Python explanation of a code

Question

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

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

def repeated(f, n):
    if n == 0:
        return identity
    else:
        return compose(f, repeated(f, n - 1))

def sq(x): return x**2

1) print(thrice(thrice)(sq)(1))

2) print(thrice(thrice(sq)(2))

Can anyone explain to me why the first function returns 1 and the second function does not work? I was thinking thrice(thrice)(sq) will give me sq∘sq∘..... 27 times, so sq(1) is 1^27=1, is that correct? thanks.

(2) has a syntax error. A closing parenthesis is missing. Also, repeated is never used, why include it into the question? — DYZ
– DYZ, Commented Sep 10, 2017 at 3:42
What result are you expecting from the second function, exactly? — Karl Knechtel
– Karl Knechtel, Commented Sep 10, 2017 at 3:54
@coldspped - This is what functional programming looks like in Python ;). — Chinny84
– Chinny84, Commented Sep 10, 2017 at 3:55

DYZ · Accepted Answer · 2017-09-10 04:04:59Z

1

thrice(thrice)(sq)(x) is an extremely fast growing function:

thrice(thrice)(sq)(1.0000009)
#2.890634480354213e+52
thrice(thrice)(sq)(1.000001)
#1.9497974384856317e+58

When you apply it to a floating point number, it quickly overflows:

thrice(thrice)(sq)(1.000006)
# OverflowError: (34, 'Numerical result out of range')

Edited (thanks to @KarlKnechtel) However, Python implements arbitrary-precision integer numbers. When you apply the function to an integer number (say, thrice(thrice)(sq)(2)), the interpreter calculates the precise answer and then attemps to print it, which, with 40,403,562 decimal places, takes enormous time.

edited Sep 10, 2017 at 4:04

answered Sep 10, 2017 at 3:57

DYZ

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4 Comments

Karl Knechtel Over a year ago

The result should be 2^(2^27). It doesn't actually take very long on my machine to compute this value (either by OP's method or more directly), but formatting it for printing would take extremely long.

Jeri Lim Over a year ago

so for the first case, it is 1^(2^27) = 1?

DYZ Over a year ago

Correct. 1^N is always 1.

Jeri Lim Over a year ago

i see. Thanks for all of your help :)

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