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))" "no need, thanks" ++: 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)