In later years, Eugene McDonnell organized similar meetings at the Asilomar Conference Grounds near Monterey, California, and at Pajaro Dunes near Watsonville, California. The SIGAPL special interest group of the Association for Computing Machinery continues to support the APL community.

                                     

1.5. History Microcomputers

On microcomputers, which became available from the mid 1970s onwards, BASIC became the dominant programming language. Nevertheless, some microcomputers provided APL instead - the first being the Intel 8008-based MCM/70 which was released in 1974 and which was primarily used in education. Another machine of this time was the VideoBrain Family Computer, released in 1977, which was supplied with its dialect of APL called APL/S.

The Commodore SuperPET, introduced in 1981, included an APL interpreter developed by the University of Waterloo.

In 1976, Bill Gates claimed in his Open Letter to Hobbyists that Microsoft Corporation was implementing APL for the Intel 8080 and Motorola 6800 but had "very little incentive to make available to hobbyists" because of software piracy. It was never released.

                                     

1.6. History APL2

Starting in the early 1980s, IBM APL development, under the leadership of Jim Brown, implemented a new version of the APL language that contained as its primary enhancement the concept of nested arrays, where an array can contain other arrays, and new language features which facilitated integrating nested arrays into program workflow. Ken Iverson, no longer in control of the development of the APL language, left IBM and joined I. P. Sharp Associates, where one of his major contributions was directing the evolution of Sharp APL to be more in accord with his vision.

As other vendors were busy developing APL interpreters for new hardware, notably Unix-based microcomputers, APL2 was almost always the standard chosen for new APL interpreter developments. Even today, most APL vendors or their users cite APL2 compatibility, as a selling point for those products.

APL2 for IBM mainframe computers is still available. IBM cites its use for problem solving, system design, prototyping, engineering and scientific computations, expert systems, for teaching mathematics and other subjects, visualization and database access and was first available for CMS and TSO in 1984. The APL2 Workstation edition followed much later in the early 1990s.



                                     

1.7. History Modern implementations

Various implementations of APL by APLX, Dyalog, et al., include extensions for object-oriented programming, support for.NET Framework, XML-array conversion primitives, graphing, operating system interfaces, and lambda calculus expressions.

                                     

1.8. History Derivative languages

APL has formed the basis of, or influenced, the following languages:

  • MATLAB, a numerical computation tool.
  • J, which was also designed by Iverson, and which uses ASCII with digraphs instead of special symbols.
  • Wolfram Language, the programming language of Mathematica.
  • A and A+, an alternative APL, the latter with graphical extensions.
  • Nial, a high-level array programming language with a functional programming notation.
  • S, a statistical programming language.
  • Ivy, an interpreter for an APL-like language developed by Rob Pike, and which uses ASCII as input.
  • K, a proprietary variant of APL developed by Arthur Whitney.
  • Polymorphic Programming Language, an interactive, extensible language with a similar base language.
  • FP, a functional programming language.
  • Speakeasy, a numerical computing interactive environment.
  • LYaPAS, a Russian extension to APL.


                                     

2. Language characteristics

Sorting

The following expression sorts a word list stored in matrix X according to word length:

HTML tags removal

In the following example, also Dyalog, the first line assigns some HTML code to a variable txt and then uses an APL expression to remove all the HTML tags explanation:

                                     

2.1. Language characteristics Character set

APL has been both criticized and praised for its choice of a unique, non-standard character set. Some who learn it become ardent adherents, suggesting that there is some weight behind Iversons idea that the notation used does make a difference. In the 1960s and 1970s, few terminal devices and even display monitors could reproduce the APL character set. The most popular ones employed the IBM Selectric print mechanism used with a special APL type element. One of the early APL line terminals line-mode operation only, not full screen was the Texas Instruments TI Model 745 circa 1977 with the full APL character set which featured half and full duplex telecommunications modes, for interacting with an APL time-sharing service or remote mainframe to run a remote computer job, called an RJE.

Over time, with the universal use of high-quality graphic displays, printing devices and Unicode support, the APL character font problem has largely been eliminated. However, entering APL characters requires the use of input method editors, keyboard mappings, virtual/on-screen APL symbol sets, or easy-reference printed keyboard cards which can frustrate beginners accustomed to other programming languages. With beginners who have no prior experience with other programming languages, a study involving high school students found that typing and using APL characters did not hinder the students in any measurable way.

In defense of APL use, APL requires less coding to type in, and keyboard mappings become memorized over time. Also, special APL keyboards are manufactured and in use today, as are freely available downloadable fonts for operating systems such as Microsoft Windows. The reported productivity gains assume that one will spend enough time working in APL to make it worthwhile to memorize the symbols, their semantics, and keyboard mappings, not to mention a substantial number of idioms for common tasks.



                                     

2.2. Language characteristics Terminology

APL makes a clear distinction between functions and operators. Functions take arrays variables or constants or expressions as arguments, and return arrays as results. Operators similar to higher-order functions take functions or arrays as arguments, and derive related functions. For example, the sum function is derived by applying the reduction operator to the addition function. Applying the same reduction operator to the maximum function which returns the larger of two numbers derives a function which returns the largest of a group vector of numbers. In the J language, Iverson substituted the terms verb for function and adverb or conjunction for 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 versions of APL operators. However a few primitives are considered to be neither functions nor operators, most noticeably assignment.

Some words used in APL literature have meanings that differ from those in both mathematics and the generality of computer science.

                                     

2.3. Language characteristics Syntax

APL has explicit representations of functions, operators, and syntax, thus providing a basis for the clear and explicit statement of extended facilities in the language, and tools to experiment on them.



                                     

2.4. Language characteristics Hello, World

This displays "Hello, world":

Hello World, sample user session on YouTube

A design theme in APL is to define default actions in some cases that would produce syntax errors in most other programming languages.

The Hello, world string constant above displays, because display is the default action on any expression for which no action is specified explicitly e.g. assignment, function parameter.

                                     

2.5. Language characteristics Exponentiation

Another example of this theme is that exponentiation in APL is written as 2⋆3 ", which indicates raising 2 to the power 3 this would be written as 2^3 in some other languages and 2**3 in FORTRAN and Python: many languages use * to signify multiplication as in 2*3 but APL uses 2×3 for that. However, if no base is specified as with the statement ⋆3 in APL, or ^3 in other languages, in most other programming languages one would have a syntax error. APL however assumes the missing base to be the natural logarithm constant e 2.71828., and so interpreting ⋆3 as 2.71828⋆3 ".

                                     

2.6. Language characteristics Simple statistics

Suppose that X is an array of numbers. Then +/X÷⍴X gives its average. Reading right-to-left, ⍴X gives the number of elements in X, and since ÷ is a dyadic operator, the term to its left is required as well. It is in parenthesis since otherwise X would be taken so that the summation would be of X÷⍴X, of each element of X divided by the number of elements in X, and +/X adds all the elements of X. Building on this, + / X - + / X ÷⍴ X) * 2) ÷⍴ X) * 0.5 calculates the standard deviation. Further, since assignment is an operator, it can appear within an expression, so

would place suitable values into T, AV and SD. Naturally, one would make this expression into a function for repeated use rather than retyping it each time.

                                     

2.7. Language characteristics Pick 6 lottery numbers

This following immediate-mode expression generates a typical set of Pick 6 lottery numbers: six pseudo-random integers ranging from 1 to 40, guaranteed non-repeating, and displays them sorted in ascending order:

The above does a lot, concisely; although it seems complex to a new APLer. It combines the following APL functions also called primitives and glyphs:

  • Then the output of ⍋ is used to index the variable x, which we saved earlier for this purpose, thereby selecting its items in ascending sequence.
  • This vector is then sorted in ascending order by a monadic ⍋ function, which has as its right argument everything to the right of it up to the next unbalanced close-bracket or close-parenthesis. The result of ⍋ is the indices that will put its argument into ascending order.
  • This vector is then assigned ← to the variable x, because it is needed later.
  • The first to be executed APL executes from rightmost to leftmost is dyadic function? named deal when dyadic that returns a vector consisting of a select number left argument: 6 in this case of random integers ranging from 1 to a specified maximum right argument: 40 in this case, which, if said maximum ≥ vector length, is guaranteed to be non-repeating; thus, generate/create 6 random integers ranging from 1-40.

Since there is no function to the left of the left-most x to tell APL what to do with the result, it simply outputs it to the display on a single line, separated by spaces without needing any explicit instruction to do that.

? also has a monadic equivalent called roll, which simply returns one random integer between 1 and its sole operand, inclusive. Thus, a role-playing game program might use the expression?20 to roll a twenty-sided die.

                                     

2.8. Language characteristics Prime numbers

The following expression finds all prime numbers from 1 to R. In both time and space, the calculation complexity is O R 2 {\displaystyle OR^{2}\,\!} in Big O notation.

Executed from right to left, this means:

  • Set R to the new vector ←, assignment primitive, i.e., 2 3 4 5 6
  • Iota ι creates a vector containing integers from 1 to R if R= 6 at the start of the program, ιR is 1 2 3 4 5 6
  • Generate outer product of R multiplied by R, i.e., a matrix that is the multiplication table of R by R °.× operator, i.e.,
  • The / reduction operator is dyadic binary and the interpreter first evaluates its left argument fully in parentheses
  • Drop first element of this vector ↓ function, i.e., 1. So 1↓ιR is 2 3 4 5 6
  • Logically negate not values in the vector change zeros to ones and ones to zeros ∼, logical not or Tilde operator, i.e., 1 0 1 0
  • Select the items in R for which the corresponding element is 1 / reduction operator, i.e., 2 3 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 or element of or Epsilon operator, i.e., 0 1 0 1

                                     

2.9. Language characteristics Sorting

The following expression sorts a word list stored in matrix X according to word length:

                                     

2.10. Language characteristics Game of Life

The following function "life", written in Dyalog APL, takes a boolean matrix and calculates the new generation according to Conways Game of Life. It demonstrates the power of APL to implement a complex algorithm in very little code, but it is also very hard to follow unless one has advanced knowledge of APL.

                                     

2.11. Language characteristics HTML tags removal

In the following example, also Dyalog, the first line assigns some HTML code to a variable txt and then uses an APL expression to remove all the HTML tags explanation:

                                     

3. Use

APL is used for many purposes including financial and insurance applications, artificial intelligence,neural networks and robotics. It has been argued that APL is a calculation tool and not a programming language; its symbolic nature and array capabilities have made it popular with domain experts and data scientists who do not have or require the skills of a computer programmer.

APL is well suited to image manipulation and computer animation, where graphic transformations can be encoded as matrix multiplications. One of the first commercial computer graphics houses, Digital Effects, produced an APL graphics product named Visions, which was used to create television commercials and animation for the 1982 film Tron. Latterly, the Stormwind boating simulator uses APL to implement its core logic, its interfacing to the rendering pipeline middleware and a major part of its physics engine.

Today, APL remains in use in a wide range of commercial and scientific applications, for example investment management,asset management,health care, and DNA profiling, and by hobbyists.

                                     

4. Notable implementations

APL\1130

In 1968, APL\1130 became the first publicly available APL system, created by IBM for the IBM 1130. It became the most popular IBM Type-III Library software that IBM released.

                                     

4.1. Notable implementations APL\360

The first implementation of APL using recognizable APL symbols was APL\360 which ran on the IBM System/360, and was completed in November 1966 though at that time remained in use only within IBM. In 1973 its implementors, Larry Breed, Dick Lathwell and Roger Moore, were awarded the Grace Murray Hopper Award from the Association for Computing Machinery ACM. It was given "for their work in the design and implementation of APL\360, setting new standards in simplicity, efficiency, reliability and response time for interactive systems."

In 1975, the IBM 5100 microcomputer offered APL\360 as one of two built-in ROM-based interpreted languages for the computer, complete with a keyboard and display that supported all the special symbols used in the language.

Significant developments to APL\360 included CMS/APL, which made use of the virtual storage capabilities of CMS and APLSV, which introduced shared variables, system variables and system functions. It was subsequently ported to the IBM System/370 and VSPC platforms until its final release in 1983, after which it was replaced by APL2.

                                     

4.2. Notable implementations APL\1130

In 1968, APL\1130 became the first publicly available APL system, created by IBM for the IBM 1130. It became the most popular IBM Type-III Library software that IBM released.

                                     

4.3. Notable implementations APL*Plus and Sharp APL

APL*Plus and Sharp APL are versions of APL\360 with added business-oriented extensions such as data formatting and facilities to store APL arrays in external files. They were jointly developed by two companies, employing various members of the original IBM APL\360 development team.

The two companies were I. P. Sharp Associates IPSA, an APL\360 services company formed in 1964 by Ian Sharp, Roger Moore and others, and STSC, a time-sharing and consulting service company formed in 1969 by Lawrence Breed and others. Together the two developed APL*Plus and thereafter continued to work together but develop APL separately as APL*Plus and Sharp APL. STSC ported APL*Plus to many platforms with versions being made for the VAX 11, PC and UNIX, whereas IPSA took a different approach to the arrival of the Personal Computer and made Sharp APL available on this platform using additional PC-XT/360 hardware. In 1993, Soliton Incorporated was formed to support Sharp APL and it developed Sharp APL into SAX Sharp APL for Unix. As of 2018, APL*Plus continues as APL2000 APL+Win.

In 1985, Ian Sharp, and Dan Dyer of STSC, jointly received the Kenneth E. Iverson Award for Outstanding Contribution to APL.

                                     

4.4. Notable implementations Dyalog APL

Dyalog APL was first released by British company Dyalog Ltd. in 1983 and, as of 2018, is available for AIX, Linux including on the Raspberry Pi, macOS and Microsoft Windows platforms. It is based on APL2, with extensions to support object-oriented programming and functional programming. Licences are free for personal/non-commercial use.

In 1995, two of the development team - John Scholes and Peter Donnelly - were awarded the Iverson Award for their work on the interpreter. Gitte Christensen and Morten Kromberg were joint recipients of the Iverson Award in 2016.



                                     

4.5. Notable implementations NARS2000

NARS2000 is an open-source APL interpreter written by Bob Smith, a prominent APL developer and implementor from STSC in the 1970s and 1980s. NARS2000 contains advanced features and new datatypes and runs natively on Microsoft Windows, and other platforms under Wine.

                                     

4.6. Notable implementations APLX

APLX is a cross-platform dialect of APL, based on APL2 and with several extensions, which was first released by British company MicroAPL in 2002. Although no longer in development or on commercial sale it is now available free of charge from Dyalog.

                                     

4.7. Notable implementations GNU APL

GNU APL is a free implementation of Extended APL as specified in ISO/IEC 13751:2001 and is thus an implementation of APL2. It runs on GNU/Linux and on Windows using Cygwin, and uses Unicode internally. It was written by Jurgen Sauermann.

Richard Stallman, founder of the GNU Project, was an early adopter of APL, using it to write a text editor as a high school student in the summer of 1969.

                                     

5. Interpretation and compilation of APL

APL is traditionally an interpreted language, having language characteristics such as weak variable typing not well suited to compilation. However, with arrays as its core data structure it provides opportunities for performance gains through parallelism, parallel computing, massively parallel applications, and very-large-scale integration VLSI, and from the outset APL has been regarded as a high-performance language - for example, it was noted for the speed with which it could perform complicated matrix operations "because it operates on arrays and performs operations like matrix inversion internally".

Nevertheless, APL is rarely purely interpreted and compilation or partial compilation techniques that are, or have been, used include the following:

                                     

5.1. Interpretation and compilation of APL Idiom recognition

Most APL interpreters support idiom recognition and evaluate common idioms as single operations. For example, by evaluating the idiom BV/⍳⍴A as a single operation where BV is a Boolean vector and A is an array, the creation of two intermediate arrays is avoided.

                                     

5.2. Interpretation and compilation of APL Optimised bytecode

Weak typing in APL means that a name may reference an array of any datatype, a function or an operator. In general, the interpreter cannot know in advance which form it will be and must therefore perform analysis, syntax checking etc. at run-time. However, in certain circumstances, it is possible to deduce in advance what type a name is expected to reference and then generate bytecode which can be executed with reduced run-time overhead. This bytecode can also be optimised using compilation techniques such as constant folding or common subexpression elimination. The interpreter will execute the bytecode when present and when any assumptions which have been made are met. Dyalog APL includes support for optimised bytecode.

                                     

5.3. Interpretation and compilation of APL Compilation

Compilation of APL has been the subject of research and experiment since the language first became available; the first compiler is considered to be the Burroughs APL-700 which was released around 1971. In order to be able to compile APL, language limitations have to be imposed. APEX is a research APL compiler which was written by Robert Bernecky and is available under the GNU Public License.

The STSC APL Compiler is a hybrid of a bytecode optimiser and a compiler - it enables compilation of functions to machine code provided that its sub-functions and globals are declared, but the interpreter is still used as a runtime library and to execute functions which do not meet the compilation requirements.

                                     

6. Standards

APL has been standardized by the American National Standards Institute ANSI working group X3J10 and International Organization for Standardization ISO and International Electrotechnical Commission IEC, 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.

                                     
  • A is an array programming language descended from the programming language A, which in turn was created to replace APL in 1988. Arthur Whitney developed
  • The programming language APL uses a number of symbols, rather than words from natural language to identify operations, similarly to mathematical symbols
  • APLX is a cross - platform dialect of the programming language APL created by British company Micro APL Ltd. APLX is intended for uses such as financial
  • skills APL programming language an array - based programming language created by Kenneth E. Iverson APL codepage the character set for programming in
  • financial products. The language originally developed in 1993, is a variant of APL and contains elements of Scheme. Advocates of the language emphasize its speed
  • The programming language APL is distinctive in being symbolic rather than lexical: its primitives are denoted by symbols, not words. These symbols were
  • non - array - oriented programming languages It is also a generalization of mapcar in the language Lisp and map in modern functional programming languages and a generalization
  • J programming language developed in the early 1990s by Kenneth E. Iverson and Roger Hui, is an array programming language based primarily on APL also
  • Shared Variables are a feature of the programming language APL which allows APL programs running on one processor to share information with another processor
  • extensible language with a base language similar to the language APL The assignment operator - or has influenced the language S. Standish, Thomas A. August
  • ELI is an interactive array programming language system based on the programming language APL It has most of the functions of the International Organization