Dyalog APL

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"Dyalog" redirects here. For the company, see Dyalog Ltd.

Dyalog APL, or simply Dyalog, is a nested APL based on NARS and APL2, first released by British company Dyadic Systems Ltd. (now Dyalog Ltd.) in 1983 for the Zilog Z8000 processor. (The name Dyalog is a portmanteau of Dyadic and Zilog). Continuously developed since, Dyalog has added support for many programming paradigms including object-oriented programming based on .NET, Lisp-style lexically scoped anonymous functions (dfns), and leading axis and tacit programming support based on J. It supports several platforms and interoperability between them, and interfaces with other languages and runtimes including native shared libraries, .NET, the JVM, R, and Python.

Although it initially received very little commercial interest, Dyalog has steadily grown in prominence and in the 2010s has been the basis of several new APL dialects including ngn/apl, APL\iv, and dzaima/APL. Even in APLs not derived from Dyalog such as GNU APL and NARS2000, dfn-style function syntax has become common, and Dyalog has also popularised SHARP APL and J innovations such as the Rank operator and trains among nested APLs.


See also: Dyalog Ltd.

Work on Dyalog was begun in 1981 by APL consulting company Dyadic Systems, which by that time had grown to support about 15 employees. In partnership with Zilog UK, Dyadic developed an interpreter using the C programming language for the Zilog Z8000's UNIX operating system—both obscure technologies at the time. Dyadic employees John Scholes and Geoff Streeter worked full-time on the implementation, while David Crossley managed its development as a part-time role. Initially aiming to produce something like SHARP APL, they eventually chose a nested model rather than adding boxes to the flat array model like SHARP, and drew most design decisions from STSC's experimental NARS dialect and the material available at the time regarding IBM's plans for APL2.[1]

Released at APL83, Dyalog sold very few copies due to the lack of interest in either Unix or the nested array model. Subsequent sales were also limited, with only a single licence sold through Zilog partly due to the Z8000's limited popularity. Supported by Dyadic's APL consulting and later by sales of Unix hardware, Scholes and Streeter continued work on Dyalog by porting it to a wide variety of Unix systems in response to requests from users; in 1995, Scholes was awarded the Iverson Award jointly with Peter Donnelly for his work on the Dyalog interpreter. Although it continued to run significant losses every year, Dyalog slowly acquired users during the 1980s, including current client SimCorp. In 1991, Dyadic hired John Daintree to begin work on the ⎕WC graphical user interface for Microsoft Windows; Dyalog for Windows debuted at APL92 and quickly become Dyalog's main platform.[1]

In 1996, John Scholes introduced a new form of functional definition to Dyalog based on his studies of the functional programming language Scheme, which he called dfns, for "direct functions". Another major addition to the language began in 2000, when John Daintree was invited to participate in the design of Microsoft's .NET. Based on this work, and the namespaces which he had added to the language in 1994 to deliver a Windows GUI API and an interface to COM/OLE, Daintree developed an object model for Dyalog, based on concepts from C# and Visual Basic.

In 2005, Dyadic transferred management to CEO Gitte Christensen and CTO Morten Kromberg, and sold ownership of the company to a group of investors including their company Insight Systems. With this arrangement, the development team at Dyalog grew rapidly. Dfns were promoted as "mainstream" APL features, with the result that many newer APLs only support dfns, abandoning traditional defined functions completely. Daintree's work on objects resulted in the addition of full object oriented programming capabilities to Dyalog APL in 2006. The influence of the Microsoft's .NET Framework also led to a project to create a new language called APL#, prototypes of which were released in 2010. The project was abandoned in 2012 when Microsoft deprecated Silverlight.

In addition to functional and object oriented language features, Dyalog APL folded concepts and features from the SHARP APL and J side of the APL family tree back into what fundamentally remains a dialect of APL2. In 2011 the company hired Roger Hui, developer of J, and in 2016 it also hired J programmer and language implementer Marshall Lochbaum. Both developers improved performance of Dyalog's primitives on flat arrays, and brought concepts such as the Rank operator, trains, and composition operators, namely Atop and Over, from J to APL.

In the 2010s, Dyalog development began to focus on performance, which had been improved out of necessity in early releases but had not been a major focus. In 2010 Dyalog Ltd. hired Jay Foad, a compiler developer who initially created a bytecode compiler for APL and later improved performance in other ways, and served as CTO from 2016 until his departure in 2019. Hui and Lochbaum also improved performance of Dyalog's primitives on flat arrays.

The Dyalog interpreter has also incorporated significant components written in APL in the 2000s and 2010s. Dan Baronet, hired in 2006, introduced the SALT (Simple APL Library Toolkit) system to distribute APL code, and user commands based on it, in version 12.0 in 2008. Work on APL components of Dyalog has also been done by Brian Becker and Adám Brudzewsky. Brudzewsky, hired in 2015, has also driven the adoption of new functionality such as Nest and array notation in Dyalog.


Besides for working out-of-the-box on Windows, macOS, and AIX, Dyalog APL runs on many Linuxes. However, to function, some require additional action beyond simple installation. As of 2019-05-15, the necessary actions for versions 16.0, 17.0, and 17.1 are:

Distribution Action
Debian 8.2, 9.8, 9.9 no pre-reqs
Fedora 29, 30 dnf install ncurses-compat-libs
Linux Mint 18.0, 19.0 no pre-reqs
openSUSE 15.0 zypper install libncurses5
CentOS/RedHat 6 not supported for 17.1 as glibc is at too low a level
CentOS/RedHat 7 no pre-reqs
RedHat 8 rpm -Uvh ncurses-compat-libs (note: RH8 would not install in a VM)
Ubuntu 16.04, 18.04 no pre-reqs
Ubuntu 19.04 apt-get install libtinfo5


Main article: Dyalog APL versions

Dyalog lists historical versions, along with release notes since 14.0, on its website. Its early history is recounted in more detail by Pete Donnelly in Dyalog APL: A Personal History (pdf).

Number Year Month Features
1 1983 April (Zilog S8000 only)
2 1984 (Many more platforms)
3.0 1985 (More platforms) Rectangular display of arrays
4.0 1986 October User-defined operators, function assignment (including for derived functions), ⎕MONITOR
5.0 1987 April Nested array editor
5.1 1988 April (first version for DOS) User-defined input/output tables, ⎕SM and ⎕SR, windowed editor/tracer, interface to GSS/CGI
5.2 1990 January Naked trace
6.0 1990 April GUI IDE
6.1 1990 October ⎕ED
6.2.1 1992 July (first version for Windows) ⎕WC, ⎕DQ, etc.
6.3.1 1993 April ⎕NA, graphical, clipboard and printer objects
7.0.1 1994 August Namespaces, additional GUI objects
7.1 1995 May ⎕CS, GUI objects as namespaces, greater APL2 compatibility
8.0 1996 May Keywords (:If/:Else, :Repeat/:Until, :Trap, and so on), ⎕PATH, additional GUI objects, OLE
8.1 1997 March dfns with lexical scope, syntax colouring, TCPSocket object, OLE client/server, automatic file tie numbers
8.2 1999 January Windowed Reduction and scalar functions with axis (from APL2), Threading with Spawn (&), ActiveX, :With, additional GUI objects
9.0 2000 September Namespace references (instead of string names) and dot syntax, context-sensitive help (F1), aditional GUI objects with animation
9.0.1 2001 January (Windows CE) Pocket APL
9.0.2 2002 January .NET support
9.5 2002 September
10.0 2003 March ⎕NULL, ⎕MAP (mapped files), idiom recognition, retained hash tables, .NET support built-in, run-time workspace as .exe, auto-completion, mapped
10.1 2004 July Multiple arguments in tradfn headers, thread tokens, 64-bit component files, value tips
11.0 2006 October Object-oriented programming (classes, objects, interfaces) modelled after C#, Index (), Power operator (), GCD (), LCM ()
12.0 2008 August Unicode support (⎕AVU, ⎕UCS), ⎕FCOPY, ⎕FPROPS
12.1 2009 November I-beam (), Table (), ⎕XML, ⎕FCHK, User commands
13.0 2011 April Left (), Right (), Variant (), ⎕OPT, ⎕R, ⎕S, ⎕PROFILE, ⎕RSI, complex number and decimal float support, short arguments for Take, Drop, and Index (, , )
13.1 2012 April ⎕DMX, ⎕FHIST
13.2 2013 January Array Editor
14.0 2014 June Trains, Tally (), Key (), Rank operator (), high-rank Index Of (), multi-threading with futures and isolates
14.1 2015 June :Disposable .NET objects and resources, gesture support, many new I-beams
16.0 2017 June At (@), Interval Index (), Where (), Nest (), Partition (), Stencil (), ⎕JSON, ⎕CSV
17.0 2018 July ⎕NCOPY, ⎕NMOVE, total array ordering, high-rank Unique ()
17.1 2019 October Duplicates in Interval Index () look-up array
18.0 2020 June Atop (), Over (), Constant (), Unique Mask (), duplicates from Where (), empty partitions from Partitioned Enclose (), date-time conversion (⎕DT), case folding/mapping (⎕C), launching with text source file, .NET Core support
18.2 2022 March ⎕ATX, shell scripting



Glyph Monadic Dyadic
+ Conjugate Plus
- Negate Minus
× Direction Times
÷ Reciprocal Divide
| Magnitude Residue
Floor Minimum
Ceiling Maximum
* Exponential Power
Natural Logarithm Logarithm
! Factorial Binomial
Pi Times Circular
~ Not Without
? Roll Deal
< Less
Less Or Equal
= Equal
Greater Or Equal
> Greater
Unique Mask Not Equal
Shape Reshape
, Ravel Catenate
Table Catenate First
Reverse Rotate
Reverse First Rotate First
Mix/First Take
Split Drop
Enclose Partitioned Enclose
Nest Partition
Enlist/Type Membership
First/Mix Pick
/ Replicate
Replicate First
\ Expand
Expand First
Unique Union
Same Left
Same Right
Index Generator Index Of
Where Interval Index
Grade Down
Grade Up
Depth Match
Tally Not Match
Matrix Inverse Matrix Divide
Materialise Index


Syntax Monadic call Dyadic call
f/ Reduction Windowed Reduction
f⌿ Reduction First Windowed Reduction First
f\ Scan
f⍀ Scan First
f⍨ Commute
A⍨ Constant
f⍣v Power
f.g Inner Product
∘.f Outer Product
A∘g Bind
f∘g Beside
f⍤B Rank
f⍤g Atop
f⍥g Over
f@v At
f⍠B Variant
f⌸ Key
f⌺B Stencil
A⌶ I-beam
f& Spawn
f[B] Axis


Dyalog APL is implemented primarily in C with some parts implemented in C++ in order to use templates. C intrinsics are used to access instruction set extensions. Some architecture-specific assembly, both compiled separately and inline from C, is used for functionality like exception flags which is not easily accessible in C. Prior to version 17.0, assembly was also used for vectorized arithmetic. In 17.0, this code was replaced by a new C++ implementation.

Internal types

Dyalog uses the following numeric types:

  • 1-bit packed Boolean
  • 1-byte integer
  • 2-byte integer
  • 4-byte integer
  • 8-byte double
  • 16-byte complex (one double for each component)
  • 16-byte decimal float "decf" (BID or DPD)

Character encodings differ for classic and unicode interpreters: classic interpreters use a custom 1-byte encoding for all characters, and are limited to a 256-character set, while characters in unicode interpreters are 1-, 2-, or 4-byte unsigned unicode code point values.

Nested and mixed arrays (that is, pointer arrays) are always stored as arrays of pointers, while simple numeric or character arrays are always stored using one of the above types. For both numbers and characters, an array may be represented using any type that can contain all the values. The interpreter may reduce the type of an array to the minimum possible ("squeeze" the array) during execution.

Because there is no complex representation using decimal floats for the components, arrays containing both decimal floats and complex numbers have no common representation. Dyalog converts such arrays to complex numbers, resulting in a loss of precision for decf elements.

Instruction set usage

Dyalog makes heavy use of vector instructions on all platforms, as well as other special instruction sets primarily on x86. Instruction set availability is checked at runtime, so that the minimum required instruction set remains low:

  • For 32-bit x86, only SSE2 is required.
  • For x86_64, there is no minimum requirement as every processor supports SSE2. SSE4.1 is required on macOS as all x86 Apple machines support this instruction set.
  • For ARM32, there is no minimum requirement.
  • As of version 17.1, POWER7 and above are supported. Support for older systems is dropped because Dyalog compiles separate binaries for each POWER architecture.

In Dyalog 17.0, the code for vectorized scalar functions was unified and extended to allow Intel AVX2 and ARM NEON in addition to Intel SSE2 and SSE4.1, and AltiVec VMX for IBM POWER. This code is also used for operations involving the scalar dyadics Plus, Minus, Times, Divide, Maximum, Minimum, and comparison functions, as well as some functions derived from operators applied to these functions, such as the Outer Product and Inner Product.

Dyalog also uses many other x86 extensions:

It also uses the POWER8 gather-bits-by-bytes instruction, which is equivalent to transposing an 8x8 bit matrix for Boolean Transpose since version 15.0 (expanded in applicability in 16.0) and the fused multiply-add instruction for division like x86 FMA3 in 18.0.

External links


  1. 1.0 1.1 Stephen Taylor. "How we got here". Vector journal Volume 23 special supplement "Dyalog at 25". 2008-09.

APL dialects [edit]
Maintained APL+WinAPL2APL64APL\ivApletteAprilCo-dfnsDyalog APLDyalog APL Visiondzaima/APLGNU APLKapNARS2000Pometo
Historical A Programming LanguageA+ (A) ∙ APL#APL2CAPL\360APL/700APL\1130APL\3000APL.68000APL*PLUSAPL.jlAPL.SVAPLXExtended Dyalog APLIverson notationIVSYS/7090NARSngn/aplopenAPLOperators and FunctionsPATRowanSAXSHARP APLRationalized APLVisualAPL (APLNext) ∙ VS APLYork APL
Derivatives AHPLBQNCoSyELIGleeIIvyJJellyK (Goal, Klong, Q) ∙ KamilaLispLang5LilNialRADUiua
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