Dyalog APL

Dyalog APL
Developer	Dyalog Ltd.
Released	1983
Latest release	17.1 / 2019
Array model	nested
Index origin	0 or 1
Function styles	tradfn, dfn, tacit
Numeric types	complex floats, decimal floats
Unicode support	full
File extensions	.dws, .dse, .dcf, .dyalog, .dyapp, .apl, .apla, .aplf, .aplo, .apln, .aplc, .apli
Implementation languages	C, C++, APL
Platforms	x86, x86_64, IBM POWER, ARM32
Operating systems	Windows, Linux, macOS, AIX
License	Free for personal use / Proprietary commercial software
Website	dyalog.com/dyalog/index.htm
Forum	Dyalog Forums
Download	Non-commercial download
Documentation	Documentation Centre
Run online	TryAPL
Influenced by	APL2, J, SHARP APL, Scheme, C#
Influenced	NARS2000, GNU APL, ngn/apl, dzaima/APL, APL\iv

For the chat bot, see APL Orchard#Chat bot.

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.

Platforms

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

Versions

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
15.0	2016	June	⎕MKDIR, ⎕NDELETE, ⎕NEXISTS, ⎕NGET, ⎕NINFO, ⎕NPARTS, ⎕NPUT
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	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)

Primitives

Functions

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	Deal
∧		And
∨		Or
⍲		Nand
⍱		Nor
<		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
⍉	Transpose
↑	Mix/Disclose	Take
↓	Split	Drop
⊂	Enclose	Partitioned Enclose
⊆	Nest	Partition
∊	Enlist/Type	Membership
⊃	Disclose/Mix	Pick
/		Replicate
⌿		Replicate First
\		Expand
⍀		Expand First
∩		Intersection
∪	Unique	Union
⊣	Same	Left
⊢	Same	Right
⍳	Index Generator	Index Of
⍸	Where	Interval Index
⍒	Grade Down
⍋	Grade Up
⍷		Find
≡	Depth	Match
≢	Tally	Not Match
⍎	Execute
⍕	Format
⊥		Base
⊤		Represent
⌹	Matrix Inverse	Matrix Divide
⌷	Materialise	Squad Indexing

Operators

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
f⍣v	Power
f.g		Inner Product
∘.f		Outer Product
A∘g	Bind
f∘B
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

Implementation

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:

• Since at least 12.1, SSE2 is used for scalar dyadics.
• Since 17.0, AVX2 is used for scalar dyadics if available.
• Since 14.1, SSE4.1 is used for Minimum and Maximum, and finding the range of an array. AVX2 can also be used for these purposes in 18.0.
• Since 17.0, SSSE3 is used primarily for the shuffle instruction for permuting arrays and searching small lookup tables.
• Since 14.0, SSE4.2 POPCNT is used to sum Boolean arrays.
• Since 14.0, SSE4.2 CRC32 is used to compute fast hash functions.
• Since 15.0, BMI2 is used for Boolean matrix transpose. Since 16.0, it is used for Boolean Compress and Expand, and several structural functions on Boolean arrays.
• Since 18.0, CLMUL is used for xor reductions and scans.
• Since 18.0, FMA3 is used to implement division by a singleton.

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

• Try APL
• Try It Online
• Download