⍨ — Self / Commute

Monadic operator. Keys: Alt-1 Backtick

f⍨Y is Y f Y.

×⍨3                ⍝ 9

X f⍨ Y is Y f X.

2-⍨10              ⍝ 8

A subject operand makes a constant function: A⍨Y and X A⍨Y return A.

42⍨0               ⍝ 42

Inverse

With one argument fixed, f⍨⁻¹ inverts f with that argument on the other side. +⍨⁻¹Y halves Y, ×⍨⁻¹Y takes its square root, and ⌊⍨⁻¹Y, ⌈⍨⁻¹Y and ⊢⍨⁻¹Y give back Y. For an array k, k⍨⁻¹Y gives back Y, which must match k.

+⍨⁻¹10   ⍝ 5
×⍨⁻¹9    ⍝ 3