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how a function in python is getting called by just typing the name of function and not using brackets

First of all to find "lcm" of two numbers I made a function lcm(a, b). Then I thought of finding "hcf" too so I made a decorator decor and defined a function hcf(a, b) in it. And then I returned this function by just typing the name of the function and I didn't put brackets with it but it is still working. I cant understand why this function is working even though I didn't used brackets.
def decor(lcm_arg): # just to practice decorators
def hcf(a, b):
if a > b:
a, b = b, a
while True:
if b % a == 0:
print("hcf is", a)
break
else:
a, b = b % a, a
return lcm_arg(a, b)
return hcf # how hcf function is working without using brackets
#decor
def lcm(a, b):
if a > b:
a, b = b, a
for x in range(b, a*b+1, b):
if x % a == 0:
print("lcm is", x)
break
lcm(2, 4)
Output:
hcf is 2
lcm is 4

I don't think you understand decorators. Let's make a minimal example.
def my_decorator(some_function):
def new_function(*args, **kwargs):
'announces the result of some_function, returns None'
result = some_function(*args, **kwargs)
print('{} produced {}'.format(some_function.__name__, result))
return new_function # NO FUNCTION CALL HERE!
#my_decorator
def my_function(a, b):
return a + b
my_function(1, 2) # will print "my_function produced 3"
We have a simple function my_function which returns the sum of its two arguments and a decorator which will just print out the result of whatever function it decorates.
Note that
#my_decorator
def my_function(a, b):
return a + b
is equivalent to
def my_function(a, b):
return a + b
my_function = my_decorator(my_function)
Since my_decorator accepts a function as an argument (here we are giving it my_function) and returns a new function new_function (without calling it!), we effectively override my_function because we reassign the name to whatever my_decorator returns.
In action:
>>> my_function(1, 2)
my_function produced 3
Note that at every point in the example when a function is called, it happens with the parentheses-syntax. Here are all the function calls that happen in the first block of code I posted, in order:
my_decorator(my_function) is called and the return value is reassigned to the name my_function. This either happens through the # syntax or more explicitly in the equivalent code snippet.
my_function(1, 2) is called. At this point, my_function is the new_function that got returned by the decorator. Brain-parse it as new_function(1, 2).
Inside the body of new_function, the argument we gave to my_decorator is called (result = some_function(*args, **kwargs)) which happens to be the value of my_function before the reassignment that happened in step 1.
print is called.
If you want to understand how new_function is holding on to some_function despite my_decorator already having returned from its call, I suggest looking into the topics free variables and closures.

return hcf does not call the function because there are no parentheses, as you noticed. The decor function is used as a decorator which reassigns the name lcm to refer to the returned function. What I mean by this is that
#decor
def lcm(a, b):
// ...
is equivalent to
def lcm(a, b):
// ...
lcm = decor(lcm)
After this executes, lcm refers to the function hcf. So calling lcm(2, 4) now executes the code in hcf. I think the key here is to understand that at the line lcm(2, 4), lcm and hcf are two names which refer to the same function.

Nested function(Python 3)

a function (funcA) that takes a function (funcB) and returns a function that can be evaluated to produce the same value that funcB would produce (if given the same arguments) plus 1
returned_func(x) = funcB(x) + 1
What could be the possible way of doing this? I am confused with the second part of the question as to how can a function return a value and function at the same time. Any code example would be much appreciated! Thanks!

The concept you're looking for is, essentially, a function decorator. In Python, functions are first-class objects, just like class instances are in other languages. That means that you can pass them around, just like any other object. For example:
def foo(x):
return x + 1
print(foo) # <function foo at 0x0000024202F43EA0>
bar = foo
print(bar) # <function foo at 0x0000024202F43EA0>
Here we created a reference to the function object itself. We can, using the same idea, make a function which returns a function:
def foo(x):
def inner(y):
return x + y
return inner
func = foo(5)
print(func(3)) # 8
func is assigned to the return value of foo, which is itself a function that we can evaluate. You want to return a function A that adds 1 to the result of another function, B. So, pass B to a function make_A:
def make_A(b):
def inner(x):
return b(x) + 1
return inner
def B(x):
return x
A = make_A(B)
print(A(1)) # 2
Python has excellent syntactic sugar for this type of function. See this primer for more information.

def func1(x):
#operations go here:
return(x + 1)
def func2():
#operations go here:
return(x - 1)
if func1(2) == func2(4):
print("Hooray")
Does this help? It is a demonstration of how parameters and return values can interact.
A segment like func(1) implies the return value with the parameter as 1.

Python currying with any number of variables

I am trying to use currying to make a simple functional add in Python. I found this curry decorator here.
def curry(func):
def curried(*args, **kwargs):
if len(args) + len(kwargs) >= func.__code__.co_argcount:
return func(*args, **kwargs)
return (lambda *args2, **kwargs2:
curried(*(args + args2), **dict(kwargs, **kwargs2)))
return curried
#curry
def foo(a, b, c):
return a + b + c
Now this is great because I can do some simple currying:
>>> foo(1)(2, 3)
6
>>> foo(1)(2)(3)
6
But this only works for exactly three variables. How do I write the function foo so that it can accept any number of variables and still be able to curry the result? I've tried the simple solution of using *args but it didn't work.
Edit: I've looked at the answers but still can't figure out how to write a function that can perform as shown below:
>>> foo(1)(2, 3)
6
>>> foo(1)(2)(3)
6
>>> foo(1)(2)
3
>>> foo(1)(2)(3)(4)
10

Arguably, explicit is better than implicit:
from functools import partial
def example(*args):
print("This is an example function that was passed:", args)
one_bound = partial(example, 1)
two_bound = partial(one_bound, 2)
two_bound(3)
#JohnKugelman explained the design problem with what you're trying to do - a call to the curried function would be ambiguous between "add more curried arguments" and "invoke the logic". The reason this isn't a problem in Haskell (where the concept comes from) is that the language evaluates everything lazily, so there isn't a distinction you can meaningfully make between "a function named x that accepts no arguments and simply returns 3" and "a call to the aforementioned function", or even between those and "the integer 3". Python isn't like that. (You could, for example, use a zero-argument call to signify "invoke the logic now"; but that would break special cases aren't special enough, and require an extra pair of parentheses for simple cases where you don't actually want to do any currying.)
functools.partial is an out-of-box solution for partial application of functions in Python. Unfortunately, repeatedly calling partial to add more "curried" arguments isn't quite as efficient (there will be nested partial objects under the hood). However, it's much more flexible; in particular, you can use it with existing functions that don't have any special decoration.

You can implement the same thing as the functools.partial example for yourself like this:
def curry (prior, *additional):
def curried(*args):
return prior(*(args + additional))
return curried
def add(*args):
return sum(args)
x = curry(add, 3,4,5)
y = curry(b, 100)
print y(200)
# 312
It may be easier to think of curry as a function factory rather than a decorator; technically that's all a decorator does but the decorator usage pattern is static where a factory is something you expect to be invoking as part of a chain of operations.
You can see here that I'm starting with add as an argument to curry and not add(1) or something: the factory signature is <callable>, *<args> . That gets around the problem in the comments to the original post.

FACT 1: It is simply impossible to implement an auto currying function for a variadic function.
FACT 2: You might not be searching for curry, if you want the function that will be passed to it * to know* that its gonna be curried, so as to make it behave differently.
In case what you need is a way to curry a variadic function, you should go with something along these lines below (using your own snipped):
def curryN(arity, func):
"""curries a function with a pre-determined number of arguments"""
def curried(*args, **kwargs):
if len(args) + len(kwargs) >= arity:
return func(*args, **kwargs)
return (lambda *args2, **kwargs2:
curried(*(args + args2), **dict(kwargs, **kwargs2)))
return curried
def curry(func):
"""automatically curries a function"""
return curryN(func.__code__.co_argcount, func);
this way you can do:
def summation(*numbers):
return sum(numbers);
sum_two_numbers = curryN(2, summation)
sum_three_numbers = curryN(3, summation)
increment = curryN(2, summation)(1)
decrement = curryN(2, summation)(-1)

I think this is a decent solution:
from copy import copy
import functools
def curry(function):
def inner(*args, **kwargs):
partial = functools.partial(function, *args, **kwargs)
signature = inspect.signature(partial.func)
try:
signature.bind(*partial.args, **partial.keywords)
except TypeError as e:
return curry(copy(partial))
else:
return partial()
return inner
This just allow you to call functools.partial recursively in an automated way:
def f(x, y, z, info=None):
if info:
print(info, end=": ")
return x + y + z
g = curry_function(f)
print(g)
print(g())
print(g(2))
print(g(2,3))
print(g(2)(3))
print(g(2, 3)(4))
print(g(2)(3)(4))
print(g(2)(3, 4))
print(g(2, info="test A")(3, 4))
print(g(2, info="test A")(3, 4, info="test B"))
Outputs:
<function curry.<locals>.inner at 0x7f6019aa6f28>
<function curry.<locals>.inner at 0x7f6019a9a158>
<function curry.<locals>.inner at 0x7f6019a9a158>
<function curry.<locals>.inner at 0x7f6019a9a158>
<function curry.<locals>.inner at 0x7f6019a9a0d0>
9
9
9
test A: 9
test B: 9

Creating a new function as return in python function?

I was wondering if it is possible in python to do the following:
def func1(a,b):
return func2(c,d)
What I mean is that suppose I do something with a,b which leads to some coefficients that can define a new function, I want to create this function if the operations with a,b is indeed possible and be able to access this outside of func1.
An example would be a simple fourier series, F(x), of a given function f:
def fourier_series(f,N):
...... math here......
return F(x)
What I mean by this is I want to creat and store this new function for later use, maybe I want to derivate it, or integrate or plot or whatever I want to do, I do not want to send the point(s) x for evaluation in fourier_series (or func1(..)), I simply say that fourier_series creates a new function that takes a variable x, this function can be called later outside like y = F(3)... if I made myself clear enough?

You should be able to do this by defining a new function inline:
def fourier_series(f, N):
def F(x):
...
return F
You are not limited to the arguments you pass in to fourier_series:
def f(a):
def F(b):
return b + 5
return F
>>> fun = f(10)
>>> fun(3)
8

You could use a lambda (although I like the other solutions a bit more, I think :) ):
>>> def func2(c, d):
... return c, d
...
>>> def func1(a, b):
... c = a + 1
... d = b + 2
... return lambda: func2(c,d)
...
>>> result = func1(1, 2)
>>> print result
<function <lambda> at 0x7f3b80a3d848>
>>> print result()
(2, 4)
>>>

While I cannot give you an answer specific to what you plan to do. (Looks like math out of my league.)
I can tell you that Python does support first-class functions.
Python may return functions from functions, store functions in collections such as lists and generally treat them as you would any variable.
Cool things such as defining functions in other functions and returning functions are all possible.
>>> def func():
... def func2(x,y):
... return x*y
... return func2
>>> x = func()
>>> x(1,2)
2
Functions can be assigned to variables and stored in lists, they can be used as arguments for other functions and are as flexible as any other object.

If you define a function inside your outer function, you can use the parameters passed to the outer function in the definition of the inner function and return that inner function as the result of the outer function.
def outer_function(*args, **kwargs):
def some_function_based_on_args_and_kwargs(new_func_param, new_func_other_param):
# do stuff here
pass
return some_function_based_on_args_and_kwargs

I think what you want to do is:
def fourier_series(f,N):
#...... math here......
def F(x):
#... more math here ...
import math #blahblah, pseudo code
return math.pi #whatever you want to return from F
if f+N == 2: #pseudo, replace with condition where f,N turn out to be useful
return F
else:
return None
Outside, you can call this like:
F = fourier_series(a,b)
if F:
ans = F(x)
else:
print 'Fourier is not possible :('
The important thing from Python's point of view are:
Yes, you can write a function inside a function
Yes, you can return a function from a function. Just make sure to return it using return F (which returns the function object) as compared to return F(x) which calls the function and returns the value

I was scraping through some documentation and found this.
This is a Snippet Like your code:
def constant(a,b):
def pair(f):
return f(a,b)
return pair
a = constant(1,2) #If You Print variable-> a then it will display "<function constant.
#<locals>.pair at 0x02EC94B0>"
pair(lambda a, b: a) #This will return variable a.
Now, constant() function takes in both a and b and return a function called "Anonymous Function" which itself takes in f, and calls f with a and b.
This is called "closures". Closures is basically an Instance of a Function.

You can define functions inside functions and return these (I think these are technically closures):
def make_f(a, b):
def x(a, b):
return a+b
return x(a, b)

function pointers in python

I would like to do something like the following:
def add(a, b):
#some code
def subtract(a, b):
#some code
operations = [add, subtract]
operations[0]( 5,3)
operations[1](5,3)
In python, is it possible to assign something like a function pointer?

Did you try it? What you wrote works exactly as written. Functions are first-class objects in Python.

Python has nothing called pointers, but your code works as written. Function are first-class objects, assigned to names, and used as any other value.
You can use this to implement a Strategy pattern, for example:
def the_simple_way(a, b):
# blah blah
def the_complicated_way(a, b):
# blah blah
def foo(way):
if way == 'complicated':
doit = the_complicated_way
else:
doit = the_simple_way
doit(a, b)
Or a lookup table:
def do_add(a, b):
return a+b
def do_sub(a, b):
return a-b
handlers = {
'add': do_add,
'sub': do_sub,
}
print handlers[op](a, b)
You can even grab a method bound to an object:
o = MyObject()
f = o.method
f(1, 2) # same as o.method(1, 2)

Just a quick note that most Python operators already have an equivalent function in the operator module.