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Assignment0220.md

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521030910331 梁亚伦 [email protected]

1. (\f n. f (f (f n))) (\f x. f (x + 1)) (\x. x) 0 = (\n. (\z. (\y. (\x. n (x + 1)) (y + 1)) (z + 1))) (\x. x) 0 = (\n. (\z. n (z + 3))) (\x. x) 0 = (\z. (z + 3)) 0 = 3.

2. (\f n. f (f (f n))) (\f x. f (x + 1)) (\x. x - 2) 0 = (\n. (\z. n (z + 3))) (\x. x - 2) 0 = (\z. (z + 3) - 2) 0 = 1.

3. (\f n. f (f (f n))) (\f x. f (x + 1)) (\x. x * x) 0 = (\n. (\z. n (z + 3))) (\x. x * x) 0 = (\z. (z + 3) * (z + 3)) 0 = 9.

4. (\f g x. f (g x)) (\x. x - 2) (\x. x * x) 10 = (\g x. (g x) - 2) (\x. x * x) 10 = (\x. x * x - 2) 10 = 98.

5. (\f g x. f (g x)) (\x. x * x) (\x. x - 2) 10 = (\g x. (g x) * (g x)) (\x. x - 2) 10 = (\x. (x - 2) * (x - 2)) 10 = 64.

6. (\f n. f (f (f n))) (\f x y. f y x) = \f x y. f y x. (\f x y. f y x) (\f g x. f (g x)) = \f g x. g (f x). (\f g x. g (f x)) (\x. x * x) = \g x. g (x * x). (\g x. g (x * x)) (\x. x - 2) = \x. (x * x) - 2. (\x. (x * x) - 2) 10 = 98.