Question 3-3
Reduce the following lambda expression, showing your intermediate steps.
It should reduce to a number.
(λf.λa.f(a + 3) - (f a) - (f 3)) (λx.x * x)) 7
Solution
(λf.λa.f(a + 3) - (f a) - (f 3)) (λx.x * x)) 7
(λa.(λx.x * x) (a + 3) - (λx.x * x) a - (λx.x * x) 3) 7
(λx.x * x) (7 + 3) - (λx.x * x) 7 - (λx.x * x) 3
(7 + 3) * (7 + 3) - (λx.x * x) 7 - (λx.x * x) 3
(7 + 3) * (7 + 3) - 7 * 7 - (λx.x * x) 3
(7 + 3) * (7 + 3) - 7 * 7 - 3 * 3
10 * 10 - 7 * 7 - 3 * 3
100 - 7 * 7 - 3 * 3
100 - 49 - 3 * 3
51 - 3 * 3
51 - 9
42
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