BQN for birdwatchers

Some people consider it reasonable to name combinators after types of birds. Here's one compendium of such names, and another that lacks its obsessive completeness. There is something wrong with these people. Some of these birds are not even real. "Quixotic bird"? Have you not heard of a quail? Nonetheless, I don't judge such afflicted souls (certainly not publicly), and have provided this translation table to explain BQN in terms they can understand.

BQN Bird 1 1 Bird 2 2
Identity I Kestrel K
Identity I KI
Bluebird B Blackbird B
Bluebird B Psi ψ
˙ Kestrel K KK
Starling S ~Dove D-like:
˜ Warbler W Cardinal C
k G H Dove D Eagle E
F G H Phoenix S' Golden Eagle Ê-like: labcde.a(bde)(cde)

The name "Golden Eagle" is a fever dream of bird enthusiast Conor Hoekstra, who saw it emerge disordered from the Bald Eagle when arguments fg are set equal to cd.

Lambda calculus doesn't have BQN's polymorphism on one or two arguments, so each BQN combinator corresponds to two lambda calculus forms depending on the number of arguments, giving the two columns of birds above.

Inputs are mapped to lambda calculus arguments according to the ordering 𝔽𝔾𝕨𝕩, and GFH for a 3-train F G H. For example, when I write that the combination 𝕨 𝔽˜ 𝕩 corresponds to a call of C or labc.acb, a is 𝔽 and bc are 𝕨𝕩.