Language overview

This page gives a structured overview of the APL programming language.

Development

APL development [edit]
Interface	Session ∙ Typing glyphs (on Linux) ∙ Fonts ∙ Text editors
Publications	Introductions ∙ Learning resources ∙ Simple examples ∙ Advanced examples ∙ Mnemonics ∙ Standards ∙ A Dictionary of APL ∙ Case studies ∙ Documentation suites ∙ Books ∙ Papers ∙ Videos ∙ Periodicals ∙ Terminology (German) ∙ Neural networks
Sharing code	Backwards compatibility ∙ APLcart ∙ APLTree ∙ APL-Cation ∙ Dfns workspace ∙ Tatin
Vendors	APL2000 ∙ Dyalog ∙ GNU APL community ∙ IBM ∙ IPSA ∙ STSC

Features

APL features [edit]
Built-ins	Primitives (functions, operators) ∙ Quad name
Array model	Shape ∙ Rank ∙ Depth ∙ Bound ∙ Index (Indexing) ∙ Axis ∙ Ravel ∙ Ravel order ∙ Element ∙ Scalar ∙ Vector ∙ Matrix ∙ Simple scalar ∙ Simple array ∙ Nested array ∙ Cell ∙ Major cell ∙ Subarray ∙ Empty array ∙ Prototype
Data types	Number (Boolean, Complex number) ∙ Character (String) ∙ Box ∙ Namespace
Concepts and paradigms	Leading axis theory ∙ Scalar extension ∙ Conformability ∙ Leading axis agreement ∙ Scalar function ∙ Pervasion ∙ Glyph ∙ Identity element ∙ Complex floor ∙ Total array ordering
Errors	LIMIT ERROR ∙ RANK ERROR ∙ SYNTAX ERROR ∙ DOMAIN ERROR ∙ LENGTH ERROR ∙ INDEX ERROR ∙ VALUE ERROR

Syntax

APL syntax [edit]
General	Comparison with traditional mathematics ∙ Precedence ∙ Tacit programming
Array	Numeric literal ∙ String ∙ Strand notation ∙ Object literal ∙ Array notation
Function	Argument ∙ Function valence ∙ Derived function ∙ Derived operator ∙ Niladic function ∙ Monadic function ∙ Dyadic function ∙ Ambivalent function ∙ Defined function (traditional) ∙ Dfn ∙ Function train
Operator	Operand ∙ Operator valence ∙ Tradop ∙ Dop ∙ Derived operator
Assignment	Multiple ∙ Indexed ∙ Selective ∙ Modified
Other	Function axis ∙ Branch ∙ Quad name ∙ System command ∙ User command ∙ Keyword ∙ Dot notation ∙ Function-operator overloading ∙ Control structure

Dialects

APL dialects [edit]
Maintained	APL+Win ∙ APL2 ∙ APL64 ∙ APL\iv ∙ Aplette ∙ April ∙ Co-dfns ∙ Dyalog APL ∙ dzaima/APL ∙ Extended Dyalog APL ∙ GNU APL ∙ KAP ∙ NARS2000 ∙ Pometo
Historical	A Programming Language ∙ A+ (A) ∙ APL# ∙ APL\360 ∙ APL/700 ∙ APL\1130 ∙ APL\3000 ∙ APL.68000 ∙ APL*PLUS ∙ APL.jl ∙ APL.SV ∙ APLX ∙ Iverson notation ∙ IVSYS/7090 ∙ NARS ∙ ngn/apl ∙ openAPL ∙ PAT ∙ Rowan ∙ SAX ∙ SHARP APL ∙ Rationalized APL ∙ VisualAPL (APLNext) ∙ VS APL ∙ York APL
Derivatives	AHPL ∙ BQN ∙ CoSy ∙ ELI ∙ Glee ∙ I ∙ Ivy ∙ J ∙ Jelly ∙ Jellyfish ∙ K (Q, KDB+) ∙ Nial ∙ RAD
Overviews	Timeline of array languages ∙ Timeline of influential array languages ∙ Family tree of array languages

Community

APL community [edit]
Activities	Conferences ∙ Advent of Code ∙ APL Campfire ∙ APL Cultivation ∙ APL Meetup (Portuguese) ∙ APL Problem Solving Competition ∙ APL Seeds ∙ Array Cast ∙ BAA sessions ∙ Code golf ∙ Dyalog user meetings ∙ Dyalog webinars ∙ Iverson Award ∙ Sharing code
User groups	APL Borealis (Canada) ∙ APL et J (France) ∙ APL Germany (terminology) ∙ BAA (UK) ∙ FinnAPL (Finland) ∙ JAPLA (Japan) ∙ SAUG (Switzerland) ∙ SIGAPL (USA) ∙ SwedAPL (Sweden)
People	Phil Abrams ∙ Brian Becker ∙ Bob Bernecky ∙ Larry Breed ∙ Charles Brenner ∙ Jim Brown ∙ Adám Brudzewsky ∙ Gitte Christensen ∙ Peter Donnelly ∙ Adin Falkoff ∙ Garth Foster ∙ Aaron Hsu ∙ Roger Hui ∙ Ken Iverson ∙ Morten Kromberg ∙ Marshall Lochbaum ∙ Eugene McDonnell ∙ Jon McGrew ∙ Donald McIntyre ∙ Roger Moore ∙ Alan Perlis ∙ Henry Rich ∙ Al Rose ∙ William Rutiser ∙ John Scholes ∙ Ian Sharp ∙ Bob Smith ∙ Geoff Streeter ∙ Roy Sykes ∙ Arthur Whitney
Other	APL Orchard ∙ APL Quote Quad ∙ APL Wiki ∙ Blogs ∙ Books ∙ Famous APL users ∙ Forums ∙ Humour ∙ Jobs ∙ Papers ∙ Subreddits ∙ TryAPL ∙ Try It Online

Built-ins

APL built-ins [edit]
Primitive functions
	Scalar
		Monadic	Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root
		Dyadic	Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
	Non-Scalar
		Structural	Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
		Selection	First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index
		Selector	Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal
		Computational	Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Primitive operators	Monadic	Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-beam ∙ Spawn ∙ Function axis
Primitive operators	Dyadic	Bind ∙ Compositions (Compose, Reverse Compose, Beside, Atop, Over) ∙ Inner Product ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut (J)
Quad names
	Arrays	Index origin ∙ Migration level ∙ Atomic vector
	Functions	Name class ∙ Case convert ∙ Unicode convert
	Operators	Search ∙ Replace

Glyphs

APL glyphs [edit]
Information	Glyph ∙ Typing glyphs (on Linux) ∙ Unicode ∙ Fonts ∙ Mnemonics ∙ Overstrikes
Individual glyphs	Jot (`∘`) ∙ Right Shoe (`⊃`) ∙ Up Arrow (`↑`) ∙ Zilde (`⍬`) ∙ High minus (`¯`) ∙ Dot (`.`) ∙ Del (`∇`)

Language overview

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