x, y, u, v: Arrays m, n: Monadic functions d, e: Dyadic functions a: Monadic operators c: Dyadic operators
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 | x√y | APL Wiki | ExDDVidzN2kKap | |
⍟ | Natural Logarithm | ⍟y | APL Wiki | DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS |
| Logarithm | x⍟y | APL Wiki | DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS | |
⌹ | Matrix Inverse | ⌹y | APL Wiki | DyExDDViN2kA2GNU'89'01AXngnKapA+WSVAprCoSAXA64A+NARS |
| Matrix Division | x⌹y | 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 | x○y | 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 | x⌈y | 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 | x⌊y | The smallest argument APL Wiki | DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS | |
| To Lowercase | ⌊y | GitHub | ExDdz | |
⊥ | Decode | x⊥y | 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 | x⊤y | 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 | x⊢y | The right argument, unchanged APL Wiki | DyExDDVidzN2kGNU'01AXngnKapAprCoSAX | |
⊣ | Same | ⊣y | The argument, unchanged APL Wiki | DyExDDVidzN2kngnCo |
| Left | x⊣y | 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 | x≠y | 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 | x≤y | 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 | x≥y | 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 | x≡y | 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 | x≢y | APL Wiki | DyExDDVidzN2kAXngnKapA+WAprCoA64NARS |
| Tally | ≢y | The amount of major cells APL Wiki | DyExDDVidzN2kngnKapAprCo | |
| Not Simple | ≢y | NARS | ||
∨ | Or | x∨y | APL Wiki | DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS |
| Greatest Common Divisor | x∨y | 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 | x∨y | 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 | x∧y | APL Wiki | DyExDDVidzN2kGNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS |
| Least Common Multiple | x∧y | 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 | x⍱y | APL Wiki | DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64NARS |
| Not All Equal To Type | ⍱y | GitHub | ExD | |
| None | ⍱y | All 0? GitHub | dz | |
⍲ | Nand | x⍲y | 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 | x↑y | 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 | x↓y | 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 | |
↓y | Print a value and return it | A+ | ||
⊂ | Enclose | ⊂y | Wrap the argument into a nested scalar APL Wiki | DyExDDVidzN2kA2GNU'01AXngnKapA+WAprCoA64NARS |
| Partitioned Enclose | x⊂y | Split the right argument into pieces specified by the left argument APL Wiki | DyExDDVidzngnAprCoNARS | |
| Partition | x⊂y | 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 | x⊂y | ??? | A+ | |
| Partition Count | ⊂y | ??? | A+ | |
⊃ | First | ⊃y | The first element of the argument APL Wiki | DyExDDVidzngnAprCoNARS |
| Pick | x⊃y | 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 | x⊃y | 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 | x⊆y | Split the right argument into pieces specified by the left argument APL Wiki | DyExDDViAprCo | |
| Subset | x⊆y | Is subset? NARS2000 Wiki | N2k | |
| Partitioned Enclose | x⊆y | Split the right argument into pieces specified by the left argument APL Wiki | Kap | |
⊇ | Disclose If Scalar | ⊇y | GitHub | ExD |
| From | x⊇y | Function form of bracket indexing APL Wiki | ExDDVidzKap | |
| Last | ⊇y | Last element in ravel order | DVi | |
| Superset | x⊇y | Is superset? NARS2000 Wiki | N2k | |
⌷ | Index | x⌷y | 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 | x⍋y | Indices that sort the right argument in ascending order, according to the left argument APL Wiki | DyExDDViN2kA2GNU'01AXngnA+WAprCoSAXA64 | |
| Interval Index | x⍋y | 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 Up | x⍒y | 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 | x⍳y | APL Wiki | DyExDDVidzN2kA2GNU'89'01AXngnA+W360SVAprCoSAXA64A+NARS | |
⍸ | Where | ⍸y | True indices in the argument mask APL Wiki | DyExDDVidzN2kAprCo |
| Interval Index | x⍸y | Determine fitting interval, left argument giving beginning points APL Wiki | DyExDDViAprCo | |
| Array Lookup | x⍸y | Like ⍳, but on major cells NARS2000 Wiki | N2k | |
| Find Index | x⍸y | Index of the first true value in the array returned by calling Find on the arguments | SAX | |
∊ | Element Of | x∊y | APL Wiki | DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS |
| Enlist | ∊y | All simple elements of the argument, traversing nested elements APL Wiki | DyExDDVidzN2kA2GNU'01AXngnA+WAprCoA64A+ | |
⍷ | Find | x⍷y | 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 | x∪y | 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 | x∪y | Produce qualified names from context names and unqualified names | A+ | |
| Separate Symbols | ∪y | Split symbols on the last dot | A+ | |
∩ | Intersection | x∩y | 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 | x⌿y | Select elements of the right argument marked by the left argument mask APL Wiki | DyExDDVidzN2kGNU'89'01ngn360SVAprCoNARS | |
| Replicate First | x⌿y | 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 | x⍀y | 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 | x⍪y | 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 | x⍴y | APL Wiki | DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS | |
⌽ | Reverse | ⌽y | APL Wiki | DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS |
| Rotate | x⌽y | APL Wiki | DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS | |
⊖ | Reverse First | ⊖y | APL Wiki | DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64 |
| Rotate First | x⊖y | APL Wiki | DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64 | |
⍉ | Transpose | ⍉y | APL Wiki | DyExDDVidzN2kA2GNU'89'01AXngnKapA+W360SVAprCoSAXA64A+NARS |
| Reorder Axes | x⍉y | 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 | (m⍣v)yx(d⍣v)y | Repeat a function a specified number of times APL Wiki | DyExDDVidzN2kngnKapAprCoNARS |
| Repeat Until | (m⍣e)yx(d⍣e)y | Repeat a function until a predicate is satisfied APL Wiki | DyExDDVidzN2kngnKapAprCo | |
⍡ | Cumulative Repeat | (m⍡v)yx(d⍡v)y(m⍡e)yx(d⍡e)y | Like ⍣, but collect intermediary results | dz |
| Convolution | x(d⍡e)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(d∙e)y | Apply a function to each pair in the arguments and combine the results with another function APL Wiki | ExD |
| Alternant | (d∙e)y | Generalized determinant APL WikiNARS2000 Wiki | ExD | |
• | Inner Product | x(d•e)y | Apply a function to each pair in the arguments and combine the results with another function APL Wiki | Kap |
∘. | 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 | (m∘n)y | Apply a function after another APL Wiki | DyExDDVidzN2kngnAprCoNARS |
| After | x(d∘e)y | Preprocess the right argument to a function with another function APL Wiki | DyExDDVidzN2kngnKapAprCoNARS | |
| Bind | (d∘v)y(u∘e)y | Bind an argument to a dyadic function, making it monadic APL Wiki | DyExDDVidzN2kngnAprCoNARS | |
| Matrix Product | x∘y | Like +.× but faster (and only for matrices) GNU APL Documentation | GNU | |
| Withe | (d∘n)y | Right hook APL Wiki | Kap | |
⍛ | Before | (m⍛e)yx(m⍛e)y | Preprocess the left argument to a function with another function APL Wiki | ExDDVidzKapApr |
⍤ | Compose | (m⍤n)y | Apply a function after another APL Wiki | DyExDDVidzN2kAprCoSAX |
| Atop | x(m⍤e)y | Call a monad using the result of a dyad as the argument APL Wiki | DyExDDVidzN2kAprCo | |
| Rank | (m⍤v)yx(d⍤v)y | Apply a function at a specified rank APL Wiki | DyExDDViN2kGNU'01KapAprCoSAX | |
| Over | x(d⍤n)y | Preprocess all arguments to a function with another function APL Wiki | SAX | |
| Cut | x(u⍤n)y(u⍤n)y | Apply a function to cuts of an array APL Wiki | SAX | |
⍥ | Compose | (m⍥n)y | Apply a function after another APL Wiki | DyExDDVidzN2kKapAprCoSAX |
| Over | x(d⍥n)y | Preprocess all arguments to a function with another function APL Wiki | DyExDDVidzN2kKapAprCo | |
| Depth | (m⍥v)yx(d⍥v)y | Apply a function at a specified depth APL Wiki | ExDDVi | |
| Atop | x(m⍥e)y | Call a monad using the result of a dyad as the argument APL Wiki | SAX | |
⍢ | Under | (m⍢n)yx(d⍢n)y | Apply a function, then another function, then the first function's inverse APL Wiki | ExDDVidzKapNARS |
ᐵ | Each Left | x(dᐵ)y | Each, only on the left argument GitHub | dz |
ᑈ | Each Right | x(dᑈ)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 | (m⍫n)yx(d⍫e)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 | (m⍠v)yx(d⍠v)y | Select a related function APL WikiDyalog ReferenceNARS2000 Wiki | DyExDDViN2k |
| Valences | (m⍠e)yx(m⍠e)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 | x⌸y | 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 | (d⍁v)y | Set the identity element for a function | ngn | |
⌺ | Stencil | (d⌺v)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 | x⍎y | ??? | A+ | |
| Protected Execute | x⍎y | ??? | A+ | |
⍕ | Format | ⍕y | APL Wiki | DyExDDVidzN2kA2GNU'89'01AXngnKapA+WSVAprSAXA64A+NARS |
| Format With Specification | x⍕y | Format specifying column widths, decimal places and optionally scientific notation APL Wiki | DyExDDViN2kA2GNU'89'01AXA+WSVAprSAXA64A+NARS | |
| Format By Example | x⍕y | 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 | x⌾y | 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 | x…y | 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 | x⍧y | 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 | x⍮y | APL Wiki | ExDdz |
| Half Pair | ⍮y | GitHub | ExDdz | |
⍭ | Factors | ⍭y | GitHub | ExD |
| Prime Related Functions | x⍭y | 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 | x⍇y | Read information from a file selected by the left argument APLX Reference | AX | |
| Rename File | x⍇y | APLX Reference | AX | |
⍈ | Write File | x⍈y | 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 | x⍐y | Lock or unlock a file APLX Reference | AX | |
⍗ | Delete File | x⍗y | APLX Reference | AX |
| Delete File Component | ⍗y | APLX Reference | AX | |
≈ | Approximately Equal To | x≈y | GitHub | ngn |
↗ | Raise | ↗y | Raise an exception | ngn |
⫽ | Compress | x⫽y | Select elements of the right argument marked by the left argument mask APL Wiki | Kap |
| Replicate | x⫽y | 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 | x⍺y | 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(u∇v)yx(u∇∘)yx(u∇v)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 |