BQN primitives

Primitives are functions and modifiers that are built into the language.

Functions

Functions that have significant differences from APL functions are marked with an asterisk. Links for these entries go to dedicated BQN documentation while other links go to the APL Wiki.

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*

Modifiers

Combinators only control the application of functions. Because a non-function operand applies as a constant function, some combinators have extra meanings when passed a constant. For example, 0˜ is identical to 0˙—a constant function that always returns 0—and 0⊸< is the function that tests whether its right argument is greater than 0.

Glyph	Name(s)	Definition	Description
`˙`	Constant	`{𝕩⋄𝕗}`	Return a function that returns the operand
`˜`	Self/Swap	`{𝕩𝔽𝕨⊣𝕩}`	Duplicate one argument or exchange two
`∘`	Atop	`{𝔽𝕨𝔾𝕩}`	Apply `𝔾` to both arguments and `𝔽` to the result
`○`	Over	`{(𝔾𝕨)𝔽𝔾𝕩}`	Apply `𝔾` to each argument and `𝔽` to the results
`⊸`	Before/Bind	`{(𝔽𝕨⊣𝕩)𝔾𝕩}`	`𝔾`'s left argument comes from `𝔽`
`⟜`	After/Bind	`{(𝕨⊣𝕩)𝔽𝔾𝕩}`	`𝔽`'s right argument comes from `𝔾`
`⌾`	Under	`{𝔾⁼∘𝔽○𝔾}` OR `{(𝔾𝕩)↩𝕨𝔽○𝔾𝕩⋄𝕩}`	Apply `𝔽` over `𝔾`, then undo `𝔾`
`⊘`	Valences	`{𝔽𝕩;𝕨𝔾𝕩}`	Apply `𝔽` if there's one argument but `𝔾` if there are two
`◶`	Choose	`{f←(𝕨𝔽𝕩)⊑𝕘 ⋄ 𝕨F𝕩}`	Select one of the functions in list `𝕘` based on `𝔽`

Choose isn't really a combinator since it calls the function ⊑, and Under is not a true combinator since it has an "undo" step at the end. This step might be implemented using the left operand's inverse (computational Under) or its structural properties (structural Under).

Other modifiers control array traversal and iteration. In three cases a simpler 1-modifier is paired with a generalized 2-modifier: in each case the 1-modifier happens to be the same as the 2-modifier with a right operand of ¯1.

1-Modifier	Name	2-Modifier	Name
`˘`	Cells	`⎉`	Rank
`¨`	Each	`⚇`	Depth
`⌜`	Table
`⁼`	Undo	`⍟`	Repeat
`´`	Fold
`˝`	Insert
`	Scan