So start with the question i.e. Why and how are Python functions hashable? First, one should know what actually hashable means in Python. So, hashable is a feature of Python objects that tells if the object has a hash value or not. If the object has a hash value then it can be used as a key for a dictionary or as an element in a set.
An object is hashable if it has a hash value that does not change during its entire lifetime. Python has a built-in hash method ( __hash__() ) that can be compared to other objects. For comparing it needs __eq__() or __cmp__() method and if the hashable objects are equal then they have the same hash value. All immutable built-in objects in Python are hashable like tuples while the mutable containers like lists and dictionaries are not hashable.
Objects which are instances of the user-defined class are hashable by default, they all compare unequal, and their hash value is their id().
Example: Consider two tuples t1, t2 with the same values, and see the differences:
t1 = (1, 5, 6)
t2 = (1, 5, 6)
# show the id of object
print(id(t1))
print(id(t2))
Output:
140040984150664 140040984150880
In the above example, two objects are different as for immutable types the hash value depends on the data stored not on their id.
Example: Let's see lambda functions are hashable or not.
# create a one-line function
l = lambda x : 1
# show the hash value
print(hash(l))
# show the id value
print(id(l))
# show the hash value
print (l.__hash__())
Output:
-9223363246992694337 140637793303544 -9223363246992694337
Hence, lambda functions are hashable.
Example: Let's see user defined def based function are hashable or not.
# create an empty function
def fun():
pass
# print types of function
print(type(fun))
# print hash value
print(fun.__hash__())
# print hash value
print(hash(fun))
Output:
<class 'function'> -9223363242199589441 -9223363242199589441
Therefore, any user defined function is hashable as its hash value remains same during its lifetime.