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(\ zero one two three succ plus mult pred minus isZero yComb .
(\ fac .
fac three
-- NOTE: the y-combinator does not have a normal form
) (yComb (\ f n . (isZero n) one (mult n (f (pred n)))))
)
-- zero
(\ f x . x)
-- one
(\ f x . f x)
-- two
(\ f x . f (f x))
-- three
(\ f x . f (f (f x)))
-- succ
(\n f x . f (n f x))
-- plus
(\m n f x . m f (n f x))
-- mult
(\m n f . m (n f))
-- pred
(\n f x . n (\ g h . h (g f)) (\ u . x) (\ u . u))
-- minus
(\ m n . n (\n f x . n (\ g h . h (g f)) (\ u . x) (\ u . u)) m)
-- isZero
(\ n . n (\ x . (\ x y . y)) (\ x y . x))
-- yComb
(\ f . (\ x . f (x x)) (\ x . f (x x)))
|
