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BQN is an APL-family language designed primarily by Marshall Lochbaum. Although it maintains the concept of array-driven computing and much of APL's array functionality, BQN discards all compatibility with other array languages and changes many fundamental concepts. It uses the based array model with dedicated array notation, distinguishes between data types and expression roles to give the language a context-free grammar with first-class functions, and uses a new set of glyphs with different primitive pairings. The language uses the leading axis model and tacit programming as core paradigms. Its implementation is largely self-hosted, with an array-based compiler like Co-dfns.


BQN has several implementations,[1] with all complete ones based on self-hosted sources, which are compiled to bytecode and included as literal arrays or similar in the implementation's source. CBQN, developed by dzaima in C, is the primary implementation with the best performance. A JavaScript version can be run online. It's slower than CBQN compiled to Wasm, but easier to connect with browser functionality.

The Singeli language was developed in order to implement BQN more effectively. CBQN uses Singeli for primitive code that uses vector instructions, and can be built with or without these optimized implementations. The Singeli implementation is written in BQN and currently targets C.


Now largely replaced by CBQN, dzaima/BQN is dzaima's independent implementation in Java, based on dzaima/APL. While dzaima/APL adds significant new functionality and is different from any other APL, dzaima/BQN follows the BQN specification closely and sometimes extends it with system functions. It has often been the first implementation to support new functionality, particularly syntax such as block headers, and was the fastest implementation before CBQN was created. It introduced the bytecode format now shared with self-hosted BQN, and was used for development and bootstrapping.



Glyph Monadic Dyadic
+ Conjugate Add
- Negate Subtract
× Sign Multiply
÷ Reciprocal Divide
Exponential Power
Square Root Root
Floor Minimum
Ceiling Maximum
Sort Up And
Sort Down Or
¬ Not Span
| Absolute Value Modulus
Less Than or Equal to
< Enclose Less Than
> Merge Greater Than
Greater Than or Equal to
= Rank Equals
Length Not Equals
Depth Match
Shape Not Match
Identity Left
Identity Right
Deshape Reshape
Join Join to
Solo Couple
Prefixes Take
Suffixes Drop
Range Windows
» Nudge Shift Before
« Nudge Back Shift After
Reverse Rotate
Transpose Reorder axes
/ Indices Replicate
Grade Up Bins Up
Grade Down Bins Down
First Cell Select
First Pick
Classify Index of
Occurrence Count Progressive Index of
Unique Mask Member of
Deduplicate Find
Group Indices Group


1-modifiers in BQN use superscript symbols, while 2-modifiers use symbols with a circle, but not one with a line through it like and .

Glyph Name(s)
˙ Constant
˜ Self/Swap
˘ Cells
¨ Each
´ Fold
˝ Insert
` Scan
Glyph Name(s)

Some modifiers are closely related, and some of their glyphs are intended to allude to this:

  • The three 1-modifers Cells (𝔽˘), Each (𝔽¨), and Undo (𝔽⁼) are equivalent to using a right-operand of ¯1 with the 2-modifiers Rank (𝔽⎉¯1), Depth (𝔽⚇¯1), and Repeat (𝔽⍟¯1). Therefore the 2-modifiers are circled versions of the 1-modifiers (except in the case of Undo/Repeat).
  • Under (𝔽⌾𝔾) is in principle equivalent to 𝔾⁼∘𝔽○𝔾. Therefore, is a combination of the glyphs and .

The Name BQN

The name "BQN" was originated as a forward iteration of the letters of APL, and "happens to match the capitals in 'Big Questions Notation'"[3].

Lochbaum recounts, "I obtained 'BQN' by moving each letter in 'APL' forward by one in the alphabet. I'd come up with the backronym 'Big Questions Notation' by the time I realized N doesn't come after L."[4]

Lochbaum commented further on this, saying:

...the way I came up with the name BQN was I thought, ... alright, I'm working on this next APL. What do I call [it?] ... I took took APL and I moved it forward and I got BQN. And I said, well, BQN, that sounds pretty good... [B]ig Questions Notation is what I ended up with. I like it 'cause it suggests that not only you're solving big questions, but you have big questions about the notation, so it's a little tongue in cheek. And I said also, you can pronounce it like bacon, so there's even a food pun like Apple. And after some half hour or an hour of thinking about this, I realized that the letter that comes after L is M, not N. I think it would be much more logical for N to come first, because it's the letter with two humps. BQM is a horrible, horrible name, and so I stuck with BQN. [5]


APL dialects [edit]
Maintained APL+WinAPL2APL64APL\ivApletteAprilCo-dfnsDyalog APLdzaima/APLExtended Dyalog APLGNU APLKAPNARS2000Pometo
Historical A Programming LanguageA+ (A) ∙ APL#APL\360APL/700APL\1130APL\3000APL.68000APL*PLUSAPL.jlAPL.SVAPLXIverson notationIVSYS/7090NARSngn/aplopenAPLOperators and FunctionsPATRowanSAXSHARP APLRationalized APLVisualAPL (APLNext) ∙ VS APLYork APL
Derivatives AHPLBQNCoSyELIGleeIIvyJJellyJellyfishK (Q, KDB+) ∙ Lang5NialRAD
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