How to make a function composer

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up vote
6
down vote

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I am trying to make a function that rounds other functions for my university degree . For example I would like to call the round_sqrt = round(sqrt)
and when i call the round_sqrt(5) it has to shows me 2 instead of 2.23606797749979. What I am trying is this one:



def rounding(funct):
return round(funct)


but this doesnt work. Can anyone help me with this one?
Any help will be appreciated:)



EDIT: The function should have only one parameter. For example
the start of the function should be



def rounding(func):


so in this function i have to make the func fuction to be rounded.
so when I call the rounding(abs)(3.2) it has to shows me 3










share|improve this question



















  • 2




    You are looking for function composition. Mathematically, h = f ∘ g is defined as h(x) = f(g(x)). While it would be nice if Python a composition operator were available in Python, practical concerns require you to define the composed function yourself.
    – chepner
    18 mins ago






  • 2




    playing with composition is one of the reasons I quickly fell in love with (then hated, then fell in love with, then hated, then...) Haskell.
    – Adam Smith
    13 mins ago










  • Haskell is easy because everything fits into a theoretically sound mathematical framework. Haskell is hard because we are aren't use to conforming to said framework. :)
    – chepner
    3 mins ago










  • You can either leave the question to help other people or delete it, but please don't just remove all the content.
    – Alex
    2 mins ago














up vote
6
down vote

favorite
1












I am trying to make a function that rounds other functions for my university degree . For example I would like to call the round_sqrt = round(sqrt)
and when i call the round_sqrt(5) it has to shows me 2 instead of 2.23606797749979. What I am trying is this one:



def rounding(funct):
return round(funct)


but this doesnt work. Can anyone help me with this one?
Any help will be appreciated:)



EDIT: The function should have only one parameter. For example
the start of the function should be



def rounding(func):


so in this function i have to make the func fuction to be rounded.
so when I call the rounding(abs)(3.2) it has to shows me 3










share|improve this question



















  • 2




    You are looking for function composition. Mathematically, h = f ∘ g is defined as h(x) = f(g(x)). While it would be nice if Python a composition operator were available in Python, practical concerns require you to define the composed function yourself.
    – chepner
    18 mins ago






  • 2




    playing with composition is one of the reasons I quickly fell in love with (then hated, then fell in love with, then hated, then...) Haskell.
    – Adam Smith
    13 mins ago










  • Haskell is easy because everything fits into a theoretically sound mathematical framework. Haskell is hard because we are aren't use to conforming to said framework. :)
    – chepner
    3 mins ago










  • You can either leave the question to help other people or delete it, but please don't just remove all the content.
    – Alex
    2 mins ago












up vote
6
down vote

favorite
1









up vote
6
down vote

favorite
1






1





I am trying to make a function that rounds other functions for my university degree . For example I would like to call the round_sqrt = round(sqrt)
and when i call the round_sqrt(5) it has to shows me 2 instead of 2.23606797749979. What I am trying is this one:



def rounding(funct):
return round(funct)


but this doesnt work. Can anyone help me with this one?
Any help will be appreciated:)



EDIT: The function should have only one parameter. For example
the start of the function should be



def rounding(func):


so in this function i have to make the func fuction to be rounded.
so when I call the rounding(abs)(3.2) it has to shows me 3










share|improve this question















I am trying to make a function that rounds other functions for my university degree . For example I would like to call the round_sqrt = round(sqrt)
and when i call the round_sqrt(5) it has to shows me 2 instead of 2.23606797749979. What I am trying is this one:



def rounding(funct):
return round(funct)


but this doesnt work. Can anyone help me with this one?
Any help will be appreciated:)



EDIT: The function should have only one parameter. For example
the start of the function should be



def rounding(func):


so in this function i have to make the func fuction to be rounded.
so when I call the rounding(abs)(3.2) it has to shows me 3







python python-3.x python-decorators function-composition






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share|improve this question













share|improve this question




share|improve this question








edited 12 secs ago

























asked 24 mins ago









php kubrick

333




333







  • 2




    You are looking for function composition. Mathematically, h = f ∘ g is defined as h(x) = f(g(x)). While it would be nice if Python a composition operator were available in Python, practical concerns require you to define the composed function yourself.
    – chepner
    18 mins ago






  • 2




    playing with composition is one of the reasons I quickly fell in love with (then hated, then fell in love with, then hated, then...) Haskell.
    – Adam Smith
    13 mins ago










  • Haskell is easy because everything fits into a theoretically sound mathematical framework. Haskell is hard because we are aren't use to conforming to said framework. :)
    – chepner
    3 mins ago










  • You can either leave the question to help other people or delete it, but please don't just remove all the content.
    – Alex
    2 mins ago












  • 2




    You are looking for function composition. Mathematically, h = f ∘ g is defined as h(x) = f(g(x)). While it would be nice if Python a composition operator were available in Python, practical concerns require you to define the composed function yourself.
    – chepner
    18 mins ago






  • 2




    playing with composition is one of the reasons I quickly fell in love with (then hated, then fell in love with, then hated, then...) Haskell.
    – Adam Smith
    13 mins ago










  • Haskell is easy because everything fits into a theoretically sound mathematical framework. Haskell is hard because we are aren't use to conforming to said framework. :)
    – chepner
    3 mins ago










  • You can either leave the question to help other people or delete it, but please don't just remove all the content.
    – Alex
    2 mins ago







2




2




You are looking for function composition. Mathematically, h = f ∘ g is defined as h(x) = f(g(x)). While it would be nice if Python a composition operator were available in Python, practical concerns require you to define the composed function yourself.
– chepner
18 mins ago




You are looking for function composition. Mathematically, h = f ∘ g is defined as h(x) = f(g(x)). While it would be nice if Python a composition operator were available in Python, practical concerns require you to define the composed function yourself.
– chepner
18 mins ago




2




2




playing with composition is one of the reasons I quickly fell in love with (then hated, then fell in love with, then hated, then...) Haskell.
– Adam Smith
13 mins ago




playing with composition is one of the reasons I quickly fell in love with (then hated, then fell in love with, then hated, then...) Haskell.
– Adam Smith
13 mins ago












Haskell is easy because everything fits into a theoretically sound mathematical framework. Haskell is hard because we are aren't use to conforming to said framework. :)
– chepner
3 mins ago




Haskell is easy because everything fits into a theoretically sound mathematical framework. Haskell is hard because we are aren't use to conforming to said framework. :)
– chepner
3 mins ago












You can either leave the question to help other people or delete it, but please don't just remove all the content.
– Alex
2 mins ago




You can either leave the question to help other people or delete it, but please don't just remove all the content.
– Alex
2 mins ago












3 Answers
3






active

oldest

votes

















up vote
2
down vote



accepted










For your specific example, you can write



def round_sqrt(x):
return round(sqrt(x))


Alex's answer generalizes this; he defines a function that creates round_sqrt for you. If the function is already defined, you just pass it as an argument to rounder:



round_sqrt = rounder(sqrt)


Of course, you don't need to define round_sqrt if you don't want to. rounder(sqrt)(3.2) can be called directly, although it's far more efficient to safe the return value of rounder if you expect to use it multiple times, rather than redefining it each time.



Otherwise, the decorator syntax is just short for (using Alex's example)



def adder(x, y):
return x + y

adder = rounder(adder)



As I said in my comment, this is an example of implementing composition. Mathematically, composition is simple, because mathematical functions always take a single argument and return a single argument. As such, the composition of two functions f and g could always be defined simply as



def compose(f, g):
def h(x): # The name doesn't matter
return f(g(x))
return h


Then



round_sqrt = compose(round, sqrt)


(Ignoring all sorts of practical concerns around the implementation, Python could in theory even provide a Unicode operator ∘ for functions: round_sqrt = round ∘ sort. Explaining why this won't happen is beyond the scope of this answer.)



In Python, though, functions are far more complicated. They can take multiple arguments, they can accept arbitrary numbers of arguments and arbitrary keyword arguments, and while each technically returns a single value, that value can be a tuple which is thought of as multiple values or a dict. As a result, there may be many ways you might expect to pass the return value of g to a function f, more than can easily be accommodated in a simple compose function.






share|improve this answer






















  • Shouldn't return f(g(z)) be return f(g(x))?
    – slider
    3 mins ago










  • Yeah, I don't know where z came from.
    – chepner
    2 mins ago

















up vote
9
down vote













You should check out closures:



def rounder(func):
def inner(*args, **kwargs):
return round(func(*args, **kwargs))
return inner


Then you can decorate functions using the @ character:



@rounder
def adder(x, y):
return x + y

print(adder(1.1, 2.2))


outputs 3



Supplementary:



  1. You can use functools.wraps in your closure so you don't lose information (e.g. docstring, function name) about the original function.

  2. There are a bunch of resources for learning about closures (e.g. 1, 2) and decorators (e.g. 1, 2) that you can find by Googling those terms.





share|improve this answer


















  • 6




    Hey look, a decorator!
    – Adam Smith
    20 mins ago










  • I cant understand anything. The answer should be more easier I think
    – php kubrick
    17 mins ago










  • @phpkubrick what? It's 3 lines of code and a function header? How much more simple would you like it? You mentioned you're in university -- you can understand this.
    – Adam Smith
    17 mins ago











  • I cant understand the *args, **kwargs
    – php kubrick
    16 mins ago










  • @phpkubrick I guess that's the next bit of research you should do then, because they're used all over the place in Python and are incredibly useful. stackoverflow.com/questions/36901/…
    – Adam Smith
    15 mins ago

















up vote
0
down vote













Function composition isn't supported natively in Python. You can use a decorator as per @Alex's solution. You can define a new function explicitly as per @chepner's solution.



Or you can use a 3rd party library. For example, via toolz.compose:



from toolz import compose

def adder(x, y):
return x + y

round_adder = compose(round, adder)

round_adder(1.1, 2.2) # 3





share|improve this answer




















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    3 Answers
    3






    active

    oldest

    votes








    3 Answers
    3






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    2
    down vote



    accepted










    For your specific example, you can write



    def round_sqrt(x):
    return round(sqrt(x))


    Alex's answer generalizes this; he defines a function that creates round_sqrt for you. If the function is already defined, you just pass it as an argument to rounder:



    round_sqrt = rounder(sqrt)


    Of course, you don't need to define round_sqrt if you don't want to. rounder(sqrt)(3.2) can be called directly, although it's far more efficient to safe the return value of rounder if you expect to use it multiple times, rather than redefining it each time.



    Otherwise, the decorator syntax is just short for (using Alex's example)



    def adder(x, y):
    return x + y

    adder = rounder(adder)



    As I said in my comment, this is an example of implementing composition. Mathematically, composition is simple, because mathematical functions always take a single argument and return a single argument. As such, the composition of two functions f and g could always be defined simply as



    def compose(f, g):
    def h(x): # The name doesn't matter
    return f(g(x))
    return h


    Then



    round_sqrt = compose(round, sqrt)


    (Ignoring all sorts of practical concerns around the implementation, Python could in theory even provide a Unicode operator ∘ for functions: round_sqrt = round ∘ sort. Explaining why this won't happen is beyond the scope of this answer.)



    In Python, though, functions are far more complicated. They can take multiple arguments, they can accept arbitrary numbers of arguments and arbitrary keyword arguments, and while each technically returns a single value, that value can be a tuple which is thought of as multiple values or a dict. As a result, there may be many ways you might expect to pass the return value of g to a function f, more than can easily be accommodated in a simple compose function.






    share|improve this answer






















    • Shouldn't return f(g(z)) be return f(g(x))?
      – slider
      3 mins ago










    • Yeah, I don't know where z came from.
      – chepner
      2 mins ago














    up vote
    2
    down vote



    accepted










    For your specific example, you can write



    def round_sqrt(x):
    return round(sqrt(x))


    Alex's answer generalizes this; he defines a function that creates round_sqrt for you. If the function is already defined, you just pass it as an argument to rounder:



    round_sqrt = rounder(sqrt)


    Of course, you don't need to define round_sqrt if you don't want to. rounder(sqrt)(3.2) can be called directly, although it's far more efficient to safe the return value of rounder if you expect to use it multiple times, rather than redefining it each time.



    Otherwise, the decorator syntax is just short for (using Alex's example)



    def adder(x, y):
    return x + y

    adder = rounder(adder)



    As I said in my comment, this is an example of implementing composition. Mathematically, composition is simple, because mathematical functions always take a single argument and return a single argument. As such, the composition of two functions f and g could always be defined simply as



    def compose(f, g):
    def h(x): # The name doesn't matter
    return f(g(x))
    return h


    Then



    round_sqrt = compose(round, sqrt)


    (Ignoring all sorts of practical concerns around the implementation, Python could in theory even provide a Unicode operator ∘ for functions: round_sqrt = round ∘ sort. Explaining why this won't happen is beyond the scope of this answer.)



    In Python, though, functions are far more complicated. They can take multiple arguments, they can accept arbitrary numbers of arguments and arbitrary keyword arguments, and while each technically returns a single value, that value can be a tuple which is thought of as multiple values or a dict. As a result, there may be many ways you might expect to pass the return value of g to a function f, more than can easily be accommodated in a simple compose function.






    share|improve this answer






















    • Shouldn't return f(g(z)) be return f(g(x))?
      – slider
      3 mins ago










    • Yeah, I don't know where z came from.
      – chepner
      2 mins ago












    up vote
    2
    down vote



    accepted







    up vote
    2
    down vote



    accepted






    For your specific example, you can write



    def round_sqrt(x):
    return round(sqrt(x))


    Alex's answer generalizes this; he defines a function that creates round_sqrt for you. If the function is already defined, you just pass it as an argument to rounder:



    round_sqrt = rounder(sqrt)


    Of course, you don't need to define round_sqrt if you don't want to. rounder(sqrt)(3.2) can be called directly, although it's far more efficient to safe the return value of rounder if you expect to use it multiple times, rather than redefining it each time.



    Otherwise, the decorator syntax is just short for (using Alex's example)



    def adder(x, y):
    return x + y

    adder = rounder(adder)



    As I said in my comment, this is an example of implementing composition. Mathematically, composition is simple, because mathematical functions always take a single argument and return a single argument. As such, the composition of two functions f and g could always be defined simply as



    def compose(f, g):
    def h(x): # The name doesn't matter
    return f(g(x))
    return h


    Then



    round_sqrt = compose(round, sqrt)


    (Ignoring all sorts of practical concerns around the implementation, Python could in theory even provide a Unicode operator ∘ for functions: round_sqrt = round ∘ sort. Explaining why this won't happen is beyond the scope of this answer.)



    In Python, though, functions are far more complicated. They can take multiple arguments, they can accept arbitrary numbers of arguments and arbitrary keyword arguments, and while each technically returns a single value, that value can be a tuple which is thought of as multiple values or a dict. As a result, there may be many ways you might expect to pass the return value of g to a function f, more than can easily be accommodated in a simple compose function.






    share|improve this answer














    For your specific example, you can write



    def round_sqrt(x):
    return round(sqrt(x))


    Alex's answer generalizes this; he defines a function that creates round_sqrt for you. If the function is already defined, you just pass it as an argument to rounder:



    round_sqrt = rounder(sqrt)


    Of course, you don't need to define round_sqrt if you don't want to. rounder(sqrt)(3.2) can be called directly, although it's far more efficient to safe the return value of rounder if you expect to use it multiple times, rather than redefining it each time.



    Otherwise, the decorator syntax is just short for (using Alex's example)



    def adder(x, y):
    return x + y

    adder = rounder(adder)



    As I said in my comment, this is an example of implementing composition. Mathematically, composition is simple, because mathematical functions always take a single argument and return a single argument. As such, the composition of two functions f and g could always be defined simply as



    def compose(f, g):
    def h(x): # The name doesn't matter
    return f(g(x))
    return h


    Then



    round_sqrt = compose(round, sqrt)


    (Ignoring all sorts of practical concerns around the implementation, Python could in theory even provide a Unicode operator ∘ for functions: round_sqrt = round ∘ sort. Explaining why this won't happen is beyond the scope of this answer.)



    In Python, though, functions are far more complicated. They can take multiple arguments, they can accept arbitrary numbers of arguments and arbitrary keyword arguments, and while each technically returns a single value, that value can be a tuple which is thought of as multiple values or a dict. As a result, there may be many ways you might expect to pass the return value of g to a function f, more than can easily be accommodated in a simple compose function.







    share|improve this answer














    share|improve this answer



    share|improve this answer








    edited 2 mins ago

























    answered 14 mins ago









    chepner

    236k29222317




    236k29222317











    • Shouldn't return f(g(z)) be return f(g(x))?
      – slider
      3 mins ago










    • Yeah, I don't know where z came from.
      – chepner
      2 mins ago
















    • Shouldn't return f(g(z)) be return f(g(x))?
      – slider
      3 mins ago










    • Yeah, I don't know where z came from.
      – chepner
      2 mins ago















    Shouldn't return f(g(z)) be return f(g(x))?
    – slider
    3 mins ago




    Shouldn't return f(g(z)) be return f(g(x))?
    – slider
    3 mins ago












    Yeah, I don't know where z came from.
    – chepner
    2 mins ago




    Yeah, I don't know where z came from.
    – chepner
    2 mins ago












    up vote
    9
    down vote













    You should check out closures:



    def rounder(func):
    def inner(*args, **kwargs):
    return round(func(*args, **kwargs))
    return inner


    Then you can decorate functions using the @ character:



    @rounder
    def adder(x, y):
    return x + y

    print(adder(1.1, 2.2))


    outputs 3



    Supplementary:



    1. You can use functools.wraps in your closure so you don't lose information (e.g. docstring, function name) about the original function.

    2. There are a bunch of resources for learning about closures (e.g. 1, 2) and decorators (e.g. 1, 2) that you can find by Googling those terms.





    share|improve this answer


















    • 6




      Hey look, a decorator!
      – Adam Smith
      20 mins ago










    • I cant understand anything. The answer should be more easier I think
      – php kubrick
      17 mins ago










    • @phpkubrick what? It's 3 lines of code and a function header? How much more simple would you like it? You mentioned you're in university -- you can understand this.
      – Adam Smith
      17 mins ago











    • I cant understand the *args, **kwargs
      – php kubrick
      16 mins ago










    • @phpkubrick I guess that's the next bit of research you should do then, because they're used all over the place in Python and are incredibly useful. stackoverflow.com/questions/36901/…
      – Adam Smith
      15 mins ago














    up vote
    9
    down vote













    You should check out closures:



    def rounder(func):
    def inner(*args, **kwargs):
    return round(func(*args, **kwargs))
    return inner


    Then you can decorate functions using the @ character:



    @rounder
    def adder(x, y):
    return x + y

    print(adder(1.1, 2.2))


    outputs 3



    Supplementary:



    1. You can use functools.wraps in your closure so you don't lose information (e.g. docstring, function name) about the original function.

    2. There are a bunch of resources for learning about closures (e.g. 1, 2) and decorators (e.g. 1, 2) that you can find by Googling those terms.





    share|improve this answer


















    • 6




      Hey look, a decorator!
      – Adam Smith
      20 mins ago










    • I cant understand anything. The answer should be more easier I think
      – php kubrick
      17 mins ago










    • @phpkubrick what? It's 3 lines of code and a function header? How much more simple would you like it? You mentioned you're in university -- you can understand this.
      – Adam Smith
      17 mins ago











    • I cant understand the *args, **kwargs
      – php kubrick
      16 mins ago










    • @phpkubrick I guess that's the next bit of research you should do then, because they're used all over the place in Python and are incredibly useful. stackoverflow.com/questions/36901/…
      – Adam Smith
      15 mins ago












    up vote
    9
    down vote










    up vote
    9
    down vote









    You should check out closures:



    def rounder(func):
    def inner(*args, **kwargs):
    return round(func(*args, **kwargs))
    return inner


    Then you can decorate functions using the @ character:



    @rounder
    def adder(x, y):
    return x + y

    print(adder(1.1, 2.2))


    outputs 3



    Supplementary:



    1. You can use functools.wraps in your closure so you don't lose information (e.g. docstring, function name) about the original function.

    2. There are a bunch of resources for learning about closures (e.g. 1, 2) and decorators (e.g. 1, 2) that you can find by Googling those terms.





    share|improve this answer














    You should check out closures:



    def rounder(func):
    def inner(*args, **kwargs):
    return round(func(*args, **kwargs))
    return inner


    Then you can decorate functions using the @ character:



    @rounder
    def adder(x, y):
    return x + y

    print(adder(1.1, 2.2))


    outputs 3



    Supplementary:



    1. You can use functools.wraps in your closure so you don't lose information (e.g. docstring, function name) about the original function.

    2. There are a bunch of resources for learning about closures (e.g. 1, 2) and decorators (e.g. 1, 2) that you can find by Googling those terms.






    share|improve this answer














    share|improve this answer



    share|improve this answer








    edited 12 mins ago

























    answered 22 mins ago









    Alex

    9,45422252




    9,45422252







    • 6




      Hey look, a decorator!
      – Adam Smith
      20 mins ago










    • I cant understand anything. The answer should be more easier I think
      – php kubrick
      17 mins ago










    • @phpkubrick what? It's 3 lines of code and a function header? How much more simple would you like it? You mentioned you're in university -- you can understand this.
      – Adam Smith
      17 mins ago











    • I cant understand the *args, **kwargs
      – php kubrick
      16 mins ago










    • @phpkubrick I guess that's the next bit of research you should do then, because they're used all over the place in Python and are incredibly useful. stackoverflow.com/questions/36901/…
      – Adam Smith
      15 mins ago












    • 6




      Hey look, a decorator!
      – Adam Smith
      20 mins ago










    • I cant understand anything. The answer should be more easier I think
      – php kubrick
      17 mins ago










    • @phpkubrick what? It's 3 lines of code and a function header? How much more simple would you like it? You mentioned you're in university -- you can understand this.
      – Adam Smith
      17 mins ago











    • I cant understand the *args, **kwargs
      – php kubrick
      16 mins ago










    • @phpkubrick I guess that's the next bit of research you should do then, because they're used all over the place in Python and are incredibly useful. stackoverflow.com/questions/36901/…
      – Adam Smith
      15 mins ago







    6




    6




    Hey look, a decorator!
    – Adam Smith
    20 mins ago




    Hey look, a decorator!
    – Adam Smith
    20 mins ago












    I cant understand anything. The answer should be more easier I think
    – php kubrick
    17 mins ago




    I cant understand anything. The answer should be more easier I think
    – php kubrick
    17 mins ago












    @phpkubrick what? It's 3 lines of code and a function header? How much more simple would you like it? You mentioned you're in university -- you can understand this.
    – Adam Smith
    17 mins ago





    @phpkubrick what? It's 3 lines of code and a function header? How much more simple would you like it? You mentioned you're in university -- you can understand this.
    – Adam Smith
    17 mins ago













    I cant understand the *args, **kwargs
    – php kubrick
    16 mins ago




    I cant understand the *args, **kwargs
    – php kubrick
    16 mins ago












    @phpkubrick I guess that's the next bit of research you should do then, because they're used all over the place in Python and are incredibly useful. stackoverflow.com/questions/36901/…
    – Adam Smith
    15 mins ago




    @phpkubrick I guess that's the next bit of research you should do then, because they're used all over the place in Python and are incredibly useful. stackoverflow.com/questions/36901/…
    – Adam Smith
    15 mins ago










    up vote
    0
    down vote













    Function composition isn't supported natively in Python. You can use a decorator as per @Alex's solution. You can define a new function explicitly as per @chepner's solution.



    Or you can use a 3rd party library. For example, via toolz.compose:



    from toolz import compose

    def adder(x, y):
    return x + y

    round_adder = compose(round, adder)

    round_adder(1.1, 2.2) # 3





    share|improve this answer
























      up vote
      0
      down vote













      Function composition isn't supported natively in Python. You can use a decorator as per @Alex's solution. You can define a new function explicitly as per @chepner's solution.



      Or you can use a 3rd party library. For example, via toolz.compose:



      from toolz import compose

      def adder(x, y):
      return x + y

      round_adder = compose(round, adder)

      round_adder(1.1, 2.2) # 3





      share|improve this answer






















        up vote
        0
        down vote










        up vote
        0
        down vote









        Function composition isn't supported natively in Python. You can use a decorator as per @Alex's solution. You can define a new function explicitly as per @chepner's solution.



        Or you can use a 3rd party library. For example, via toolz.compose:



        from toolz import compose

        def adder(x, y):
        return x + y

        round_adder = compose(round, adder)

        round_adder(1.1, 2.2) # 3





        share|improve this answer












        Function composition isn't supported natively in Python. You can use a decorator as per @Alex's solution. You can define a new function explicitly as per @chepner's solution.



        Or you can use a 3rd party library. For example, via toolz.compose:



        from toolz import compose

        def adder(x, y):
        return x + y

        round_adder = compose(round, adder)

        round_adder(1.1, 2.2) # 3






        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 14 mins ago









        jpp

        78.7k184592




        78.7k184592



























             

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