BQN

Table of Contents

1. Function

= is for APL Equivalent.

BQN follows Leading Axis Theory

  • ↕: Range/Windows. Outer product of Iotas. Slices of the given size.
  • ≠: Length/Not Equal. = Monadic ≢. = Dyadic ≠.
  • ≢: Shape/Not Match. = Monadic ⍴. = Dyadic ≢.
  • ≍: Solo/Couple. Monadic: Increase the rank with an axis of length 1. Dyadic: Mix the two arguments.
  • ⋈: Enlist/Pair. Monadic: Single element list. Dyadic: Pair in a two element list.
  • <: Enclose/Lesser Than. Monadic: Unit array (scalar array), = Monadic ⊂.
  • >: Merge/Greater Than. = Monadic ↑.
  • ∾: Join/Join To. Denest once, without changing the rank. Join along the first axis (Dyadic , does this on the last axis).
  • ↑: Prefixes/Take. List of prefixes. Take portion of the array specifies by the range.
  • ↓: Suffixes/Drop. List of suffixes.
  • /: Indices/Replicate. Repeat the indices. Repeat the elements.
  • ⊏: First Cell/Select. First major cell (array, possibly a unit array). Major cells at the given indices.
  • ⊑: First/Pick. First Element (the atom). Element at the given index.
  • ⊐: Classify/Index Of. Map to the order of the first occurrences. Index of first occurrence.
  • ⊒: Occurrence Count/Progressive Index Of. Occurrence before. Index of next occurrence each time.
  • ∊: Mark Firsts/Member Of. = Monadic =≠=(Unique Mask), Map first occurrence to 1.
  • ⍷: Deduplicate/Find. = Monadic ∪, Unique major cells. Mark the top left location with 1 if found.
  • ⊔: Group Indices/Group. Group Indices by the values. Group major cells by the given indices.

2. Operator

  • ´: Fold. = /.
  • `: Scan. = \.
  • ¨: Each. = ¨
  • ˜: Self/Swap. = ⍨
  • ⊸: Bind Left, Before/Dyadic Before. ⟜: Bind Right, After/Dyadic After.
    • Bind = ∘x. Dyadic After = ∘f
  • ○: Over. = ⍥.
  • ⌾: Under. f⌾g apply g to both arguments and perform f and then do g⁼=(=g inverse).
  • ⌜: Table. = ∘..

Author: Jeemin Kim

Created: 2026-09-29 Tue 00:17