Who introduced the Kite to Smullyan's combinator birds?

883 Views Asked by At

I am reading To Mock a Mockingbird by Raymond Smullyan. I was led to it by various people describing the lambda calculus combinators using Smullyan's ornithological notation, such as this video and this paper. but I am confused about one thing. Both people use the bird "kestrel" for true and "kite" for false. Kestrel is the bird where A(Bx) = B, and Smullyan does indeed include that bird in the "Hopeless Egocentricity" section. Keenan, in the first link, describes the Kite as "The Kite ignores what it hears and always responds with the Idiot song, so it is the KI bird." The Kite is the Kestrel(Idiot) bird, which in the second link is described as a bird where Ki(Ax) = x.

But I have looked and as far as I can tell Smullyan never mentions the kite, nor does he mention a bird that is the Kestrel listening to the Idiot or where A(Bx) = x in the "Who's Who Among the Birds" section. I searched for 'Kite' in the Google Books version of TMAM and came up with nothing.

My question: Is the kite in TMAM and I missed it? And if Smullyan didn't invent the Kite, who did? And why do people describe it as if it came from TMAM when it didn't?

1

There are 1 best solutions below

1
On

I found this (here) by googling.

;; A few birds and aliases not necessarily given in the book
  ;; but discussed in David Keenan's http://dkeenan.com/Lambda/
  (define identity-bird*   (λ (x y) (x y)))
  (define kite             (λ (x y) y))
  (define konstant-mocker  (λ (x y) (y y)))
  (define crossed-konstant-mocker (λ (x y) (x x)))
  (define idiot-bird* identity-bird*)
  (define pairing vireo))