问题
A regular function can contain a call to itself in its definition, no problem. I can\'t figure out how to do it with a lambda function though for the simple reason that the lambda function has no name to refer back to. Is there a way to do it? How?
回答1:
The only way I can think of to do this amounts to giving the function a name:
fact = lambda x: 1 if x == 0 else x * fact(x-1)
or alternately, for earlier versions of python:
fact = lambda x: x == 0 and 1 or x * fact(x-1)
Update: using the ideas from the other answers, I was able to wedge the factorial function into a single unnamed lambda:
>>> map(lambda n: (lambda f, *a: f(f, *a))(lambda rec, n: 1 if n == 0 else n*rec(rec, n-1), n), range(10))
[1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880]
So it's possible, but not really recommended!
回答2:
without reduce, map, named lambdas or python internals:
(lambda a:lambda v:a(a,v))(lambda s,x:1 if x==0 else x*s(s,x-1))(10)
回答3:
Contrary to what sth said, you CAN directly do this.
(lambda f: (lambda x: f(lambda v: x(x)(v)))(lambda x: f(lambda v: x(x)(v))))(lambda f: (lambda i: 1 if (i == 0) else i * f(i - 1)))(n)
The first part is the fixed-point combinator Y that facilitates recursion in lambda calculus
Y = (lambda f: (lambda x: f(lambda v: x(x)(v)))(lambda x: f(lambda v: x(x)(v))))
the second part is the factorial function fact defined recursively
fact = (lambda f: (lambda i: 1 if (i == 0) else i * f(i - 1)))
Y is applied to fact to form another lambda expression
F = Y(fact)
which is applied to the third part, n, which evaulates to the nth factorial
>>> n = 5
>>> F(n)
120
or equivalently
>>> (lambda f: (lambda x: f(lambda v: x(x)(v)))(lambda x: f(lambda v: x(x)(v))))(lambda f: (lambda i: 1 if (i == 0) else i * f(i - 1)))(5)
120
If however you prefer fibs to facts you can do that too using the same combinator
>>> (lambda f: (lambda x: f(lambda v: x(x)(v)))(lambda x: f(lambda v: x(x)(v))))(lambda f: (lambda i: f(i - 1) + f(i - 2) if i > 1 else 1))(5)
8
回答4:
You can't directly do it, because it has no name. But with a helper function like the Y-combinator Lemmy pointed to, you can create recursion by passing the function as a parameter to itself (as strange as that sounds):
# helper function
def recursive(f, *p, **kw):
return f(f, *p, **kw)
def fib(n):
# The rec parameter will be the lambda function itself
return recursive((lambda rec, n: rec(rec, n-1) + rec(rec, n-2) if n>1 else 1), n)
# using map since we already started to do black functional programming magic
print map(fib, range(10))
This prints the first ten Fibonacci numbers: [1, 1, 2, 3, 5, 8, 13, 21, 34, 55],
回答5:
Yes. I have two ways to do it, and one was already covered. This is my preferred way.
(lambda v: (lambda n: n * __import__('types').FunctionType(
__import__('inspect').stack()[0][0].f_code,
dict(__import__=__import__, dict=dict)
)(n - 1) if n > 1 else 1)(v))(5)
回答6:
I have never used Python, but this is probably what you are looking for.
回答7:
This answer is pretty basic. It is a little simpler than Hugo Walter's answer:
>>> (lambda f: f(f))(lambda f, i=0: (i < 10)and f(f, i + 1)or i)
10
>>>
Hugo Walter's answer:
(lambda a:lambda v:a(a,v))(lambda s,x:1 if x==0 else x*s(s,x-1))(10)
回答8:
def recursive(def_fun):
def wrapper(*p, **kw):
fi = lambda *p, **kw: def_fun(fi, *p, **kw)
return def_fun(fi, *p, **kw)
return wrapper
factorial = recursive(lambda f, n: 1 if n < 2 else n * f(n - 1))
print(factorial(10))
fibonaci = recursive(lambda f, n: f(n - 1) + f(n - 2) if n > 1 else 1)
print(fibonaci(10))
Hope it would be helpful to someone.
回答9:
Well, not exactly pure lambda recursion, but it's applicable in places, where you can only use lambdas, e.g. reduce, map and list comprehensions, or other lambdas. The trick is to benefit from list comprehension and Python's name scope. The following example traverses the dictionary by the given chain of keys.
>>> data = {'John': {'age': 33}, 'Kate': {'age': 32}}
>>> [fn(data, ['John', 'age']) for fn in [lambda d, keys: None if d is None or type(d) is not dict or len(keys) < 1 or keys[0] not in d else (d[keys[0]] if len(keys) == 1 else fn(d[keys[0]], keys[1:]))]][0]
33
The lambda reuses its name defined in the list comprehension expression (fn). The example is rather complicated, but it shows the concept.
回答10:
For this we can use Fixed-point combinators, specifically Z combinator, because it will work in strict languages, also called eager languages:
const Z = f => (x => f(v => x(x)(v)))(x => f(v => x(x)(v)))
Define fact function and modify it:
1. const fact n = n === 0 ? 1 : n * fact(n - 1)
2. const fact = n => n === 0 ? 1 : n * fact(n - 1)
3. const _fact = (fact => n => n === 0 ? 1 : n * fact(n - 1))
Notice that:
fact === Z(_fact)
And use it:
const Z = f => (x => f(v => x(x)(v)))(x => f(v => x(x)(v)));
const _fact = f => n => n === 0 ? 1 : n * f(n - 1);
const fact = Z(_fact);
console.log(fact(5)); //120See also: Fixed-point combinators in JavaScript: Memoizing recursive functions
回答11:
Lambda can easily replace recursive functions in Python:
For example, this basic compound_interest:
def interest(amount, rate, period):
if period == 0:
return amount
else:
return interest(amount * rate, rate, period - 1)
can be replaced by:
lambda_interest = lambda a,r,p: a if p == 0 else lambda_interest(a * r, r, p - 1)
or for more visibility :
lambda_interest = lambda amount, rate, period: \
amount if period == 0 else \
lambda_interest(amount * rate, rate, period - 1)
USAGE:
print(interest(10000, 1.1, 3))
print(lambda_interest(10000, 1.1, 3))
Output:
13310.0
13310.0
回答12:
By the way, instead of slow calculation of Fibonacci:
f = lambda x: 1 if x in (1,2) else f(x-1)+f(x-2)
I suggest fast calculation of Fibonacci:
fib = lambda n, pp=1, pn=1, c=1: pp if c > n else fib(n, pn, pn+pp, c+1)
It works really fast.
Also here is factorial calculation:
fact = lambda n, p=1, c=1: p if c > n else fact(n, p*c, c+1)
回答13:
If you were truly masochistic, you might be able to do it using C extensions, but to echo Greg (hi Greg!), this exceeds the capability of a lambda (unnamed, anonymous) functon.
No. (for most values of no).
来源：https://stackoverflow.com/questions/481692/can-a-lambda-function-call-itself-recursively-in-python