TL;DR
g(f(x)) means applying f to x first, then applying g to the output.
Omit the parentheses, add @ before and line break after each function name:
@g
@f
x
(Syntax only valid if x is the definition of a function/class.)
Abstract explanation
The reasoning behind this design decision becomes fairly obvious IMHO, if you remember what the decorator syntax - in its most abstract and general form - actually means. So I am going to try the abstract approach to explain this.
It is all about syntax
To be clear here, the distinguishing factor in the concept of the "decorator" is not the object underneath it (so to speak) nor the operation it performs. It is the special syntax and the restrictions for it. Thus, a decorator at its core is nothing more than feature of Python grammar.
The decorator syntax requires a target to be decorated. Initially (see PEP 318) the target could only be function definitions; later class definitions were also allowed to be decorated (see PEP 3129).
Minimal valid syntax
Syntactically, this is valid Python:
def f(): pass
@f
class Target: pass # or `def target: pass`
However, this will (perhaps unsuprisingly) cause a TypeError upon execution. As has been reiterated multiple times here and in other posts on this platform, the above is equivalent to this:
def f(): pass
class Target: pass
Target = f(Target)
Minimal working decorator
The TypeError stems from the fact that f lacks a positional argument. This is the obvious logical restriction imposed by what a decorator is supposed to do. Thus, to achieve not only syntactically valid code, but also have it run without errors, this is sufficient:
def f(x): pass
@f
class Target: pass
This is still not very useful, but it is enough for the most general form of a working decorator.
Decoration is just application of a function to the target and assigning the output to the target's name.
Chaining functions ⇒ Chaining decorators
We can ignore the target and what it is or does and focus only on the decorator. Since it merely stands for applying a function, the order of operations comes into play, as soon as we have more than one. What is the order of operation, when we chain functions?
def f(x): pass
def g(x): pass
class Target: pass
Target = g(f(Target))
Well, just like in the composition of purely mathematical functions, this implies that we apply f to Target first and then apply g to the result of f. Despite g appearing first (i.e. further left), it is not what is applied first.
Since stacking decorators is equivalent to nesting functions, it seems obvious to define the order of operation the same way. This time, we just skip the parentheses, add an @ symbol in front of the function name and a line break after it.
def f(x): pass
def g(x): pass
@g
@f
class Target: pass
But, why though?
If after the explanation above (and reading the PEPs for historic background), the reasoning behind the order of operation is still not clear or still unintuitive, there is not really any good answer left, other than "because the devs thought it made sense, so get used to it".
PS
I thought I'd add a few things for additional context based on all the comments around your question.
Decoration vs. calling a decorated function
A source of confusion seems to be the distinction between what happens when applying the decorator versus calling the decorated function.
Notice that in my examples above I never actually called target itself (the class or function being decorated). Decoration is itself a function call. Adding @f above the target is calling the f and passing the target to it as the first positional argument.
A "decorated function" might not even be a function
The distinction is very important because nowhere does it say that a decorator actually needs to return a callable (function or class). f being just a function means it can return whatever it wants. This is again valid and working Python code:
def f(x): return 3.14
@f
def target(): return "foo"
try:
target()
except Exception as e:
print(repr(e))
print(target)
Output:
TypeError("'float' object is not callable")
3.14
Notice that the name target does not even refer to a function anymore. It just holds the 3.14 returned by the decorator. Thus, we cannot even call target. The entire function behind it is essentially lost immediately before it is even available to the global namespace. That is because f just completely ignores its first positional argument x.
Replacing a function
Expanding this further, if we want, we can have f return a function. Not doing that seems very strange, considering it is used to decorate a function. But it doesn't have to be related to the target at all. Again, this is fine:
def bar(): return "bar"
def f(x): return bar
@f
def target(): return "foo"
print(target())
print(target is bar)
Output:
bar
True
It comes down to convention
The way decorators are actually overwhelmingly used out in the wild, is in a way that still keeps a reference to the target being decorated around somewhere. In practice it can be as simple as this:
def f(x):
print(f"applied `f({x.__name__})`")
return
@f
def target(): return "foo"
Just running this piece of code outputs applied f(target). Again, notice that we don't call target here, we only called f. But now, the decorated function is still target, so we could add the call print(target()) at the bottom and that would output foo after the other output produced by f.
The fact that most decorators don't just throw away their target comes down to convention. You (as a developer) would not expect your function/class to simply be thrown away completely, when you use a decorator.
Decoration with wrapping
This is why real-life decorators typically either return the reference to the target at the end outright (like in the last example) or they return a different callable, but that callable itself calls the target, meaning a reference to the target is kept in that new callable's local namespace . These functions are what is usually referred to as wrappers:
def f(x):
print(f"applied `f({x.__name__})`")
def wrapper():
print(f"wrapper executing with {locals()=}")
return x()
return wrapper
@f
def target(): return "foo"
print(f"{target()=}")
print(f"{target.__name__=}")
Output:
applied `f(target)`
wrapper executing with locals()={'x': <function target at 0x7f1b2f78f250>}
target()='foo'
target.__name__='wrapper'
As you can see, what the decorator left us is wrapper, not what we originally defined as target. And the wrapper is what we call, when we write target().
Wrapping wrappers
This is the kind of behavior we typically expect, when we use decorators. And therefore it is not surprising that multiple decorators stacked together behave the way they do. The are called from the inside out (as explained above) and each adds its own wrapper around what it receives from the one applied before:
def f(x):
print(f"applied `f({x.__name__})`")
def wrapper_from_f():
print(f"wrapper_from_f executing with {locals()=}")
return x()
return wrapper_from_f
def g(x):
print(f"applied `g({x.__name__})`")
def wrapper_from_g():
print(f"wrapper_from_g executing with {locals()=}")
return x()
return wrapper_from_g
@g
@f
def target(): return "foo"
print(f"{target()=}")
print(f"{target.__name__=}")
Output:
applied `f(target)`
applied `g(wrapper_from_f)`
wrapper_from_g executing with locals()={'x': <function f.<locals>.wrapper_from_f at 0x7fbfc8d64f70>}
wrapper_from_f executing with locals()={'x': <function target at 0x7fbfc8d65630>}
target()='foo'
target.__name__='wrapper_from_g'
This shows very clearly the difference between the order in which the decorators are called and the order in which the wrapped/wrapping functions are called.
After the decoration is done, we are left with wrapper_from_g, which is referenced by our target name in global namespace. When we call it, wrapper_from_g executes and calls wrapper_from_f, which in turn calls the original target.
