Language Features

At the moment, the following sections describe only those language features that are New or Enhanced relative to the Extended APL Standard, or that deserve special comment.

Syntax

• Strand Assignment: (A1 A2 ... An)←R
• Modified Assignment: Af←R
• Modify Strand Assignment: (A1 A2 ... An)f←R
• Hyperators: ∇ Z←L (LO (LH dhdo RH) RO) R
• Function/Operator/Hyperator Assignment: A←f,      A←op1,      A←op2
• Binding Strength: How Variables, Functions, Operators, Hyperators and other syntactic elements combine
• Sink: ←R
• Point Notation:
  • Base — 16b10FFFF is a shorthand for 16⊥1 0 15 15 15 15 and 10b45v is a shorthand for 10⊥4 5 31.
  • Euler — 2x3 is a shorthand for 2∙e³ or 2×(*1)*3 where e is Euler's Number (2.718281828459045...).
  • Pi — 2p3 is a shorthand for 2∙π³ or 2×(○1)*3 where π is Archimedes' constant (3.141592653589793...).
  • Gamma — 2g3 is a shorthand for 2∙γ³ where γ is Euler-Mascheroni's Constant (0.5772156649015329...).
  • Zeta — 2z3 is a shorthand for 2∙ζ(3) where ζ(x) is the Riemann Zeta function.
  • Hypercomplex — 2i3, 2J3 (both equal to 2+3×√¯1), 2ad3 (Angle in Degrees), 2ar3 (Angle in Radians), 2au3 (Angle in Unit Normalized), or 2ah3 (Angle in Half Unit Normalized) for a Complex number, 1i2j3k4 for a Quaternion number, and 1i2j3k4l5ij6jk7kl8 for an Octonion number.
  • Rational — 2r3 is a shorthand for 2÷3 as a Multiple-Precision Integer/Rational number.
  • Variable-Precision Floating — 2.3v is a shorthand for 2.3 as a Multiple-Precision Floating Point number.
  • Ball Arithmetic — 2.3±1E¯17 is a shorthand for a Ball whose Midpoint and Radius are 2.3 and 1E¯17, respectively.
• Trains: e.g., avg←(+⌿ ÷ ≢) applies the functions to its argument(s) in a particular way (in this case, to compute the average of a numeric scalar or vector).
• Anonymous Functions/Operators/Hyperators: multi-line grouping of one or more statements all enclosed in braces such as {(+⌿⍵)÷≢⍵}.

Primitive Functions

Name	Symbol/Syntax	Function Valence
Array Lookup	L⍸R	dyadic
Condense	<[X] R	monadic
Dilate	>[X] R	monadic
Expand	L\[X] R	dyadic
Find	L⍷R	dyadic
Index Generator	⍳R	monadic
Index Of	L⍳R	dyadic
Indexing	R[L],   R[L]←A,   R[L]f←A,   L⌷[X] R,    L⍉R,   L⊃R	dyadic
Indices	⍸R	monadic
Matrix Inverse/Divide	⌹R,   L⌹R	ambivalent
Mismatch	L≢R	dyadic
Partitioned Enclose	L⊂[X] R	dyadic
Primes	πR,   LπR	ambivalent
Reshape	L⍴R	dyadic
Root	√R,   L√[X] R	ambivalent
Sequence	L..R	dyadic
Sets	L§R,   L⊆R,   L⊇R	dyadic
Tally	≢R	monadic
Without	L~R	dyadic

where L is the Left argument, R is the Right argument, and [X] is an optional Axis value.

Primitive Operators

Name	Symbol/Syntax	Derived Function Valence
Axis	{L} f[X] R,   {L} f op1[X] R,   {L} f op2[X] g R	ambivalent
Combinatorial	a‼ R	monadic
Commute	L f⍨ R ←→ R f L	dyadic
Compose	{L} f∘g R,   f∘b R,   a∘g R	ambivalent/monadic
Composition	{L} f⍥g R	ambivalent
Convolution	L f⍡g R	dyadic
Determinant	f.g R	monadic
Duplicate	f⍨ R ←→ R f R	monadic
Integral	{L} f∫ R	ambivalent
Inverses	{L} f⍣¯1 R	ambivalent
Mask	L (a∘/) R,   L (a∘⌿) R,   L (a∘/[X]) R	dyadic
Matrix	{L} f⌻ R,   ∘⌻ R	ambivalent/monadic
Mesh	L (a∘\) R,   L (a∘⍀) R,   L (a∘\[X]) R	dyadic
Multisets	{L} f⍦ R	ambivalent
Nth Derivative	{L} f∂ R,   {L} f∂∂ R, etc.	ambivalent
Null	{L} f⊙ R	ambivalent
Power	{L} f⍣g R,   {L} f⍣b R	ambivalent
Rank	{L} f⍤[X] b R	ambivalent
Variant	{L} f⍠b R	ambivalent

where {L} is an optional Left argument, R is the Right argument, f and g represent Functions, a and b represent Variables, and [X] is an optional Axis value.

Primitive Hyperators

Name	Symbol/Syntax	Derived Function Valence
Transform	f h⍑g R	monadic

where {L} is an optional Left argument, R is the Right argument, f and g represent Functions, h represents a Function/Operator, and [X] is an optional Axis value.

Also, see Hyperators.

Datatypes

• Infinity: ∞ and ¯∞
• Arithmetic Progression Arrays: 2 3 4⍴⍳24
• Unicode Characters
• Array Predicates
• Rational Numbers: 1r3 and 12345x
• Variable-precision Floating Point (VFP) Numbers: 1.234v and 12v
• Complex Numbers: 1i2 or 3.4i5 or 2ad90 or 22ar.1 or 20au.5
• Quaternion Numbers: 1i2j3k4
• Octonion Numbers: 1i2j3k4l5ij6jk7kl8
• Ball Arithmetic: 2.3± is a shorthand for a Ball whose Midpoint and Radius are 2.3 and 2*¯53, respectively, because the Midpoint (2.3) cannot be represented exactly in double-precision floating point format with the standard 53 bits of precision.

System Commands

System Commands provide features to the user of the APL system, separate from actual workspaces, variables or APL operators. These provide such features as accessing files, saving a workspace, and exiting the APL interpreter. The commands are not case sensitive, so )IN and )in do the same thing.

NARS2000 currently has the following system commands:

)BOX Turn ON/OFF box around output )CLEAR Start a new session manager window with an empty workspace )CLOSE )COPY )DROP )EDIT Create a new function in the workspace or edit an existing function )ERASE Delete a variable or function in the current workspace )EXIT Close down the interpreter and exit the program. Same as )OFF )FNS )FOP Display functions, operators, and hyperators. Same as )FOPS )FOPS )HYP Display hyperators only )IN )INASCII     )LIB )LAOD Alternative spelling of )LOAD )LOAD Load an existing workspace )NEWTAB

)NMS )OFF Close down the interpreter and exit the program. Same as )EXIT )OPEN )OPS Display operators only )OUT )RESET )SAVE Save the current workspace )SVAE Alternative spelling for )SAVE )SI workspace State Indicator )SIC State Indicator Clear )SINL )SYMB )ULIB )VARS )XLOAD )WSID

System Variables and Functions

System Variables (A value may be assigned to these except for ⎕DM)
⎕ALX	⎕CT	⎕DM	⎕DT	⎕ELX	⎕FC	⎕FEATURE	⎕FPC	⎕IC	⎕IO
⎕LR	⎕LX	⎕PP	⎕PR	⎕PW	⎕RL	⎕SA	⎕WSID
Niladic System Functions (a value cannot be assigned to these)
⎕A	⎕AV	⎕EM	⎕ET	⎕LC	⎕NNAMES	⎕NNUMS	⎕SI	⎕SYSID	⎕SYSVER
⎕T	⎕TC	⎕TCBEL	⎕TCBS	⎕TCESC	⎕TCFF	⎕TCHT	⎕TCLF	⎕TCNL	⎕TCNUL
⎕TS	⎕WA
Monadic or dyadic system functions (a value cannot be assigned to these)
⎕AT	⎕CR	⎕DC	⎕DFT	⎕DL	⎕DR	⎕EA	⎕EC	⎕ERROR	⎕ES
⎕EX	⎕FMT	⎕FX	⎕MF	⎕NAPPEND	⎕NC	⎕NCREATE	⎕NERASE	⎕NINFO	⎕NL
⎕NLOCK	⎕NREAD	⎕NRENAME	⎕NREPLACE	⎕NRESIZE	⎕NSIZE	⎕NTIE	⎕NUNTIE	⎕STOP	⎕TF
⎕TRACE	⎕UCS	⎕VR
Note that quad functions and variables (except for the ⎕A family of functions) are case insensitive