Background: In Python, I'm trying writing a generator function that yields functions that are repeated applications of a one-argument function f. The first function yielded should apply f 0 times (the identity function), the second function yielded should apply f once, etc. The function's doctest string is in the following.
def repeated(f):
"""
>>> double = lambda x: 2 * x
>>> funcs = repeated(double)
>>> identity = next(funcs)
>>> double = next(funcs)
>>> quad = next(funcs)
>>> oct = next(funcs)
>>> quad(1)
4
>>> oct(1)
8
>>> [g(1) for _, g in
... zip(range(5), repeated(lambda x: 2 * x))]
[1, 2, 4, 8, 16]
"""
def repeated(f):
g = lambda x: x
while 1:
yield g
g = lambda x: f(g(x))
Problem: In the code above, max recursion depth error on line "g = lambda x: f(g(x))". But when I change that line to "g = (lambda h: lambda x: f(h(x)))(g)", it works. Why does this happen? What's the difference between these two statements?
def repeated(f):
g = lambda x: x
while 1:
yield lambda x: g(x)
g = (lambda h: lambda x: f(h(x)))(g)
Extra Problem:The code block above almost passes the doctest, but still fails. Failed example: quad(1) Expected: 4 Got: 8
However, when I replace the "yield lambda x: g(x)" to "yield g", it passes the doctest. What's the difference between "lambda x: g(x)" and "g"?
