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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 I y Identity ⊣/⊢ K \mathrm K K x Kestrel ⊣ κ \kappa κ y Kite ⊢ W \mathrm W W y F y Warbler ⍨ C \mathrm C C y F x Cardinal ⍨ B \mathrm B B F (G y) Bluebird ∘/⍤/⍥ Q \mathrm Q Q G (F y) Queer ⍛ B 1 {\mathrm B}_1 B1​ F (x G y) Blackbird ⍤ Ψ \Psi Ψ (G x) F (G y) Psi ⍥ S \mathrm S S y F (G y) Starling ⟜/⇽ Σ \Sigma Σ (F y) G y Violet Starling ⊸/⇾ D \mathrm D D x F (G y) Dove ∘/⟜ Δ \Delta Δ (F x) G y Zebra Dove ⍛/⊸ Φ \Phi Φ (F y) G (H y) Phoenix «» Φ 1 \Phi_1 Φ1​ (x F y) G (x H y) Pheasant «» D 2 {\mathrm D}_2 D2​ (F x) G (H y) Dovekie ⊸ + ⟜ P \mathrm P P (y G x) F (x G y) Parrot(2) ⸚ N \mathrm N N x F (x G y) Eastern Nicator ⇽ ν \mathrm \nu ν (x F y) G y Western Nicator ⇾ Additionally, some other primitives have combinator-like behavior: APL expression TinyAPL Diagram n ⍨ n ⍨ F y ⁖ x G y ⁖ Footnotes 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. I made this one up.

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