Explanation of a code

Question

def compose(f, g):
    return lambda x:f(g(x))

def thrice(f):
    return compose(f, compose(f, f))

add1 = lambda x: x + 1


print(thrice(thrice)(add1)(6)) = 33

Can anyone explain to me why is this 33? which side of the composite function should i start reading?

The function thrice(thrice) takes a function and returns the same function composited 3^3=27 times. Hence, thrice(thrice)(add1) is a function that adds 27 to its input. Calling it with 6 returns 33. — Bach
– Bach, Commented Feb 6, 2014 at 12:56

bereal · Accepted Answer · 2014-02-06 13:04:05Z

1

1) In terms of math, compose(f, g) = f ∘ g

2) Then thrice(f) = f ∘ f ∘ f.

3) Then T := thrice(thrice) = thrice ∘ thrice ∘ thrice

4) Then T(f) = f ∘ f ∘ f ∘ f ∘ f ∘ ... # 27 times

5) Then thrice(thrice)(add1) = T(add1) = add1 ∘ add1 ∘ ... # 27 times

6) Then thrice(thrice(add1))(x) = x + 27

answered Feb 6, 2014 at 13:04

bereal

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JirkaV · Accepted Answer · 2014-02-06 13:08:17Z

0

First call of thrice(thrice) reuturns a function. To that function you pass add1 function and as a result you will again get a function. If you pass 6 to that function you will get 33 as result.

f1 = thrice(thrice)
f2 = f1(add1)
print(f2(6))

answered Feb 6, 2014 at 13:08

JirkaV

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