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Dyalog APL Extended

Extended domains of existing primitives/quad-names, and a few new ones. Requires Dyalog APL version 16.0 or higher.

How to use

These extensions are available on Try it Online, but can easily be used offline:


Replacing ns with your target namespace (e.g. #), do

]Load path/dyalog-apl-extended/* -target=ns


]Link ns path/dyalog-apl-extended


]Link.Create ns path/dyalog-apl-extended

Running code

Now you have three options:

  1. Use the extensions directly with the glyph names.
  2. Use ns.Extended.FIX as a drop in for ⎕FIX.
  3. Use ns.Extended.Repl '' to start a (limited) session where the glyphs work. Enter to exit.


Name Glyph Type* Extension
BackSlash \ 🔶 ∘.f when dyadic, allows short and/or multiple left args
BackSlashBar 🔶 ⊢∘f when dyadic, allows short and/or multiple left args
Bullet 🔺 Inner product and Alternant
CircleDiaeresis 🔺 Over and Depth
CircleJot 🔺 Complex/Imaginary
DelDiaeresis 🔺 Under (a.k.a. Dual)
DelTilde 🔺 Obverse; ⍺⍺ but with inverse ⍵⍵
Diaeresis ¨ 🔵 allows constant operand
Divide ÷ 🔵 monadic converts letters to title case when possible
DollarSign $ 🔺 string enhancement ${1}:1⊃⍺, ${expr}:⍎expr, \n:JSON
DownArrow 🔵 allows long
DownShoe 🔵 allows rank>1
Downstile 🔵 monadic lowercases letters
DownTack 🔶 2s as default left argument
Ellipsis 🔺 fill sequence gaps (dfns's to⍤1)
EpsilonUnderbar 🔶 monadic is Type with ⎕ML←0
Equals = 🔶 with TAO; monad: is-type
GreaterThan > 🔶 with TAO; monad: is-strictly-negative/is-visible
GreaterThanOrEqualTo 🔶 with TAO; monad: is non-positive/is-not-control-character
house 🔺 prefix for contents of dfns
infinity 🔺 largest integer (for use with and )
Iota 🔵 Unicode version of dfns's iotag
IotaUnderbar 🔵 allows duplicates/non-Booleans
IotaUnderbarInverse ⍸⍣¯1 🔵 given r, finds n so that r≡⍸n
JotDiaeresis 🔵 allows constant left operand, Atop with function right operand
JotUnderbar 🔺 reverse composition X f⍛g Y is (f X) g Y
LeftShoe 🔵 allows partitioning along multiple trailing axes, with short ⍺s, and inserting/appending empty partitions
LeftShoeStile 🔺 monad: nub-sieve; dyad: count-in
LeftShoeWithAxis ⊂[k] 🔵 as , but called with left operand
LessThan < 🔶 with TAO; monad: is-strictly-positive/is-control-character
LessThanOrEqualTo 🔶 with TAO ; monad: is-non-negative/is-invisible
Minus - 🔵 monadic flips letter case
macron ¯ 🔵 as prefix to name or primitive means its inverse
negativeInfinity ¯∞ 🔺 smallest integer (for use with )
Nand 🔶 monad: not all equal to type
Nor 🔶 monad: not any equal to type
NotEqualTo 🔶 with TAO; monad: is-non-type
Percent % 🔺 f% and A%: probability-logical function (mapping arrays)
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
QuestionMark ? 🔵 ⍺?¯⍵ as norm dist stddev and optional mean ⍺←0
Rho 🔵 allows omitting one dimension length with ¯1
RightShoeUnderbar 🔺 monadic discloses if scalar, dyadic indexes sanely
RightShoeUnderbarWithAxis ⊇[k] 🔺 as above, but called with left operand
Root 🔺 (Square) Root
SemicolonUnderbar 🔺 (Half) Pair; use ↑⍤⍮ to add axis
Slash / 🔵 allows short and/or multiple left args
SlashBar 🔵 allows short and/or multiple left args
StarDiaeresis 🔵 allows non-scalar right operand incl. and ¯∞ and array left operand
Stile | 🔵 monadic normalises letters to lowercase (upper then lower)
StileTilde 🔺 monadic is factors; dyadic depends on : 0=non-prime?, 1=prime?, ¯1=primes less than , ¯2=th prime, 4=next prime, ¯4=prev prime
Tilde ~ 🔵 monadic allows probabilities, dyadic allows rank>1
TildeDiaeresis 🔵 allows constant operand
Times × 🔵 set/query letter case (lower: ¯1, title: 0, upper: 1)
UpArrow 🔵 allows long
UpShoe 🔶 monadic is self-classify; dyadic allows rank>1
Upstile 🔵 monadic uppercases letters
UpTack 🔶 2 as default left argument
Vel 🔶 monadic is Descending Sort
Wedge 🔶 monadic is Ascending Sort
∆C ⎕C 🔺 fn ⎕C applies case-insensitively, array ⎕C case-folds
∆EM ⎕EM 🔺 Self-inverse ⎕EM
∆NS ⎕NS 🔵 allows ⎕NS names values (tries to resolve ⎕ORs)
∆NSinverse ⎕NS⍣¯1 🔺 allows (names values)←⎕NS⍣¯1⊢ns (returns ⎕ORs for ns/fns)
∆UCS ⎕UCS 🔵 scalar when monadic

* 🔺 means new feature 🔶 means added valence 🔵 means expanded domain

17.0 Requires Dyalog APL version 17.0
17.1 Requires Dyalog APL version 17.1