⍨) is a monadic operator that takes a dyadic function as operand and modifies how the argument(s) of its derived functions are used. If the derived function is used monadically, the argument is also used as left argument. This usage is also known as Self or, more informally, Selfie. If the derived function is used dyadically, the arguments are swapped. This usage is also known as Swap. The glyph is also used for Constant.
This decrements from the vector:
1 -⍨ 1 2 3 0 1 2
+⍨1 2 3 2 4 6
Commute can be used to emulate a monadic
f g h Fork when combined with Compose (note the following code is not workable APL, but a series of evaluations):
g⍨∘f⍨∘h⍨ x x g⍨∘f⍨∘h x ⍝ the last ⍨ is being used monadically, i.e. Selfie x g⍨∘f⍨ h x (h x) g⍨∘f x ⍝ the last ⍨ is being used dyadically, i.e. Swap (h x) g⍨ (f x) (f x) g (h x) ⍝ the last ⍨ is being used dyadically, i.e. Swap
The Commute operator was defined in Operators and Functions in 1978, and taken up by NARS as a result. Dyalog, influenced by NARS, included the operator early on. While it didn't appear in SHARP APL, it was included in J as "Reflex/Passive" (