not directed, and so orderly at that. with all its inherent problems: church's bottles . (nil, true, false, functions, numbers,... may be implemented in the outside place...) Y: f.(x.(f x x)x.(f x x)) Y g . x.(g x x)x.(g x x) g x.(g x x)x.(g x x) g g (...) . recursion by forgetting itself A DRa`gon to be bound to something, someone, in dear heart, or just illusioned will. (a light and mocking heart, but g has to see it all, all that it's done... to itself though...) . it's fixed-point combinator à la Curry. O: (x.y.y(x x y))(x.y.y(x x y)) . (y.y((x.y.y(x x y))(x.y.y(x x y))y))" O g . g((x.y.y(x x y))(x.y.y(x x y))g) g(O g) . recursion by remembering itself (in never-ending tragedy, deepest sorrow) fixed-piont combinator à la Turing. "additional notes." 0:(f.x.x) "1:(f.x.(f x))" "2:(f.x.(f (f x)))" "3:(f.x.(f (f (f x))))" ++:(n.f.x.(f (n f x))) --:("i don't know...") +:(m.n.(m ++ n)) -:(m.n.(m -- n)) *:(m.n.(m (+ n) 0)) ^:(b.e.(e b)) f.x.(f (f (f x))) (f.x.(f (f (f x))) a) TA:(x.y.x "boolean true") FA:(x.y.y "boolean false") /\:(p.q.(p q p) "on 2 FA/TA") \/:(p.q.(p p q) "on 2 FA/TA") ~:(p.(p FA TA) "on 1 FA/TA") -<:(p.a.b.(p a b) "on 1 FA/TA some some") 0?:(n.(n x.FA TA)) <=:(m.n.(0? (- m n))) /\ TA FA FA TA "true and false, is false, is true." PIR:(x.y.f.(f x y)) FIR:(p.(p TA)) SIR:(p.(p FA)) NIL:(x.TA) NUL:(p.(p x.y.FA)) #:(x.(PIR (SIR x) (++ (SIR x)))) --:(n.(FIR (n # (PIR 0 0)))) "more moist à la Curry" I:(x.x) S:(x.y.z.(x z(y z))) K:(x.y.(x)) B:(x.y.z.(x(y z))) C:(x.y.z.(x z y)) W:(x.y.(x y y)) U:(x.(x x)) Y:(B U(C B U))