Hashable, immutable

Hashing is the process of converting some large amount of data into a much smaller amount (typically a single integer) in a repeatable way so that it can be looked up in a table in constant-time (O(1)), which is important for high-performance algorithms and data structures.

Immutability is the idea that an object will not change in some important way after it has been created, especially in any way that might change the hash value of that object.

The two ideas are related because objects which are used as hash keys must typically be immutable so their hash value doesn't change. If it was allowed to change then the location of that object in a data structure such as a hashtable would change and then the whole purpose of hashing for efficiency is defeated.

To really grasp the idea you should try to implement your own hashtable in a language like C/C++, or read the Java implementation of the HashMap class.

• Are there mutable objects that are hashable or immutable objects that are not hashable?

In Python, tuple is immutable, but it is hashable only if all its elements are hashable.

>>> tt = (1, 2, (30, 40))
>>> hash(tt)
8027212646858338501
>>> tl = (1, 2, [30, 40])
>>> hash(tl)
TypeError: unhashable type: 'list'

Hashable Types

• The atomic immutable types are all hashable, such as str, bytes, numeric types
• A frozen set is always hashable(its elements must be hashable by definition)
• A tuple is hashable only if all its elements are hashable
• User-defined types are hashable by default because their hash value is their id()

From the Python Glossary:

An object is hashable if it has a hash value which never changes during its lifetime (it needs a __hash__() method), and can be compared to other objects (it needs an __eq__() or __cmp__() method). Hashable objects which compare equal must have the same hash value.

Hashability makes an object usable as a dictionary key and a set member, because these data structures use the hash value internally.

All of Python’s immutable built-in objects are hashable, while no mutable containers (such as lists or dictionaries) are. Objects which are instances of user-defined classes are hashable by default; they all compare unequal, and their hash value is their id().

Dicts and sets must use a hash for efficient lookup in a hash table; the hash values must be immutable, because changing the hash will mess up the data structures and cause the dict or set to fail. The easiest way to make the hash value immutable is to make the whole object immutable, which is why the two are often mentioned together.

While none of the built-in mutable objects are hashable, it is possible to make a mutable object with a hash value that's not mutable. It's common for only a portion of the object to represent its identity, while the rest of the object contains properties that are free to change. As long as the hash value and comparison functions are based on the identity but not the mutable properties, and the identity never changes, you've met the requirements.