Dyalog APL

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Dyalog APL, or simply Dyalog, is a modern APL in the APL2 tradition, first released by British company Dyadic Systems Ltd. (now Dyalog Ltd.) in 1983 for the Zylog Z80 processor (the name Dyalog is a portmanteau of Dyadic and Zylog). Dyalog supports several platforms and interfaces with many languages and runtimes including native shared libraries, .NET, the JVM, R, and Python. It is actively developed and has introduced many new primitives and concepts to array programming. Major categories of features introduced to APL by Dyalog are tacit programming by allowing named derived functions and later trains, lexically-scoped functional programming using dfns, namespaces and object-oriented programming, and the addition of leading axis theory and the Rank operator to the nested array paradigm.

In 1995, two Dyalog developers—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.


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, Assignment for functions (including 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, idiom recognition (mapped files), 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
17.1 2019 October Duplicates in Interval Index () look-up array
18.0 Unreleased Atop (), Over (), Constant (), Unique Mask (), duplicates from Where (), empty partitions from Partitioned Enclose (), multi-line session input, date-time conversion, case folding/mapping (⎕C)



Glyph Monadic Dyadic
+ Conjugate Plus
- Negate Minus
× Signum Times
÷ Reciprocal Divide
| Magnitude Residue
Floor Minimum
Ceiling Maximum
* Exponential Power
Natural Logarithm Logarithm
! Factorial Binomial
Pi Times Circular
~ Not Without
? Roll Query
< 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/Disclose Take
Split Drop
Enclose Partitioned Enclose
Nest Partition
Enlist/Type Membership
Disclose/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 Squad Indexing


Syntax Monadic call Dyadic call
f/ Reduction Windowed Reduction
f Reduction First Windowed Reduction First
f\ Scan
f Scan First
f¨ Each
f Commute
A Constant
fv Power
f.g Inner Product
∘.f Outer Product
Ag Bind
fg Beside
fB Rank
fg Atop
fg Over
f@v At
fB Variant
f Key
fB 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

APL dialects [edit]
Maintained APL+Win (APL*PLUS) ∙ APL2APL64APL\ivAprilCo-dfnsDyalog APLdzaima/APLExtended Dyalog APLGNU APLNARS2000ngn/apl
Historical Iverson notationA Programming LanguageA+ (A) ∙ APL#APL.68000APL.SVAPLXAPL\1130APL\3000APL\360NARSopenAPLRowanSAXSHARP APLVisualAPL (APLNext) ∙ VS APLYork APL
Derivatives AHPLAPL\ivELIIIvyJJellyK (Q, KDB+) ∙ LYaPASNialRAD