Omnibar GitHub

Omnibar: the ultimate language toolbar with support for all (?) APL dialects, and currently has 436 meanings. Many dialects call the same primitive different names; in this list they are all grouped under a common name. You can also Download a JSON file that contains all glyphs and meanings.
Monadic functionDyadic functionMonadic operatorDyadic operatorArrayHyperatorSyntax

x, y, u, v: Arrays m, n: Monadic functions d, e: Dyadic functions a: Monadic operators c: Dyadic operators

Dy Dyalog APL ExD Extended Dyalog APL DVi Dyalog APL Vision dz dzaima/APL N2k NARS2000 A2 APL2 GNU GNU APL '89 ISO 8485:1989 '01 ISO/IEC 13751:2001 AX APLX ngn ngn/apl Kap Kap A+W APL+WIN 360 APL\360 SV APL.SV Apr April Co Co-dfns SAX SAX A64 APL64 A+ A+ NARS NARS
Use short names for dialects (listed above, plus all), | for union, & for intersection, ~ for difference.
Glyph Meaning name Meaning pattern Meaning description Meaning dialects
+ Identity
+y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Conjugate
+y
(Hyper)complex conjugate APL Wiki DyExDDViN2kA2GNU'01ngnKapAprCo
Addition
x+y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Join Strings
x+y
Catenate two strings A64
- Negate
-y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Subtraction
-y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Flip Letter Case
-y
GitHub ExDdz
× Signum
×y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Direction
×y
Complex signum APL Wiki DyExDDViN2kA2GNU'01ngnKapAprCo
Multiplication
x×y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Query Letter Case
×y
GitHub ExDdz
Set Letter Case
x×y
GitHub ExD
÷ Reciprocal
÷y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Division
x÷y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
To Title Case
÷y
GitHub ExD
* Exponential
*y
Power with Euler's number as the base APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Power
x*y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Square Root
y
APL Wiki ExDDVidzN2kKap
Root
xy
APL Wiki ExDDVidzN2kKap
Natural Logarithm
y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Logarithm
xy
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Matrix Inverse
y
APL Wiki DyExDDViN2kA2GNU'89'01AXngnKapA+WSVAprCoSAXA64A+NARS
Matrix Division
xy
APL Wiki DyExDDViN2kA2GNU'89'01AXngnKapA+WSVAprCoSAXA64A+NARS
QR Factorization
[v]y
GNU APL Documentation GNU
Pi Times
y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnA+W360SVAprCoSAXA64A+NARS
Circular Functions
xy
A range of trigonometric and related functions selected using the left argument APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnA+W360SVAprCoSAXA64A+NARS
! Factorial
!y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64NARS
Binomial Coefficient
x!y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64NARS
Demote
!y
Combine two leading axes (like ,[⍳2]) Kap Reference A+
Restructure
x!y
??? A+
? Roll
?y
Random numbers as specified by the argument APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Deal
x?y
Right argument random selections from the range defined by the left argument APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
| Absolute Value
|y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Magnitude
|y
APL Wiki DyExDDViN2kA2GNU'01ngnKapAprCo
Residue
x|y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Case Fold
|y
GitHub ExD
Ceiling
y
The smallest integer greater than or equal to the argument APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Maximum
xy
The largest argument APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
To Uppercase
y
GitHub ExDdz
Floor
y
The largest integer less than or equal to the argument APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Minimum
xy
The smallest argument APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
To Lowercase
y
GitHub ExDdz
Decode
xy
Evaluate the right argument in the base defined by the left argument APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Base-2 Decode
y
GitHub ExDdz
Pack
y
Turn character vectors into symbols A+
Encode
xy
Represent the right argument in the base defined by the left argument APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Base-2 Encode
y
GitHub ExDdz
Type
y
Prototype array corresponding to the argument APL Wiki N2kNARS
Unpack
y
Turn symbols into character vectors A+
Same
y
The argument, unchanged APL Wiki DyExDDVidzN2kGNUAXngnKapAprCoSAXA+
Right
xy
The right argument, unchanged APL Wiki DyExDDVidzN2kGNU'01AXngnKapAprCoSAX
Same
y
The argument, unchanged APL Wiki DyExDDVidzN2kngnCo
Left
xy
The left argument, unchanged APL Wiki DyExDDVidzN2kGNU'01AXngnKapAprCoSAX
Stop
y
Return an empty matrix APL WikiAPLX Reference GNUAXKapAprSAXA+
= Equal To
x=y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Is Type?
=y
Equal to type GitHub ExD
Rank
=y
APL Wiki DVi
Dimension
=y
Hypercomplex dimension (1, 2, 4, or 8) N2k
Nub In
=y
Table of which elements are their unique APL Wiki SAX
Not Equal To
xy
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Nub Sieve
y
Mask that marks the first occurrence of each element APL Wiki DyDViAprCoSAX
Is Not Type?
y
Not equal to type GitHub ExD
Norm
y
Argument times the conjugate of the argument N2k
Less Than or Equal To
xy
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Is Nonnegative?
y
GitHub ExD
Is Invisible Character?
y
GitHub ExD
Sort Ascending
y
GitHub DVi
< Less Than
x<y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Is Positive?
<y
GitHub ExD
Is Control Character?
<y
GitHub ExD
Major Cells
<y
APL Wiki DVi
Sort Ascending
<y
GitHub dz
Condense
<y
Compress a real array into an array of hypercomplex numbers NARS2000 Wiki N2k
Promote
<y
Add a length-1 axis before the other axes APL Wiki Kap
Enclose
<y
Wrap the argument into a nested scalar APL Wiki SAXA+
To String
<y
Turn a character vector into a string A64
> Greater Than
x>y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Is Negative?
>y
GitHub ExD
Is Visible Character?
>y
GitHub ExD
Join
>y
Merge array of arrays into single array APL Wiki DVi
Sort Descending
>y
GitHub dz
Dilate
>y
Expand an array of hypercomplex numbers into an array of reals NARS2000 Wiki N2k
Demote
>y
Combine two leading axes (like ,[⍳2]) Kap Reference Kap
Mix
>y
Combine all elements into a single array APL Wiki SAXA+
From String
>y
Turn a string into a charcter vector A64
Greater Than or Equal To
xy
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Is Nonpositive?
y
GitHub ExD
Is Not Control Character?
y
GitHub ExD
Sort Descending
y
GitHub DVi
Match
xy
Compare the whole arrays for equality APL Wiki DyExDDVidzN2kA2GNU'01AXngnKapA+WAprCoSAXA64A+NARS
Depth
y
Level of nesting APL Wiki DyExDDVidzN2kA2GNU'01AXngnKapA+WAprCoA64A+
Simple
y
Whether the argument is simple (non-nested) NARS
Not Match
xy
APL Wiki DyExDDVidzN2kAXngnKapA+WAprCoA64NARS
Tally
y
The amount of major cells APL Wiki DyExDDVidzN2kngnKapAprCo
Not Simple
y
NARS
Or
xy
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Greatest Common Divisor
xy
APL Wiki DyExDDVidzN2kGNU'01ngnCoSAX
Sort Descending
y
GitHub ExDKap
Demote
y
Combine two leading axes (like ,[⍳2]) Kap Reference DVi
Monadic GCD
y
GCD reduction (any 1?) GitHub dz
Cast
xy
Cast the right argument to the type specified by the left argument symbol A+
Type
y
Prototype array corresponding to the argument APL Wiki A+
And
xy
APL Wiki DyExDDVidzN2kGNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Least Common Multiple
xy
APL Wiki DyExDDVidzN2kGNU'01ngnCoSAX
Sort Ascending
y
GitHub ExDKap
Promote
y
Add a length-1 axis before the other axes APL Wiki DVi
Monadic LCM
y
LCM reduction (all 1?) GitHub dz
Stop
y
Perform an action based on the `stop system variable A+
^ And
x^y
APL Wiki A2
Nor
xy
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64NARS
Not All Equal To Type
y
GitHub ExD
None
y
All 0? GitHub dz
Nand
xy
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64NARS
Not Any Equal To Type
y
GitHub ExD
Not All
y
Any 0? GitHub dz
Mix
y
Combine all elements into a single array APL Wiki DyExDDVidzngnAprCoNARS
Take
xy
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
First
y
The first element of the argument APL Wiki N2kA2GNU'01AXKapA+WA64
Unique
y
Unique elements APL Wiki SAX
Raise
y
Raise an exception A+
Split
y
Convert an axis to a level of nesting APL Wiki DyExDDVidzngnAprCoNARS
Drop
xy
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Drop First
y
Kap Reference Kap
Join
y
Merge array of arrays into single array APL Wiki SAX
Print
y
Print a value and return it A+
Enclose
y
Wrap the argument into a nested scalar APL Wiki DyExDDVidzN2kA2GNU'01AXngnKapA+WAprCoA64NARS
Partitioned Enclose
xy
Split the right argument into pieces specified by the left argument APL Wiki DyExDDVidzngnAprCoNARS
Partition
xy
Split the right argument into pieces specified by the left argument APL Wiki N2kA2AXKapA+WA64
Duplicate
(d)y
Call the operand with the argument as both left and right APL Wiki SAX
Commute
x(d)y
Call the operand with the arguments swapped APL Wiki SAX
Partition
xy
??? A+
Partition Count
y
??? A+
First
y
The first element of the argument APL Wiki DyExDDVidzngnAprCoNARS
Pick
xy
Extract a value through layers of nesting APL Wiki DyExDDVidzN2kA2GNU'01AXngnKapA+WAprCoA64A+NARS
Mix
y
Combine all elements into a single array APL Wiki N2kA2GNU'01AXKapA+WA64
Nest
y
Enclose if simple APL Wiki SAX
Link
xy
Catenate the enclose of the left argument and the nest of the right argument APL Wiki SAX
Join
y
Merge array of arrays into single array APL Wiki A+
Nest
y
Enclose if simple APL Wiki DyExDDViAprCo
Partition
xy
Split the right argument into pieces specified by the left argument APL Wiki DyExDDViAprCo
Subset
xy
Is subset? NARS2000 Wiki N2k
Partitioned Enclose
xy
Split the right argument into pieces specified by the left argument APL Wiki Kap
Disclose If Scalar
y
GitHub ExD
From
xy
Function form of bracket indexing APL Wiki ExDDVidzKap
Last
y
Last element in ravel order DVi
Superset
xy
Is superset? NARS2000 Wiki N2k
Index
xy
Items of the right argument as specified by the left argument APL Wiki DyExDDVidzN2kA2GNUAXngnKapA+WAprCoA64
Materialize
y
Cast the argument to an array APL Wiki DyExDDViCo
Map Key/Value Pairs
y
GitHub dz
Grade Up
y
Indices that sort the argument in ascending order APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Dyadic Grade Up
xy
Indices that sort the right argument in ascending order, according to the left argument APL Wiki DyExDDViN2kA2GNU'01AXngnA+WAprCoSAXA64
Interval Index
xy
Determine fitting interval, left argument giving beginning points APL Wiki A+
Grade Down
y
Indices that sort the argument in descending order APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Dyadic Grade Down
xy
Indices that sort the right argument in descending order, according to the left argument APL Wiki DyExDDViN2kA2GNU'01AXngnA+WAprCoSAXA64
Index Generator (Range)
y
Numbers in range defined by the argument APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnA+W360SVAprCoSAXA64NARS
Index Generator (Indices)
y
Indices with shape specified by the argument APL Wiki DyExDDVidzN2kGNU'01ngnAprCoA64NARS
Index Of
xy
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnA+W360SVAprCoSAXA64A+NARS
Where
y
True indices in the argument mask APL Wiki DyExDDVidzN2kAprCo
Interval Index
xy
Determine fitting interval, left argument giving beginning points APL Wiki DyExDDViAprCo
Array Lookup
xy
Like ⍳, but on major cells NARS2000 Wiki N2k
Find Index
xy
Index of the first true value in the array returned by calling Find on the arguments SAX
Element Of
xy
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Enlist
y
All simple elements of the argument, traversing nested elements APL Wiki DyExDDVidzN2kA2GNU'01AXngnA+WAprCoA64A+
Find
xy
Mask of the start corners of the appearances of the left argument in the right argument APL Wiki DyExDDVidzN2kA2AXngnKapA+WAprCoSAXA64
Type
y
Prototype array corresponding to the argument APL Wiki ExDDVi
Union
xy
The left argument catenated with the elements of the right argument that don't appear in the left argument APL Wiki DyExDDVidzN2kAXngnKapAprCoNARS
Unique
y
Unique elements APL Wiki DyExDDVidzN2kA2AXngnA+WAprCoA64NARS
Combine Symbols
xy
Produce qualified names from context names and unqualified names A+
Separate Symbols
y
Split symbols on the last dot A+
Intersection
xy
All elements of the left argument that appear in the right argument APL Wiki DyExDDVidzN2kAXngnKapAprCoNARS
Nub In
y
Table of which elements are their unique APL Wiki ExD
~ Not
~y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Without
x~y
All elements of the left argument that don't appear in the right argument APL Wiki DyExDDVidzN2kA2GNU'01AXngnKapAprCoSAXNARS
1 Minus
~y
Like Not but extended to floats [0; 1] GitHub ExD
Laminate
x~y
Join two arrays along a new axis APL Wiki A+
§ Symmetric Difference
x§y
Elements that appear in exactly one of the arguments NARS2000 Wiki N2k
/ Reduce
(d/)y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Windowed Reduce
x(d/)y
APL Wiki DyExDDVidzN2kA2GNU'01AXngnKapAprCoNARS
Compress
x/y
Select elements of the right argument marked by the left argument mask APL Wiki DyExDDViN2kGNU'89'01ngn360SVAprCoNARS
Replicate
x/y
APL Wiki DyExDDViN2kGNU'01ngnAprCoA+NARS
Compress
(u/)y
Select elements of the argument marked by the operand mask APL Wiki A2AXA+WSAXA64
Replicate
(u/)y
APL Wiki A2AXA+WA64
Reduce First
(d)y
APL Wiki DyExDDViN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64NARS
Windowed Reduce First
x(d)y
APL Wiki DyExDDViN2kA2GNU'01AXngnKapAprCoNARS
Compress First
xy
Select elements of the right argument marked by the left argument mask APL Wiki DyExDDVidzN2kGNU'89'01ngn360SVAprCoNARS
Replicate First
xy
APL Wiki DyExDDVidzN2kGNU'01ngnAprCoNARS
Compress First
(u)y
Select elements of the argument marked by the operand mask APL Wiki A2AXA+WSAXA64
Replicate First
(u)y
APL Wiki A2AXA+WA64
\ Scan
(d\)y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+WSVAprCoSAXA64A+NARS
Expand
x\y
APL Wiki DyExDDVidzN2kGNU'89'01ngn360SVAprCoA+NARS
Outer Product
x(d\)y
Apply a function to the cartesian product of the two arguments APL Wiki ExD
Expand
(u\)y
APL Wiki A2AXA+WSAXA64
Dyadic Scan
x(d\)y
Scan on windows of length of at most the left argument NARS
Scan First
(d)y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+WSVAprCoSAXA64NARS
Expand First
xy
APL Wiki DyExDDVidzN2kGNU'89'01ngn360SVAprCoNARS
Apply To Right Argument (?)
x(m)y
⊢∘f GitHub ExD
Expand First
(u)y
APL Wiki A2AXA+WSAXA64
Dyadic Scan First
x(d)y
NARS
, Ravel
,y
All elements of the argument as a vector APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Catenate
x,y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Ravel Items
y
APL Wiki DyExDDVidzN2kGNU'01ngnKapAprCoSAX
Catenate First
xy
APL Wiki DyExDDVidzN2kGNU'01AXngnKapA+WAprCoSAXA64NARS
Ravel
y
All elements of the argument as a vector APL Wiki AX
Shape
y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Reshape
xy
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Reverse
y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Rotate
xy
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Reverse First
y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64
Rotate First
xy
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64
Transpose
y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Reorder Axes
xy
APL Wiki DyExDDViN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
¨ Each
(m¨)y
Apply a function to each element of an array APL Wiki DyExDDVidzN2kA2GNU'01AXngnKapAprCoA+NARS
Each
x(d¨)y
Apply a function to each element of two arrays APL Wiki DyExDDVidzN2kA2GNU'01AXngnKapAprCoA+NARS
Under
(m¨n)yx(d¨n)y
Apply a function, then another function, then the first function's inverse APL Wiki SAX
Bind
(d¨v)y(u¨e)y
Bind an argument to a dyadic function, making it monadic APL Wiki SAX
Apply
(u¨)yx(u¨)y
Apply the operand function object to the arguments A+
Constant
(u)yx(u)y
A function that always returns the operand APL Wiki DyExDDVidzAprCo
Commute
x(d)y
Call the operand with the arguments swapped APL Wiki DyExDDVidzN2kGNU'01ngnKapA+WAprCoA64NARS
Duplicate
(d)y
Call the operand with the argument as both left and right APL Wiki DyExDDVidzN2kGNU'01ngnKapAprCo
Bitwise
x(d)y(m)y
Derive a bitwise function from a boolean function Kap Reference A+
Repeat
(mv)yx(dv)y
Repeat a function a specified number of times APL Wiki DyExDDVidzN2kngnKapAprCoNARS
Repeat Until
(me)yx(de)y
Repeat a function until a predicate is satisfied APL Wiki DyExDDVidzN2kngnKapAprCo
Cumulative Repeat
(mv)yx(dv)y(me)yx(de)y
Like ⍣, but collect intermediary results dz
Convolution
x(de)y
NARS2000 Wiki N2kNARS
. Inner Product
x(d.e)y
Apply a function to each pair in the arguments and combine the results with another function APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Alternant
(d.e)y
Generalized determinant APL WikiNARS2000 Wiki N2kSAX
Member Access
Access an entry of a namespace/object DyExDDVidzGNUA+WCoA64
Decimal Point
DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64
Tie
x(u.e)y
Restrict number of axes used in Cartesian product SAX
Repeat
(m.v)yx(d.v)y
Repeat a function a specified number of times APL Wiki SAX
Inner Product
x(de)y
Apply a function to each pair in the arguments and combine the results with another function APL Wiki ExDKap
Alternant
(de)y
Generalized determinant APL WikiNARS2000 Wiki ExD
∘. Outer Product
x(∘.d)y
Apply a function to the cartesian product of the two arguments APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS
Function Table
(∘.d)y
Outer product between ranges defined by the argument NARS
∘∙ Outer Product
x(d∘∙)y
Apply a function to the cartesian product of the two arguments APL Wiki Kap
Compose
(mn)y
Apply a function after another APL Wiki DyExDDVidzN2kngnAprCoNARS
After
x(de)y
Preprocess the right argument to a function with another function APL Wiki DyExDDVidzN2kngnKapAprCoNARS
Bind
(dv)y(ue)y
Bind an argument to a dyadic function, making it monadic APL Wiki DyExDDVidzN2kngnAprCoNARS
Matrix Product
xy
Like +.× but faster (and only for matrices) GNU APL Documentation GNU
Withe
(dn)y
Right hook APL Wiki Kap
Before
(me)yx(me)y
Preprocess the left argument to a function with another function APL Wiki ExDDVidzKapApr
Compose
(mn)y
Apply a function after another APL Wiki DyExDDVidzN2kAprCoSAX
Atop
x(me)y
Call a monad using the result of a dyad as the argument APL Wiki DyExDDVidzN2kAprCo
Rank
(mv)yx(dv)y
Apply a function at a specified rank APL Wiki DyExDDViN2kGNU'01KapAprCoSAX
Over
x(dn)y
Preprocess all arguments to a function with another function APL Wiki SAX
Cut
x(un)y(un)y
Apply a function to cuts of an array APL Wiki SAX
Compose
(mn)y
Apply a function after another APL Wiki DyExDDVidzN2kKapAprCoSAX
Over
x(dn)y
Preprocess all arguments to a function with another function APL Wiki DyExDDVidzN2kKapAprCo
Depth
(mv)yx(dv)y
Apply a function at a specified depth APL Wiki ExDDVi
Atop
x(me)y
Call a monad using the result of a dyad as the argument APL Wiki SAX
Under
(mn)yx(dn)y
Apply a function, then another function, then the first function's inverse APL Wiki ExDDVidzKapNARS
Each Left
x(d)y
Each, only on the left argument GitHub dz
Each Right
x(d)y
Each, only on the right argument GitHub dz
@ At
(m@n)y(m@v)y(u@n)y(u@v)y
Transform selected elements of an array APL Wiki DyExDDVidzAprCo
Character
A literal for a single scalar character Kap Reference Kap
From
x@y
Function form of bracket indexing APL Wiki SAX
All
@y
Cartesian product by catenation of all elements of the argument APL Wiki SAX
Rank
@y
APL Wiki A+
Obverse
(mn)yx(de)y
Specify the inverse function for a function GitHub ExDDVidz
Lock
Lock a function definition, so that it can't be read or modified APLX Reference A2AX
Return
Return early from a dfn ngn
Evaluated Input
Input and evaluate as an APL expression APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnA+W360SVAprCoA64
Standard Output
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnA+W360SVAprCoA64
System Name
First character of a system name APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnA+WSVAprCoA64
String Input
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnA+W360SVAprCoA64
Standard Error
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnA+W360SVAprCoA64
Apply Function Reference
Call a function wrapped in a reference Kap Reference Kap
Variant
(mv)yx(dv)y
Select a related function APL WikiDyalog ReferenceNARS2000 Wiki DyExDDViN2k
Valences
(me)yx(me)y
Apply the left function if called monadically and the right function if called dyadically ngn
Key (Indices)
(d)y
Apply a function to unique elements of an array and their indices APL Wiki DyExDDVidzngnAprCo
Key (Values)
x(d)y
Apply a function to unique elements of the left array and the corresponding entries in the right array APL Wiki DyExDDVidzngnAprCo
Key With Vocabulary (Indices)
(u)y
Locations of each element in the vocabulary in the argument GitHub DVi
Key With Vocabulary (Values)
x(u)y
Elements of the left argument corresponding to locations of elements in the vocabulary in the right argument GitHub DVi
Get In Map
(u)y
GitHub dz
Set In Map
x(u)y
GitHub dz
Key
xy
Unique values of the left array, each paired with the list of corresponding entries from the right array Kap Reference Kap
Diagonals
(m)y
Apply a function to each diagonal of a matrix GitHub dz
Identity Element
(dv)y
Set the identity element for a function ngn
Stencil
(dv)y
Apply a function to windows of an array APL Wiki DyExDDViAprCo
I-Beam
(u)yx(u)y
Access non-primitive, implementation specific functions APL WikiDyalog Reference DyExDDViCo
Execute
y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+WSVAprSAXA64A+NARS
Execute in Context
xy
??? A+
Protected Execute
xy
??? A+
Format
y
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+WSVAprSAXA64A+NARS
Format With Specification
xy
Format specifying column widths, decimal places and optionally scientific notation APL Wiki DyExDDViN2kA2GNU'89'01AXA+WSVAprSAXA64A+NARS
Format By Example
xy
Format the right argument accoding to the left argument "example" APL Wiki A2AXSAX
Zilde
Empty numeric vector APL Wiki DyExDDVidzN2kAXngnA+WAprCoA64NARS
Infinity
The largest number GitHub ExDdzN2kngn
¯∞ Negative Infinity
¯∞
The smallest number GitHub ExDdzN2kngn
Not a Number
NARS2000 Wiki N2k
# Root Namespace
#
Dyalog Reference DyExDDViCo
From
x#y
Function form of bracket indexing APL Wiki A+
Tally
#y
The amount of major cells APL Wiki A+
## Parent Namespace
##
Dyalog Reference DyExDDViCo
Complex
xy
left + i × right APL Wiki ExD
Imaginary
y
i × arg APL Wiki ExD
Outer Product
x(d)y
Apply a function to the cartesian product of the two arguments APL Wiki dz
$ String Enhancement (Monadic)
$y
${expr} inside a string is evaluated GitHub ExDDVi
String Enhancement (Dyadic)
x$y
${idx} is replaced with the corresponding item in the argument GitHub ExDDVi
Hexadecimal Number
GNU APL Documentation GNU
Conditional
??? GNU APL Documentation Apr
Range
xy
APL Wiki ExDdz
.. Range
x..y
APL Wiki N2k
Multisets
(m)yx(d)y
Turns set functions into multiset functions NARS2000 Wiki N2k
Nub Sieve
y
Mask that marks the first occurrence of each element APL Wiki ExDdz
Count In
xy
Count occurrences of each of the left argument in the right argument GitHub ExDdz
% Probability-logical Function
x(d%)y
Multiplicative fuzzy logic (probabalistic) function corresponding to the Boolean function given GitHub ExD
Merge
x%y
Compose array by choosing each element from the corresponding element in each of a set of sources APL Wiki dzKap
Value
%y
??? A+
Value in Context
x%y
??? A+
Pair
xy
APL Wiki ExDdz
Half Pair
y
GitHub ExDdz
Factors
y
GitHub ExD
Prime Related Functions
xy
Prime-related functions on the right argument, selected by left argument GitHubNARS2000 Wiki ExD
π Prime Factors
πy
NARS2000 Wiki N2k
Prime Related Functions
xπy
Prime-related functions on the right argument, selected by left argument GitHubNARS2000 Wiki N2k
Null
(m)yx(d)y
The identity operator, useful for casting hybrids to functions NARS2000 Wiki N2k
Combinatorial
x(u)y
Combinatorial functions selected by the operand NARS2000 Wiki N2k
Matrix
(m)yx(d)y
Apply a function to a diagonalizable matrix NARS2000 Wiki N2k
Outer Product
x(d)y
Apply a function to the cartesian product of the two arguments APL Wiki Kap
Derivative
(m)yx(d)y
NARS2000 Wiki N2k
Integral
x(m)y
NARS2000 Wiki N2k
Transform
(d(m)e)y
Paper N2k
& Spawn
(m&)yx(d&)y
Run the operand in a green thread APL Wiki DyExDDVi
Select
(m&)y
Apply a function that selects a subset of the elements of an array SAX
Merge
x(m&)y
Replace elements of the right argument with elements of the left argument as selected by the operand SAX
⊤∧ Bitwise And
x⊤∧y
GNU APL Documentation GNU
Bitwise And With 0
⊤∧y
GNU APL Documentation GNU
⊤∨ Bitwise Or
x⊤∨y
GNU APL Documentation GNU
Bitwise Or With 0
⊤∨y
GNU APL Documentation GNU
⊤⍲ Bitwise Nand
x⊤⍲y
GNU APL Documentation GNU
⊤⍱ Bitwise Nor
x⊤⍱y
GNU APL Documentation GNU
Bitwise Nor With 0
⊤⍱y
GNU APL Documentation GNU
⊤≠ Bitwise Xor
x⊤≠y
GNU APL Documentation GNU
⊤= Bitwise Xnor
x⊤=y
GNU APL Documentation GNU
Read File
y
Read a component from a file APLX Reference AX
File Info
xy
Read information from a file selected by the left argument APLX Reference AX
Rename File
xy
APLX Reference AX
Write File
xy
Write a component to a file APLX Reference AX
Set File Allocation Quota
y
Set how much a file can hold APLX Reference AX
File Hold
xy
Lock or unlock a file APLX Reference AX
Delete File
xy
APLX Reference AX
Delete File Component
y
APLX Reference AX
Approximately Equal To
xy
GitHub ngn
Raise
y
Raise an exception ngn
Compress
xy
Select elements of the right argument marked by the left argument mask APL Wiki Kap
Replicate
xy
APL Wiki Kap
Bitwise
x(d)y(m)y
Derive a bitwise function from a boolean function Kap Reference Kap
Parallel
(m)yx(d)y
Apply a function in parallel (with multiple threads) Kap
˝ Inverse
(m˝)yx(d˝)y
Kap Reference Kap
⍣∘ Power Limit
x(d⍣∘)y(m⍣∘)y
Repeat a function until a result is returned twice NARS
∘/ Mask
x(u∘/)y
APL Wiki N2kNARS
∘⌿ Mask First
x(u∘⌿)y
APL Wiki N2kNARS
∘\ Mesh
x(u∘\)y
APL Wiki N2kNARS
∘⍀ Mesh First
x(u∘⍀)y
APL Wiki N2kNARS
{} Dfn
Wrap a dfn (anonymous function) definition Wikipedia DyExDDVidzN2kGNUngnKapAprCo
Dop
Wrap a dop (anonymous operator) definition Wikipedia DyExDDVidzN2kGNUngnAprCo
Dhyp
Wrap a dhyp (anonymous hyperator) definition NARS2000 Wiki N2k
Shy Result
Indicate that a tradfn result is shy APL Wiki DyExDDViN2kA2GNUCo
Optional Left Argument
Indicate that a tradfn's left argument is optional APL Wiki DyExDDViCo
Left Argument
Wikipedia DyExDDVidzN2kGNUngnKapAprCo
Picture Format
xy
APLX Reference AX
Right Argument
Wikipedia DyExDDVidzN2kGNUngnKapAprCo
⍺⍺ Left Operand
WikipediaGitHub DyExDDViN2kAprCo
Left Operand
WikipediaGitHub dzGNUngn
⍵⍵ Right Operand
WikipediaGitHub DyExDDViN2kAprCo
Right Operand
WikipediaGitHub dzGNUngn
⍺⍺⍺ Left Hyperand
NARS2000 Wiki N2k
⍵⍵⍵ Right Hyperand
NARS2000 Wiki N2k
χ Axis Argument
NARS2000 Wiki N2kGNU
: Guard
Dfn guard: run RHS if LHS is true Dyalog Reference DyExDDVidzN2kCo
Control Structure
Begin a control structure name APL Wiki DyExDDViN2kA+WA64
Label
Target for a branch Dyalog Reference DyExDDViGNU'01A+WCoSAXA64
:: Error Guard
If an error of the LHS category occurs, return the RHS Dyalog Reference DyExDDVi
[] Index
Index into an array APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+Wngn360SVAprCoSAXA64A+NARS
Function Axis
Specify an axis for a function APL Wiki DyExDDViN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64NARS
; Axis Separator
Inside a bracket index, separates the different axes APL Wiki DyExDDVidzN2kA2GNU'89'01AXA+WngnKap360SVAprCoSAXA64A+
Local Variable
Mark a variable as local inside a tradfn APL Wiki DyExDDViN2kA2GNU'89'01AXA+W360SVA64
Tuple
Separates entries in a tuple literal Kap Reference Kap
Adjacent Output
Print multiple arrays next to each other 360SV
Assignment
APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+
Return
Return early from a dfn dzA+
Sink
Don't print the result of an expression NARS2000 Wiki N2kA+WA64NARS
Assign Function
Bind a function to a name Kap Reference Kap
Branch
APL Wiki DyExDDViN2kA2GNU'01AXA+WAprSAXA64
Return
Return early from a dfn Kap
Tradfn Definition
APL Wiki DyExDDViN2kA2GNU'89'01AXA+W360SVSAXA64
Recurse Function
In a dfn, refer to the dfn itself WikipediaDyalog Reference DyExDDVidzN2kngnAprCo
Global Function
Kap Reference Kap
Direct Definition
(∘v)y(uv)yx(u∘)yx(uv)y
Define an anonymous function APL Wiki NARS
∇∇ Recurse Operator
In a dop, refer to the dop itself WikipediaDyalog Reference DyExDDViN2kCo
∇∇∇ Recurse Hyperator
In a dhyp, refer to the dhyp itself NARS2000 Wiki N2k
¯ Negative
Mark a number as negative APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64
Inverse
The inverse of a function ExD
Dfns Workspace
First character of a dfns workspace name APL Wiki ExD
E Exponential Separator
Separates the multiplier and exponent of a number DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64
e Exponential Separator
Separates the multiplier and exponent of a number DyExDDVidzN2kngnKapCoSAX
J Complex Separator
Separates the real and imaginary part of a complex number DyExDDViN2kA2GNU'01ngnKapCo
j Complex Separator
Separates the real and imaginary part of a complex number DyExDDVingnKapCo
i Complex Separator
Separates the real and imaginary part of a complex number N2k
D Complex Angle Degrees
A2
R Complex Angle Radians
A2
ad Complex Angle Degrees
N2k
ah Complex Angle Signed Half Unit
N2k
ar Complex Angle Radians
N2k
au Complex Angle Unsigned Unit
N2k
b Base Point Notation
N2k
g Gamma Point Notation
N2k
p Pi Point Notation
N2k
r Rational Notation
N2kApr
v Multiprecision Float
N2k
x Euler Point Notation
N2k
z Zeta Point Notation
N2k
± Ball Arithmetic Notation
N2k
ijk Quaternion Notation
N2k
ijkl Octonion Notation
N2k
0x Hexadecimal Number
GNU APL Documentation KapA+WA64
0X Hexadecimal Number
GNU APL Documentation A+WA64
0b Binary Number
A+WA64
0B Binary Number
A+WA64
0r IEEE Float
Floating point number as a hex representation of an IEEE double A+WA64
0R IEEE Float
Floating point number as a hex representation of an IEEE double A+WA64
Statement Separator
DyExDDVidzN2kA2GNU'01AXngnA+WAprCoSAXA64
Comment
Start a comment that ends at the end of the line APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64
⟃⟄ Inline Comment
A64
⟃⟃⟄⟄ Multiline Comment
A comment that can span multiple lines A64
' Character Literal
Character vector/scalar delimiter APL Wiki DyExDDVidzN2kA2GNU'89'01AXngnA+W360SVAprCoSAXA64
" String Literal
Like a character literal, but with escapes and always a vector dzGNUKap
Character Literal
Character vector/scalar delimiter APL Wiki AXA+WA64
""" Multiline String
A string that can span multiple lines GNU
λ Create Function Reference
Turn a function into a primitive Kap Reference Kap
«» Fork
Kap Reference Kap
Scalar String
A string literal that makes a string scalar, instead of a vector of characters A64
««»» Multiline String
A string that can span multiple lines A64
_ Digit Separator
Ignored, separates digits for readability Apr
Line Continuation
N2k