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: 2026-07-16 Thu 21:33