BQN–Dyalog APL dictionary

A few tables to help users of Dyalog APL (or similar) get started quickly on BQN. For a higher-level comparison, check Why BQN?. Here we assume ML is 1 for Dyalog.


Array model

BQN uses the based array model, so that a Dyalog simple scalar corresponds to many BQN values: an atom, its enclose, and so on.

Dyalog BQN
Simple scalar Atom
Scalar Unit
Vector List
Matrix Table

BQN shares the terms "cell" and "major cell" with Dyalog, and uses "element" (which may mean different things to different Dyalog users) not for a 0-cell but for the value it contains.


Dyalog uses value types (array, function, and so on) to determine syntax while BQN uses a separate concept called syntactic roles. See context-free grammar.

Dyalog type BQN role
Array Subject
Function Function
Monadic operator 1-modifier
Dyadic operator 2-modifier
Niladic function go away


BQN comments are written with #, not . BQN strings use double quotes "" while single quotes '' enclose a character.

BQN's block functions use {}, like Dyalog's dfns. The names for inputs and self-reference are different:

Dyalog BQN
⍺⍺ 𝔽
⍵⍵ 𝔾
∇∇ 𝕣

Blocks don't have guards exactly, but headers and predicates support some similar functionality (first-class functions can also be used for control structures). Headers can also be used to make a block more explicit about its inputs, more like a tradfn.

The assignment arrow defines a new variable in a block, while modifies an existing one.

BQN uses the ligature character for stranding, instead of plain juxtaposition. It also has a list notation using ⟨⟩, and [] for higher-rank arrays.

For reading

Glyphs +-×÷⌊⌈|⊣⊢⍉ have nearly the same meaning in BQN as APL. The other primitive functions (except !, Assert) are translated loosely to Dyalog APL below.

BQN Monad Dyad
* *
*(÷2) *÷
¬ ~ 1+-
= ⍤⍴ =
< <
> >
,⍥⊂ ,⍥⊂
,⍥⊂ ,⍥⊂
» ≢↑(¯1-≢)↑⊢ ⊢↑
« -≢↑(1+≢)↑⊢ -⊢↑⍪⍨
, reversed order
+..<() {R⍺⍳⍪⍨(R⍨⍳R)}
{⊂⍵} {⊂⍵} or

Modifiers are a little harder. Many have equivalents in some cases, but Dyalog sometimes chooses different functionality based on whether the operand is an array. In BQN an array is always treated as a constant function.

BQN ¨ ˝ ` ˜
Dyalog ¨ . A ⍤f

Some other BQN modifiers have been proposed as future Dyalog extensions:

Dyalog proposed Under Depth Reverse Compose

For writing

The tables below give approximate implementations of Dyalog primitives for the ones that aren't the same. First- and last-axis pairs are also mostly omitted. BQN just has the first-axis form, and you can get the last-axis form with 1.

The form FG (Power with a function right operand; Power limit) must be implemented with recursion instead of primitives because it performs unbounded iteration. The modifier _while_ {𝔽𝔾𝔽_𝕣_𝔾𝔽𝔾𝕩} provides similar functionality without risk of stack overflow. It's discussed here and called as Fn _while_ Cond arg.

Glyph Monadic Dyadic
! ×´1+↕ ((×´)1+)˜
π× •math
~ ¬ ¬∊/⊣
? •rand.Range0 •rand.Deal
, 1
< +`
<(1≥≡) (¬-˜⊢×·+`»>)
Inverse, Solve from here
Syntax Monadic Dyadic
, or ` if associative
¨ ¨
f.g f˝g1
.f f
Ag Ag
fB fB
fg fg
f⍤B fB
f⍤g fg
f⍥g fg
f@v f(v)
f⍠B Uh
f⌸ ⊐⊔↕
A •Something
f& Nothing yet