# Dyalog APL Vision

Dyalog APL Vision continues the role of Extended Dyalog APL, but tries to provide realistic extensions of Dyalog APL rather than simply extending the language as much as possible. It extends the domains of existing primitives and quad names and adds a few new ones.

## Features

All scalar functions support leading axis agreement.

• All set functions support arguments of any rank.
• `⎕C` and monadic `⎕UCS` are scalar functions.
• In addition, the following is included:
Name Symbol Type* Extension Examples
CircleDiaeresis `⍥` 🔵 ✅ Depth when right operand is array. This is similar to Rank (`⍤`) but applies at nesting level. `f⍥0` applies `f` like a scalar function and `f⍥1` applies to flat subarrays. `f⍤1⍥1` applies to flat vectors.
DelDiaeresis `⍢` 🔺 Under (a.k.a. Dual). Like `f⍥g` but conceptually inverts the right operand when done. If `g` is a selection function, it puts the data back where it came from `-⍢(2 3∘⊃)` negates the 2nd element's 3rd element.
DelTilde `⍫` 🔺 Obverse; `⍺⍺` but with inverse `⍵⍵` `×⍢(FFT⍫iFFT)`
DollarSign `\$` 🔺 string enhancement `\${1}`:`1⊃⍺`, `\${expr}`:`⍎expr`, `\n`:JSON `'Dyer' 'Bob'\$'Hi, \${2} \${1}!`
`\$'Hi, \${first} \${last}!`
`\$'2×3=\${2×3}'`
DownArrow `↓` 🔵 dyad allows long `⍺` `0 1↓'abc'` gives `1 2⍴'bc'`
DownTack `⊤` `⊥⍣¯1` when left argument is scalar `2⊤123` gives `1 1 1 1 0 1 1`
EpsilonUnderbar `⍷` 🔶 monad: Type (like `∊` with `⎕ML←0`) `⍷1'a'#` gives `0' '#`'
Equal `=` 🔶 monad: Rank (`≢⍴`) `=10 20 30` gives `1`'
GreaterOrEqual `≥` 🔵 monad: sort descending `≥3 1 4 1 5` gives `5 4 3 1 1`
GreaterThan `>` 🔵 monad: Join `>2 2⍴⍪¨1 2 3 4` gives `2 2⍴1 2 3 4`
JotUnderbar `⍛` 🔺 ✅ reverse composition `X f⍛g Y` is `(f X) g Y` and default argument `⌽⍛≡` checks for palindromes.
`a-⍛↑b` takes the last `a` from `b`.
LeftShoe `⊂` 🔵 dyad allows partitioning along multiple leading axes `(⊂1 1)⊂matrix` separates out the first row and column.
LeftShoeUnderbar `⊆` 🔵 dyad allows partitioning along multiple leading axes `(⊂1 0 1 1)⊆4 4⍴⎕A` splits off the first row and column, and removes the second.
LessOrEqual `≤` 🔵 monad: sort ascending `≤3 1 4 1 5` gives `1 1 3 4 5`
LessThan `<` 🔵 monad: Major Cells `<2 2 2⍴⎕A` gives `(2 2⍴'ABCD')(2 2⍴'EFGH')`
QuadEqual `⌸` 🔵 allow array operand to be vocabulary (then uses `{⊂⍵}` as internal operand) `≢¨'ACGT'⌸'ATT-ACA'` gives `3 1 0 2`
QuadDiamond `⌺` 🔶 auto-extended `⍵⍵`, allows small `⍵`, optional edge spec(s) (0:Zero; 1:Repl; 2:Rev; 3:Mirror; 4:Wrap; -:Twist) with masks as operand's `⍺` Life on a cylinder: `0 4 Life⌺3 3`
QuestionMark `?` 🔵 dyadic allows `⍺` to be any shape (not just vector shape) and `⍵` is shape of array to select indices from `3 5?4 13` deals 3 hands of 5 cards from deck of 4 suits from A to K
Rho `⍴` 🔵 dyad: negatives reverse axis, `0.5` auto-size rounding down, `1.5` auto-size rounding up, `2.5` auto-size with padding Reshape into two columns: `0.5 2⍴data`
RightShoeUnderbar `⊇` 🔺 monad: last (`⊃⌽,⍵`)
✅ dyad: select (`⌷⍨∘⊃⍨⍤0 99`)
`3 1 2⊇'abc'` gives `'cab'`
Root `√` 🔺 (Square) Root `√25` gives `5`
`3√27 gives 3`
UpArrow `↑` 🔵 allows long `⍺` `2 3↑4 5` gives `2 3⍴4 5 0 0 0 0`
Vel `∨` 🔶 monad: demote (`,[⍳2]`) `∨2 3 4⍴⎕A` gives `6 4⍴⎕A`
Wedge `∧` 🔶 monad: promote (`⍵⍴⍨1,⍴⍵`) `'ABC'⍪⍥∧'DEF'` gives `2 3⍴⎕A`
Event Message `⎕EM` 🔵 Self-inverse `⎕EM` `⎕EM'RANK ERROR' 'WS FULL'` gives `4 1`
Name Get `⎕NG` 🔺 Name Get `ref⎕NG'Bea' 'Abe'`
Name Set `⎕NS` 🔵 Accepts ref left arg. Name Set: The list of values to copy into the new/target namespace can have 2-element name-value vectors, setting the name to the given value `ref←⎕NS('Abe' 10)('Bea' 12)`
`ref⎕NS⊂'Carl' 8`
Name Value `⎕NV` 🔺 Names and Values `ref⎕NV -2 9
Signal Event `⎕SIGNAL` 🔵 Allows `⎕DMX`-style ref argument `⎕SIGNAL ⎕DMX`

* 🔺 new feature 🔶 added valence 🔵 expanded domain ⚠ breaking change ✅ scheduled for 20.0

APL dialects 
Maintained APL+WinAPL2APL64APL\ivApletteAprilCo-dfnsDyalog APLDyalog APL Visiondzaima/APLGNU APLKapNARS2000Pometo
Historical A Programming LanguageA+ (A) ∙ APL#APL2CAPL\360APL/700APL\1130APL\3000APL.68000APL*PLUSAPL.jlAPL.SVAPLXExtended Dyalog APLIverson notationIVSYS/7090NARSngn/aplopenAPLOperators and FunctionsPATRowanSAXSHARP APLRationalized APLVisualAPL (APLNext) ∙ VS APLYork APL
Derivatives AHPLBQNCoSyELIGleeIIvyJJellyK (Goal, Klong, Q) ∙ KamilaLispLang5LilNialRADUiua
Overviews Comparison of APL dialectsTimeline of array languagesTimeline of influential array languagesFamily tree of array languages