Combinators

A combinator is a function or operator that only refers to its arguments and operands without modifying them in any way.

Symbol APL expression Bird(1) TinyAPL Diagram
I \mathrm I y Identity / Same diagram
K \mathrm K x Kestrel Left diagram
κ \kappa y Kite Right diagram
W \mathrm W y F y Warbler Duplicate diagram
C \mathrm C y F x Cardinal Commute diagram
B \mathrm B F (G y) Bluebird // Compose diagram
Q \mathrm Q G (F y) Queer Reverse Compose diagram
B 1 {\mathrm B}_1 F (x G y) Blackbird Atop diagram
Ψ \Psi (G x) F (G y) Psi Over diagram
S \mathrm S y F (G y) Starling Right Hook diagram
Σ \Sigma (F y) G y Violet Starling Left Hook diagram
D \mathrm D x F (G y) Dove / After diagram
Δ \Delta (F x) G y Zebra Dove / Before diagram
Φ \Phi (F y) G (H y) Phoenix «» Fork (monad) diagram
Φ 1 \Phi_1 (x F y) G (x H y) Pheasant «» Fork (dyad) diagram
D 2 {\mathrm D}_2 (F x) G (H y) Dovekie + Bracket diagram
P \mathrm P (y G x) F (x G y) Parrot(2) Mirror diagram

Additionally, some other primitives have combinator-like behavior:

APL expression TinyAPL Diagram
n Constant (monad) diagram
n Constant (dyad) diagram
F y Valences (monad) diagram
x G y Valences (dyad) diagram

Footnotes

  1. Some combinators have bird names, originating from To Mock a Mockingbird by Raymond Smullyan. Some of the bird names are taken from the Uiua combinator page.

  2. I made this one up.