- Curry's fixed point combinator:
Init = Y;
Y = \f.(\x.f (x x))(\x.f (x x));
- Turings's fixed point combinator:
Init = Y;
Y = (\x.\f.f (x x f))(\x.\f.f (x x f));
- Building new fixed point combinators using the generating vector (S(AI))I:
Init = Y (S (A I)) I;
S = \a.\b.\c. a c (b c);
I = \a.a;
A = B S;
B = \a.\b.\c. a (b c);
Y = \f.(\x.f (x x))(\x.f (x x));
- First term in Scott's [75] equation BY = BYS with Curry's fixed point combinator Y:
Init = B Y;
S = \a.\b.\c. a c (b c);
B = \a.\b.\c. a (b c);
Y = \f.(\x.f (x x))(\x.f (x x));
- Second term in Scott's [75] equation BY = BYS with Curry's fixed point combinator Y:
Init = B Y S;
S = \a.\b.\c. a c (b c);
B = \a.\b.\c. a (b c);
Y = \f.(\x.f (x x))(\x.f (x x));
- A lambda term generating the Thue--Morse sequence:
Init = Y (\Morse.P A (zip (inv Morse) (tail Morse)));
zip = Y (\z.\l.\r.P (l A) (P (r A) (z (l B) (r B))));
inv = Y (\i.\s. P (s A B A) (i (s B)));
tail = \s.s B;
P = \x.\y.\c.c x y; A = \x.\y.x; B = \x.\y.y;
Y = \f.(\x.f (x x))(\x.f (x x));